Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

The Truth Operator and the Truth Predicate

This is an addendum to our earlier discussion which I hope will advance it a step or two.  We heard Alan Rhoda claim that the following sentence is false: 'If nothing exists, then it is true that nothing exists.'  Let's think further about this.  We first note that 'If nothing exists, then it is true that nothing exists' can be parsed in two ways:

1. If nothing exists, then it is true that (nothing exists).

2. If nothing exists, then it is true (that nothing exists).

Call (1) the operator construal.  'It is true that ( )' is a sentential operator the operand of which is a sentence.  The result of the operation is itself a sentence.  If the operand is true, then the resulting sentence  is true.  If the operand is false, then the resulting sentence is false. Please note that prefixing 'It is true that' to a sentence cannot change the truth-value of the sentence.  In this respect, the truth operator 'It is true that ( )' is unlike the negation operator 'It is not the case that ( ).'  Assuming Bivalence — as I have been doing throughout — if you negate a true sentence you get a false one, and vice versa.

Call (2) the predicate construal.  The consequent of (2) is of course a sentence, but it is not the result or product of a sentential operator operating upon a sentence. For what is within the parentheses is not a sentence.  'That nothing exists' is not a sentence.  It does not have a truth-value.  If I assertively utter it I do not convey a complete thought to my audience.  'That nothing exists' is the name of a proposition.  It follows that 'it is true' in the consequent of (2) functions as a predicate as one can more clearly see from the equivalent

3.  If nothing exists, then that nothing exists is true.

In (2) and (3)  a predicate is attached to a name, whereas in (1) this is not the case: a sentential operator is attached to a sentence.

Not only are the parsings different, the ontological commitments are as well.  (2) commits us to propositions while (1) doesn't.  And (1) seems to commit us to operators while (2) doesn't. 

Here is the place to comment on my asterisks convention.  Putting asterisks around a declarative sentence forms a name of the proposition expressed by the sentence.  'The Moon is uninhabited' is a declarative sentence.  '*The Moon is uninhabited*' is not a sentence but a name.  It names an entity that has a truth-value, but it itself does not have a truth-value.  (2) and (3) can also be rendered as

4. If nothing exists, then *Nothing exists* is true.

With the operator/predicate distinction under our belts we may be in a position to see how one philosopher (Alan)  could reasonably reject 'If nothing exists, then it is true that nothing exists' while another accepts it.  The one philosopher gives the original sentence the predicate construal which is committed to propositions.  This philosopher then reasons that, if nothing exists, then no propositions exist either, and are therefore not available to instantiate the property of being true.  The other philosopher gives the original sentence the operator construal and finds it impossible to understand how anyone could reject the original sentence so construed.  This philosopher insists that if nothing exists, then it is true that nothing exists; that this truth is not nothing, and that therefore it is something, which implies that it cannot be the case that nothing exists.

 

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Bill Vallicella

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12 responses to “The Truth Operator and the Truth Predicate”

  1. William Woking Avatar
    William Woking

    This is an excellent post. As you know I have long argued for an ‘operator’ theory of truth. This looks like a further argument against a predicate theory of truth. If ‘true’ is a predicate, then every predicate must have a subject, and so the subject of ‘that nothing exists / is true’ must paradoxically name something.
    The operator theory I have defended here in the past is that 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).

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  2. William Woking Avatar
    William Woking

    To avoid possible confusion, I maintain that 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 relation form ‘X believes Y’. Note that in the belief sentence the verb ‘falls’ is no longer the main verb. The sentence truth of 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 semantic composition. The main verb is now the ‘is’ of ‘it is true’, and the verb ‘falls’ is a subordinate verb. The assertoric component of (3) is in ‘it is true’, the assertoric component of (1) is 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 removes any 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?

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  3. Bill Vallicella Avatar
    Bill Vallicella

    WW,
    Thanks for the commentary. You and I may be able to find some common ground after all. But I still have trouble with your claim that ‘snow falls’ asserts something. What you displayed above is a sentence-type which, as far as I can see, doesn’t assert anything. Persons assert, not sentences. Assertion is a speech act. I make an assertion by producing a token of the type ‘snow is white.’ E.g., I assertively utter the sentence.
    So that’s one problem I have with your view. A second is your use of ‘assertoric.’ You want to say that the sentence is assertoric in virtue of the assertoric component embedded in ‘falls.’ I suggest that ‘assertoric’ as used by you elides the distinction between the grammatical mood of a sentence (which does not belong to pragmatics) and the pragmatic question as to the use to which the sentence is put.
    One can utter (or otherwise token) an indicative sentence in oratio recta and not make an assertion. Suppose Johnny is picking his nose in public, and Mommy says to Johnny, ‘We don’t do that.’ Mommy utters an indicative sentence, and yet does not make an assertion; she issues a command. A second example. ‘Obama sucks’ is an indicative sentence. But a tokening of this sentence type will not typically express a proposition or convey an assertion; it will typically be used to express dislike or contempt.
    What I am saying, then, is that pragmatics and semantics have to be kept distinct. Assertion belongs on the side of pragmatics. The grammatical moods belong on the semantic side. Your use of ‘assertoric’ tends to blur matters, or so it seems to me.
    See my post (which may have been written against you), “Assertion and Grammatical Mood”: http://maverickphilosopher.typepad.com/maverick_philosopher/2010/03/assertion-and-grammatical-mood.html

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  4. Bill Vallicella Avatar
    Bill Vallicella

    WW writes, >>This removes any temptation to suppose that there are such things as ‘truthmakers’.<< Are you perhaps confusing truthmakers with truthbearers? Propositions are truthbearers. And I take it your nominalism forbids propositions. I can see how the parsing 'It is true that / snow falls' does not commit us ontologically to propositions in the way 'It is true / that snow falls' does. But this is separate from the truthmaker question. Furthermore, you favor the parsing 'John believes / that snow falls' which makes of believing a dyadic relation that connects a person with a proposition (that which is named by the 'that' clause.) So are you for propositions or against them? Your view is not clear to me.

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  5. William Woking Avatar
    William Woking

    Hi –
    >>Persons assert, not sentences.
    We have certainly been over this ground before, indeed on my hard drive I may still have a point by point discussion of the issue.
    For now, and to clarify, I am claiming that there is a part of the semantics of the sentence which we can call ‘assertoric’, and this belongs to the sentence as part of its meaning, just as much as any other meaningful part. However, like the atom, it cannot be seen directly, indeed if I am right it cannot be referred to. For a sentence is always more than a list of referring terms (I think we agree this). But the meaning of the sentence amounts to more than that. We have to add a verb, whose semantics includes the magical component which I call ‘assertoric’.
    You say we have to ‘assertively utter’ the sentence. But how else would we use language to express meaning? Your argument applies to any part of speech. You might as well argue that a noun like ‘snow’ has no meaning of itself, because we have to utter the word ‘snow’ to express its meaning.
    >>Mommy utters an indicative sentence, and yet does not make an assertion; she issues a command.
    I agree that in certain contexts we can utter the same string of words and express a different meaning by means of the mode of expression, rather than the syntactics. But my argument remains: the component X (the ‘assertoric’ component) belongs to the sentence in virtue of its syntax, not its pragmatics. Specificaly, we add a verb to a noun to make a sentence. The verb contains the magic component. So it is syntax, not pragmatics, that determines the semantics.
    >> ‘Obama sucks’ …
    I also agree that many ideas, moods and so on can be conveyed by a sentence that do not belong to its semantics, properly understood. But this is not an argument against my position.
    >> Assertion belongs on the side of pragmatics.
    Disagree, when ‘assertion’ is understood in the sense I have explained. The sense I have explained is what is included only in a verb, and is what converts a noun phrase into a sentence, and which enables us to express what is capable of truth or falsity.
    Or perhaps I should withdraw that last remark above, or qualify it. The whole mess is caused by imagining there are things ‘bearing’ or ‘being capable of’ truth and falsity. Not at all. Adding ‘it is true’ to a ‘that clause’ doesn’t predicate truth or falsity to the content named by the ‘that’clause. It is simply a way of converting a noun phrase (the ‘that’clause) into a sentence.
    I use the term ‘assertoric’ because traditionally assertion is what is associated with the ideas of truth and falsity.

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  6. William Woking Avatar
    William Woking

    I have located my original set of points, which are in the form of a scholastic Quaestio – “Utrum assertio est pars significationis propositionis” – is assertion a part of the signification of a proposition?
    Perhaps I will post it on my blog. The ‘rationes’ were arguments put by you and ‘Spur’ and others in October 2007.
    I will add the rationes that you mention here, and in the post that you link to, and think of some ad rationes

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  7. William Woking Avatar
    William Woking

    Consider again
    (1) Snow falls
    (2) that snow falls
    (3) It is true that snow falls
    Which of the following propositions do you not agree with?
    (A) (1) has the same truth-conditions as (3)
    (B) (1) has a similar meaning to (3), except for the location of the main verb
    (C) (2) has a different meaning
    (D) (3) is formed by the successive addition of operators to (1).
    (E) The change in meaning caused by the operators is determined by the linguistic meaning of the terms. Specifically, one who understands the meaning of the operator ‘that’, and of the operator ‘it is true’, and of the rules of their use, understands what (3) means. This is independent of the context or the way the sentence is used, or of the intentions of the person who speaks or writes it.
    (F) Since (3) returns us to a sentence close or the same in meaning to (1), it follows that whatever change was induced by ‘that’, is reversed by ‘it is true’.
    (G) The operator ‘that’ removes some semantic component from (1). This is because it converts a noun-phrase into a sentence, and a noun phrase is in some sense less than a sentence.
    (H) From (F) and (G) it follows that ‘it is true’ replaces what ‘that’ removes.
    (I) Hence there is some semantic component corresponding to ‘it is true’ embedded in the original sentence (1).
    (J) The semantic component is determined by the linguistic meaning of the sentence. What we call this semantic component (e.g. ‘assertoric’) is a matter of indifference to the phenomenon in question.
    I can’t think of any clearer way of putting this, and the validity of the argument seems unassailable.

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  8. David|Brightly Avatar
    David|Brightly

    I’m attracted to WW’s position on this and the case he makes in his latest comment, eschewing all reference to ‘objects of belief or judgement’, is convincing. However, there’s a second noun phrase we can form from ‘snow falls’, viz, ‘snow’s falling’ (=’the falling of snow’). This too lacks the assertoric element of ‘snow falls’, but we can retreive it by appending ‘occurs’ or ‘happens’. It would seem that an analogous argument could then be made that ‘occurs’ is a sentence operator that undoes the work of an implicit operator that ‘gerundises’ ‘snow falls’ into ‘snow’s falling’. Hence if WW’s argument vitiates ‘is true’ as a genuine predicate the analogous argument would also seem to vitiate ‘occurs’. But we are quite happy with gerundive phrases like ‘snow’s falling’, thinking them names for event or process types, just as common nouns are names for object types, and using them in causal explanations: ‘Joe was winded by his running for a bus’. And it seems we cannot do without ‘occurs’ since it plays the role of ‘is instantiated’.

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  9. William Woking Avatar
    William Woking

    >>It would seem that an analogous argument could then be made that ‘occurs’ is a sentence operator that undoes the work of an implicit operator that ‘gerundises’ ‘snow falls’ into ‘snow’s falling’.
    I suggest that ‘occurs’ has a bit of residual content left in it, over and above the assertion/is-true operator. E.g. we can turn
    (1) a snowfall has occurred
    into
    (2) that a snowfall has occurred
    and then into
    (3) it is true that a snowfall has occurred
    which suggests that the verb ‘occur’ contains extra information over and above the ‘assertoric’ component.

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  10. David|Brightly Avatar
    David|Brightly

    WW, I’m not sure I see how your latest example brings out the extra content in ‘occurs’, nor am I sure it makes sense to talk about an ‘assertory element’ bare of asserting something, but I think you are right. The assertory element in ‘occurs’ seems to have the form of an existence claim, that the concept ‘snow’s falling’, say, is instantiated.
    Could you say a bit more about how you see the meaning of ‘that snow falls’? The suggestion is that it means the same as ‘snow falls’ minus the sense of assertion which can be added back by appending ‘is true’. I take it that this is not the same as ‘snow’s falling’ since to get back to ‘snow falls’ we have to append ‘occurs’ and this adds more than mere assertion? I note also that we would say ‘John believes that snow falls’ but ‘John believes in snow’s falling’, so perhaps these surface differences overlay deeper distinctions. For it seems that we can decompose ‘snow falls’ in two distinct ways: ‘that snow falls’ + ‘is true’, and ‘snow’s falling’ + ‘occurs’.

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  11. William Woking Avatar
    William Woking

    >>Could you say a bit more about how you see the meaning of ‘that snow falls’? The suggestion is that it means the same as ‘snow falls’ minus the sense of assertion which can be added back by appending ‘is true’.
    That is absolutely correct.
    >>I take it that this is not the same as ‘snow’s falling’ since to get back to ‘snow falls’ we have to append ‘occurs’ and this adds more than mere assertion?
    Yes. That is because, in my view, there is more stuff embedded in ‘occurs’ than just the assertoric content. What would that be? Difficult, but an ‘occurrence’ is something that comes into existence, then possibly stops existing. Contrast that with ‘Socrates is wise’. Being wise is not an occurrence, a snowfall is.
    David, I remember you from the previous incarnation of ‘Maverick Philosopher’, when everything had a comment box, but I can’t remember what your background was. Computing? Logic? Philosophy?

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  12. David|Brightly Avatar
    David|Brightly

    But we could also say something like this (with apologies for schoolboy Latin).
    Theorem. The sentence “Nix descendet” is true.
    Proof. A sentence of the form noun verb means that the referent of the noun performs the action referenced by the verb. ‘Nix’ refers to snow and ‘descendet’ refers to falling. That snow falls is true and hence “Nix descendet” is true.
    Corollary. The sentence “Snow falls” is true.
    Proof. “Snow falls” and “Nix descendet” have the same meaning. Apply the above theorem.
    Compare the the two sentences
    1. That snow falls is true.
    2. That nix descendet is true.
    Sentence (1) seems quite natural but I have the feeling that the change of language in (2) somehow prevents the that _ is true operator from doing its job. (2) seems to have lost its assertive force and feels to me closer to the unassertive ‘that snow falls’. How do others read it? Perhaps the more one is familiar with Latin the more the operator can ‘penetrate’ the alien phrase?
    This suggests the following hypothesis: In any language rich enough to serve as its own metalanguage the construction that _ is true, aka the sentence “_” is true, necessarily has a dual interpretation as both disquotational and metalinguistic oparator.

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