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MORE ABOUT FREGE’S
PHILOSOPHY OF LANGUAGE
Extending Frege’s story from singular terms!
‘BUCEPHALUS IS A HORSE’
Bucephalus is a horse
What does this sentence mean?
Breaks down into two questions:
What does ‘Bucephalus’ mean? What does ‘is a horse’ mean?
DILEMMA ABOUT IDENTITYFrege’s opening question:
‘Equality gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A
relation between objects, or between names or signs of objects?’
When we express ‘Hesperus is Phosphorus’ using the ‘is’ of identity, ought we to write it as
(1) Hesperus = Phosphorus
(2) ‘Hesperus’ = ‘Phosphorus’
IDENTITY AS A RELATION BETWEEN THINGS
Frege points out the following:
‘a=a and a=b are obviously statements of differing cognitive value; a=a holds a priori and, according to Kant, is to be labelled analytic, while statements of
the form a=b often contain very valuable extensions of our knowledge and cannot always be
established a priori.’
a=a is analytic, a priori,
of negligible cognitive value
a=bis synthetic, a posteriori,of high cognitive value
IDENTITY AS A RELATION BETWEEN THINGS
Frege now objects:
‘Now if we were to regard identity as a relation between that which the names ‘a’ and ‘b’
designate, it would seem that a=b could not differ from a=a.’
Relevantly, the two expressions could not differ in cognitive value!
IDENTITY AS A RELATION BETWEEN THINGSThe argument
(P1) Given the Naive Theory, if identity is a relation between objects, ‘a=a’ and ‘a=b’ must have the same meaning.
(P2) If two expressions mean the same thing, they do not differ in cognitive value.
(P3) ‘a=a’ and ‘a=b’ differ in cognitive value.
(4) ‘a=a’ and ‘a=b’ do not mean the same thing.
∴ (C1): Identity is not a relation between objects.
IDENTITY AS A RELATION BETWEEN NAMES
So on to the second option, where ‘Hesperus is Phosphorus’ should be written as
(2) ‘Hesperus’ = ‘Phosphorus’
Of course, not this (as it is obviously false), but really
(3) The terms ‘Hesperus’ and ‘Phosphorus’ designate the same thing.
This is the Metalinguistic Thesis.
IDENTITY AS A RELATION BETWEEN NAMES
(P1) If identity is a relation between names, then what we learn from identity statements is that two
terms designate the same thing
(P2) If what term we use to designate an object is arbitrary, then learning that two terms
designate the same thing does not give us proper knowledge
(P3) What term we use to designate an object is arbitrary
(4) Learning that two terms designate the same thing does not give us proper knowledge
(5) If identity is a relation between names, then identity statements do not give us proper knowledge
(P6) Identity statements do give us proper knowledge about the world
∴ (C2) Identity is not a relation between names.
IDENTITY AS A RELATION BETWEEN NAMES
DILEMMA ABOUT IDENTITYFrege’s Puzzle: Identity cannot be a relation
between objects, nor can it be a relation between names.
But clearly identity is a relation between something!
So what should we do?
Frege’s Answer: Reject the Naive Theory & the claim that the meaning of a singular term is nothing
but the referent.
SOLUTION TO THE PROBLEMFrege:
‘A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated.’
In other words:
Find some element which captures the mode of presentation of an object via the employed singular term
A SHORT ADVENTUREExplorer 1 (call him ‘Marco’), traveling in an
unexplored area, sees a snow-capped mountain on the northern horizon.
A SHORT ADVENTURE
Talking to natives, Marco learns it is called ‘Aphla’.
Sighting different points, Marco enters it onto a map of the area.
Measuring, he writes ‘Aphla is at least 5000 metres high.’
A SHORT ADVENTUREExplorer 2 (call him ‘Christopher’) sees a snow-
capped mountain on the southern horizon.
A SHORT ADVENTURE
Speaking to a few natives, Christopher learns that it is called ‘Ateb’.
Sighting different points, he enters it into a map of the area.
Measuring, he writes ‘Ateb is at least 5000 metres high.’
A SHORT ADVENTURE People go on using Marco & Christopher’s maps
for several years, navigating around this distant land wonderfully.
Over a few drinks at the Explorers Club, Marco and Christopher meet up & discuss their respective discoveries. Gradually, they come to realize that they saw the same mountain.
At this point, they agree that ‘Ateb is Aphla’
This proposition is a ‘valuable piece of geographic knowledge’.
A SHORT ADVENTUREIf all there was to the name ‘Aphla’ was the
reference – the mountain itself – then
(1)Aphla is Aphla
(2)Ateb is Aphla
would express the same thought.
But then how could Christopher & Marco have gained any geographic knowledge?
A SHORT ADVENTUREProblem: these two expressions differ in cognitive value – they express different thoughts – but they have the same reference.
So what corresponds to the name ‘Ateb’ as part of the thought must therefore be different from what
corresponds to ‘Aphla’
Can’t be their reference, because that is the same
Frege’s answer: must be the senses!
A SHORT ADVENTUREThus Frege:
‘…I say accordingly that the sense of the name ‘Ateb’ is different from the sense of the name
‘Aphla’.’
Further, ‘An object can be determined in different ways, and every one of those ways of determining it can give rise to a special name, and these different names then have different senses; for it is not self-evident that it is the same object which is being determined in different ways.’ [Frege, LtJ]
A SHORT ADVENTUREOnce we have sense, we can explain why the thoughts
a. Ateb is at least 5000 metres high
b. Aphla is at least 5000 metres high
are different: they contain parts which have different senses. So the sense of the complex
expression is itself different because the senses of the parts are different – even though the truth-
conditions are the same!
A SHORT ADVENTUREThe sense of a singular term can’t be subjective, however.
If it were, the sense of the thought in which the sense of a name occurs would then be subjective as well.
So, e.g. ‘Ateb is at least 5000 metres high’ would be subjective.
If this was subjective, the thought one man connects with the expression would be different from the thought another man connects with it
A SHORT ADVENTUREThat’s bad – then, ‘a common store of thoughts, a
common science’ would be impossible.
Thus Frege:
‘It would be impossible for something one man said to contradict what another man said, because the two would not express the same thought at all, but
each his own.’ [LtJ]
MAKING SENSE OF IT ALLFrege’s suggestion:
‘It is natural, now, to think of there being connected with a sign (name, combination of words, letter),
besides that to which the sign refers, which may be called the reference of the sign, also what I should like to call the sense of the sign, wherein the mode
of presentation is contained. ... The reference of ‘Hesperus’ would be the same as that of ‘Phosphorus’, but not the sense’ (OS&R)
MAKING SENSE OF IT ALLSenses for Singular Terms
In the case of a=b
Singular Terms a and b each have a sense and a referent; the sense of a is different from the sense of b, though the referent of a is the same as the referent of b.
The difference in sense explains how a = a and a = b can differ in cognitive value (or meaning) even when a = b is true.
FREGE’S STORY FOR SINGULAR G-UNITS‘50 Cent’
DETERMINES
DENOTES
EX
PR
ES
SE
S
Sense of ‘50 Cent’
FREGE’S STORY FOR SINGULAR G-UNITS‘Curtis Jackson’
DETERMINES
DENOTESEX
PR
ES
SE
S
Sense of ‘Curtis Jackson’
FREGE’S STORY FOR SINGULAR TERMS ‘Curtis
‘50 Cent’ Jackson’
E
XPR
ES
SE
S
EX
PR
ES
SE
S
DETER
MINES DETERMINES
Sense of ‘50 Cent’
Sense of‘CJ’
WHAT TO DO WITH THE DUDE?What about singular terms that fail to refer?
The Dude, unfortunately, is just a fictional character – he does not really exist.
WHAT TO DO WITH THE DUDE?‘The Dude’
DETERMINES
DENOTESEX
PR
ES
SE
S
Sense of ‘The Dude’
FREGE ON NON-REFERRING SINGULAR TERMS
Thus both things seem to me necessary: (1) the reference of a name, which is that about which
something is being said, and (2) the sense of name, which is part of the thought. Without reference, we
could indeed have a thought, but only a mythological or literary thought, not a thought that could further scientific knowledge. Without a sense, we would have no thought, and hence also nothing
that we could recognize as true. [Frege, LtJ]
FREGE ON NON-REFERRING SINGULAR TERMS
…this is not to say that to the sense there also corresponds a reference. The words ‘the celestial
body most distant from the Earth’ have a sense, but it is very doubtful they also have a reference. The
expression ‘the least rapidly convergent series’ has a sense; but it is known to have no reference… In grasping a sense, one is not certainly assured of a
reference.’ [OS&R]
SINGULAR TERMS WITH UNKNOWN REFERENCE
Frege:
The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it
belongs; but this serves to illuminate only a single aspect of the reference, supposing it to have one. Comprehensive knowledge of the reference would require us to be able to say immediately whether any given sense belongs to it. To such knowledge
we never attain. [OS&R]
????
SINGULAR TERMS WITH UNKNOWN REFERENCE
‘The Tallest Person in the room’
DETERMINES
DENOTES
EX
PR
ES
SE
S
Sense of 'The Tallest Person in the room’
SENSIBLE LESSONS(1) Each meaningful singular term has a determinate sense (‘Sinn’) and (at most) a single referent (‘Bedeutung’)
No sense, not meaningful No referent, then either
(a) not a singular term (no single referent)(b) a non-referring name (no referent at all)
SENSIBLE LESSONS(2) The referent of a singular term is the ‘definite object’ that it stands for.
(3) The sense of a singular term contains a “mode of presentation” and is what determines the term’s referent (if any).
(4) Sense ≠ idea (‘Vorstellung’)Telescope analogySubjectivity point above
SENSIBLE LESSONS(5) Some theoretical work for sense:
(a) Someone who understands a singular term knows the sense of the term
(b) Two singular terms s and s’ in L are synonyms in L iff the sense of s in L = the sense of s’ in L (similar criterion for translation across languages!)
(c) A singular term is ambiguous in L iff more than one sense is associated with it
FREGE ON PREDICATESPredicates express senses and denote concepts (like singular terms, just different denotation)
Concepts are unsaturated – they need objects to instantiate them in order to exist.
Think of a concept like a donut hole
A concept cannot exist without an object saturating it.
FREGE’S STORY FOR PREDICATES!
The story centres on a circular animal-like creature that is missing a wedge-shaped piece of itself. It doesn’t like this,and sets out to find its missing piece, singing:
Oh, I'm lookin' for my missin' pieceI'm lookin' for my missin' pieceHi-dee-ho, here I golookin' for my missin' piece
FREGE’S STORY FOR PREDICATES!
Concepts are like the circle that’s missing a piece – something central to what they are is absent when they are unsaturated.
Only by being saturated by an object is a concept completely whole.
Importantly, predicates express senses and denote concepts (like singular terms, just different denotation)
‘BUCEPHALUS IS A HORSE’
Bucephalus is a horse
What does this sentence mean?
What does ‘Bucephalus’ mean? Determined/constituted by the sense of ‘Bucephalus’
What does ‘is a horse’ mean? Determined/constituted by the sense of ‘is a horse’
A SENSE FOR SENTENCESThe sense of a complete declarative sentence is a
thought (‘Gedanke’)
‘By a thought I understand not the subjective performance of thinking but its objective content, which is capable of being the common property of
several thinkers.’ (Frege, OS&R, footnote 7)
What makes up the thought of a sentence?
A SENSE FOR SENTENCESAnswer: the senses of the constituent expressions!
(Psst! - Remember COMPOSITIONALITY: The meaning of a complex
expression depends on the meaning and arrangement of its constituent parts?)
The thought of the sentence
‘Bucephalus is a horse’
is composed of the senses of ‘Bucephalus’ and ‘is a horse’
A SENSE FOR SENTENCES
Sentence Bucephalus is a horse
Thought {[Bucephalus] + [is a horse]}
Reference??????????
A REFERENCE FOR SENTENCES(1) Frege endorses a compositionality thesis about reference: the reference of a complex expression is determined by the references of its constituent expressions.
(2) So reference of a sentence is determined by reference and structure of its constituent expressions.
(3) But two sentences whose expressions are all co-referential (and arranged in the same way) can express different thoughts.
(4) So the reference of a sentence thought it expresses
A REFERENCE FOR SENTENCES(5) We care about reference of constituent expressions of a sentence just when we care about truth value of sentence: “It is striving for truth that drives us always to advance from the sense to the referent”.
(C) ‘We are therefore driven into accepting the truth value of a sentence as its referent’.
The reference of a sentence is its truth-value
A REFERENCE FOR SENTENCESThere are two truth values
True FalseEvery sentence that has a referent refers to one of these
We are therefore driven into accepting the truth value of a sentence as constituting its reference. By the truth
value of a sentence I understand the circumstance that it is true or false. There are no further truth values. For
brevity I call the one the True, the other the False. Every declarative sentence concerned with the reference of its words is therefore to be regarded as a proper name, and its reference, if it has one, is either the True or the False.
[OS&R, emphasis mine]
A REFERENCE FOR SENTENCESThree comments
(1) This means that Truth Values are objects, just like people, tables, chairs, etc.
(2) Sentences are just really complex singular terms, picking out truth values
(3) The difference in cognitive value between two sentences must be explained by difference in thought (since they might have the same referent)
A REFERENCE FOR SENTENCES
Sentence Bucephalus is a horse
Thought {[Bucephalus] + [is a horse]}
Reference The True
A REFERENCE FOR SENTENCES
Sentence Prince is a horse
Thought {[ ] + [is a horse]}
Reference The False
WHAT LOIS & GEORGE BELIEVE
‘Superman’ & ‘Clark Kent’ refer to the same object
Lois believes that Clark Kent is a reporter.
Lois does not believe that Superman is a reporter.
How to explain the difference between Lois’ beliefs, given that Superman is Clark Kent?!?
WHAT LOIS & GEORGE BELIEVEIf a is identical with b, whatever is true of the one is true of the other, and either may be substituted for
the other in any proposition without altering the truth or falsehood of that proposition. Now George IV wished to know whether Scott was the author of
Waverley; and in fact Scott was the author of Waverley. Hence we may substitute Scott for ‘the
author of Waverley’, and thereby prove that George IV wished to know whether Scott was Scott. Yet an
interest in the law of identity can hardly be attributed to the first gentleman of Europe. -Russell
George believes that Scott wrote Waverly. George doesn’t believe that Walter wrote Waverly.
WHAT LOIS & GEORGE BELIEVEFrege's concept of indirect discourse:
In indirect (oblique) discourse we speak of the sense, e.g., of the words of someone else. From this it becomes clear that also in indirect discourse words do not have their customary reference; they here name what customarily would be their sense. (Frege, OSR)
Distinguish: Indirect speech: talk regarding the sense of words Direct speech: talk regarding the reference of
words
WHAT LOIS & GEORGE BELIEVEIn the sentence, ‘Columbus inferred from the
roundness of the earth that he could, travelling westward, reach India,’ we have, as reference of its parts two propositions: that the earth is round, and
that Columbus traveling westward could reach India. What matters here is only that Columbus was convinced of the one as well as the other and that
the one conviction furnishes the ground for the other. It is irrelevant to the truth of our sentence whether the earth is really round and whether
Columbus could have reached India in the manner he fancied.
-Frege, OSR
WHAT LOIS & GEORGE BELIEVE
In cases of this type it is not permissible to replace in the clause one expression by another of the same reference. Such replacement may be made only by expressions of the same indirect reference, i.e. of
the same customary sense. … The only correct conclusion is that the reference of a sentence is not always its truth-value, and that ‘morning star’ does
not always refer to the planet Venus; for this is indeed not the case when the word is used with its
indirect reference.-Frege, OSR
WHAT LOIS & GEORGE BELIEVESo, when we engage in indirect discourse, an expression does not refer to referent, but rather to its sense.
This applies to everything – singular terms, predicates, & sentences!
Rule of thumb: if a sentence occurs within a ‘that’-clause, it’s an instance of indirect discourse
Lois believes that Clark Kent is a reporter. George believes that Scott wrote Waverly.
WHAT LOIS & GEORGE BELIEVEThis gives us the tools to explain Lois & George’s beliefs:
What they believe is different in the two cases!
Lois believes that {Clark Kent is a reporter}.Lois does not believe that {Superman is a
reporter}.
George believes that {Scott wrote Waverly}. George doesn’t believe that {Walter wrote
Waverly}.
WHAT LOIS & GEORGE BELIEVE
Sentence Lois believes [CK is a reporter]
Thought {[Lois] + [believes]+ [[CK is a reporter]]}
Reference
The True
WHAT LOIS & GEORGE BELIEVE
Sentence Lois believes [SM is a reporter]
Thought {[Lois] + [believes]+ [[SM is a reporter]]}
Reference
The False
WHAT TO DO WITH THE DUDE?What about sentences that contain singular terms
that fail to refer?
Odysseus was set ashore at Ithaca while sound asleep.
The Dude abides.
WHAT TO DO WITH THE DUDE?
Sentence The Dude abides
Thought {[The Dude] + [abides]} (No problem so far: both have senses,
so sentence clearly expresses a thought)
Reference??????????
WHAT TO DO WITH THE DUDE?According to Frege, if a constituent expression in a
sentence has a sense but lacks reference, the sense of the sentence lacks reference too.
Hence, ‘The Dude abides’ lacks a reference.
Frege says that such a sentence expresses a thought all the same: ‘The thought remains the same whether
‘Odysseus’ has a referent or not’.
Problem: Frege is committed to there being meaningful sentences that lack a truth value – i.e. to there being meaningful expressions that are neither
true nor false
PROBLEMS WITH FRENCH ROYALTY? The Present King of France: is or isn’t he bald?
By the law of excluded middle, either ‘A is B’ or ‘A is not B’ must be true. Hence either ‘The present King of France is bald’ or ‘The present King of France is not bald’ must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of
France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a
wig.-Russell, On Denoting
PROBLEMS WITH FRENCH ROYALTY?
A related problem
The Present King of France does not exist.
Is this true, false, or neither?
‘…it would appear, it must always be self-contradictory to deny the being of anything…’
(Russell, On Denoting)
WRAPPING UPThree Puzzles the Naïve Theory was unable to solve:
(1)How can two identity statements differ in cognitive value, if the terms involved refer to the
same thing?
(2)How can two predicational statements differ in cognitive value if the singular terms involved
refer to the same thing?
(3)How can Lois believe something of the same object under one designation, but not another?
WRAPPING UP(1) How can two identity statements differ in cognitive
value, if the terms involved refer to the same thing?FREGE’S ANSWER: Because the terms have different
senses!
(2) How can two predicational statements differ in cognitive value if the singular terms involved refer to
the same thing?FREGE’S ANSWER: Because the terms have different
senses!
(3) How can Lois believe something of the same object under one designation, but not another?
FREGE’S ANSWER: Because the thoughts involved differ!
WRAPPING UPHowever, we’ve seen two potential problems
with Frege’s account
(4) How do we account for complex expressions which contain singular terms that don’t refer?
(5) How can we assert that ‘x doesn’t exist’ without contradicting ourselves?
NEXT WEEK – RUSSELL’S ON DENOTING
Reading for next week:
(1)Russell’s Descriptions
(2) Russell’s On Denoting p. 481, paragraph beginning ‘It remains to interpret…’
