Signification and assertion

Every departmental science has a subject, and its literature talks about or refers to that subject. Physics talks about heavy bodies and momentum and energy, chemistry talks about compounds, biology talks about flora and fauna etc. What does semantics, the science of meaning, talk about?

And there is the problem. Sometimes we cannot refer to what we signify.






Frege recognised this problem in 1892, in his essay ‘On Concept and Object’. A sentence consists of words, each of which has a signification or sense. What the whole sentence signifies is thus a compound of the senses corresponding to the words. (See e.g. his undated letter to Jourdain, in Frege’s Philosophical and Mathematical Correspondence, ed Gabriel and Hermes, 1980). The possibility of understanding a sentence we have never heard before depends on this property. What the sentence signifies is something new and perhaps previously unknown to us, but the signification of the words of which it is composed must be known, otherwise we would be incapable of understanding the sentence. For example ‘Socrates is a man’ is composed of the expressions ‘Socrates’ and ‘is a man’, both of which we know and understand.

The problem that Frege grapples with in ‘On Concept and Object’ is that while we can talk about what ‘Socrates’ signifies, namely Socrates himself, we can’t talk about what ‘is a man’ signifies. Or suppose we can. Let’s refer to it by the expression ‘The signification of “is a man”’. Will that do? No, because that expression is what Frege calls an Object term, an expression that refers to an object like Socrates. Thus the sentence ‘The signification of “is a man” is an Object’ is true. But it cannot signify an object, otherwise the sentence ‘Socrates is a man’ would be composed of two terms for objects. But two such terms cannot compose a sentence, any more than ‘Socrates Plato’ can. The sentence would be a mere list of words. Frege says, enigmatically ‘the concept horse is not a concept’, and attributes it to ‘an awkwardness of language’.

There is a similar problem regarding what I call signs of assertion. Consider

It is false that Socrates is a horse

I have not asserted that Socrates is a horse. On the contrary, I have denied it. Yet the four words ‘Socrates is a horse’ occur inside the eight word sentence ‘It is false that Socrates is a horse’. Perhaps we can explain this as follows. The eight word sentence can be split into ‘It is false’ and ‘that Socrates is a horse’. The latter is what Frege calls an object term. It refers to something a mad person might assert as true, the very thing I stand in the relation of denying to. So the meaning of the eight word sentence is changed by putting ‘It is false’ in front, and so if the meaning of the whole sentence is a composite of the meaning of ‘it is false’ and ‘that Socrates is a horse’, the composite is what ‘It is false that Socrates is a horse’ signifies. But of course that can’t be so, for the very fact that we could signify that Socrates was not a horse, would require that Socrates not being a horse was a fact. Worse, ‘It is true that Socrates is a horse’ would signify Socrates being a horse, so would require the existence of Socrates being a horse. Both those contradictory facts would have to exist in order for the contradictory sentences to be significant. Impossible!

Frege alludes to this problem in a much later essay (‘Negation’) published in 1918. He distinguishes between a question (my example is ‘is Socrates a horse’) from the thought corresponding to an answer like ‘yes’ or ‘no’. For if the sense of the question contained the sense of ‘yes’ or ‘no’, then the question would contain its own answer. The question would express a thought ‘whose being consists in its being true’.

Grasping the sense [of the question] would at the same time be an act of judging, and the utterance of the interrogative sentence would at the same time be an assertion, and so an answer to the question. But in an interrogative sentence neither the truth nor the falsity of the sense may be asserted.

Fair enough, but Frege does not see this as a challenge to his compositional semantics. Consider ‘Is Socrates a horse? No’. The first part signifies the question. If adding the sign ‘No’ completes the sense, then what is signified by the whole thing, namely question plus answer, must indeed be something whose being consists in being true, which Frege apparently denies.

In summary, if the signification of the whole is made up of the signification of the parts, then we should be able to refer to the signification of the whole, if semantics is to be a proper science. But we can’t, otherwise the subject of our science would include items like Socrates not being a horse, as well as Socrates being a horse. Which is impossible. Therefore semantics is not a science, at least not a proper science.

Sic et non

What do the words ‘yes’ and ‘no’ mean? Well, I can explain how their meanings add up. If I add the word ‘yes’ to the question ‘is it raining’ I get something with the same meaning as the assertion ‘it is raining’

“Is it raining? – yes” = ‘it is raining’

Similarly adding the word ‘no’ to the same question gives the corresponding denial:

“Is it raining? – no” = ‘it is not raining’

Does this shed any light on the question about negation and the principles of contradiction and excluded middle? I think so. For I suggested that one who questions either of these principles hasn’t really understood the meaning (or rather, the use) of words like ‘not’. Certainly, one who thinks that both ‘yes’ and ‘no’ are simultaneous replies to the same question, hasn’t understood the meaning of these interjections. For example, suppose someone utters ‘no’ then ‘yes’ in close succession.

“Is it raining? – no… yes” = ‘it is raining’

We would naturally take him or her to have changed their mind. I.e. At the time of uttering ‘no’ they were saying it was not raining, and then retracted it by uttering ‘yes’. 

That deals with the principle of contradiction, namely is that it is impossible meaningfully to assert and deny the same thing.  As for excluded middle, that follows from the fact that nothing else apart from ‘yes’ and ‘no’ counts as a reply to a question. Note that ‘not sure’ is not a relevant reply, for it is really the reply ‘no’ to the question ‘are you sure that it is raining?’, rather to the question 'is it raining?'.  I.e.

"Is it raining? - not sure" = "are you sure it is raining? - no" = "I am not sure it is raining"

Failing to answer is failing to answer. Bullshitting is also failing to answer the question, but by means of asserting all sorts of other irrelevant things, or just outright nonsense.

On the true nature of reality

I have finished the first draft of a translation of Chapter 51 of Ockham's Summa. To put this in context, it is part of chapters 40-62 which cover Aristotle's ten categories or 'praedicamenta' or 'genera'. In this part of the book, Ockham argues that the categories are not ten kinds of thing that exist in reality, outside the mind, but rather they are kinds of term - ten terms that signify the same thing in different ways. He writes (my translation)

For it should not be thought that the ten genera are things outside the soul, or that they signify ten things, each of which is signified by only one of the genera, but rather the teaching of the Peripatetics shows that the ten genera are ten terms signifying the same things in different ways. For just as the eight parts of speech can be distinct, and yet signify the same thing, e.g. 'white', 'whitening', 'to whiten', 'go white', so the identity of the things which they convey can be consistent with the distinctness of the categories.

Is that right? It is consistent with Ockham's strategy throughout this part of the book. Instead of saying 'Socrates has wisdom' we should say 'Socrates is wise'. We should not suppose that the abstract term 'wisdom' is some king of thing outside the soul, which bears some odd relation to Socrates such as 'instantiation' or 'inherence'.

Someone will object (perhaps they are from Phoenix) doesn't this miss something out? Is 'wise' just another way of referring to or 'suppositing for' Socrates? Surely not. Socrates himself - per se ipsum - is not the referent of 'wise'. There must be something in reality which, in addition to Socrates, makes 'Socrates is wise' true. There must be some difference between the fact that 'Socrates' refers to Socrates, and the fact that 'wise' refers to Socrates. And that difference would be wisdom itself. Whereas it is part of the meaning of 'Socrates' that it signifies him, it is not part of the meaning of 'wise'. There must be something more to reality than the referent of subject and predicate.

I reply: there may well be something more, but as I have argued before, this 'missing part' of reality cannot be conveyed by noun phrase. I won't repeat these arguments in detail, but briefly, Socrates and wisdom gives us two separate things, but not Socrates being wise. And Socrates being wise is not enough, since we want to know whether his being wise is a fact, is the case etc. There is always something missing from a noun phrase that makes it incapable of expressing reality. To express reality we need a verb. But realists always insist on talking about reality using noun phrases. What do they have against verbs?  Why this discrimination? If verbs were a part of society, they would be a disadvantaged minority, socially excluded, if realists had their way.

And note also that it is not the nature of the verb to express action. For 'action' is an abstract noun phrase. For there to be action, the action must take place, or happen.  In any case, there are verbs that do not signify actions at all, such as 'to rest', 'to remain', 'to endure' and so on. As Arnauld says in his Logic, Part II chapter 2, "On the verb", 'Peter lives' is a proposition and 'Peter living' is not. If you add 'is' to 'Peter living' to get 'Peter is living', you get a proposition, and this is because the participle 'living' does not signify affirmation, whereas the verb 'is' does. "From this it appears that the affirmation that does or does not exist in a word is what makes it a verb or not".

Is there something in reality that corresponds to the noun-verb structure that is essential to all language? If so, we could not talk about it, at least, not using nouns. We could express reality, but not signify it.

Flirting with linguistic idealism

Vallicella concedes to David Brightly here that the only way to get at 'truthmakers' is via the nominalisation of sentences.  For example

Tom is fat ==> Tom's fatness
Tom is seated ==> Tom's being seated

All we seem to be doing is turning a verb and noun phrase into a verbal noun or gerundive.  I agree.  This has a an affinity with my position on assertion.  The verb contains something that turns a noun phrase such as 'Caesar's death' into 'Caesar died'.  This cannot be nominalised, for if it could be, the verb would no longer be a verb.  All the philosophical difficulties connected with the notion of assertion, truth, truthmaking, extralinguistic reality, Bradley's regress etc etc are down to this simple, almost trivial fact.  The reality that we are trying to communicate by means of a sentence must include what we are communicating by a verb, and not just a verbal noun.  Thus we cannot name or designate or refer to this reality.  For naming or designation or reference is a function of noun phrases, not of verbs, and we can only communicate what is real - what is the case - by means of a verb.

Which means that it cannot be 'a reality' at all.  For the demonstrative noun phrase 'that reality' is ipso facto a noun phrase.  We need to add that this putative reality is a reality, that it really is the case.  But 'is the case' is a verb phrase.  If we nominalise it, we are back to 'its being the case', which does not quite capture 'the reality'.  Is its being the case a fact? Or is it something merely claimed by John, or Freddy?  To convey the reality, we need a verb, and thus convey more than 'the reality'.

Yet Vallicella still wants more, so it seems.

And yet surely we cannot rest content with saying that 'Tom is seated' is just true. Surely there is more to a true sentence than the sentence that is true. It can't be language all the way down. Or all the way out. I get the sense that nominalists like Ed are flirting with linguistic idealism.

Not really.  There clearly is more to a true sentence than the sentence that is true.  It's just that we can't name it or refer to it.

What does not agree with reality, does not exist.

We might have got there at last with Anthony, who now says "what does not agree with reality, does not exist".  I rather thought it was heading in that direction.  What a false statement asserts, does not agree with reality.  "Snow is black" says that snow is black. But snow being black does not agree with reality. Ergo, snow being black does not exist.  Ergo, "snow is black" does not state anything at all, for if it did, it would have to express a state of affairs that is not real, a non-enity, a nullity, a void.  Ergo, there are no false statements: all statements are true.

Nailed it at last.

Some questions for Anthony

Some questions for Anthony, who is still not convinced that any statements are false, yet (paradoxically) seems inclined to disagree with absolutely anything I say. I.e. for pretty much any x that I say, he strongly disagrees with x, yet will not admit that x is false (for he sees that if he says that what I say is false, he will have contradicted himself, given his implicit position that no statement is false, not even the statements of mine that he disagrees with). Well, some more questions for him.

Anthony, please remain seated (I assume you are sitting at a computer terminal while you are reading this).

1. Do you agree that ‘Anthony is sitting’ is true?

Now stand up, please.

2. Do you agree that ‘Anthony is sitting’ is no longer true?

3. If so, do you also agree that ‘Anthony is sitting’ is now false?

Sentences as names

I regularly visit Vallicella’s place although no longer comment there due to the sometimes alarming responses. Today’s one caught my eye. I stopped right at the first leg of his aporetic triad, and went no further.

1. 'Al is fat' is the name of the fact of Al's being fat.

Come off it. The expression ‘the name of the fact of Al's being fat’ is the name of the fact of Al's being fat. As for 'Al is fat', it names nothing. Although it does express the proposition that Al is fat.

Gospel truth

In my last post, I mentioned two fundamental differences between the account of fiction I have defended here, and the account given by Peter van Inwagen in "Creatures of fiction". The first is that, according to me, sentences in fiction have a truth value. They are typically false (although works of fiction may contain many true statements, such as that Napoleon was short, that Paris is a city in France, that Baker street is in London etc). The second is that fictional names refer. Van Inwagen, by contrast, holds that (i) sentences in fiction typically assert nothing at at all and (ii) fictional names do not refer.

Taking the first point first. Van Inwagen's position is essentially the neo-Fregean view of assertion, namely that the same thought or proposition may occur now asserted, now unasserted, that I have criticised in many places, particularly here, arguing that assertion is part of the semantics of a sentence, and that every complete sentence (i.e. one that is not a subordinate or noun clause) can be analysed into a sign for the content of the sentence - that which it states or expresses, usually signified by a 'that' clause, and a sign for assertion or denial.  Thus "Snow is white" = "It is the case / that snow is white".  If this is correct, then even fictional sentences contain an assertoric component, and hence are capable of truth or falsity, independent of what the narrator means or intends when he or she utters them.  This is exactly what Van Inwagen denies, and it is, of course, why he calls sentences vehicles of assertion. 

The same view is defended by Alvin Plantinga (The Nature of Necessity, Oxford, 1974, Ch. VIII, pp. 153-163 especially), who cites a famous passage by the English poet Sir Philip Sidney (1554-1586).

Now for the poet, he nothing affirmeth, and therefore never lieth. For, as I take it, to lie is to affirm that to be true which is false; so as the other artists, and especially the historian, affirming many things, can, in the cloudy knowledge of mankind, hardly escape from many lies. But the poet, as I said before, never affirmeth. The poet never maketh any circles about your imagination, to conjure you to believe for true what he writeth. He citeth not authorities of other histories, but even for his entry calleth the sweet Muses to inspire into him a good invention; in troth, not laboring to tell you what is or is not, but what should or should not be. And therefore though he recount things not true, yet because he telleth them not for true he lieth not; without we will say that Nathan lied in his speech, before alleged, to David; which, as a wicked man durst scarce say, so think I none so simple would say that Aesop lied in the tales of his beasts; for who thinketh that Aesop wrote it for actually true, were well worthy to have his name chronicled among the beasts he writeth of.

This is not right. For it is not true, as Sidney implies, that there is absolutely no gap between saying something false, and lying. There are at least two things in between. The dictionary definition of ‘to lie’ is ‘to utter something that is false with the intention to deceive’. Thus (1) in the case of stories, the narrator utters something he knows to be false, but with no intention to deceive. There is a compact between the narrator and his audience. The audience knows that these are falsehoods, the narrator knows that they know this, and both sides agree the same. This does not change the fact that the things said are (typically) falsehoods. And (2) in many cases a person uttering falsehoods does not know they are false, but rather believes sincerely in their truth, and so does not intend to deceive either. For example, a story about some miracle that (we will assume) cannot be true, but which the teller genuinely and sincerely and believes, and which, to paraphrase Sidney “he telleth for true”.

Someone who is not a Biblical fundamentalist must deal with the possibility that some or all of the events recounted in the Gospel are not literally true. If so, then according to Inwagen’s neo-Fregean view of assertion, one who recounts the Gospels is not asserting anything, and is not saying anything true or false. Clearly not: the fundamentalist, for one, will strenuously defend the literal truth of everything that is stated there. The ‘truth’ of the Resurrection is fundamental to Christian belief, and is even something a Christian has to publicly state they believe in.

Nor can Van Inwagen exclude such texts from his account. For his account is designed to explain the truth and falsity of statements of textual criticism, in which Biblical criticism must be included. For example, in “Discipleship and minor characters in mark's gospel” Joel Williams writes.

The main character groups in Mark's Gospel are the disciples, the opponents of Jesus, and the crowd. In addition to these groups, a number of individual characters are included in Mark's narrative. Some of them, such as Andrew or Peter, are disciples, while others, such as the high priest or Pilate, oppose Jesus. Also a number of minor characters function neither as Jesus' disciples nor as His opponents.

The statements are clearly true, and they include the sort of quantification (“some of them … others…”) that Inwagen’s account is designed to explain. But they are inconsistent with one of his key assumptions, which is that ‘textual criticism’ statements are vehicles of assertion, whereas the sentences in the texts they are criticising are not.

I will discuss the second point about 'reference' later.

Impersonal assertion

A fundamental objection to my position on assertion (that assertion is a part of the semantics of a declarative sentence) is that assertion must be personal. That is, the subject of verbs like 'assert', 'state', 'say' and suchlike must be a person. Thus no sentence - which is an impersonal, inanimate linguistic item - can assert anything. Thus assertion cannot be part of the semantics of a sentence.

I shall argue against this in two ways.

1. Even if we concede that the subject of an assertion must be personal, it does not follow that we cannot analyse a sentence in such a way that a sign for assertion is made visible. I claim that we can analyse the sentence 'Tom runs' as

It is true / that Tom runs

which means the same, but which contains the sign 'it is true'. The other part is the that-clause 'that Tom runs', which signifies the content of the sentence. This is the same content referred to in sentences such as 'Alice believes that Tom runs', 'Carol hopes that Tom runs', 'Bob doubts that Tom runs' and so on. But no one who utters these sentences asserts that content. If I utter 'Alice believes that Tom runs', I have asserted that Alice believes something. But I have not asserted the thing that she believes: I have not asserted that Tom runs, only that Alice believes this. But when I utter 'It is true that Tom runs', I have asserted that Tom runs. Which suggests that 'it is true' is a sign indicating that I am asserting the content itself, rather than saying something about it (such that it is a belief, or a hope, of someone). The sign 'it is true' is a symbol which, suitably connected with a symbol for the content, signifies assertion.

2. In any case, we need the idea of impersonal assertion for statements whose author is unknown. For example "The next sentence in Genesis says the earth was without form and void, and darkness over it.

In summary. We can analyse a declarative sentence into another sentence which means the same, but which has two main parts: a sign for the content of the sentence and another sign which is used to indicate or signify that the speaker is personally asserting the content, rather than saying something about the content. It is not unreasonable to call this an assertion sign. And sometimes - when the author of the original sentence is unknown - it is equally reasonable to say that the sentence impersonally asserts its content.

Frege's Point

What Geach calls 'Frege's point' is the claim that the same thought or proposition may occur now asserted, now unasserted. Frege expresses this very clearly in a short essay*, posthumously published, probably written in 1915, where he argues that asserting a sentence is a matter of the assertoric force with which the sentence is uttered, and that assertion is not the function of the word 'true'.

His argument is as follows. Uttering a sentence 'sea water is salt' merely expresses a thought. Nothing is meant to be asserted (behauptet werden solle). This becomes clear when turn the sentence into a that-clause: 'that sea-water is salty'. The that-clause does not assert anything. Or we could have the sentence spoken by an actor on a stage, where the actor does not speak with 'assertoric force' (or at least only seems to).

We can make this even clearer, he says, by adding the words 'it is true' to the expression 'that seawater is salty'. This forms a sentence that we can also turn into a that-clause: 'that it is true that sea-water is salty'. Thus the sense of the word 'true' does not make any essential contribution to the thought. If I assert 'it is true that sea-water is salty', I assert the same thing as if I assert 'sea-water is salty'. Thus the assertion is not to be found in the word 'true', but in the assertoric force with which the sentence is uttered.

Readers of this blog will recognise this as the thesis that William Vallicella has been defending from his website in Arizona. I shall discuss Frege's argument in my next post.

* "My Basic Logical Insights" (Posthumous Writings, transl. P. Long and R. White, 251-2. This is a translation of Nachgelassene Schriften 271-2).

Thought is quick

"Enthymeme" is a form of argument where one or more of the assumptions is so obvious that it need not be stated. Suppose at a party my wife says "It's past eleven". I know what she means, which can be expressed by the following syllogism.

(Major) If it is past eleven and we are out, then leave now!
(Minor) It is past eleven and we are out
(Conclusion) Leave now!

She does not need to state the major premiss, nor even the conclusion, but I catch her drift. Note both the major and the conclusion contain an imperative. Arthur Prior investigated the logic of arguments containing imperatives in his paper "On Some Proofs of the Existence of God" , published in Papers in Logic and Ethics, Duckworth 1976.

Note also that the minor premiss is an assertion, and must be understood as such for the argument to be valid. If by contrast it meant something like "Would you like another large gin and tonic?" her conclusion would not follow. The point being, "linguistic meaning" is king. If it were not for the meaning we assign to expression types, we would not be able to express ourselves in ways like this, that superficially suggest that meaning constantly fluctuates, and that some expressions have no linguistic meaning.

Thomas Hobbes gives an entertaining example in Leviathan Chapter III (my emphasis).

"For in a discourse of our present civil war, what could seem more impertinent than to ask, as one did, what was the value of a Roman penny. Yet the coherence to me was manifest enough. For the thought of the war introduced the thought of the delivering up the king to his enemies; the thought of that brought in the thought of the delivering up of Christ; and that again the thought of the thirty pence, which was the price of that treason; and thence easily followed that malicious question; and all this in a moment of time—for thought is quick."

The Prosentential Theory of Truth

In a comment to Vallicella here I mentioned an article on the pro-sentential theory in the Internet Encyclopedia of Philosophy, and said that the theory has 'some affinity' with the 'assertoric' theory of truth I have sketched out here (as well as fiercely defended at Vallicella's place.

Here, I will take some of the claims made for the prosentential theory in that article and compare them with the corresponding claims of the assertoric theory, to see how close the affinity is.

The Assertoric Theory
The assertoric theory of truth is that the copula 'is' of a simple declarative subject-predicate sentence, such as

Tom is running

contains two components. One is the copula, whose function is to join subject and predicate to form the 'content' of the sentence. The content we can signify by a noun phrase such as 'that Tom is running' or the verbal noun 'Tom's running'. The other is the assertoric component, whose function is to signal assertion, i.e. to signal that the person uttering the sentence is saying something capable of being true or false. We can make the internal structure of such a declarative sentence transparent by parsing it as follows:

It is true / that Tom is running

The Prosentential Theory compared to the Assertoric Theory
1. "According to the prosentential theory of truth, whenever a referring expression (for example, a definite description or a quote-name) is joined to the truth predicate, the resulting statement contains no more content than the sentence(s) picked out by the referring expression."

Although the theories are similar, the fundamental difference is that, according to the assertoric theory, the 'truth predicate' (actually the truth operator) operates on a noun phrase signifying the content of the sentence, not the sentence.

2. "The central claim of the prosentential theory is that ‘x is true’ functions as a prosentence-forming operator rather than a property-ascribing locution."

The central claim of the assertoric theory is that 'x is true' functions as an operator on a 'that'-clause that forms a normal sentence (not a 'prosentence'). It claims also that this operator is implicit, though not lexically visible, in a sentence that does not use the words 'is true'.

3. "According to the prosentential theory, the statement ‘p is true’ says no more than the statement ‘p,’

The corresponding claim in the assertion theory is that 'it is true that p' says no more than that p. I.e. 'It is true that Tom runs' says that Tom runs. However, the theory distinguishes between the operator 'it is true that', which operates on a sentence to produce another sentence (of equivalent meaning), the operator 'that' which operates on sentences to produce a noun phrase, and the operator 'it is true' which operates on 'that' clauses to form sentences. This is a crucial feature of the theory which is necessary to prevent the 'substitution problem'. If we substitute the noun phrase 'that Tom runs' for 'p' in 3 above, we get the nonsensical

(*) The statement 'that Tom runs is true' says no more than the statement 'that Tom runs'

which is nonsensical because 'that Tom runs' is not a statement, but a noun phrase. If by contrast we substitute the sentence 'Tom runs', we get

(**) The statement 'Tom runs is true' says no more than the statement 'Tom runs'

which is nonsensical because 'Tom runs is true' is not a well-formed sentence (it would be well-formed if we read it as 'that Tom runs is true', i.e. read the sentence as a that-clause, but then we are not substituting the same thing salva significatione. (To be fair, the IEP article does note the problem of substitution, but does not sufficiently explain how the prosentential theory overcomes it).

4. " The prosentential theory of truth counts as a ‘deflationary’ theory because it denies that any analysis of truth of the form "(x)(x is true iff x is F)" can be given, where ‘x is F’ expresses a property that is conceptually or explanatorily more fundamental than ‘x is true.’ "

The assertoric theory is also a deflationary theory on this criterion. According to the assertoric theory, 'is true' operates on a noun phrase (a that-clause) to form a sentence. This operator is present, explicitly or implicitly, in the main verb of every declarative sentence. It is fundamental to the semantics of the declarative sentence, and no more fundamental explanation is available.

5. "The prosentential theory of truth implies a solution to the liar paradox. Consider the following sentence.- This sentence is false - if it says something true, it is false ... if it says something false ... it is true. [... ] Some attempts to solve the liar paradox involve extreme measures. Tarski, for example, thought that the paradox could be avoided only by eschewing ‘semantically closed languages’ [...] Tarski succeeds in avoiding the basic form of the liar paradox—but only at a very high price. He must content himself with providing an account of ‘true-in-Li’ rather than an account of truth. And, since natural languages like English are semantically closed, Tarski’s theory also has the weakness of applying only to artificial languages. ... According to the prosentential theory, (43) is neither true nor false because it fails to pick up an anaphoric antecedent. Just as I cannot inherit my own wealth, a prosentence cannot inherit its content from itself. "

The assertoric theory solves the Paradox in essentially the same way. 'is true' is fundamentally an operator, not a predicate. When attached to a 'that'-clause, it does not predicate anything or attribute anything to anything named by the clause. It merely signals that the speaker is asserting the content signified by the clause. In the case of the Liar sentence, there is no content to be asserted. According to the assertoric theory, we must analyse every declarative sentence into a content-part, and an assertoric part. Thus the Liar sentence must be analysed as

What this sentence says is false.

where the content part is signified by 'What this sentence says', and the assertoric part to the denial 'is false'. But the sentence says nothing, because the attempt to locate a referent for it fails.

Deflationary theories of Truth

A common objection to deflationary theories of truth is sentences like 'Everything Tom says is true'. Analysing this as

(A) For all p, if he asserts p, then p.

results in incoherence when we attempt to substitute. If we substitute sentences like 'snow is white', we get

(B) If he asserts 'snow is white', then 'snow is white'.

which is nonsense. If we substitute propositional content, signified by a 'that' clause, we get

(C) If he asserts that snow is white, then that snow is white.

which is also nonsense. However, we can evade this difficulty along the lines I have suggested in earlier posts. The first insight is that 'it is true that' is a complex operator built from 'it is true', which operates on 'that' clauses to form declarative sentences, and 'that' which operates on sentences to form 'that' clauses. Then it is coherent to hold that the semantics of any declarative sentence can be represented formally as

(D) |- c

where the operator |- corresponds to the 'it is true' part, and 'c' to a that-clause. I.e. we parse 'it is true that Tom runs' as 'it is true / that Tom runs'. Then the problem sentence 'He is always right' can be analysed as

(E) If he says c, |- c

Suppose for example that he says that Tom runs. then c = that Tom runs (note I substitute a 'that' clause, not a sentence), and |- = 'it is true', as above. This yields

(F) If he says that Tom runs, it is true that Tom runs = if he says that Tom runs, Tom runs

which makes perfect sense.

Why truth is not a predicate

As I have argued below and elsewhere, the copula 'is', as in

(1) Tom is running

has a twofold function. The first is to join subject and predicate together into a single content that is expressible by the sentence. For example 'Tom's running' or 'that Tom runs'. The second - and this is something only a verb can do - is actually to express this content. Thus

(2) Tom's running is the case

or 'That Tom runs is a fact' or 'it is true that Tom runs'. Now as it happens the operator 'it is true' which we attach to the that-clause 'that Tom runs' or 'is the case' which we attach to 'Tom's running' also contains the verb 'is'. But this, I argue, is a grammatical accident. The 'is' in 'is the case' is mere filling. The operator 'is the case' is a unitary element of the sentence. It would be better expressed by a single verb 'isthecase' or 'itistrue'. If it is essentially complex, then of course it contains the verb 'is', and if it functions as a copula, then it will have the twofold function described above. 'the case' would be a predicate that we could attach to the subject 'Tom's running' to form the noun-phrase 'Tom's running being the case'. And we could further assert this to form a new sentence 'Tom's running being the case is the case' and so on ad infinitum.

This is obvious with 'is the case'. We are not tempted into supposing that 'the case' is a predicate that qualifies Tom's running in any way. It is less obvious with 'it is true'. It is more tempting to suppose that the noun-phrase 'that Tom is running' refers to some content, a thing, and that in forming 'that Tom is running is true' we are predicating 'truth' of this content. Bad things lie in that direction.

See also Maverick Philosopher for a different take on why truth is not a predicate

Semantic cancellation

The dispute about assertion continues at William Vallicella's house here. To recap. I hold that every declarative sentence contains an 'assertoric component'. This is part of the semantics of the sentence. Vallicella objects that one token of the same sentence-type may be used to make an assertion, another not. "Therefore, there cannot be an assertoric component in indicative sentence types ... whether there is anything assertoric about a token depends on how it is used in a concrete situation."

My reply to this is that the phenomena Vallicella has in mind can easily be explained by the possibility of 'semantic cancellation' i.e. the use of a sign added to an expression to cancel out part of the semantics of the expression. If we agree that semantics is compositional, and if we agree that verbal composition does not always reflect semantic composition (as in 'Tom runs' = 'Tom is running'), then we allow for the possibility of 'semantic cancellation'.

If we allow for semantic cancellation, we automatically allow that one token may have a different semantics from another of the same type, because of the presence of semantic cancellation in the latter case. For example, in

(A) Tom runs
(B) Sarah believes that Tom runs.

(B) has a different semantics from (A). (A) is true iff Tom runs. But (B) can be true or false whether or not Tom runs. But this is not an argument against the existence of an assertoric component which relates 'Tom' and 'runs'. Semantic cancellation explains this. The operator 'that' cancels out the assertoric component in (A), and converts its semantics into that of a noun-phrase. This phrase is object to 'Sarah believes', where the assertoric component is now located inside the main verb 'believes'. We can further cancel this out by adding another 'that' operator to create another that-clause, as in:

(C) that Sarah believes that Tom runs.

and so on. Note that semantic cancellation can be non-verbal. If I utter 'Tom runs' together with a nod and a wink (meaning that Tom is a lazy fellow who takes no exercise at all), the nod and wink is a cancellation operator on the verbal part of the assertion. I.e. the utterance of the sentence accompanied by the nod and wink is equivalent to

It is not the case that / Tom runs

where 'Tom runs' is the verbal component, and 'It is not the case that' corresponds to the non-verbal nod or wink. Ironic or arch modes of expression can also be used to the same effect ('Tom runs - oh yeah right').

In summary. Vallicella's argument against an 'assertoric component' is that a token of the same sentence-type may be used without making an assertion. My reply to his argument is that this is because of semantic cancellation, which removes the assertoric component. The fact that this componet is removed in the one case, does not prove that it did not exist in the other.

The ultimate goal of this is a nominalistic theory of truth which is a version of the redundancy theory of truth. i.e. a theory which denies the existence of both truthbearers and truthmakers. There is something else at stake also, nothing to do with truthbearing and truthmaking. Vallicella's type-token argument is a general argument against 'semantic determinism'. Semantic determinism is the thesis that the same tokens of a type-identical set of signs will always have the same meaning. If this were not true, it would destroy the possibility of communication. Given that we cannot bring things that are not directly known to speaker and hearer (such as other people's thoughts, or things that are not perceptible to us) into the discussion, we have to use words as symbols of things - nominibus utimur pro rebus notis, quia non possumus nobiscum ferre res ad disputandum. If different tokens of these symbols (or rather sets of symbols) did not have a fixed and constant meaning, how could we communicate at all?

Now I agree that a subset of the symbols we use can change their meaning depending on context. But when we include the whole context, and if we regard the context itself as part of the symbol-set, then I claim that the semantics is deterministic. For example, when I use the word 'this', pointing to an animal, then 'this is a tree' is false. When I point to a tree, the same sentence (i.e. a different token of the type 'this is a tree') is true. So it may appear that the semantics of 'this is a tree' is indeterminate. But if we include the act of pointing, i.e. the gesture, and the tree-appearance, as all included in the symbol-set, then the semantics is determinate. Any token of 'this is a tree' accompanied by the act of pointing, and a representation of the demonstrated object, will have the same meaning (and the sentence will be true when the representation is in fact of a tree, false otherwise).

So, quite a lot is at stake.

The Truth Operator

A modified version of my comment on Maverick Philosopher, about the distinction between truth as a predicate, which as Bill argues seems to commit us to realism about truthmakers, and truth as an operator, which does not appear to lead to such a commitment.

I subscribe to an 'operator' theory of truth. Each sentence has a syncategoric semantic component which corresponds to assertion. This component is always locked inside the main verb of the sentence. The operator 'that', which forms a that-clause from the sentence, strips out this assertoric component to convert the sentence into a categorematic expression signifying a possible object of thought, belief, assert, judgment etc. The operator 'it is true' replaces the assertoric component again to give us back the sentence (although the main verb is now the 'is' of 'it is true' rather than the verb of the operated-on sentence).

Thus the expression 'it is true that' is a sentence-operator that contains two operators, namely 'is true' and 'that'. The operator 'that' operates on sentences to produce a that-clause:a noun-phrase that names a content, a possible object of belief and judgment. It does this by removing the assertoric element from the sentence. The operator 'it is true' operates upon that-clauses, to form whole sentences. Such sentences have the same truth-conditions as the original sentence. Thus:

(1) Snow falls

is a sentence that asserts something, via the assertoric component embedded in the main verb 'falls'.

(2) that snow falls

is a that-clause naming a possible object of judgment or belief, such as in the sentence 'John believes that snow falls', which we parse as 'John / believes / that snow falls' to clarify its relational form 'X believes Y'. Note that in the belief sentence the verb 'falls' is no longer the main verb. The truth or falsity of 'John believes / that snow falls' no longer depends on whether snow does fall or not. Rather it depends on whether John believes this or not. Finally

(3) It is true that snow falls

Gets us back to a sentence with the same truth-conditions as (1), but with a different semantics. The main verb is now the 'is' of 'it is true', and the verb 'falls' is a subordinate verb. The assertoric component of (3) lies in the 'is' of 'it is true', the assertoric component of (1) lies in 'falls'. We can parse (3) as 'It is true / that / snow falls' to make it clear that there are two operators rather than one (Frege's mistake was to think there is only one). Or we can parse it as 'It is true that / snow falls' to make it clear that the combination of 'it is true' and 'that' gives us a further operator.

This may remove the temptation to suppose that there are such things as 'truthmakers'. (Well it won't, I imagine the supporters of truthmaking will continue in the deep error of their ways, but that is the way). The operator approach is of course consistent with a thoroughgoing nominalist program. I wonder whether, if ordinary language had the right synactic structure so that operators and existence-verbs and the like were clearly identified, the users of that language would be so committed to realist semantics. Could we even 'do' metaphysics in such a language?

Existence and assertion

Bill Vallicella's otherwise excellent discussion of 'thin' theories of existence in a series of posts at the Maverick Philosopher website has so far ignored the difference between theories where the existence of a singular referent is presupposed, and theories where it is asserted.

Consider 'Socrates is wise'. This affirms wisdom of Socrates. Does it also affirm existence of him? Does it then consist of two propositions, one of which affirms existence, the other of which affirms wisdom? Or does it consist of just one, that affirms wisdom without affirming existence? The latter view, sometimes called the 'Strawsonian' or 'presupposition' view, involves the following problem.

If Socrates does not exist, the negation of 'Socrates is wise', i.e. 'It is not the case that Socrates is wise' must be true. But if 'Socrates is wise' does not assert the existence of Socrates, neither does its negation (for a negation can deny no more than the corresponding affirmation affirmed). In which case the negation expresses exactly the same thing as if Socrates had existed, and wisdom was being denied of him, i.e. expresses exactly what 'Socrates is non-wise' expresses. But then it affirms non-wisdom of something, and so requires the existence of Socrates. But that cannot be, if Socrates does not exist.

But there is no such problem with the view that existence, as well as wisdom, is asserted. Then the negation of 'Socrates is wise' is the negation of a conjunction, and so is equivalent to the disjunction 'There is no such person as Socrates, or wisdom does not apply to Socrates'. There are different facts corresponding to Socrates' not existing, and Socrates existing but not having wisdom, and so the falsity of 'Socrates is wise' does not imply that a non-wise Socrates exists.

[edit] For an early defence of assertionism, see my translation of chapters 12 and 14 of the Ockham's Summa Logicae II here. For a later one that should be familiar to almost everyone, see Russell's Theory of Descriptions.