Freges and Russells views are obviously different but because of certain superficial similarities in how they handle certain famous puzzles about proper names they are often assimilated Where proper names are concerned both Frege and Russell are often described together as descriptivists But their views are fundamentally different To see that lets look at the puzzle of names without bearers as it arises in the context of Mills purely referential theory of proper names aka the Fido-Fido theoryAccording to Mill a proper name is but an unmeaning mark which we connect in our minds with the idea of the object in order that whenever the mark meets our eyes or occurs to our thoughts we may think of that individual object (1872 22) The function of proper names Mill thought is not to convey general information but rather to enable individuals to be made the subject of discourse names are attached to the objects themselves and are not dependent on hellip any attribute of the object (1872 20) As a result our use of names in communication can accommodate such pervasive facts as that a person place or thing can change over time that ones conception of something can change over time that we can be mistaken in our conceptions of it and that different peoples conceptions of the same thing can differ All this is possible if using a name in thinking of or referring to an object is not a matter of representing it as having certain properties but as Russell said merely to indicate what we are speaking about [the name] is no part of the fact asserted hellip it is merely part of the symbolism by which we express our thought (1919 175)An obvious problem with this simple view is that if the role of names were simply to refer to their bearers names without bearers would be meaningless Yet names without bearers seem perfectly meaningful and sentences in which they occur seem to express propositions Otherwise how could a sentence like Santa Claus does not exist be not only meaningful but true Descriptivism

about proper names avoids this problem as well as Freges two famous puzzles (about the informativeness of identity statements and about failure of substitution in indirect quotation and attitude reports) Descriptivism is often referred to as the Frege-Russell view1 However their views were quite different Ill call Freges view sense descriptivism and Russells view abbreviational descriptivism Lets take up Russells view first although it came secondRussells view concerned ordinary proper names like Bill Clinton and Santa Claus He contrasted these with logically proper names ie the individual constants of formal logic which he regarded as Millian For reasons connected with his doctrine of acquaintance he thought that the only logically proper names of ordinary language English in particular are the demonstratives this and that as used to refer to ones current sense data and the pronoun I (1917 216) He held that ordinary proper names are really abbreviated or disguised definite descriptions Definite descriptions in turn according to Russells famous Theory of Descriptions function not as referring expressions but as quantificational phrases We should not be misled by Russells characterization of them denoting phrases because for Russell denotation is a semantically inert property That is the proposition expressed by a sentence in which a description occurs is the same whether the description has a denotation or not So its denotation does not enter into that proposition2 As Russell explainsThe actual object (if any) which is the denotation is not hellip a constituent of propositions in which descriptions occur3 and this is the reason why in order to understand such propositions we need acquaintance with the constituents of the description but do not need acquaintance with its denotation4 (1917 222)Thus for any sentence containing a definite description grammatical form is misleading as to logical form For example The inventor of silly putty got rich is of subject-predicate form grammatically but not logically-it is not really about the inventor of silly putty According to Russells famous theory of

descriptions a simple subject-predicate sentence of the form The F is G does not express a singular proposition of the subject-predicate form a is G but a general existential proposition what might be called a uniqueness proposition The quantificational structure of such a proposition is revealed only after the definite description is broken up to yield (in modern notation) the form (x)((y)(Fy y=x) amp Gx) in which the description not being a semantic unit does not even appear5 Accordingly for Russell if a proper name is a disguised description eg if George Kistiakowski is short for the inventor of silly putty the bearer of the name does not enter into the proposition expressed by a sentence in which the name occurs This is not because the name has a sense (in Freges sense of sense) but because it abbreviates a definite descriptionRussells view is clear from what he says about the name Bismarck In his view the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description (1917 208) Russell makes allowances for the fact that the requisite descriptionwill vary for different people or for the same person at different times (the description in our minds will probably be some more or less vague mass of historical knowledge far more in most cases than is required to identify him) hellip but so long as the object to which the name applies remains constant the particular description involved usually makes no difference to the truth or falsehood of the proposition in which the name appears (1917 208-9)For purposes of illustration he uses the description the first Chancellor of the German Empire Russell first considers the situation of Bismarck himself who might have used the name directly to designate [himself] hellip to ma[k]e a judgment about himself with himself as a constituent (209) Here the proper name has the direct use which it always wishes to have as simply standing for a certain object and not for a description of the object But our situation in referring to Bismarck is different from his

when we make a statement about something known only by description we often intend to make our statement not in the form involving the description but about the actual thing described That is when we say anything about Bismarck we should like if we could to make the judgment which Bismarck alone can make namely the judgment of which he himself is a constituent [But] in this we are necessarily defeated hellipWhat enables us to communicate in spite of the varying descriptions we employ is that we know there is a true proposition concerning the actual Bismarck and that however we may vary the description (as long as the description is correct) the proposition described is still the same This proposition which is described and is known to be true is what interests us but we are not acquainted with the proposition itself and do not know it though we know it is true (1917 210-11)The proposition that interests us is a singular proposition but we cannot actually think it-we can know it only by description that is by entertaining a general (uniqueness) proposition which is if true made true by a fact involving Bismarck But this general proposition does not itself involve Bismarck and would be thinkable even if Bismarck never existedFrege is a descriptivist of a different sort than Russell He claims not that proper names are disguised descriptions but that they have senses as well as references The sense of a name is both the mode of presentation and the determinant of its referent (it also functions for Frege as the indirect (as opposed to customary) reference when the name is embedded in a context of indirect quotation or propositional attitude ascription) Frege agrees with Russell and with Mill for that matter that words are ordinarily used to talk about things not ideas If words are used in the ordinary way what one intends to speak of is their reference (1892 58) Even so in so using them we must associate reference-determining properties with our words Moreover insofar as our words also express our thoughts they must correspond to constituents of those thoughts Thus for Frege the semantic and the cognitive

significance of expressions are intimately related Indeed because an expression can have a sense without having a reference Frege holds that the constituents of thoughts are senses not referencesFrege does not hold that every proper name is equivalent to some definite description but rather that expressions of both kinds are of the same semantic genus which he calls Eigennamen (literally translated as proper names but better paraphrased as singular terms) Unlike Russell he does not assimilate definite descriptions to quantificational phrases but treats them like proper names (properly so-called) as semantic units capable of having individuals as semantic values determined by their senses The sense of such an expression plays the semantic role of imposing a condition that an individual must satisfy in order to be the referent A proper name like a definite description contributes its sense to that of a sentence in which it occurs regardless of which individual actually is its referent and even if it has no referent at all This is because the condition imposed by sense the determinant of reference is independent of that which it determines For example Frege says the thought remains the same whether Odysseus has reference or not (1892 63) The same object can be presented in different ways under different modes of presentation but it is not essential to any mode of presentation that it actually present anything at allFreges conception of sense does not entail that every proper name has the sense of some definite description or that the sense of every proper name is an individual concept expressible by some definite description His conception of sense leaves open the possibility of non-descriptive senses such as percepts If one thinks of an object by means of a percept as one does when visually attending to it this is not equivalent to thinking of it under a description of the form the thing that looks thus-and-so One might verbally express a thought about an object one is looking at by saying something of the form the thing that looks thus-and-so is hellip but as Frege says about indexical thoughts the mere wording does not suffice for the expression of the thought

(1918 24) He does not explicitly make the analogous point in regard to proper names but nowhere does he explicitly assert that each proper name is equivalent to some definite description and his overall theory of sense and reference does not require this equivalenceRussells conception of presentation is quite different from what Frege means by presentation (in mode of presentation) For Russell any object that can be presented at all cannot be presented in different ways Russells restrictive notion of acquaintance is a direct cognitive relation and indeed is simply the converse of the relation of object and subject which constitutes presentation (1917 202) Notoriously Russell disqualifies public objects as objects of acquaintance but this is the price he is willing to pay to avoid the problem of names without bearers as well as Freges puzzles (about identity statements and about indirect quotation and attitude reports) He avoids having to appeal to senses to solve them The notion of sense as the determinant of reference has no place in Russells theory of language or thought Constituents of propositions are individuals (particulars and universals) and the Principle of Acquaintance requires that every proposition which we can understand must be composed wholly of constituents with which we are acquainted (1917 211) For Frege modes of presentation are the constituents of thoughts and the objects which modes of presentation present are not Because the relation between subject to object is mediated by a sense this relation is indirect unlike Russellian acquaintance6 So the difference between Freges two-tiered and Russells one-tiered semantics is reflected in their different epistemological views on presentation They are in their respective ways descriptivists about singular thought as well as about proper names

Russell held that ordinary proper names are abbreviated definite descriptions but he denied that definite descriptions (or expressions of any other sort) have two levels of semantic significance This was the central point of On Denoting (1905) For Russell what distinguishes both definite

descriptions and ordinary proper names from genuine logically proper names like the individual constants of logic is not that they do have senses but that they do not have references (they do have denotations but these are not their semantic values) For Frege there are two levels of semantic significance sense and reference and sense is primary Despite their differences neither Freges sense-descriptivism nor Russells abbreviational descriptivism is susceptible as Mills view is to the problem of names without bearers On both views a proper name can play its (primary) semantic role whether or not it belongs to anything But this is so for different reasons For Russell the reason is the semantic inertness of denotation for Frege it is the independence of sense from reference

2 Fregersquos Theory of Sense and Reference

Although Frege accepted something like the Naive Theory in his early work he later rejected it for reasons like those given above He formulated a radical alternative his famous theory of Sinn and Bedeutung We here translate Fregersquos terms into English as lsquosensersquo and lsquoreferencersquo respectively The distinction between sense and reference is most easily illustrated using sentences containing definite descriptions Consider (11)

11 The inventor of the bifocals is the first Postmaster General of the United States The definite descriptions in (11) refer to the same object Benjamin Franklin Yet they seem to present and determine that object in different ways for instance one presents him as an inventor whereas the other presents him as a Postmaster General Frege held that these definite descriptions differ in sense A sense according to Frege is a mode of presentation of an object and a way of thinking of an object A sense presents or determines an object Each of the above definite descriptions expresses a sense and each refers to whatever object its sense presents

Frege claimed that proper names also express senses The sense of a proper name like the sense of a definite description presents an object which is the referent of the name In that respect the sense of a proper name is like that of a definite description Frege often used definite descriptions to express the senses of proper names For instance he claimed that the sense of lsquoAristotlersquo (for some speakers) can be expressed by the definite description lsquothe Stagirite teacher of Alexander the Greatrsquo Thus some philosophers claim that Frege thought that the sense of any name can be expressed by a definite description

Whether or not this is so we shall initially be concerned with this descriptive version of Fregersquos theory (Non-descriptive Fregean theories will be discussed later)

Frege extended the theory of sense and reference to all expressions A predicate expresses a sense that presents a set of objects (or more accurately the characteristic function of a set of objects) This set is the referent of the predicate The truth value of a sentence is determined by the references of its parts for instance lsquoMark Twain is humanrsquo is determined to be true because the referent of the name is a member of the referent of the predicate lsquois humanrsquo that is the set of humans Thus Frege held that the reference of a sentence is its truth value (So the Bedeutung of an expression is comparable to its extension or reference in modern terminology) The sense of a full indicative sentence is a Gedanke or Thought The Thought that a sentence expresses presents the truth value of the sentence Thoughts are also the things that people assert and believe in this respect they are like the propositions of the Naive Theory

Fregersquos theory was largely motivated by the Objection from Cognitive Significance and deals handily with the examples used in that objection lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo differ in sense for most speakers The sense of the first for some speakers can be expressed by lsquothe author of Huckleberry Finnrsquo while the sense of the second for some speakers can be

expressed by lsquothe person who published US Grantrsquos autobiographyrsquo Thus sentences (1) and (2) express different senses or Thoughts So the sentences can differ in informativeness a priority and analyticity and a rational person can think that (1) and (2) differ in truth value Similarly for (3) and (4) and (5) and (6)

According to Fregersquos theory of attitude ascriptions the lsquothatrsquo-clauses that appear in belief ascriptions (9) and (10) refer to the Thoughts that (1) and (2) express

9 Mary believes that Mark Twain is Mark Twain10 Mary believes that Mark Twain is Samuel Clemens 1 Mark Twain is Mark Twain2 Mark Twain is Samuel Clemens

Thus (9) attributes to Mary belief in one Thought whereas (10) attributes to her belief in a different Thought Itrsquos possible for Mary to believe one of these Thoughts without believing the other so itrsquos possible for (9) and (10) to differ in truth value

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

about proper names avoids this problem as well as Freges two famous puzzles (about the informativeness of identity statements and about failure of substitution in indirect quotation and attitude reports) Descriptivism is often referred to as the Frege-Russell view1 However their views were quite different Ill call Freges view sense descriptivism and Russells view abbreviational descriptivism Lets take up Russells view first although it came secondRussells view concerned ordinary proper names like Bill Clinton and Santa Claus He contrasted these with logically proper names ie the individual constants of formal logic which he regarded as Millian For reasons connected with his doctrine of acquaintance he thought that the only logically proper names of ordinary language English in particular are the demonstratives this and that as used to refer to ones current sense data and the pronoun I (1917 216) He held that ordinary proper names are really abbreviated or disguised definite descriptions Definite descriptions in turn according to Russells famous Theory of Descriptions function not as referring expressions but as quantificational phrases We should not be misled by Russells characterization of them denoting phrases because for Russell denotation is a semantically inert property That is the proposition expressed by a sentence in which a description occurs is the same whether the description has a denotation or not So its denotation does not enter into that proposition2 As Russell explainsThe actual object (if any) which is the denotation is not hellip a constituent of propositions in which descriptions occur3 and this is the reason why in order to understand such propositions we need acquaintance with the constituents of the description but do not need acquaintance with its denotation4 (1917 222)Thus for any sentence containing a definite description grammatical form is misleading as to logical form For example The inventor of silly putty got rich is of subject-predicate form grammatically but not logically-it is not really about the inventor of silly putty According to Russells famous theory of

descriptions a simple subject-predicate sentence of the form The F is G does not express a singular proposition of the subject-predicate form a is G but a general existential proposition what might be called a uniqueness proposition The quantificational structure of such a proposition is revealed only after the definite description is broken up to yield (in modern notation) the form (x)((y)(Fy y=x) amp Gx) in which the description not being a semantic unit does not even appear5 Accordingly for Russell if a proper name is a disguised description eg if George Kistiakowski is short for the inventor of silly putty the bearer of the name does not enter into the proposition expressed by a sentence in which the name occurs This is not because the name has a sense (in Freges sense of sense) but because it abbreviates a definite descriptionRussells view is clear from what he says about the name Bismarck In his view the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description (1917 208) Russell makes allowances for the fact that the requisite descriptionwill vary for different people or for the same person at different times (the description in our minds will probably be some more or less vague mass of historical knowledge far more in most cases than is required to identify him) hellip but so long as the object to which the name applies remains constant the particular description involved usually makes no difference to the truth or falsehood of the proposition in which the name appears (1917 208-9)For purposes of illustration he uses the description the first Chancellor of the German Empire Russell first considers the situation of Bismarck himself who might have used the name directly to designate [himself] hellip to ma[k]e a judgment about himself with himself as a constituent (209) Here the proper name has the direct use which it always wishes to have as simply standing for a certain object and not for a description of the object But our situation in referring to Bismarck is different from his

when we make a statement about something known only by description we often intend to make our statement not in the form involving the description but about the actual thing described That is when we say anything about Bismarck we should like if we could to make the judgment which Bismarck alone can make namely the judgment of which he himself is a constituent [But] in this we are necessarily defeated hellipWhat enables us to communicate in spite of the varying descriptions we employ is that we know there is a true proposition concerning the actual Bismarck and that however we may vary the description (as long as the description is correct) the proposition described is still the same This proposition which is described and is known to be true is what interests us but we are not acquainted with the proposition itself and do not know it though we know it is true (1917 210-11)The proposition that interests us is a singular proposition but we cannot actually think it-we can know it only by description that is by entertaining a general (uniqueness) proposition which is if true made true by a fact involving Bismarck But this general proposition does not itself involve Bismarck and would be thinkable even if Bismarck never existedFrege is a descriptivist of a different sort than Russell He claims not that proper names are disguised descriptions but that they have senses as well as references The sense of a name is both the mode of presentation and the determinant of its referent (it also functions for Frege as the indirect (as opposed to customary) reference when the name is embedded in a context of indirect quotation or propositional attitude ascription) Frege agrees with Russell and with Mill for that matter that words are ordinarily used to talk about things not ideas If words are used in the ordinary way what one intends to speak of is their reference (1892 58) Even so in so using them we must associate reference-determining properties with our words Moreover insofar as our words also express our thoughts they must correspond to constituents of those thoughts Thus for Frege the semantic and the cognitive

significance of expressions are intimately related Indeed because an expression can have a sense without having a reference Frege holds that the constituents of thoughts are senses not referencesFrege does not hold that every proper name is equivalent to some definite description but rather that expressions of both kinds are of the same semantic genus which he calls Eigennamen (literally translated as proper names but better paraphrased as singular terms) Unlike Russell he does not assimilate definite descriptions to quantificational phrases but treats them like proper names (properly so-called) as semantic units capable of having individuals as semantic values determined by their senses The sense of such an expression plays the semantic role of imposing a condition that an individual must satisfy in order to be the referent A proper name like a definite description contributes its sense to that of a sentence in which it occurs regardless of which individual actually is its referent and even if it has no referent at all This is because the condition imposed by sense the determinant of reference is independent of that which it determines For example Frege says the thought remains the same whether Odysseus has reference or not (1892 63) The same object can be presented in different ways under different modes of presentation but it is not essential to any mode of presentation that it actually present anything at allFreges conception of sense does not entail that every proper name has the sense of some definite description or that the sense of every proper name is an individual concept expressible by some definite description His conception of sense leaves open the possibility of non-descriptive senses such as percepts If one thinks of an object by means of a percept as one does when visually attending to it this is not equivalent to thinking of it under a description of the form the thing that looks thus-and-so One might verbally express a thought about an object one is looking at by saying something of the form the thing that looks thus-and-so is hellip but as Frege says about indexical thoughts the mere wording does not suffice for the expression of the thought

(1918 24) He does not explicitly make the analogous point in regard to proper names but nowhere does he explicitly assert that each proper name is equivalent to some definite description and his overall theory of sense and reference does not require this equivalenceRussells conception of presentation is quite different from what Frege means by presentation (in mode of presentation) For Russell any object that can be presented at all cannot be presented in different ways Russells restrictive notion of acquaintance is a direct cognitive relation and indeed is simply the converse of the relation of object and subject which constitutes presentation (1917 202) Notoriously Russell disqualifies public objects as objects of acquaintance but this is the price he is willing to pay to avoid the problem of names without bearers as well as Freges puzzles (about identity statements and about indirect quotation and attitude reports) He avoids having to appeal to senses to solve them The notion of sense as the determinant of reference has no place in Russells theory of language or thought Constituents of propositions are individuals (particulars and universals) and the Principle of Acquaintance requires that every proposition which we can understand must be composed wholly of constituents with which we are acquainted (1917 211) For Frege modes of presentation are the constituents of thoughts and the objects which modes of presentation present are not Because the relation between subject to object is mediated by a sense this relation is indirect unlike Russellian acquaintance6 So the difference between Freges two-tiered and Russells one-tiered semantics is reflected in their different epistemological views on presentation They are in their respective ways descriptivists about singular thought as well as about proper names

Russell held that ordinary proper names are abbreviated definite descriptions but he denied that definite descriptions (or expressions of any other sort) have two levels of semantic significance This was the central point of On Denoting (1905) For Russell what distinguishes both definite

descriptions and ordinary proper names from genuine logically proper names like the individual constants of logic is not that they do have senses but that they do not have references (they do have denotations but these are not their semantic values) For Frege there are two levels of semantic significance sense and reference and sense is primary Despite their differences neither Freges sense-descriptivism nor Russells abbreviational descriptivism is susceptible as Mills view is to the problem of names without bearers On both views a proper name can play its (primary) semantic role whether or not it belongs to anything But this is so for different reasons For Russell the reason is the semantic inertness of denotation for Frege it is the independence of sense from reference

2 Fregersquos Theory of Sense and Reference

Although Frege accepted something like the Naive Theory in his early work he later rejected it for reasons like those given above He formulated a radical alternative his famous theory of Sinn and Bedeutung We here translate Fregersquos terms into English as lsquosensersquo and lsquoreferencersquo respectively The distinction between sense and reference is most easily illustrated using sentences containing definite descriptions Consider (11)

11 The inventor of the bifocals is the first Postmaster General of the United States The definite descriptions in (11) refer to the same object Benjamin Franklin Yet they seem to present and determine that object in different ways for instance one presents him as an inventor whereas the other presents him as a Postmaster General Frege held that these definite descriptions differ in sense A sense according to Frege is a mode of presentation of an object and a way of thinking of an object A sense presents or determines an object Each of the above definite descriptions expresses a sense and each refers to whatever object its sense presents

Frege claimed that proper names also express senses The sense of a proper name like the sense of a definite description presents an object which is the referent of the name In that respect the sense of a proper name is like that of a definite description Frege often used definite descriptions to express the senses of proper names For instance he claimed that the sense of lsquoAristotlersquo (for some speakers) can be expressed by the definite description lsquothe Stagirite teacher of Alexander the Greatrsquo Thus some philosophers claim that Frege thought that the sense of any name can be expressed by a definite description

Whether or not this is so we shall initially be concerned with this descriptive version of Fregersquos theory (Non-descriptive Fregean theories will be discussed later)

Frege extended the theory of sense and reference to all expressions A predicate expresses a sense that presents a set of objects (or more accurately the characteristic function of a set of objects) This set is the referent of the predicate The truth value of a sentence is determined by the references of its parts for instance lsquoMark Twain is humanrsquo is determined to be true because the referent of the name is a member of the referent of the predicate lsquois humanrsquo that is the set of humans Thus Frege held that the reference of a sentence is its truth value (So the Bedeutung of an expression is comparable to its extension or reference in modern terminology) The sense of a full indicative sentence is a Gedanke or Thought The Thought that a sentence expresses presents the truth value of the sentence Thoughts are also the things that people assert and believe in this respect they are like the propositions of the Naive Theory

Fregersquos theory was largely motivated by the Objection from Cognitive Significance and deals handily with the examples used in that objection lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo differ in sense for most speakers The sense of the first for some speakers can be expressed by lsquothe author of Huckleberry Finnrsquo while the sense of the second for some speakers can be

expressed by lsquothe person who published US Grantrsquos autobiographyrsquo Thus sentences (1) and (2) express different senses or Thoughts So the sentences can differ in informativeness a priority and analyticity and a rational person can think that (1) and (2) differ in truth value Similarly for (3) and (4) and (5) and (6)

According to Fregersquos theory of attitude ascriptions the lsquothatrsquo-clauses that appear in belief ascriptions (9) and (10) refer to the Thoughts that (1) and (2) express

9 Mary believes that Mark Twain is Mark Twain10 Mary believes that Mark Twain is Samuel Clemens 1 Mark Twain is Mark Twain2 Mark Twain is Samuel Clemens

Thus (9) attributes to Mary belief in one Thought whereas (10) attributes to her belief in a different Thought Itrsquos possible for Mary to believe one of these Thoughts without believing the other so itrsquos possible for (9) and (10) to differ in truth value

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

descriptions a simple subject-predicate sentence of the form The F is G does not express a singular proposition of the subject-predicate form a is G but a general existential proposition what might be called a uniqueness proposition The quantificational structure of such a proposition is revealed only after the definite description is broken up to yield (in modern notation) the form (x)((y)(Fy y=x) amp Gx) in which the description not being a semantic unit does not even appear5 Accordingly for Russell if a proper name is a disguised description eg if George Kistiakowski is short for the inventor of silly putty the bearer of the name does not enter into the proposition expressed by a sentence in which the name occurs This is not because the name has a sense (in Freges sense of sense) but because it abbreviates a definite descriptionRussells view is clear from what he says about the name Bismarck In his view the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description (1917 208) Russell makes allowances for the fact that the requisite descriptionwill vary for different people or for the same person at different times (the description in our minds will probably be some more or less vague mass of historical knowledge far more in most cases than is required to identify him) hellip but so long as the object to which the name applies remains constant the particular description involved usually makes no difference to the truth or falsehood of the proposition in which the name appears (1917 208-9)For purposes of illustration he uses the description the first Chancellor of the German Empire Russell first considers the situation of Bismarck himself who might have used the name directly to designate [himself] hellip to ma[k]e a judgment about himself with himself as a constituent (209) Here the proper name has the direct use which it always wishes to have as simply standing for a certain object and not for a description of the object But our situation in referring to Bismarck is different from his

when we make a statement about something known only by description we often intend to make our statement not in the form involving the description but about the actual thing described That is when we say anything about Bismarck we should like if we could to make the judgment which Bismarck alone can make namely the judgment of which he himself is a constituent [But] in this we are necessarily defeated hellipWhat enables us to communicate in spite of the varying descriptions we employ is that we know there is a true proposition concerning the actual Bismarck and that however we may vary the description (as long as the description is correct) the proposition described is still the same This proposition which is described and is known to be true is what interests us but we are not acquainted with the proposition itself and do not know it though we know it is true (1917 210-11)The proposition that interests us is a singular proposition but we cannot actually think it-we can know it only by description that is by entertaining a general (uniqueness) proposition which is if true made true by a fact involving Bismarck But this general proposition does not itself involve Bismarck and would be thinkable even if Bismarck never existedFrege is a descriptivist of a different sort than Russell He claims not that proper names are disguised descriptions but that they have senses as well as references The sense of a name is both the mode of presentation and the determinant of its referent (it also functions for Frege as the indirect (as opposed to customary) reference when the name is embedded in a context of indirect quotation or propositional attitude ascription) Frege agrees with Russell and with Mill for that matter that words are ordinarily used to talk about things not ideas If words are used in the ordinary way what one intends to speak of is their reference (1892 58) Even so in so using them we must associate reference-determining properties with our words Moreover insofar as our words also express our thoughts they must correspond to constituents of those thoughts Thus for Frege the semantic and the cognitive

significance of expressions are intimately related Indeed because an expression can have a sense without having a reference Frege holds that the constituents of thoughts are senses not referencesFrege does not hold that every proper name is equivalent to some definite description but rather that expressions of both kinds are of the same semantic genus which he calls Eigennamen (literally translated as proper names but better paraphrased as singular terms) Unlike Russell he does not assimilate definite descriptions to quantificational phrases but treats them like proper names (properly so-called) as semantic units capable of having individuals as semantic values determined by their senses The sense of such an expression plays the semantic role of imposing a condition that an individual must satisfy in order to be the referent A proper name like a definite description contributes its sense to that of a sentence in which it occurs regardless of which individual actually is its referent and even if it has no referent at all This is because the condition imposed by sense the determinant of reference is independent of that which it determines For example Frege says the thought remains the same whether Odysseus has reference or not (1892 63) The same object can be presented in different ways under different modes of presentation but it is not essential to any mode of presentation that it actually present anything at allFreges conception of sense does not entail that every proper name has the sense of some definite description or that the sense of every proper name is an individual concept expressible by some definite description His conception of sense leaves open the possibility of non-descriptive senses such as percepts If one thinks of an object by means of a percept as one does when visually attending to it this is not equivalent to thinking of it under a description of the form the thing that looks thus-and-so One might verbally express a thought about an object one is looking at by saying something of the form the thing that looks thus-and-so is hellip but as Frege says about indexical thoughts the mere wording does not suffice for the expression of the thought

(1918 24) He does not explicitly make the analogous point in regard to proper names but nowhere does he explicitly assert that each proper name is equivalent to some definite description and his overall theory of sense and reference does not require this equivalenceRussells conception of presentation is quite different from what Frege means by presentation (in mode of presentation) For Russell any object that can be presented at all cannot be presented in different ways Russells restrictive notion of acquaintance is a direct cognitive relation and indeed is simply the converse of the relation of object and subject which constitutes presentation (1917 202) Notoriously Russell disqualifies public objects as objects of acquaintance but this is the price he is willing to pay to avoid the problem of names without bearers as well as Freges puzzles (about identity statements and about indirect quotation and attitude reports) He avoids having to appeal to senses to solve them The notion of sense as the determinant of reference has no place in Russells theory of language or thought Constituents of propositions are individuals (particulars and universals) and the Principle of Acquaintance requires that every proposition which we can understand must be composed wholly of constituents with which we are acquainted (1917 211) For Frege modes of presentation are the constituents of thoughts and the objects which modes of presentation present are not Because the relation between subject to object is mediated by a sense this relation is indirect unlike Russellian acquaintance6 So the difference between Freges two-tiered and Russells one-tiered semantics is reflected in their different epistemological views on presentation They are in their respective ways descriptivists about singular thought as well as about proper names

Russell held that ordinary proper names are abbreviated definite descriptions but he denied that definite descriptions (or expressions of any other sort) have two levels of semantic significance This was the central point of On Denoting (1905) For Russell what distinguishes both definite

descriptions and ordinary proper names from genuine logically proper names like the individual constants of logic is not that they do have senses but that they do not have references (they do have denotations but these are not their semantic values) For Frege there are two levels of semantic significance sense and reference and sense is primary Despite their differences neither Freges sense-descriptivism nor Russells abbreviational descriptivism is susceptible as Mills view is to the problem of names without bearers On both views a proper name can play its (primary) semantic role whether or not it belongs to anything But this is so for different reasons For Russell the reason is the semantic inertness of denotation for Frege it is the independence of sense from reference

2 Fregersquos Theory of Sense and Reference

Although Frege accepted something like the Naive Theory in his early work he later rejected it for reasons like those given above He formulated a radical alternative his famous theory of Sinn and Bedeutung We here translate Fregersquos terms into English as lsquosensersquo and lsquoreferencersquo respectively The distinction between sense and reference is most easily illustrated using sentences containing definite descriptions Consider (11)

11 The inventor of the bifocals is the first Postmaster General of the United States The definite descriptions in (11) refer to the same object Benjamin Franklin Yet they seem to present and determine that object in different ways for instance one presents him as an inventor whereas the other presents him as a Postmaster General Frege held that these definite descriptions differ in sense A sense according to Frege is a mode of presentation of an object and a way of thinking of an object A sense presents or determines an object Each of the above definite descriptions expresses a sense and each refers to whatever object its sense presents

Frege claimed that proper names also express senses The sense of a proper name like the sense of a definite description presents an object which is the referent of the name In that respect the sense of a proper name is like that of a definite description Frege often used definite descriptions to express the senses of proper names For instance he claimed that the sense of lsquoAristotlersquo (for some speakers) can be expressed by the definite description lsquothe Stagirite teacher of Alexander the Greatrsquo Thus some philosophers claim that Frege thought that the sense of any name can be expressed by a definite description

Whether or not this is so we shall initially be concerned with this descriptive version of Fregersquos theory (Non-descriptive Fregean theories will be discussed later)

Frege extended the theory of sense and reference to all expressions A predicate expresses a sense that presents a set of objects (or more accurately the characteristic function of a set of objects) This set is the referent of the predicate The truth value of a sentence is determined by the references of its parts for instance lsquoMark Twain is humanrsquo is determined to be true because the referent of the name is a member of the referent of the predicate lsquois humanrsquo that is the set of humans Thus Frege held that the reference of a sentence is its truth value (So the Bedeutung of an expression is comparable to its extension or reference in modern terminology) The sense of a full indicative sentence is a Gedanke or Thought The Thought that a sentence expresses presents the truth value of the sentence Thoughts are also the things that people assert and believe in this respect they are like the propositions of the Naive Theory

Fregersquos theory was largely motivated by the Objection from Cognitive Significance and deals handily with the examples used in that objection lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo differ in sense for most speakers The sense of the first for some speakers can be expressed by lsquothe author of Huckleberry Finnrsquo while the sense of the second for some speakers can be

expressed by lsquothe person who published US Grantrsquos autobiographyrsquo Thus sentences (1) and (2) express different senses or Thoughts So the sentences can differ in informativeness a priority and analyticity and a rational person can think that (1) and (2) differ in truth value Similarly for (3) and (4) and (5) and (6)

According to Fregersquos theory of attitude ascriptions the lsquothatrsquo-clauses that appear in belief ascriptions (9) and (10) refer to the Thoughts that (1) and (2) express

9 Mary believes that Mark Twain is Mark Twain10 Mary believes that Mark Twain is Samuel Clemens 1 Mark Twain is Mark Twain2 Mark Twain is Samuel Clemens

Thus (9) attributes to Mary belief in one Thought whereas (10) attributes to her belief in a different Thought Itrsquos possible for Mary to believe one of these Thoughts without believing the other so itrsquos possible for (9) and (10) to differ in truth value

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

when we make a statement about something known only by description we often intend to make our statement not in the form involving the description but about the actual thing described That is when we say anything about Bismarck we should like if we could to make the judgment which Bismarck alone can make namely the judgment of which he himself is a constituent [But] in this we are necessarily defeated hellipWhat enables us to communicate in spite of the varying descriptions we employ is that we know there is a true proposition concerning the actual Bismarck and that however we may vary the description (as long as the description is correct) the proposition described is still the same This proposition which is described and is known to be true is what interests us but we are not acquainted with the proposition itself and do not know it though we know it is true (1917 210-11)The proposition that interests us is a singular proposition but we cannot actually think it-we can know it only by description that is by entertaining a general (uniqueness) proposition which is if true made true by a fact involving Bismarck But this general proposition does not itself involve Bismarck and would be thinkable even if Bismarck never existedFrege is a descriptivist of a different sort than Russell He claims not that proper names are disguised descriptions but that they have senses as well as references The sense of a name is both the mode of presentation and the determinant of its referent (it also functions for Frege as the indirect (as opposed to customary) reference when the name is embedded in a context of indirect quotation or propositional attitude ascription) Frege agrees with Russell and with Mill for that matter that words are ordinarily used to talk about things not ideas If words are used in the ordinary way what one intends to speak of is their reference (1892 58) Even so in so using them we must associate reference-determining properties with our words Moreover insofar as our words also express our thoughts they must correspond to constituents of those thoughts Thus for Frege the semantic and the cognitive

significance of expressions are intimately related Indeed because an expression can have a sense without having a reference Frege holds that the constituents of thoughts are senses not referencesFrege does not hold that every proper name is equivalent to some definite description but rather that expressions of both kinds are of the same semantic genus which he calls Eigennamen (literally translated as proper names but better paraphrased as singular terms) Unlike Russell he does not assimilate definite descriptions to quantificational phrases but treats them like proper names (properly so-called) as semantic units capable of having individuals as semantic values determined by their senses The sense of such an expression plays the semantic role of imposing a condition that an individual must satisfy in order to be the referent A proper name like a definite description contributes its sense to that of a sentence in which it occurs regardless of which individual actually is its referent and even if it has no referent at all This is because the condition imposed by sense the determinant of reference is independent of that which it determines For example Frege says the thought remains the same whether Odysseus has reference or not (1892 63) The same object can be presented in different ways under different modes of presentation but it is not essential to any mode of presentation that it actually present anything at allFreges conception of sense does not entail that every proper name has the sense of some definite description or that the sense of every proper name is an individual concept expressible by some definite description His conception of sense leaves open the possibility of non-descriptive senses such as percepts If one thinks of an object by means of a percept as one does when visually attending to it this is not equivalent to thinking of it under a description of the form the thing that looks thus-and-so One might verbally express a thought about an object one is looking at by saying something of the form the thing that looks thus-and-so is hellip but as Frege says about indexical thoughts the mere wording does not suffice for the expression of the thought

(1918 24) He does not explicitly make the analogous point in regard to proper names but nowhere does he explicitly assert that each proper name is equivalent to some definite description and his overall theory of sense and reference does not require this equivalenceRussells conception of presentation is quite different from what Frege means by presentation (in mode of presentation) For Russell any object that can be presented at all cannot be presented in different ways Russells restrictive notion of acquaintance is a direct cognitive relation and indeed is simply the converse of the relation of object and subject which constitutes presentation (1917 202) Notoriously Russell disqualifies public objects as objects of acquaintance but this is the price he is willing to pay to avoid the problem of names without bearers as well as Freges puzzles (about identity statements and about indirect quotation and attitude reports) He avoids having to appeal to senses to solve them The notion of sense as the determinant of reference has no place in Russells theory of language or thought Constituents of propositions are individuals (particulars and universals) and the Principle of Acquaintance requires that every proposition which we can understand must be composed wholly of constituents with which we are acquainted (1917 211) For Frege modes of presentation are the constituents of thoughts and the objects which modes of presentation present are not Because the relation between subject to object is mediated by a sense this relation is indirect unlike Russellian acquaintance6 So the difference between Freges two-tiered and Russells one-tiered semantics is reflected in their different epistemological views on presentation They are in their respective ways descriptivists about singular thought as well as about proper names

Russell held that ordinary proper names are abbreviated definite descriptions but he denied that definite descriptions (or expressions of any other sort) have two levels of semantic significance This was the central point of On Denoting (1905) For Russell what distinguishes both definite

descriptions and ordinary proper names from genuine logically proper names like the individual constants of logic is not that they do have senses but that they do not have references (they do have denotations but these are not their semantic values) For Frege there are two levels of semantic significance sense and reference and sense is primary Despite their differences neither Freges sense-descriptivism nor Russells abbreviational descriptivism is susceptible as Mills view is to the problem of names without bearers On both views a proper name can play its (primary) semantic role whether or not it belongs to anything But this is so for different reasons For Russell the reason is the semantic inertness of denotation for Frege it is the independence of sense from reference

2 Fregersquos Theory of Sense and Reference

Although Frege accepted something like the Naive Theory in his early work he later rejected it for reasons like those given above He formulated a radical alternative his famous theory of Sinn and Bedeutung We here translate Fregersquos terms into English as lsquosensersquo and lsquoreferencersquo respectively The distinction between sense and reference is most easily illustrated using sentences containing definite descriptions Consider (11)

11 The inventor of the bifocals is the first Postmaster General of the United States The definite descriptions in (11) refer to the same object Benjamin Franklin Yet they seem to present and determine that object in different ways for instance one presents him as an inventor whereas the other presents him as a Postmaster General Frege held that these definite descriptions differ in sense A sense according to Frege is a mode of presentation of an object and a way of thinking of an object A sense presents or determines an object Each of the above definite descriptions expresses a sense and each refers to whatever object its sense presents

Frege claimed that proper names also express senses The sense of a proper name like the sense of a definite description presents an object which is the referent of the name In that respect the sense of a proper name is like that of a definite description Frege often used definite descriptions to express the senses of proper names For instance he claimed that the sense of lsquoAristotlersquo (for some speakers) can be expressed by the definite description lsquothe Stagirite teacher of Alexander the Greatrsquo Thus some philosophers claim that Frege thought that the sense of any name can be expressed by a definite description

Whether or not this is so we shall initially be concerned with this descriptive version of Fregersquos theory (Non-descriptive Fregean theories will be discussed later)

Frege extended the theory of sense and reference to all expressions A predicate expresses a sense that presents a set of objects (or more accurately the characteristic function of a set of objects) This set is the referent of the predicate The truth value of a sentence is determined by the references of its parts for instance lsquoMark Twain is humanrsquo is determined to be true because the referent of the name is a member of the referent of the predicate lsquois humanrsquo that is the set of humans Thus Frege held that the reference of a sentence is its truth value (So the Bedeutung of an expression is comparable to its extension or reference in modern terminology) The sense of a full indicative sentence is a Gedanke or Thought The Thought that a sentence expresses presents the truth value of the sentence Thoughts are also the things that people assert and believe in this respect they are like the propositions of the Naive Theory

Fregersquos theory was largely motivated by the Objection from Cognitive Significance and deals handily with the examples used in that objection lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo differ in sense for most speakers The sense of the first for some speakers can be expressed by lsquothe author of Huckleberry Finnrsquo while the sense of the second for some speakers can be

expressed by lsquothe person who published US Grantrsquos autobiographyrsquo Thus sentences (1) and (2) express different senses or Thoughts So the sentences can differ in informativeness a priority and analyticity and a rational person can think that (1) and (2) differ in truth value Similarly for (3) and (4) and (5) and (6)

According to Fregersquos theory of attitude ascriptions the lsquothatrsquo-clauses that appear in belief ascriptions (9) and (10) refer to the Thoughts that (1) and (2) express

9 Mary believes that Mark Twain is Mark Twain10 Mary believes that Mark Twain is Samuel Clemens 1 Mark Twain is Mark Twain2 Mark Twain is Samuel Clemens

Thus (9) attributes to Mary belief in one Thought whereas (10) attributes to her belief in a different Thought Itrsquos possible for Mary to believe one of these Thoughts without believing the other so itrsquos possible for (9) and (10) to differ in truth value

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

significance of expressions are intimately related Indeed because an expression can have a sense without having a reference Frege holds that the constituents of thoughts are senses not referencesFrege does not hold that every proper name is equivalent to some definite description but rather that expressions of both kinds are of the same semantic genus which he calls Eigennamen (literally translated as proper names but better paraphrased as singular terms) Unlike Russell he does not assimilate definite descriptions to quantificational phrases but treats them like proper names (properly so-called) as semantic units capable of having individuals as semantic values determined by their senses The sense of such an expression plays the semantic role of imposing a condition that an individual must satisfy in order to be the referent A proper name like a definite description contributes its sense to that of a sentence in which it occurs regardless of which individual actually is its referent and even if it has no referent at all This is because the condition imposed by sense the determinant of reference is independent of that which it determines For example Frege says the thought remains the same whether Odysseus has reference or not (1892 63) The same object can be presented in different ways under different modes of presentation but it is not essential to any mode of presentation that it actually present anything at allFreges conception of sense does not entail that every proper name has the sense of some definite description or that the sense of every proper name is an individual concept expressible by some definite description His conception of sense leaves open the possibility of non-descriptive senses such as percepts If one thinks of an object by means of a percept as one does when visually attending to it this is not equivalent to thinking of it under a description of the form the thing that looks thus-and-so One might verbally express a thought about an object one is looking at by saying something of the form the thing that looks thus-and-so is hellip but as Frege says about indexical thoughts the mere wording does not suffice for the expression of the thought

(1918 24) He does not explicitly make the analogous point in regard to proper names but nowhere does he explicitly assert that each proper name is equivalent to some definite description and his overall theory of sense and reference does not require this equivalenceRussells conception of presentation is quite different from what Frege means by presentation (in mode of presentation) For Russell any object that can be presented at all cannot be presented in different ways Russells restrictive notion of acquaintance is a direct cognitive relation and indeed is simply the converse of the relation of object and subject which constitutes presentation (1917 202) Notoriously Russell disqualifies public objects as objects of acquaintance but this is the price he is willing to pay to avoid the problem of names without bearers as well as Freges puzzles (about identity statements and about indirect quotation and attitude reports) He avoids having to appeal to senses to solve them The notion of sense as the determinant of reference has no place in Russells theory of language or thought Constituents of propositions are individuals (particulars and universals) and the Principle of Acquaintance requires that every proposition which we can understand must be composed wholly of constituents with which we are acquainted (1917 211) For Frege modes of presentation are the constituents of thoughts and the objects which modes of presentation present are not Because the relation between subject to object is mediated by a sense this relation is indirect unlike Russellian acquaintance6 So the difference between Freges two-tiered and Russells one-tiered semantics is reflected in their different epistemological views on presentation They are in their respective ways descriptivists about singular thought as well as about proper names

Russell held that ordinary proper names are abbreviated definite descriptions but he denied that definite descriptions (or expressions of any other sort) have two levels of semantic significance This was the central point of On Denoting (1905) For Russell what distinguishes both definite

descriptions and ordinary proper names from genuine logically proper names like the individual constants of logic is not that they do have senses but that they do not have references (they do have denotations but these are not their semantic values) For Frege there are two levels of semantic significance sense and reference and sense is primary Despite their differences neither Freges sense-descriptivism nor Russells abbreviational descriptivism is susceptible as Mills view is to the problem of names without bearers On both views a proper name can play its (primary) semantic role whether or not it belongs to anything But this is so for different reasons For Russell the reason is the semantic inertness of denotation for Frege it is the independence of sense from reference

2 Fregersquos Theory of Sense and Reference

Although Frege accepted something like the Naive Theory in his early work he later rejected it for reasons like those given above He formulated a radical alternative his famous theory of Sinn and Bedeutung We here translate Fregersquos terms into English as lsquosensersquo and lsquoreferencersquo respectively The distinction between sense and reference is most easily illustrated using sentences containing definite descriptions Consider (11)

11 The inventor of the bifocals is the first Postmaster General of the United States The definite descriptions in (11) refer to the same object Benjamin Franklin Yet they seem to present and determine that object in different ways for instance one presents him as an inventor whereas the other presents him as a Postmaster General Frege held that these definite descriptions differ in sense A sense according to Frege is a mode of presentation of an object and a way of thinking of an object A sense presents or determines an object Each of the above definite descriptions expresses a sense and each refers to whatever object its sense presents

Frege claimed that proper names also express senses The sense of a proper name like the sense of a definite description presents an object which is the referent of the name In that respect the sense of a proper name is like that of a definite description Frege often used definite descriptions to express the senses of proper names For instance he claimed that the sense of lsquoAristotlersquo (for some speakers) can be expressed by the definite description lsquothe Stagirite teacher of Alexander the Greatrsquo Thus some philosophers claim that Frege thought that the sense of any name can be expressed by a definite description

Whether or not this is so we shall initially be concerned with this descriptive version of Fregersquos theory (Non-descriptive Fregean theories will be discussed later)

Frege extended the theory of sense and reference to all expressions A predicate expresses a sense that presents a set of objects (or more accurately the characteristic function of a set of objects) This set is the referent of the predicate The truth value of a sentence is determined by the references of its parts for instance lsquoMark Twain is humanrsquo is determined to be true because the referent of the name is a member of the referent of the predicate lsquois humanrsquo that is the set of humans Thus Frege held that the reference of a sentence is its truth value (So the Bedeutung of an expression is comparable to its extension or reference in modern terminology) The sense of a full indicative sentence is a Gedanke or Thought The Thought that a sentence expresses presents the truth value of the sentence Thoughts are also the things that people assert and believe in this respect they are like the propositions of the Naive Theory

Fregersquos theory was largely motivated by the Objection from Cognitive Significance and deals handily with the examples used in that objection lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo differ in sense for most speakers The sense of the first for some speakers can be expressed by lsquothe author of Huckleberry Finnrsquo while the sense of the second for some speakers can be

expressed by lsquothe person who published US Grantrsquos autobiographyrsquo Thus sentences (1) and (2) express different senses or Thoughts So the sentences can differ in informativeness a priority and analyticity and a rational person can think that (1) and (2) differ in truth value Similarly for (3) and (4) and (5) and (6)

According to Fregersquos theory of attitude ascriptions the lsquothatrsquo-clauses that appear in belief ascriptions (9) and (10) refer to the Thoughts that (1) and (2) express

9 Mary believes that Mark Twain is Mark Twain10 Mary believes that Mark Twain is Samuel Clemens 1 Mark Twain is Mark Twain2 Mark Twain is Samuel Clemens

Thus (9) attributes to Mary belief in one Thought whereas (10) attributes to her belief in a different Thought Itrsquos possible for Mary to believe one of these Thoughts without believing the other so itrsquos possible for (9) and (10) to differ in truth value

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

(1918 24) He does not explicitly make the analogous point in regard to proper names but nowhere does he explicitly assert that each proper name is equivalent to some definite description and his overall theory of sense and reference does not require this equivalenceRussells conception of presentation is quite different from what Frege means by presentation (in mode of presentation) For Russell any object that can be presented at all cannot be presented in different ways Russells restrictive notion of acquaintance is a direct cognitive relation and indeed is simply the converse of the relation of object and subject which constitutes presentation (1917 202) Notoriously Russell disqualifies public objects as objects of acquaintance but this is the price he is willing to pay to avoid the problem of names without bearers as well as Freges puzzles (about identity statements and about indirect quotation and attitude reports) He avoids having to appeal to senses to solve them The notion of sense as the determinant of reference has no place in Russells theory of language or thought Constituents of propositions are individuals (particulars and universals) and the Principle of Acquaintance requires that every proposition which we can understand must be composed wholly of constituents with which we are acquainted (1917 211) For Frege modes of presentation are the constituents of thoughts and the objects which modes of presentation present are not Because the relation between subject to object is mediated by a sense this relation is indirect unlike Russellian acquaintance6 So the difference between Freges two-tiered and Russells one-tiered semantics is reflected in their different epistemological views on presentation They are in their respective ways descriptivists about singular thought as well as about proper names

Russell held that ordinary proper names are abbreviated definite descriptions but he denied that definite descriptions (or expressions of any other sort) have two levels of semantic significance This was the central point of On Denoting (1905) For Russell what distinguishes both definite

descriptions and ordinary proper names from genuine logically proper names like the individual constants of logic is not that they do have senses but that they do not have references (they do have denotations but these are not their semantic values) For Frege there are two levels of semantic significance sense and reference and sense is primary Despite their differences neither Freges sense-descriptivism nor Russells abbreviational descriptivism is susceptible as Mills view is to the problem of names without bearers On both views a proper name can play its (primary) semantic role whether or not it belongs to anything But this is so for different reasons For Russell the reason is the semantic inertness of denotation for Frege it is the independence of sense from reference

2 Fregersquos Theory of Sense and Reference

Although Frege accepted something like the Naive Theory in his early work he later rejected it for reasons like those given above He formulated a radical alternative his famous theory of Sinn and Bedeutung We here translate Fregersquos terms into English as lsquosensersquo and lsquoreferencersquo respectively The distinction between sense and reference is most easily illustrated using sentences containing definite descriptions Consider (11)

11 The inventor of the bifocals is the first Postmaster General of the United States The definite descriptions in (11) refer to the same object Benjamin Franklin Yet they seem to present and determine that object in different ways for instance one presents him as an inventor whereas the other presents him as a Postmaster General Frege held that these definite descriptions differ in sense A sense according to Frege is a mode of presentation of an object and a way of thinking of an object A sense presents or determines an object Each of the above definite descriptions expresses a sense and each refers to whatever object its sense presents

Frege claimed that proper names also express senses The sense of a proper name like the sense of a definite description presents an object which is the referent of the name In that respect the sense of a proper name is like that of a definite description Frege often used definite descriptions to express the senses of proper names For instance he claimed that the sense of lsquoAristotlersquo (for some speakers) can be expressed by the definite description lsquothe Stagirite teacher of Alexander the Greatrsquo Thus some philosophers claim that Frege thought that the sense of any name can be expressed by a definite description

Whether or not this is so we shall initially be concerned with this descriptive version of Fregersquos theory (Non-descriptive Fregean theories will be discussed later)

Frege extended the theory of sense and reference to all expressions A predicate expresses a sense that presents a set of objects (or more accurately the characteristic function of a set of objects) This set is the referent of the predicate The truth value of a sentence is determined by the references of its parts for instance lsquoMark Twain is humanrsquo is determined to be true because the referent of the name is a member of the referent of the predicate lsquois humanrsquo that is the set of humans Thus Frege held that the reference of a sentence is its truth value (So the Bedeutung of an expression is comparable to its extension or reference in modern terminology) The sense of a full indicative sentence is a Gedanke or Thought The Thought that a sentence expresses presents the truth value of the sentence Thoughts are also the things that people assert and believe in this respect they are like the propositions of the Naive Theory

Fregersquos theory was largely motivated by the Objection from Cognitive Significance and deals handily with the examples used in that objection lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo differ in sense for most speakers The sense of the first for some speakers can be expressed by lsquothe author of Huckleberry Finnrsquo while the sense of the second for some speakers can be

expressed by lsquothe person who published US Grantrsquos autobiographyrsquo Thus sentences (1) and (2) express different senses or Thoughts So the sentences can differ in informativeness a priority and analyticity and a rational person can think that (1) and (2) differ in truth value Similarly for (3) and (4) and (5) and (6)

According to Fregersquos theory of attitude ascriptions the lsquothatrsquo-clauses that appear in belief ascriptions (9) and (10) refer to the Thoughts that (1) and (2) express

9 Mary believes that Mark Twain is Mark Twain10 Mary believes that Mark Twain is Samuel Clemens 1 Mark Twain is Mark Twain2 Mark Twain is Samuel Clemens

Thus (9) attributes to Mary belief in one Thought whereas (10) attributes to her belief in a different Thought Itrsquos possible for Mary to believe one of these Thoughts without believing the other so itrsquos possible for (9) and (10) to differ in truth value

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

descriptions and ordinary proper names from genuine logically proper names like the individual constants of logic is not that they do have senses but that they do not have references (they do have denotations but these are not their semantic values) For Frege there are two levels of semantic significance sense and reference and sense is primary Despite their differences neither Freges sense-descriptivism nor Russells abbreviational descriptivism is susceptible as Mills view is to the problem of names without bearers On both views a proper name can play its (primary) semantic role whether or not it belongs to anything But this is so for different reasons For Russell the reason is the semantic inertness of denotation for Frege it is the independence of sense from reference

2 Fregersquos Theory of Sense and Reference

Although Frege accepted something like the Naive Theory in his early work he later rejected it for reasons like those given above He formulated a radical alternative his famous theory of Sinn and Bedeutung We here translate Fregersquos terms into English as lsquosensersquo and lsquoreferencersquo respectively The distinction between sense and reference is most easily illustrated using sentences containing definite descriptions Consider (11)

11 The inventor of the bifocals is the first Postmaster General of the United States The definite descriptions in (11) refer to the same object Benjamin Franklin Yet they seem to present and determine that object in different ways for instance one presents him as an inventor whereas the other presents him as a Postmaster General Frege held that these definite descriptions differ in sense A sense according to Frege is a mode of presentation of an object and a way of thinking of an object A sense presents or determines an object Each of the above definite descriptions expresses a sense and each refers to whatever object its sense presents

Frege claimed that proper names also express senses The sense of a proper name like the sense of a definite description presents an object which is the referent of the name In that respect the sense of a proper name is like that of a definite description Frege often used definite descriptions to express the senses of proper names For instance he claimed that the sense of lsquoAristotlersquo (for some speakers) can be expressed by the definite description lsquothe Stagirite teacher of Alexander the Greatrsquo Thus some philosophers claim that Frege thought that the sense of any name can be expressed by a definite description

Whether or not this is so we shall initially be concerned with this descriptive version of Fregersquos theory (Non-descriptive Fregean theories will be discussed later)

Frege extended the theory of sense and reference to all expressions A predicate expresses a sense that presents a set of objects (or more accurately the characteristic function of a set of objects) This set is the referent of the predicate The truth value of a sentence is determined by the references of its parts for instance lsquoMark Twain is humanrsquo is determined to be true because the referent of the name is a member of the referent of the predicate lsquois humanrsquo that is the set of humans Thus Frege held that the reference of a sentence is its truth value (So the Bedeutung of an expression is comparable to its extension or reference in modern terminology) The sense of a full indicative sentence is a Gedanke or Thought The Thought that a sentence expresses presents the truth value of the sentence Thoughts are also the things that people assert and believe in this respect they are like the propositions of the Naive Theory

Fregersquos theory was largely motivated by the Objection from Cognitive Significance and deals handily with the examples used in that objection lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo differ in sense for most speakers The sense of the first for some speakers can be expressed by lsquothe author of Huckleberry Finnrsquo while the sense of the second for some speakers can be

expressed by lsquothe person who published US Grantrsquos autobiographyrsquo Thus sentences (1) and (2) express different senses or Thoughts So the sentences can differ in informativeness a priority and analyticity and a rational person can think that (1) and (2) differ in truth value Similarly for (3) and (4) and (5) and (6)

According to Fregersquos theory of attitude ascriptions the lsquothatrsquo-clauses that appear in belief ascriptions (9) and (10) refer to the Thoughts that (1) and (2) express

9 Mary believes that Mark Twain is Mark Twain10 Mary believes that Mark Twain is Samuel Clemens 1 Mark Twain is Mark Twain2 Mark Twain is Samuel Clemens

Thus (9) attributes to Mary belief in one Thought whereas (10) attributes to her belief in a different Thought Itrsquos possible for Mary to believe one of these Thoughts without believing the other so itrsquos possible for (9) and (10) to differ in truth value

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

Whether or not this is so we shall initially be concerned with this descriptive version of Fregersquos theory (Non-descriptive Fregean theories will be discussed later)

Frege extended the theory of sense and reference to all expressions A predicate expresses a sense that presents a set of objects (or more accurately the characteristic function of a set of objects) This set is the referent of the predicate The truth value of a sentence is determined by the references of its parts for instance lsquoMark Twain is humanrsquo is determined to be true because the referent of the name is a member of the referent of the predicate lsquois humanrsquo that is the set of humans Thus Frege held that the reference of a sentence is its truth value (So the Bedeutung of an expression is comparable to its extension or reference in modern terminology) The sense of a full indicative sentence is a Gedanke or Thought The Thought that a sentence expresses presents the truth value of the sentence Thoughts are also the things that people assert and believe in this respect they are like the propositions of the Naive Theory

Fregersquos theory was largely motivated by the Objection from Cognitive Significance and deals handily with the examples used in that objection lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo differ in sense for most speakers The sense of the first for some speakers can be expressed by lsquothe author of Huckleberry Finnrsquo while the sense of the second for some speakers can be

expressed by lsquothe person who published US Grantrsquos autobiographyrsquo Thus sentences (1) and (2) express different senses or Thoughts So the sentences can differ in informativeness a priority and analyticity and a rational person can think that (1) and (2) differ in truth value Similarly for (3) and (4) and (5) and (6)

According to Fregersquos theory of attitude ascriptions the lsquothatrsquo-clauses that appear in belief ascriptions (9) and (10) refer to the Thoughts that (1) and (2) express

9 Mary believes that Mark Twain is Mark Twain10 Mary believes that Mark Twain is Samuel Clemens 1 Mark Twain is Mark Twain2 Mark Twain is Samuel Clemens

Thus (9) attributes to Mary belief in one Thought whereas (10) attributes to her belief in a different Thought Itrsquos possible for Mary to believe one of these Thoughts without believing the other so itrsquos possible for (9) and (10) to differ in truth value

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

Fregersquos theory allows proper names to express senses that fail to present an object

1

For

instance the name lsquoPegasusrsquo expresses a sense that might also be expressed by the description lsquothe winged horsersquo This sense does not present an object and so the name fails to refer Nevertheless sentence (7) expresses a Thought and is (in that sense) meaningful Itrsquos not entirely clear how Fregersquos theory would deal with apparently true negative existentials At first glance Fregersquos theory seems to entail that lsquoPegasus existsrsquo has no truth value since the name lsquoPegasusrsquo fails to refer But itrsquos open to Frege to hold that when a name appears in an existential sentence it refers to its usual sense Thus lsquoPegasus existsrsquo might mean roughly the same thing as lsquoThe sense expressed by lsquoPegasusrsquo presents an objectrsquo This is false so (8) is true

3 Russellrsquos Theory

Bertrand Russell also rejected the Naive Theory for reasons much like Fregersquos But his proposed replacement was a relatively modest modification of the Naive Theory compared with Fregersquos radical alternative

Russell unlike Frege accepted the existence of singular propositions But he thought that agents entertain relatively few singular propositions and rarely express singular propositions with their utterances According to Russell an agent A can entertain a proposition P only if A is directly acquainted with all of Prsquos constituents Russell held that there are strong constraints on the things with which an agent can be directly acquainted If O is an object then A is directly acquainted with O at time T only if Arsquos experiences at T necessitate the existence of O at T Furthermore if A is directly acquainted with objects O and O at T and O is identical with O then A believes at T the singular proposition that they are identical ltO O Identitygt If O and O are distinct then A does not believe this proposition but rather its negation Similar constraints on direct acquaintance hold for the properties and relations that appear in

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

1

Gareth Evans (19xx) and John McDowell have argued that (i) Frege denied that non-

referring proper names have senses and (ii) the claim that non-referring proper names have senses is inconsistent with (the spirit of) Fregersquos theory of sense and reference in particular with his claim that a sense is a way of thinking of an object Evansrsquos and McDowellrsquos interpretations of Frege are strained In any case a Fregean theory that allows non-referring proper names to express senses is more interesting than one that does not and certainly is better able to deal with Fregersquos Puzzles Therefore this is the sort of Fregean theory we shall consider here

propositions Thus an agent is directly acquainted with very little perhaps only herself her current experiences and the properties and relations exemplified by her current experiencesThe propositions she can entertain can have only items of these sorts as constituents Furthermore a sentence in Arsquos language expresses proposition P only if A can entertain PThese doctrines have direct implications for puzzles of cognitive significance Suppose N and N are two names in Arsquos language and suppose that lsquo=rsquo expresses the relation of identity Then the sentence ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language only if A is directly acquainted with O and O Thus if ldquoN=Nrdquo expresses the singular proposition ltO O Identitygt in Arsquos language and this proposition is true then A believes it If the proposition is false then A believes its negation So if N and N are Millian names (or logically proper names as Russell puts it) in Arsquos language for the same object O then A cannot think that ldquoN=Nrdquo and ldquoN=Nrdquo differ in truth value It also seems that these sentences cannot differ in cognitive significance for A in any other respect

Russell held however that sentences containing ordinary proper names like (1) and (2) can differ in cognitive significance Thus Russell held that ordinary proper names like lsquoMark Twainrsquo and lsquoSamuel Clemensrsquo are not logically proper names They are instead abbreviations for definite descriptions For a given agent sentences (1) and (2) might be abbreviations for sentences (1d) and (2d)

1d The author of Huckleberry Finn is the author of Huckleberry Finn2d The author of Huckleberry Finn is the person who published US Grantrsquos

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

autobiographyThese sentences do not express propositions that have Twain as a constituent They instead express propositions whose constituents are the relation of authoring the property of being a person the relation of publishing and so on

2

Thus a rational agent can think

that (1) is true and (2) is false The sentences can also differ in a priority and analyticity

3

Russell furthermore held that strictly speaking no ordinary proper name refers to an individual His reason is that ordinary proper names abbreviate definite descriptions and definite descriptions (on Russellrsquos view) are semantically like quantifier phrases such as lsquoall dogsrsquo and lsquosome catsrsquo which do not refer to individuals For instance a sentence containing a definite description such as (12) expresses a complex proposition that is more perspicuously articulated by sentences (12a) and (12b)

2

Strictly speaking Russell held that predicates like lsquoauthorrsquo and lsquothinkrsquo contribute

propositional functions rather than properties and relations to the propositions expressed

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

by sentences A propositional function is a function from individuals to singular propositions We ignore this detail here

3

Sentence (2d) contains the proper name lsquoUS Grantrsquo but no agent other than Grant

entertains a proposition that has Grant as a constituent Thus for most agents the name lsquoUS Grantrsquo is itself an abbreviation for a definite description If an agent other than Grant wished to articulate in unabbreviated form the proposition that she entertains when she understands (2d) she would need to replace the name lsquoUS Grantrsquo with a definite description whose constituent singular terms (if any) refer only to items with which she is directly acquainted She would similarly need to replace the names lsquoHuckleberry Finnrsquo and the predicates lsquoauthorrsquo lsquopersonrsquo lsquopublishrsquo and lsquoautobiographyrsquo

12 The author of Huckleberry Finn thinks

1 12a There is a thing such that it authors Huckleberry Finn and everything that authors

Huckleberry Finn is identical with it and it thinks

2 12b 1113088x(Authors(x HF) amp 1113088y(Authors(y HF) 6 y=x) amp Thinks(x))

The proposition that (12) expresses has a constituent structure that is very different from the syntactic structure of sentence (12) the propositionrsquos structure is instead very much like the syntactic structure of (12b) This proposition has as constituents the relation of authoring being identical the second-order property of being an instantiated property and so on It does not have a constituent that corresponds to the definite description lsquothe author of Huckleberry Finnrsquo the contribution of the definite description to the proposition that (12) expresses is ldquoscatteredrdquo among various constituents of the proposition Furthermore there is no expression in (12a) or (12b) that strictly speaking refers to Twain similarly there is no constituent of the proposition that (12) expresses that determines or presents Twain Thus ordinary proper names do not strictly speaking refer on Russellrsquos view However Russell sometimes says that a definite description jthe Fk denotes object O if O is the unique object that is F

Russellrsquos solutions to Fregersquos Puzzles are similar to Fregersquos (1) and (2) can differ in informativeness a priority and analyticity because they express different descriptive

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it

propositions Similarly for (3) and (4) and (5) and (6) lsquoThatrsquo-clauses in belief ascriptions refer to the propositions expressed by the embedded sentences Therefore (9) and (10) attribute to Mary belief in different propositions and so can differ in truth value The name lsquoPegasusrsquo contributes a scattered complex of properties and relations to the proposition expressed by sentence (7) Therefore sentence (7) is meaningful even though lsquoPegasusrsquo fails to refer (and denote) Russell may have a more satisfactory answer to the problem of true negative existentials than Frege On Russellrsquos view sentence (8) on one understanding of it expresses a proposition that might be more perspicuously expressed by (8a)

4

8 Pegasus does not exist

8a -1113088x(Winged(x) amp Horse(x) amp 1113088y(Winged(y) and Horse(y) 6 y=x) amp 1113088zz=x) The proposition expressed by (8a) is straightforwardly true because it is not the case that there is a winged horse Therefore (8) is false on this understanding of it