The Logical Function of That or Truth Propositions and Sentences Harrison Philosophy Journal

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The Logical Function of That, orTruth, Propositions and Sentences1

JONATHAN HARRISON

(i) Introduction: The main function of the word that:

I once2 defended the (formerly popular) view that what is true orwhat is false is always a proposition, and not a sentence. A proposi-

tion is always capable of being expressed by a that clause; forexample, what it is correct to describe as true is that dogs bark, notDogs bark. It is true Dogs bark, does not make sense, involvesa category mistake, and leads to serious errors. Though one oftensays such things as It is true dogs bark, where the word that isunderstood, the result, when written rather than spoken, is usuallyslightly slovenly, and the word that can always be inserted aftertrue. (If one adopts the terminology of J. L.Austin, to say Dogsbark is to perform a phatic act; to say that dogs bark is to perform

a rhetic act. Since there is only one act, it would be better if Austinhad talked about phatic and rhetic descriptions of (verbal) acts.)Propositions are not always expressed by that clauses. One can

also say such things as Dogs bark. When one does one is usuallyasserting a proposition, in this case, the proposition that dogs bark.When one utters the words Dogs bark, one is usuallythough notif one is on the stage, teaching elocution, or merely exercising onesvocal cordsasserting the proposition that dogs bark. When oneasserts that dogs bark, what one asserts can be said to be true or

false, supported by the evidence, believed, disbelieved or doubtedby the speaker, or consistent or inconsistent with other things(propositions) the speaker has said (asserted). The words that oneuses to formulate a true proposition can be said to be true only inthe sense that the proposition they express is true. And it is that

Philosophy 79 2004 67

doi:10.1017/S0031819104000063 2004 The Royal Institute of Philosophy

1 This article was stimulated by some remarks by J. J. C. Smart in criti-cism of a piece of work (God, Freedom and Immortality, Ashgate, 1999)that he was kind enough to read for me. I am greatly indebted to my friendDavid Rees for correcting the manuscript, and making some valuable sug-gestions concerning its content.

2 Jonathan Harrison, The Trouble with Tarski, The PhilosophicalQuarterly, Vol. 48, 1998, pp. 122.
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dogs bark, not Dogs bark, that implies or entails, or from which itfollows, that dogs are not entirely silent. None of these things canbe said of sentences.

Of sentences it may be said that they are in English, shouted outloud, rehearsed silently, written on recycled paper, consist entirelyof four letter words, are long or short, written in green ink, half wayup the sheet of paper, on mouldy parchment in faded ink, undeci-pherable, badly punctuated, do not end with a full stop, are difficultto understand, meaningless, composed of protons and electrons,have been where they are a long time, were written down a long timeago, will not last, are badly written, in joined writing, and fadingrapidly. These things cannot be said of propositions.

I shall argue that the function of the word that is to enable oneto put forward a proposition in order that various things may be saidabout it without the person using these word expressing the propo-sition having to commit himself to its truth, as he usually would beif the word that were omitted.

Propositions are not (pace Frege) thoughts. In one sense ofthink propositions can be thought, because one can think (believe)that dogs bark. But, of course, there can be many propositionsamong which are an infinite number of propositions that are

instances of the schema: x+y=z, which, whether true or not, havenever been either believed or disbelieved, and which it has nevereven entered anyones mind to consider. (Naturally I cannot giveexamples.) In another sense, to think is to reason or ratiocinate; butratiocinating is an activity, and propositions are not activities,though many acts of ratiocinating may involve considering whethera proposition is true or false, probable or improbable, supported bythe evidence or unfounded. Thinking, too sometimes means delib-erating, or thinking what to do (or to say or to believe). If you

decide to do A, there will be reasons (though not necessarily goodones) for your decision, and the reasons will be propositions, butwhat the reasons were reasons for are not propositions.Propositions are not always the objects of intention or hope, foryou can intend or hope to as well as intend or hope that. To say thatthoughts are the objects of intention or hope does not seem to meto make sense.

It has become fashionable to speak of contents rather than propo-sitions. I prefer the word proposition, partly because one speaks of

the proposition that ..., not of the content that ...., partly becausethe word content suggests that contents are the contents of some-ones mind, and so mental, and perhaps also that a content is akind of entity of which one can be aware. But propositions, even

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when someone is considering them, are not the sort of thing to be thecontents of anyones mind. If one were aware of them one couldraise the old question whether it was they or our awareness of them

that was mental, but they are not the sort of thing one can be awareof. Though one can consider the ways of cooking eggs with a view todeciding which one to adopt, this does not mean that a way is thekind of thingan entitythat one can be aware of (as opposed tobeing aware that it exists), and I believe the same is true of proposi-tions. In any case applying the word content both to propositions,which could be described as the contents of thought, and to theobjects of perception, blurs an important distinction. The contentsof thought, like the thought that perhaps disaster is impending, are

capable of being true or false; the objects of perception, like trees orrainbows (or the sense-data of trees or rainbows) cannot be.

Anti-realistsand I shall discuss Anti-realism lateroften usethe word statement rather than proposition, and use itinterchangeably with sentence. A statement, however, is no more asentence than a proposition is; you can say that Tom stated that dogsbark, but not that he stated Dogs bark. In the former case, whatTom stated is a proposition.

Using statement, when it would be better to have used the word

proposition, makes the Anti-realists task easier. For though state-ments, like propositions, can be true or false, they are unlike propo-sitions in that in the required sense there cannot be any unknownstatements, or undiscovered statements. Undiscovered or unknownstatements would be things one might find in police stations. Thesewould usually not be just sentences, unless taken from a lunatic, butstatements that conveyed what the person being questioned claimed(though not in these words) to express true propositions. The factthat there cannot be unstated or unknown or unformulated state-

ments may give the illusion that there cannot be unstated truths.But there can, of course, be unasserted true propositions, or propo-sitions not known to be true, and this is what unknown truths are.

(ii) Davidsons view of that:

An alternative view has been expressed by Donald Davidson in OnSaying That.3 According to Davidson, the word that, as it occurs

in the sentence Galileo said that the earth moves is a demonstra-tive. It means Galileo said that: the earth moves. The word that

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3 Donald Davidson, Enquiries into Truth and Interpretation, (OxfordUniversity Press, 1984).


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then, according to Davidson, refers to what I utter when I say Theearth moves.

Utterance, however, is ambiguous. It can mean the sentence I

utter, or the proposition I use this sentence to assert, or the event ofmy uttering either of these. It can also designate a heterogeneouscollection of things, such as individual words or phrases or theuttering of them.

It ought not to be held that that refers to the sentenceDavidson says utterancefor Galileo could and did say that theearth moves without uttering the sentence The earth moves. Imyself would have thought that, if it were to refer to anything, itwould refer to the proposition (or statement) that I utter. The sense

in which utterance refers to the utteringof a proposition or sen-tence or some other words is irrelevant.

Pace Davidson4 He said (in the past tense) that the earth movesis not a performative utterance. If what Galileo had said had beenI say that the earth moves then he would have been uttering a per-formative, which would have enabled him to accomplish the perfor-mance of saying (asserting) that the earth moves. The performanceitself would not have had a truth valuethough that the earthmoves has a truth valuebecause Galileo is not saying that he is

saying that the earth moves, but saying it. But someone (who maybe Galileo) who says that Galileo said that the earth moves, is mak-ing a statement, which is true if Galileo did say that the earthmoves, false if he did not.

Davidson suggests that Tom said that the earth moves meansAn utterance of Toms, in the assertive mode, has the content ofthis utterance of mine: the earth moves. But Tom might perfectlywell have said that the earth moves, even though he and I do notmean the same thing by the words The earth moves. My meaning

the same as what Tom means by certain words is not a condition ofhis using these words to say something, quite possibly somethingtrue. What it is a condition of is the quite different fact that when Iuse these words after Tom said I am correctly reporting what Tomsaid. But it is perfectly possible for Tom to say that the earth moves,without my reporting what he says correctly, or having the resourcesin which to report his saying it.

It is a further fatal objection to Davidsons theory that it cannotdeal with recurrences of that such as that used in the sentence

Tom said that Mary said that the earth moves And Davidsonwould be quite unable to deal with more complicated sentences suchas this:

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4 Op. cit., note 3, 107.


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He thought me asleep; at least I knew.He thought I thought he thought I slept.5

(iii) Some more difficulties for Davidson

There are the following difficulties with Davidsons view.(a) I would myself, if I wanted to refer to an utterance (if utter-

ance is the right word) that I was about to state, use the word this,not the word that. I would say Galileo said this: the earth moves.The rules for the use of this and that are not clear-cut, but Iwould use this word for much the same reason that I would refer tothe one in my vicinity as this one, but to the one in the distance asthat one (over there). Though that is sometimes a demonstrative,but at other times has the function which I am attempting to eluci-date, this` is always a demonstrative. Galileo said this: the earthmoves would not have given rise to so much confusion. Hence hadDavidson said this (or, as I shall suggest later the following), hemight not have muddled the function of that as a demonstrativewith its function in presenting a proposition. This does not enableone to present a proposition by being put before a sentence thatexpresses one.

(b) Anyone saying Galileo said that: the earth moves, ought tobe asserting two propositions. He ought to be asserting that Galileosaid somethingin this case, though not necessarily, that the earthmoveswhich he refers to by the word that. He should then besaying (asserting) himself that the earth moves, and so endorsingwhat Galileo said (though not saying that he is endorsing it). (Hemust be asserting the proposition that the earth moves, because theword that is not used in the words that express it, i.e., the earthmoves. All that is said is the earth moves (where there ought to bea capital T). Since one function of that is to enable one to put for-ward a proposition for consideration without committing oneself toit, and The earth moves does not contain the word that, the manwho says Galileo says that; the earth moves should be assertingand so committing himself to the earths moving by saying theearth moves, which in fact he is not.) However, if one says thatGalileo said that the earth moves, one is asserting only one proposi-tionan atomic propositionabout Galileo. The truth of that theearth moves is entirely irrelevant to the truth of that Galileo saidthat the earth moves.

(c) Sometimes, as I have said, that is a demonstrative, as it is in


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5 From The Kiss by Coventry Patmore.


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Thats a big one, where that refers to a fish, or Did Galileo believethat?, where the reference of that (to, say, that the earth moves) isunderstood from the context. At other times that is not a demon-

strative, as in Galileo once believed that the earth did not move.Obviously, Galileo believed that ... where the gap must be filled tomake a complete sentence, is quite different from Galileo believedthat (when that is a demonstrative) which is a complete sentence. InHe believed that was a big one, where that does present a proposi-tion, there are in fact two occurrences of that, and it is really ratherobvious that though the first that is referential, the second is not.

(d) I actually would not use that in the way Davidson suggests,but say Galileo said (asserted) the following; that the earth moves.

(The fact that you have to put that after the following shows thatthe function of that is not demonstrative, for the demonstrating isdone by the following; but even with the following, the sentenceneeds a that in order to present the proposition that the earthmoves without asserting it.)

Hence one function of that is to remove the (I think conversa-tional) implication, which would obtain were it not for that, thatthe proposition being formulated is being asserted and is believedby the person asserting it. Hence when I say that Galileo said that

the earth moves I avoid committing myself to the proposition thatthe earth moves. But Galileo said that: that the earth movesthough, unlike Davidsons Galileo said that the earth moves,avoids my committing myself to the proposition that the earthmoves, is faced with the difficulty that it does not correctly reportwhat Galileo said. If all Galileo had said was that the earth moveshe would not have committed himself to the earths moving.Anyone saying that the earth moves is not committing himself tothis truth, and could not be reported as having said (asserted) that

the earth moves. For it to be true that Galileo said that the earthmoves, what he would have had to say would be The earth moves,not that the earth moves. He would need to have said somethingabout (the proposition) that the earth moves. To have made anassertion Galileo would have had to say some such thing as that thatthe earth moves is true.6

(Incidentally, what that` would designate, if it were to designate,

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6 It is a minor, but interesting question what the word it in It is true

that dogs bark refers to. It could be an impersonal use of it as in It israining; when the question What is raining? is inappropriate. In It istrue, said in reply to someone who has just asserted something, it refers towhat has just been asserted, and says nothing different from That is true,said in the same circumstances. (Here that is being used demonstratively.)


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could not be, as Davidson supposes, an utterance. Sometimes utter-ance refers to the event of my uttering something, which occurs at acertain time and place (the time at which I uttered it and the place at

which I was when I uttered it). But (the proposition) that the earth isflat does not occur at any time, or place. That the earth is flatoccurred in Cambridge at 7.00 p.m. on 1st July does not make sense,though it does make sense to say this of the event of my asserting it.

At other times utterance refers not to the event of my utteringsomething, but to what I utter. In that case what I utter is words ornoises, which may or may not constitute a sentence. But that can-not be followed by words which express a sentence. He said (utteredthe words) The earth is flat, is correct, but he asserted that The

earth is flat is not. He asserted that the earth is flat is also correct,but He uttered that the earth is flat is not.)

(e) That in He said that the earth moves does not refer to aproposition (or an utterance or anything else at all) but indicatesthat the proposition being formulated is going to be talked about. IfI want to say, without committing myself to its truth, that someonesaid (asserted) a proposition, or believed it or thought about it orthat it implies or is implied by some other proposition, I precede thewords expressing the proposition in question with the word that.

We have seen that the function of that is to express or formulatea proposition without committing oneself to it, with a view to talk-ing about it. Hence it is a further difficulty for Davidson that toavoid the suggestion that in Davidsons Galileo said that: the earthmoves, that the earth moves is being asserted, as opposed to mere-ly being reported, one would need two thats. Davidsons viewshould be, if it were right at all, that Galileo said that the earthmoves means Galileo said (asserted) that (said this, or said the fol-lowing); that the earth moves. But this view would presuppose a

truth incompatible with what Davidson is asserting, for the secondthat, the one that shouldbe a demonstrative if his view is correct,is not a demonstrative. And if the only words Galileo had utteredwere that the earth movesor the Italian equivalenthe wouldnot have finished his sentence.

A corollary of the view that that indicates that a proposition isbeing put forward, perhaps to be talked about, but not asserted, isthat in That two and two are four is a necessary truth, it is theproposition that two and two are four that is being said to be a nec-

essary truth, not the sentence Two and two are four. A sentencecan be a necessary truth, but only in the sense that some such sen-tence as Two and two make four is necessary, necessary to expressthe fact that two and two make four.


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(iv) That and implies

Though one can and should make assertions such as that that he is

a fool implies (or is perhaps equivalent to) that he is a knave, onecannot assert such things as If that he is a fool, then that he is aknave, or Either that he is not a fool or that he is a knave, or Notboth that he is a fool and that he is a not knave. One should say,without the that, If he is a fool, he is a knave, Either he is a notfool or he is a knave or He is not both a fool and not a knave.Whether or not you put that before p and before q in any sentencesuch as That p implies that q will depend upon what you thinkought to be substituted, when necessary, for the symbols p and q.

If you intend that sentences such as dogs bark should be substi-tuted, you have to add a that. If you wish to substitute that dogsbark, or think that implies should always be read as implies thatyou do not.

The presence of that indicates that that today is Tuesdayimplies that tomorrow is Wednesday is about propositions, forexample, propositions about someones aforesaid knavery and fool-ishness. The other three propositions are not about propositions,but directly about knavery and foolishness. One could say that they

are about the world, though this is true only in an odd sense ofworld. But they are about what might be described as extra-propositional reality, whatever might be included under thatdescription. By extra-propositional reality I mean reality outsidethe proposition being considered, for there is no reason why thereality in question should not consist of other propositions, e.g.,that if he says that he believes that, he is a liar.

Quine is therefore not right to hold7 that the difference betweenthat p implies that q, and if p then q, is that in the latter a sentence

is being used and in the former it is being mentioned.8 But it wouldbe to oversimplify to suggest that what I have said implies a dis-

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7 Willard van Orman Quine, Methods of Logic, (London: Routledge andKegan Paul, 1962) p. 38.

8 Quine says The verbs implies, is longer than, is clearer than, andrhymes with are all on a par as far as the present contrasts are concerned:they connect, not statements to form compound statements, but names ofstatements to form statements about statements. But though is longer

than, is clearer than and rhymes with are all about words, it is oneproposition or statement that implies another proposition or statement.And Dogs bark is not the name of the statement that dogs bark as itwould be if it were called George. Op. cit. note 6, 38. But Quine does heresay statement, not, as he usually does, sentence.


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tinction between using a proposition as opposed to talking about it.Indeed, one cannot use propositions (as opposed to mentioningthem), though one can use sentences for, among other things, the

purpose of formulating propositions, i.e., putting them into words.(Another use would simply be to deafen people in ones vicinity.) Itshould not be supposed that putting something into words is thesame as naming it or describing it. It is not the case that one avoidscommitting oneself to a proposition when one says that that pimplies that q, but not when one says that if p then q. In neithercase is one committed to p or to q, and in both cases one is com-mitted to the connection between p and q. But when one says thatthat p implies that q one is talking about propositions; when one

says if p, then q, one is talking about the world.This is even clearer in certain senses of if, for example as in If

it rains, England will win, which should take the truth tableTFUU, where U indicates that since the speaker has committedhimself to something only if it rains, and it has not rained, the ques-tions whether he has asserted something true or false cannot arise.If it rains England will win cannot be translated as That it rainsimplies that England will win. One is tempted to say that onlyhypothetical propositions can assert anything conditionally; implica-

tion propositions assert unconditionally that a connection holdsbetween their implicans and their implicata.

There is nevertheless a difference, though Quine gets it wrong,between that that p implies that q, and that if p, then q. One istempted to say that implication is the relation that holds betweentwopropositions, say that dogs bark and that cats purr, when a state-ment such as that if dogs bark, then cats purr, is true. For example,if it is true that if he is a knave (then) he is a fool, then it is also thecase that that he is a knave implies that he is a fool. One is tempted

to say that that p implies that q if (and only if) if p, then q.There are reasons which I shall not state, for thinking that this

view is too lax. On the other hand, the view that that p implies thatq is true only if that q is deducible from that p, or if there is someother more intimate relation between that p and that q, is fairlyobviously too stringent.

It has been said (by Quine) that confusing propositions aboutwhat implies what, which I think need the words implies that, andthose which are about the world, and expressed, among other ways,

by If ... then ..., led to Russells definition of p implies q aseither -p or q. Though Quine is right to insist that that he is aknave implies that he is a fool is on a higher level from that if he is aknave, then he is a fool, he is wrong if he supposes that this means


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that that he is a knave implies that he is a fool is not entailed by ifhe is a knave, then he is a fool. If, as I have suggested, implicationis that relation which holds between the propositions that he is a

knave and that he is a fool precisely when it is true to say that if heis a knave, then he is a fool, then the fact that implication proposi-tions are of an order one higher than hypothetical proposition doesnot mean that the latter cannot entail the former.

This is a different view from the view that that if he is a knave heis a fool is equivalent to that either he is not a knave or he is a fool,or to that he is not both a knave and not a fool, where the latterpropositions are about the world. On my view a proposition aboutpropositions is made true by propositions about the world, because

the latter propositions stand in just the relationship that the formersays they do. But this is not to say that both my view and Quinesmay not both be correct.

There is no word that stands in the relation to either ... or ... ornot both ... and ... that implies stands in to if ... then .... Onecannot say, useful though it might be to be able to, that that he is aknave disjoins that he is a fool, or that that he is a knave excludesthat he is a fool. If there is a way of translating a disjunction or thenegation of a conjunction into a statement about the relation

between the disjuncts or the propositions jointly denied, it is to saythat the negation of the first implies the second, or that the truth ofthe first conjunct implies the falsity of the second. For example,that if a syllogism has two negative premises it is invalid, and thateither a syllogism does not have two negative premises, or it isinvalid, or that a valid syllogism cannot have two negative premises,can all be put by saying that the statement that that a syllogism hastwo negative premises implies that it is invalid.

It follows that that p implies that q does not mean that either -p

or q. Whether or not that if p, then q is equivalent to either not p orq, to say that p implies that q, cannot be to say that that if p then q,for the second is about the world, and the first about a propositionabout the world. One can argue from the already known fact thatthat p implies that q to the conclusion that if p, then q. One canargue to the conclusion that p implies that q from the fact that if p,then q. In the former case that p implies q must be known eitherbecause it is an a priori proposition, or from examining similarcases. In the latter case, the truth or falsity of that p and that q must

be established by observation.If p then q, either -p or q, and not both (p & q) may well be all

equivalent (though perhaps different in their conversational impli-cations). All may entail that p implies that q (because that one or

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other of these relations holds between p and q is just what that pimplies that q asserts. And one but not the only reason for assertingany of these three is that that p implies that q, and it may be that

asserting any of these three at least sometimes implies, in the senseof presupposing, that p implies that q. If one can assert that if p,then q because one knows that p is false or knows that q is true, itmight seem that if p then q cannot presuppose that p implies thatq. But examples of cases when if p then q is implied by, say, -q arecases that presuppose that p implies that q is true. If Tom wins Iam a Dutchman, asserted on the grounds that I am not aDutchman, which is the premise of an enthymeme with the conclu-sion that Tom wont win, is precisely a case when it is presupposed

that that Tom will win implies that Im not a Dutchman.There is a question about implies that is analogous to the ques-

tion whether the word true in That dogs bark is true is redun-dant. It is the question whether in That p implies that q the wordimplies can be omitted, and if p then q substituted for it. (Weshall see later that implies just means implies true.) I shall alsoargue later that implies cannot be dropped, because it is impossi-ble to make the necessary generalizations about truth using only thewords if ... then ....

I have put forward the view that that p implies that q asserts thatif p, then q, (and perhaps also asserts that either not-p or q and notboth p & q) and that if p then qpresupposes that p implies q, but Iam not convinced that these apparently different views are incom-patible. For example, could you not say that that p presupposes thatp is true, and that what that p is true asserts is that p? I think how-ever, that the correct account of the situation may be that if p thenq does not so much imply that that p implies that q, as make that pimplies that q true because the truth of if p then q is just what that

p implies that q asserts to be the case. And it is not so much that ifp then q presupposes that that p implies that q, so much that myasserting that if p then q that presupposes that I believe that that pimplies that q.

(v) Logic about propositions, not about sentences; theRussellian view

Russell, when explaining |--q..pvq (*1.3) in ordinary words, saysthat it states that if a proposition is true, any alternative proposi-tion may be added without making it false. In other places he sayssuch things as that pvp..p (*1.2) means that if either p is true or


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p is true, then p is true; but this is not a full translation of *1.2,since it p is not an ordinary English word. But it is clear that hisview is that logic is not about propositions, but about sentences.

Quine has complained that Russells work is full of type/tokenfallacies, because he sometimes uses implies and at other timesuses if then ... . (I have argued above that the real differencebetween if p , then q ... and that p implies that q is that the for-mer is about the world, the latter about propositions about theworld.)

It is impossible to interpret formulae of the form if ... then ...... & ... and ... v ... as making, as they stand, generalizations aboutpropositions. But, as we have seen, -p v q, though it does not mean,

and should not be defined as meaning, that that p implies that qforit is about the world whereas that p implies q is about propositionsabout the worlddoes entail that if p then q, and conversely.

If p then q, then if -q then -p should be takencharitably,because the formula makes no mention of implication, and it isimpossible to make generalizations about propositions with only thewords if ... then ...to mean that whenever one propositionimplies another, the contradictory of the second implies the contra-dictory of the first. To express the fact that pvqqvp, one must say

some such things as that the order in which the disjuncts in a dis-junctive proposition occur makes no difference to its truth.

The fact that one cannot make the necessary generalizationswithout the words true or implies (which means implies thetruth of) seems to me to dispose of the redundancy theory of truth,of which more hereafter.

(vi) Logic about sentences; the Quinean view

According to Quine the formulae in the propositional (or rather sen-tential) calculus are mere schemata, not propositions. One schemaimplies another9 if it is impossible to substitute sentences for thevariables in the schemata in such a way as to make the first come outtrue and the second false. On this view, , v and & join thevariables in such a way as to demand their being interpreted as if ...then .., either ... or ... and and respectively, never as implies.Hence sentences resulting from these substitutions express

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9 Note that one does not need the word that when the proposition thatfollows is not stated, but only described. To put that in the relevant sensebefore words that do not express a proposition would not make sense.


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propositions (which are not generalizations) about the world, notpropositions about propositions. (According to Quine, of course,they are sentences about the world, rather than sentences about sen-

tences.) Implication (I would prefer to say entailment) comes inonly because some schemata imply10 others.

always means if ... then ..., and never implies; hence all sen-tences resulting from substituting a sentence for a variable in aschema are about the world. Implication is used only when one istalking about the relation between schemata, and is not used withinschemata. Hence there is no confusion between using and men-tioning it (on Quines (incorrect) view of this fallacy) or betweenstating a proposition and talking about it (on my view).

(vii) Rejection of the Quinean view

Quines view cannot be right. Schemata, qua schemata, are just con-catenations of printers ink, and, without a certain amount of conver-sation, no more express truths of logical interest than slots cut inpaper into which one may insert sentences. What is of logical interestis the statements (or propositions) about the schemata to the effect

that if you fill in the variables in the schema with certain sentencesfor propositions, you will get a sentence expressing a necessarily trueproposition. But this presupposes the view, which it is supposed torival, that the formulae express generalizations about propositions.For the statement that if you fill in p in pp with any sentence fora proposition you will get a sentence that expresses a necessarily trueproposition, presupposes the truth of the true result in question,namely, the generalization that every proposition implies itself; so youmight as well accept a view such that logical formulae express gener-

alizations about propositions in the first place.In any case, propositional logic cannot consist of generalizations

about sentences orformulae, for such generalizations are precariousin a way in which logic ought not to be. It is a necessary truth thatpp if this means that every proposition implies itself, but simply acontingent fact that whatever sentence is substituted for the variablesin pp the result expresses a (necessary) truth. This is because itis just a contingent fact that means implies and not, say, and.

Interpreting logic as being about schemata also ignores its a

prioricharacter, for it is just an empiricalfact that schema have thefunction given to them.


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10 I put imply in quotes because pvpp does not imply (-pp)p in theordinary English sense of imply; which carries truth with it.


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Taking the calculus of propositions to be about schema alsomakes it conventional in an undesirable way, for what a schemameans is entirely a matter of convention. But the fact that every

proposition implies itself is not a matter of convention, thoughwhat symbols are used to express this fact is.

Another difficulty11 with the Quinean view is that it does not evenfollow from the fact that every sentence substituted for a variable ina schema expresses a truth, that the proposition expressed is itselfnecessarily true. For example, in the schema W means W (a sub-stitution instance of which would be Cows means cows) it isimpossible to substitute any word for W and get a false result; butthe sentence Cows means cows does not express a necessary

truth.12

What it actually does is something quite different, i.e., nec-essarily express a truth. (I have argued13 that the sentences Cowsmeans cows, I am here, Snow is white means that snow iswhite, and is true if and only if snow is white, and The metre rodin Paris is a metre long are instances of schemata which necessari-ly express truths. These schemata are W means W, I am in theplace I am, s means s if and only if s expresses a truth if andonly if s. Though these schemata are such that, necessarily, everysentence in them expresses a truth, the truths they express are all

contingent.14

Hence the fact that it is impossible to substitute sen-tences for Quines schema in such a way as to make them come outfalse does not by itself mean that these sentences express necessarytruths, as they need to be if they are to be logical truths.

For all these reasons, the propositional calculus must be aboutpropositions, not about sentences (or schemata).

(viii) Propositions, sentences and the logic of propositional

functions

When it comes to propositional functions, however, though Russellmaintains the view that the logic of propositional functions stillconsists of relations of implication between propositions, he is nev-ertheless tarred with the same brush as Quine. For he says that thepropositions of traditional logicthat all men are mortal, that somemen are mortal, that no men are mortal and that some men are not

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11

Op. cit. note 2.12 Op. cit. note 2.13 Loc. cit. note 2, .14 Jonathan Harrison, The Confusions of Kripke, Erkenntnis, Vol. 27,

1986.


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mortalare all about propositional functions. For example, he saysthat that all men are mortal means that the propositional function xis mortal is a man is always true. To say that some men are mor-

tal is to say that the propositional function some men are mortal issometimes true, and so on. The logic of propositional functionsthen elucidates the logical relations between propositions such asthese.

If it is intended to be an explanation of what is meant by allRussells view is circularfor always in always true simply meansat alltimes. And as an account of what is meant by all, some,and none Russells view suffers from the defect of translatingpropositions about men into propositions about the word man. It

is just plain wrong to suppose that when one is talking about menbeing mortal one is talking about the words man and mortal, asone would be if one were talking about the propositional function xis a man. Still less could we be talking about the symbol x. (Thepropositions about men now expressed by the sentence All men aremortal would remain true, even if the word man (in the proposi-tional function x is a man) were to come to mean phoenix, thoughif the word man were to come to mean phoenix, the sentence Allmen are mortal would come to express a proposition that was false,

as would the propositional function x is a man. The same confu-sion is exemplified by Russells saying such things as that Peanosaxioms are about variables, when they are in fact about numbers.And the variable x cannot have children.

The situation could be saved by inserting the word that in anappropriate place in the function x is a man. That x is a manimplies that x is mortal does depend for its truth upon the meaningof man, for it is not about x is a man, but about men. There is aperfectly good sense in which something of the form that ... can be

said to be sometimes true. For example, it can be sometimes truethat the pub opposite is open. (It is always true to say that it is some-times open.)

(This does not escape a well-known objection to Russellsaccount of propositions like All men are mortal. If Russell wereright, the propositions that all centaurs are mortal, all centaurs arecompany directors, all centaurs are apartment blocks, etc., would allbe true, since, as there are no centaurs, the propositional function xis a centaur is always false, and material implications with false

antecedents necessarily are true. Hence the statement that the non-existent propositional function (x) is a diodopulos x is aquadrangle must always true, on the grounds that there is no suchpropositional function.


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(ix) Objectual and substitutional interpretation of variables

It follows from what I have said about propositional functions thatit is as foolish for the two ends of a worm to quarrel as for the sub-

stitutional and objectual interpretations of quantifiers to quarrel.The only thing one can substitute for a variable is a word or descrip-tion; one cannot,pace Russell, substitute a man, but only a word ordescription of a man, for the variable in the propositional functionx is a man. However, the propositional function x is a man willrange over men if words or descriptions for men are substituted forthe variable x.

(x) Propositions, sentences and descriptions

Russell says that what he calls the definite description the author ofWaverley is Scotch [sic] means among other things that the propo-sitional function x wrote Waverley is not always false. But what-ever we are talking about when we talk about the author ofWaverley, we are not talking about the words wrote Waverley. Scottwould have written Waverley, whatever had been meant by wrote,and even if he had called Waverley Gentlemen prefer Blondes.

Russells account could be improved if that x wrote Waverleywas substituted for x wrote Waverley. Then, instead of saying thatx wrote Waverley was sometimes true, one could say that that xwrote Waverley (without the quotes) was sometimes true. I myselfcannot see why one could not then just say it is true that someonewrote Waverley though, saying this, would not be equivalent tosaying that someone wrote Waverley. (Russells account of indefi-nite descriptions also cannot be correct, and for the same reason.)

For the same reason the statement that God exists cannot be, as

Russell maintains that it is, about the propositional function x isGod. Whether one is successful or not, one is trying to say suchthings as that God is omniscient, and what is omniscient cannotconsist of something having two words and one symbol. When onesays that God exists, one is talking about God, not about God,whether God exists or not. It is simply a mistake to hold that onecannot talk about the non-existent. One talks about non-existentthings all the time. One is talking about something if that thing isthe subject of ones discourse. Fairies are the subject of ones

discourse if one utters words which purport to refer to fairies,knowing what the word fairies means, and with a view to commu-nicating to others ones thoughts on this important topic.

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(xi) Some consequential remarks about truth;

When I say That snow is white is true I get through the that snow

is white part without committing myself to snows being white.When someone says (utters the words) that snow is white he isputting up a proposition for consideration without asserting it, andwith a view to saying certain things about it, such as that it is trueor false or believed or disbelieved. When he says Snow is white,without the word that, he is (normally)15 asserting that snow iswhite.

That I am putting forward a proposition for consideration whenI say that snow is white is even more clearly shown by the fact that

I could have added is false. The proposition that it is true thatsnow is white gets over no more information about the worldthandoes the proposition that snow is white, but it does state somethingabout the proposition that snow is white that that snow is white doesnot state. Of course, anyone who says that snow is white ought alsoto be prepared to say that it is true that snow is white, if he has thewords in which to do it, but this does not mean that this is what hehas said.

To say that a proposition is true is to say that things are as that

proposition says that they are. It follows that anyone saying that itis true that that proposition is true must also be saying that thingsare as it says they are; he is saying that it is a proposition that saysthat things are as they are, which, ex hypothesi, it does. The same istrue of that it is true that it is true that it is true, and so ad infini-tum.

Hence the reason why the proposition that it is true that dogsbark, unlike the proposition that Tom believes that that dogs barkimplies that dogs bark, is that to say that it is true that dogs bark is

to say that things are as anyone asserting that proposition would beasserting that they are. Then, if the person in question has suc-ceeded in saying how things are, what he has said must be16 true. Ifyou yourself think that dogs bark, then you must think that anyonesaying that they bark is saying that things are in the way that in fact,they are. (The fact that I say of what someone who says that it israining is true because I agree with him that it is raining does notmean that what I mean when I say that that it is raining is true is thatI agree with him that it is raining. If it is raining, then it is an objec-


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15 He would not be asserting it if he were on the stage, for example, orrehearsing his part.

16 L(p and A asserts that p implies that what A says is true), not (p andA asserts p) implies that what A says is true).


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tive fact that it is raining, and it will be raining whether I agree withhim or not.

(xii) Truth and correspondence

I suppose that the view that to say that a proposition is true is to saythat things are as it says that they are is a kind of correspondencetheory. It does not hold, however, that truth is correspondence to (orwith) fact. (Indeed, I have steered away from using the word cor-responds at all, as it is not clear what it means.) There is an oldfashioned sense in which fact means event or deed or crime.17 But

the true proposition that two and two are four, for example, does notcorrespond to an event or a deed or a crime. One may wish to saythat it corresponds to the fact that two and two make four, but to saythat it is a fact that two plus two make four, if it corresponds to any-thing, corresponds to the fact that two and two make four. But infact (i.e.. despite what has been supposed) that two and two are fourdoes not correspond to a fact; it is a fact.

It is either true that there is life on Mars or false that there is lifeon Mars, but neither are facts. One day, perhaps, it will become an

established fact that there is life there, and then that there is life onMars will be a fact. (Not all true propositions are facts. Saying thatsomething is true and that it is a fact have different conversationalimplications.)

Neither facts nor true propositions are contained within theworld. Wittgensteins statementthe first in the Tractatusthatthe world is the sum of everything that is the case is probably oneof the greatest howlers to be perpetrated by an eminent philoso-pher. Indeed, nothing that is a fact can be in the world, for the world

contains chairs and tables and people and stars and galaxies, andnone of these is the case. What is the case is that there are suchthings; but the fact (as well as the proposition) that there are suchthings are no more part of the world than the fact that there are notany centaurs, which is also a fact.

Perhaps a true proposition corresponds to the way things are. Forthe proposition that snow is white to be true, things must be the waythat proposition says that they are. The way things are can com-prehend snows being white, the average mans once having had 24

children, twos not having a square root, and there being more waysof getting to heaven than in a Ford coup (if there are).

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17 As a matter of fact, I do not think that fact ever means crime, thoughone species of fact, in the sense of deed, are crimes.


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(xiii) Truth and coherence

The fact that to say that a proposition is true is to say that things are

as it says that they are explains, as we have seen, why if a proposi-tion is true, it is true that it is true. If to say that a proposition is trueis to say that it coheres with other propositions, there would be nological reason why the proposition that a proposition coheres withother propositions should cohere with other propositions. Thoughevery proposition must be either true or false, there is no obviousreason why a proposition should either cohere with other proposi-tions or not cohere with other propositions. And, though if a propo-sition is true, it must be true that it is true, there is also no obvious

reason why the proposition that a proposition coheres with otherpropositions should cohere with other propositions. The truth isthat in assuming that if a proposition coheres with other proposi-tions it must be true that it coheres with other propositions, theholders of the coherence theory are, inconsistently, assuming eitherthe correspondence or the redundancy theory of truth. They areassuming that, though to say that a proposition is true is to say thatit coheres, to say that it is true that it is true that it coheres is to saythat things are as it says that they are, i.e., that it says a certain

proposition coheres and it does.

(xiv) Truth and pragmatism

According to pragmatism a proposition is true if it is one that it isuseful, or which has good consequences, to believe. This can betaken as a view that is paradoxical and immoral. If it means, as Ithink it should, that a proposition is true if the consequences of

believing it are good for the agent, it follows that some false propo-sitions, such as that the Prime Minister is always right, are true. Italso leads to some form of relativism, in that the consequences ofbelieving that the Prime Minister is always right may be good for amember of the Prime Ministers party, but not for a member of theopposition. In any case, this kind of consequence is not the result ofbelieving such things, but the consequence of asserting them outloud when you can be heard by influential people, whether onebelieves them or not.

If Pragmatists hold that if a proposition is true if the conse-quences ofacting on it are good, this is more plausible, but only par-tially true, as anyone will know who has failed to bet on a horse thatwon because he believed truly that the chances of its winning were


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remote. In any case, it is irrelevant whether the consequences of act-ing on a proposition aregood; what is relevant is its getting the agentwhat he was aiming to get by acting on it.

The belief that a proposition is true if beliefs converge upon itseems a piece of rather gross overoptimism; I can see no earthlyreason why beliefs should always converge on the truth, thoughmostly they must by and large do so or we should live uncomfort-able lives or prematurely die. As I get older I feel my beliefs con-verge away from the truth, rather than towards it, and if all theworld became old, as may happen one day, everybodys beliefswould be converging away from the truth. In any case, no-oneseems to have thought carefully about what beliefs converge on such

truths as that, say, my name is Harrison, and what is meant by con-verge. Is the belief that my name is Smith nearer the truth than thebelief that my name is Jones, so that the beliefs of someone whoreplaces the first belief with the second converge upon the truth? Inany case, it does not seem to be true of every belief that beliefsconverge upon it or do not converge upon it (the analogue of theprinciple of bivalence; see next section). Though it is useful to havetrue beliefs, there is often no particular usefulness in believing thatthey are true beliefs, and so pragmatism cannot give any account of

the fact that if a proposition is true, it must be true that it is true.Like the coherence theory, Pragmatism presupposes either thecorrespondence or the redundancy theories of truth.

Sometimes pragmatists count among the useful consequences ofa belief the fact that when tested it yields other true propositions;true propositions can be deduced from it. This success in theory isquite different from success in action. It is undoubtedly true that aproposition (or hypothesis) is rendered probably true by the factthat true consequences follow from it, but this view presupposes a

different account of the truth of the consequences from that of thetruth of the hypotheses;pace Antifoundationalists, one cannot go onsupporting truths with other truths ad infinitum. At some point onemust stop, and one must stop with a proposition which we believebecause we confront it with reality, not because true consequencescan be deduced from it (though of course true propositions can bededuced from it).

(xv) Truth and warrantable assertibility

If to say that a proposition is true is to say that things are as it saysthat they are, then the view that truth is warrantable assertibility or

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anything like it must be wrong. It is moderately obvious that anenormous number of false propositions are warrantably assertible,for example that my horse will lose, when in fact against the odds it

is going to win. The same is true of agreed, and agreed by mostpeople. In any case, the truth of a proposition should not dependupon whether one is warranted in assertingit, but on whether one iswarranted in believingit. There are lots of proposition which one iswarranted in believing, but not warranted in asserting, for examplethat the lady one is speaking to, and is within earshot, is fat.

Clearly there are lots of proposition which one is neitherwarranted in believing to be true nor warranted in believing to befalse, which fact conflicts with the principle of bivalence.

The effectiveness of the last argument depends on the truth of theprinciple of bivalence, that every proposition must be true or false,or true or not true. But though the principle of bivalence may notapply to every proposition, it is not sensible to reject the principle inmany cases when one would need to reject it to retain the view thattruth is warrantable assertibility. And one day it will be neitherwarrantably assertible that I lived nor warrantably assertible that Idid not live; but I have difficulty in believing that it will then be nei-ther true nor false that I am dead and neither true nor false that I am

alive, and equal difficulty in believing that the truth of such propo-sitions as that I am alive will change its truth value in the course oftime (from being true now to neither true nor false later). (The viewthat propositions about the future are neither true nor false (and soeventually change from being neither true nor false to being true orto be being false) will lead to the implausible conclusion that that Iwill one day die is neither true nor false, and also that, since I knowthat I will one day die, that knowledge does not imply truth.)

(xvi) That and the redundancy theory of truth: whether

Casually and informally saying Dogs bark is true or Dogs barkimplies dogs bark, and omitting the word, that gives spuriousplausibility to any variant of the redundancy theory of truthbecause the omission of the word that makes it look as if what isbeing asserted to be true is about dogs (which is what the proposi-tion that dogs bark is) not a proposition about a proposition about

dogs, which is what the proposition that that dogs bark is true is.(Note the two thats.)18


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18 But such precision is not always necessary, and Sir Ernest Gowers saysthat it is often stylistically better to omit it.


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(It is important, in order to understand what has foregone, torealize that anyone saying or uttering the words Dogs bark with-out the word that, in order to assert something, is properly

describedas asserting the proposition that dogs bark (with the wordthat). Anyone saying or uttering the words with the intention ofasserting something That dogs bark is true is properly describedas saying (two thats) that that dogs bark is true.

A proposition does not have to beformulatedin order to be said to betrue. It can be described, as in the proposition that some of the thingsTom says are true, when it is not said which these things (propositions)are. The fact that a proposition can be talked about without being stat-ed creates a difficulty for the redundancy theory of truth, for if the

proposition has not been stated, one cannot simply be reiterating itwhen one says it is true. It has not been iterated in the first place.

The stock answer to this objection is unsatisfactory. It may workfor a proposition picked out by a definite description like the firstthing Tom said on Tuesday. But with indefinite descriptions thismanoeuvre is less successful. The redundancy theory holds thatSome of the things that Tom says are true means (Ep) Tom saysp and p, where the second occurrence of p is supposed to reiter-ate the first occurrence.

Unlike Tom says that the cat is on the mat, and the cat is on themat or Tom says that the cat is on the mat, and that the cat is on themat is true, (Ep) Tom says (asserted) that p, and that p, does notmake sense. Tom asserted that the cat is on the mat makes sense.Tom asserted that p does not make sense. To make the former makesense one would have to interpret it as a propositional function, whichit cannot be, for it is supposed to be saying something true, andpropositional functions are neither true nor false. If it is regarded asa propositional function, then it itself is neither true nor false, though

it will be supposed by upholders of the redundancy theory that truthswill be obtained by substituting propositions for the variable p.

One has to make generalizations about propositions, as well asabout the world, and one needs the words true or implies (whichI have suggested means implies true) in order to do this. If theredundancy theory of truth were true, one could not make the nec-essary generalizations about propositions. One would always betalking about the world, not about propositions, for that it is truethat snow is white is, according to the redundancy theory, just as

much about snow as is that snow is white. There are obviously alarge number of words which say things about propositions ratherthan about the world, and it would be odd if true were the only oneof these words that had to be eliminated.

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The final, and I think insuperable, difficulty for the redundancytheory is that it cannot deal with true as it occurs when intentionis involved. Tom may be searching for truth without there being

any particular truth for which he is searching, so that his search fortruth cannot be analysed as (Ep) Tom wants to know p. Tom doesnot want to know that p; what he wants is to know whetherp is trueor not. That Tom wants to know whether p is true or not cannot beanalysed as: either p and Tom wants to know p or -p and Tomwants to know that -p. Tom does not want to know eitherthoughhe may, which is different, hope that p is true or hope that q is true,and ifp is true, want to know that it is.

It looks puzzling that that if Tom is going to be killed tomorrow,

he wants to know that he isperhaps so that he can make peacewith his makerand he is going to be killed tomorrow does notentail that Tom wants to know that he is going to be killed tomor-row, which is an apparent breach of modus ponendo ponens.19 Thepuzzle is solved when it is realized that If Tom is going to be killedtomorrow Tom wants to know that he is is an incorrect way of for-mulating the fact that what Tom wants is, ifhe is to be killed tomor-row, to know that he is. This is not a hypothetical with a consequentabout what Tom wants. The whole hypothetical expresses the object

of Toms wants, i.e., if he is to be killed tomorrow to know that heis.

An alternative way of solving the puzzle is to point out that thatif he is going to be killed tomorrow, Tom wants to know that he iscould also be better expressed by saying that Tom wants to knowwhetherhe is going to be killed tomorrow, so that if he is going to bekilled tomorrow, he can make peace with his maker. Here there isno breach of ponendo ponens, because that Tom wants to knowwhether he is going to be killed tomorrow or not, together with

Tom is going to be killed tomorrow, does not entail that Tom wantsto know that he is going to be killed tomorrow. Indeed, it is highlyunlikely that Tom does want to know that he will be killed tomor-row. That would entail that he was going to be killed tomorrow.

(xvii) Truth and the semantic theory

According to the so-called semantic theory, it is necessary that anysatisfactory theory of truth fulfil the condition that (s)20 s is true if


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19 Jonathan Harrison How Happy could I be with either, Ethical Essays,Vol. III, (Guildford: Ashford, 1995).

20 (s) is usually omitted, which doesnt help.


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and only if s, where s would range over sentences on the objectualview, or where one would substitute sentences for s on the substi-tutional view. It holds that truth always belongs to the metalan-

guage, which is an inflated way of saying what I have just said, thatthe proposition that something is true is about a proposition and notabout the world. (The statement that (s) s is true if and only if smust presumably be held (wrongly) to be a priori, because noempirical investigation of truth has been conducted in order toestablish it.)

The non-general statement that Snow is white is true if and onlyif snow is white is (apart from the fact that truth is improperly pred-icated of a sentence) all right linguistically as it stands. But, as is

indicated by the fact that it contains the words if, it is a statementabout the world, not as it should be in order to express a general-ization about truth, a statement about sentences or propositionsabout the world; for that one would need the words true or theword implies. The then which can normally precede the sentenceexpressing the implicate is made unnecessary and indeed impossi-ble by the presence of the words only if . Only if p, then q, asopposed to only if p, q, and unlike ifp, then q, does not make sense.If and only if that p, then that q also does not make sense.

The problem is how to formulate the generalization of which thatsnow is white is true if and only if snow is white is an instance. Itmight look as if If a proposition is true it is true that it is true, andvice versa, would do the trick, but in fact it doesnt. For here trueoccurs twice in the consequent, when it is supposed to occur only inthe antecedent. If one tries to drop truth from the consequent whatone gets is the statement that a sentence is true if and only if thatsentence, which is meaningless. (s) s is true if and only if that sen-tence is also meaningless. The truth is that since you cannot make

the required kind of generalization about a sentenceone concern-ing its truthwithout using the word true, the generalization elim-inating truth cannot be made.

The substitutionalview makes a better job of making the requiredgeneralization, for the sentence Whatever (meaningful?) sentenceone substitutes for s in the schema (s) s is true if and only if sthe result will be true does make sense. But quite apart from thefact that it turns a generalization made in a sentence to a generaliza-tion about that sentence (see above) it does not formulate what needs

to be formulated. For what needs to be formulated is a necessarytruth about the truth of such things as that snow is white, whereasthe generalization that whatever sentence is substituted for s in theformula (s) s is true if and only if s, the result will express a truth

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expresses only a contingent truth about a sentence, and not a truthabout the proposition that snow is white at all. For that snow iswhite would be true whatever was meant by snow and white. If

snow meant grass or white meant black, substituting the sentenceSnow is white for the variables in (s) s if and only if s wouldnecessarily result in a sentence that expresses a truth, but not theneeded truth about that snow is white.

That a theory of truth should entail that (s) s is true if and onlyif s has been put forward (by Tarski) as a condition which anytheory of truth must fulfil, but in fact any theory which fulfils thisalleged necessary condition must be false, as well as being improp-erly formed (because as we have seen sentences are in the wrong

category of thing to be true or false). It could be false because thereare circumstances in which the sentence Snow is white may befalse, or express what is false, even when snow is white.

For example, the sentence would be false if snow were to meangrass or white were to mean green, and it is only a historical acci-dent that these words do not mean this. (If snow were to mean grassandwhite were to mean green the sentence Snow is white wouldstill express some truth, but the different truth that grass is green.)If snow were to come to mean grass, this would not affect the truth

of the proposition that snow is white is true if and only if snow iswhite, though this proposition would then have to be expressed byusing whatever word was then the word for snow in this case theword grass. I am not sure how the generalization of which snow iswhite is true if and only if snow is white is an instance can beexpressed. It might be expressed as: whenever a situation (such assnows being white) obtains, the proposition stating that it obtainsmust be true.

(xviii) (p) ppT

It is an interesting consequence of what I have said about the func-tion of the word true in making the generalizations about truththat when it comes to putting the proposition (p) ppT into Englishwords one can say only that if a proposition is true, it is true that itis true, where there is one true in the antecedent and two in theconsequent. Without the word true in the antecedent you get a

piece of nonsense like Whenever a proposition, that proposition istrue. The particular casethat the cat is on the mat implies that itis true that the cat is on the matof a generalization that one is try-ing to formulate, can be expressed, by using the word true only


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once, but the general rule of which this is a case cannot be soexpressed. (p) ppT does not make sense; (p) pTpTT does.

It follows that that the cat is on the mat implies that it is true that

the cat is on the mat is not, despite appearances, an instance of (p)ppT, but an instance of (p) pTpTT. This is because when onegeneralizes, one has to talk about a proposition about the world, andso add a true that was not there in the singular proposition. Whenthe singular proposition (or one of its components) already con-tains the word true, one has to add a second true. The impossi-bility of doing without the word true in such situations seems tobe another fatal objection to any variant of the redundancy theory.

To return to the substitutional interpretation, the statement that

the formula (p) ppT, yields a truth whatever sentence is substi-tuted for p is true and makes sense, but again turns a statementabout truth into a statement about a sentence that may or may notbe about truth. Furthermore it is not a necessary truth that this for-mula expresses a truth, for the meaning attached to the symbols init is purely conventional and we might have chosen other conven-tions. That (p) pTpTT, however, is a necessary truth.

(xix) The principle of bivalence

The principle of bivalence is usually expressed symbolically aspTvpF or (p) pTvpF. There is no difficulty about reading this asEvery proposition is either true or false. This does not mean thatyou can make generalizations about propositions with v alone,without using the word true. (p) pv-p, has to be read as Everyproposition is either true or its negation is true. My former objec-tion to the substitutional interpretation of (p) pTvpF also appliesto the principle of bivalence. The singularproposition that eitherthat he is a fool is true or that he is not a fool is true is perfectly wellformed.

(xx) The law of the excluded middle

The law of the excluded middle is usually expressed in symbols aspv-p, or as (p) pv-p. The natural way of expressing (p) pv-p wouldbe to say that every proposition is either true or its negation is true.The formula (p) pv-p doesnt make sense unless one inserts theword true. For every proposition, that proposition or not that

proposition does not make sense. The singular proposition thateither he is a fool or not a fool, however, does make sense. (Ofcourse it is in fact a necessary truth, but it does not say of itself thatit is necessarily true.)

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(xxi) The principle of non-contradiction

The principle of non-contradiction is supposed to be expressed as

(p) -(p&-p). But since and here joins only propositions about theworld, this formula does not make sense. That one cannot have aproposition and not that proposition is very nearly gibberish. Toformulate it, again, one needs the word true. To say that a propo-sition and its negation cannot both be true makes perfectly goodsense.

(xxii) Partial Recapitulation

Briefly to summarize: the formulae in the calculus of propositionsinvolving implies (and is equivalent to) make sense provided is read as implies and not as if ... then ...; those involving only if... then ..., either ... or ... and not both ... and ... do not makesense as they stand. (p) (p&(pq))q can simply be read as sayingthat if p is true, and implies that q, then that q is (or must be) true,which is all right. But (p) if p and if p then q, then q only makesense if for if ... then ... you substitute implies. If you read the

expression as Whenever if p and if p then q then q it does notmake sense, for Whenever if ... does not make sense. You can alsomake it make sense by turning it into a proposition about the func-tion If p, and if p then q, then q which again makes the mistake ofturning it from being a generalization about the propositions to oneabout the sentence in which that generalization is expressed.

In our minds we read such formulae in whichever way makes itunderstandable, but we are sometimes doing a formula more justicethan it deserves. The formula can all be made to make sense as read-

ing them as propositions about the symbols that express them, as isdone on the substitutional interpretation of the quantifiers, but wehave seen why doing this is objectionable.

(xxiii) That and entailment21

If to say that a proposition is true is to say that things are as it saysthat they are, then to say that one proposition entails another is to say


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21 I did not know when I wrote this passage about two years ago thatFrank Jackson had expressed a similar view; (Frank Jackson, New Essayson the A Priori, Paul Boghossian and Christopher Peacocke (eds.), OxfordUniversity Press, 2000, pp. 3245).


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that if things are as the first proposition says that they are they mustbe as the second proposition says they are. The reason for this is thatthe range of thingsI cannot find any word more specific than

thing that will not be too narrowwhich would make the secondproposition true includes the range of things which make the firstproposition true. If this is so, then if things are as the first proposi-tion says they are, they must be as the second proposition says theyare. If the range of situations which make the second proposition trueincludes the range of situations which make the first proposition true,the two propositions are equivalent. For example, if that something isa man entails that he is an animal, this is because the range of thingswhich make it true to say that he is an animal includes the range of

things which make it true to say that he is a man. We have to knowwhat is meant by (among other words) man and animal to knowwhether or not this is so, but this does not mean that whether the firstproposition entails the second depends on what is meant by man andanimal. The proposition expressed by the sentence All men are ani-mals will be true, whatever the words in that sentence mean, but ifthey were not to mean what they do mean, this sentence wouldexpress a different proposition, one which might be false.

The fact that one proposition entails another can sometimes be

worked out from knowledge of the definition of the words in thesentences that express it. For example, that vixens are female can be.More often, however, one has to envisage the range of circum-stances in which would obtain if things are as one proposition saysthat they are and see if these are included in the range of situationswhich would obtain if things were as the other proposition says thatthey are.22

(xxiv) Propositions as subsistent entities

Finally, I must disclaim the view, once associated, rightly orwrongly, with Bolzano and Meinong, that propositions are subsis-tent entities.

A grin is not an entity. To speak of a grin is to speak of the wayin which someones lips are configured. Entitiescats lipsareinvolved in grinning, but are not the grin. A grin can be friendly,forced, appealing, impossible to repress, insincere, or bad for the

face. None of these epithets can be ascribed to lips.The same applies to ways. The proposition that there is a way of

Jonathan Harrison

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22 Jonathan Harrison, Humes Moral Epistemology, (Oxford UniversityPress, 1976), Chapter III.


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cooking eggs is entailed by the fact that if you put an egg with oilinto a frying pan and apply heat the result will be a cooked egg.That ways can be talked about and even countedthere are far

more eggs than there are ways of cooking eggsdoes not imply thatways are entities.

Just as that the only entities involved in grinning are lips, so theonly entities involved in that way of cooking an egg which is fryingit are eggs, cooking oil, a pan, a source of heat and perhaps people.But this does not mean that what can be predicated of ways ofcooking eggs, for example that they are slow, reliable, expensive,difficult, easy to forget or never used, can be predicated, either indi-vidually or collectively, of eggs, frying pans oil and heat. (The word

heat is itself problematic. Perhaps I should have said under a jet ofignited gas.)

Philosophers do in fact often take certain words to be about enti-tiessubstances might be a better wordand then debate theexistence of a whole menagerie of apparent entities, the possibleexistence of which careful attention to language, together with con-sidering the number of nouns in the language which cannot possi-bly be names for entities, might dispel. For example, if one thinksways are entities, it may seem that the question whether there are

such things as ways, or worse, given that there are ways, whetherways exist, is a philosophical or perhaps an ontological question. Butto doubt whether there are ways of boiling eggs in view of the factthat it is manifestly possible to boil them would be daft.

I suspect that the same thing is true of numbers. To doubt theexistence of numbers when it is manifestly true that there is a primenumber between three and seven, and that it is equally true thatpeople can add numbers, subtract numbers, multiply numbersdivide numbers, and correlate numbers with groups of entities (i.e.

count them) is like doubting the existence of ways when it is mani-festly true that there is at least one way of cooking eggs. To doubtthe existence of propositions when it is manifestly possible to dosuch things as assert that dogs bark, deny that they do, wonderwhether they do or not, advance reason for thinking that they do,draw conclusions from the fact that they do, is nearly as misguided.

It may well be the case that the world contains no entitiesinvolved in cooking eggs over and above eggs, pans, frying oil andgas jets, but this is not at all to say that ways of cooking eggs just are

eggs and pans and frying oil. Similarly, it may be that the world con-tains no entities relevant to the existence of propositions other thansentences, but this would not mean that propositions were sen-tences. But to give an account of the entities to which talk about


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propositions might be reduced, and how to reduce it, is at themoment beyond my capacity.

Cambridge

Jonathan Harrison

Documents

The Logical Function of That or Truth Propositions and Sentences Harrison Philosophy Journal