The Elusive Assertoric Component

William of Woking comments:

 Consider again

(1) Tom runs

(2) that Tom runs

(3) It is true that Tom runs

We have agreed that (1) and (3) are semantically identical. Yes, they express the very same propositional content or thought. They have the very same meaning (Sinn).   We also agree that (2) is verbally more complex than (1), likewise (3) is verbally more complex than (2). Yes, that's obvious. 

Do you agree that it logically follows that in some cases, increasing the verbal complexity can reduce the semantic complexity? I argue as follows. Either (2) is semantically more complex than (1) or less complex. If more complex, then it follows that (2) is semantically more complex than (3), because of the semantic identity we agreed. In which case it logically follows that increasing the verbal complexity (in the move from (2) to (3)) reduces the semantic complexity. Therefore &c. Or (2) is semantically less complex than (1). In which case it logically follows that increasing the verbal complexity (from (1) to (2)) reduces the semantic complexity.

Your argument seems correct: in some cases increasing verbal complexity reduces semantic complexity.  But what exactly do you mean by 'semantic complexity'?  Verbal complexity seems clear: if one expression contains more words than another, then the first expression is verbally more complex.  But you need to explain to us exactly what you mean when you say that one expression is semantically more complex than another.  For example, (1) and (2) are semantically distinct.  The first has a truth-value, the second doesn't.  But which is semantically more complex?  What criterion do you use to decide that?  I don't see that (2) is semantically more complex than (1).  If you think of 'that' as a sentential operator, then you can say that (2) results from (1) when 'that' operates upon (1).  But that is not to say that (2) is semantically more complex than (1).  For 'that' by itself carries no meaning.  It is syncategorematical as opposed to autocaregorematical to use some Medieval lingo.

If you agree to this, then I have a large part of what I propose, for nearly all your negative arguments rest on the observation that a token of the same verbal expression (i.e. with the same verbal complexity) may appear to lack the assertoric component that the other has. My reply here is that this is consistent with 'semantic subtraction' operators. The token of the expression (1) above ('Tom runs') is identical to the token included in the that-clause in (2).   No, they are distinct tokens; they are only type-identical. Yet (2) as a whole appears not to be an assertion. To be precise: (2), by itself, cannot be used to make an assertion.  You would argue, in general, that this is because there is no such thing as a semantic component of assertion. I reply, in general, that this is because of the 'negative effect' of the 'that operator'.

I'm afraid this is still very unclear.  Consider the sentence 'Tom sucks.'  Now consider two tokens of this sentence type.  (T1)  'Tom sucks' uttered by Tanya to express contempt for Tom. (T2) 'Tom sucks' uttered by Tony to describe how Tom is ingesting his cola.  From the point of view of grammar, both tokens are in the indicative mood.  But only one is being used to make an assertion.  Therefore, there cannot be an assertoric component in indicative sentence types.  And whether there is anything assertoric about a token depends on how it is used in a concrete situation.

In any case, what is the wider relevance of all this?  What's at stake here?  Where are you going with this?

Comments

[William]

>>But which is semantically more complex? What criterion do you use to decide that?

If you read my argument, you see that it does not require a criterion. The argument begins 'Either ...', which is a signal that alternatives are in question. Both imply the conclusion I propose. I.e. if A implies p, and B implies p, and A and B are the only alternatives, p follows. Strictly speaking, the alternatives are contraries, not contradictories. "A is more complex than B" "A is less complex than B" can both be false, if A or B or both do not admit of complexity. But we agreed at the very beginning of this disputatio that semantic compositionality can be assumed.

>>But you need to explain to us exactly what you mean when you say that one expression is semantically more complex than another.

I don't have to, for the reasons explained above. If the two expressions in question admit of complexity at all (i.e. we assume semantic compositionality), it follows that one is more complex than the other. The argument I gave does not require us to say which one is th more complex. However I will attempt a definition: A is semantically more complex than B

>>Consider the sentence 'Tom sucks.'

That is not a good example in my view because it relies on equivocation. The word 'suck' has the meaning of drawing liquid into the mouth. Also (in the US only, this meaning is not even in my British dictionary), it is a verb meaning 'to be disgustingly disagreeable or offensive'. So (in my view) they are different words, i.e. different types of word, even though their orthography is the same). Also, and this is odd, why do you consider that the sentence 'Tom is disgustingly disagreeable' is not being used to make an assertion? One person may disagree with this, another person may agree. And it may be true (perhaps Tom is so) or not.

>>In any case, what is the wider relevance of all this? What's at stake here? Where are you going with this?

I have several goals. I wanted you to take a position on 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'.

And 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

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

We agree that (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 also explains this. The operator 'that' (on this view) 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

(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.

It is not the case that / Tom runs

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

That is the first goal. The ultimate goal: 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. I won't give the arguments here, as things are already busy enough.

There is something else at stake also, which is nothing to do with truthbearing and truthmaking. Your type-token argument is a general argument against 'semantic determinism', namely the thesis that different tokens of a type-identical set of signs can always have a different meaning. If true, this destroys 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) could suddenly change their meaning, the possibility of communication is destroyed.

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.

[William]

Sorry, I missed the definition of 'semantically complex'. A is more semantically complex than B when A has more semantic components than B. A special case of this is when all the components of B are also contained in A. But my definition, and my argument above, do not depend on assuming this special case.

[William]

I have posted a modified version of the comment above at my place here http://ocham.blogspot.com/2010/05/semantic-cancellation.html .

[Bill Vallicella]

Well, old friend, it looks like we've bogged down again. But I'll continue thinking about it.

[William]

Is it that the idea of semantic cancellation is obscure or unclear? Then I will think of ways to clarify it, with your help.

[T. Hanson]

"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)."

Why is this determinate? I could point to the tree, say "this is a tree," gesture, etc. and it could be legitimately be understood by the listener as "this is bark." These little indeterminacies often pop up in teaching my toddler words.

[William]

>>I could point to the tree, say "this is a tree," gesture, etc. and it could be legitimately be understood by the listener as "this is bark."

It is determinate for anyone who correctly understands the rules of the language, and its vocabulary.

[T. Hanson]

"It is determinate for anyone who correctly understands the rules of the language, and its vocabulary."

If they correctly understand the rules of the language and vocabulary why would you "point to it and gesture and say 'this is a tree'" in the first place? They would already know what a tree is.

Pointing to something, gesturing, and saying this is a tree does not have a determinate truth value unless the listener knows you are pointing to the tree and not the bark on the tree.

[William]

>>If they correctly understand the rules of the language and vocabulary why would you "point to it and gesture and say 'this is a tree'" in the first place? They would already know what a tree is.

The example was purposely chosen to show how exactly the same sentence type could have a different meaning depending on what was pointed to.