Monday, May 31, 2010

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.