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02/16/2010

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Irmela Wagner

I'll just try to reconstruct, please correct me if I'm wrong-

Ok, so the question seems to be:

Can the axioms be taken to be interpretive?

No, because

1) competence of a language has to be presupposed before we even get in a position to find the axioms governing it
2) natural languages have characteristics which evade 'catching' in axioms

Nevertheless we 'know' that there ARE rules governing sentences and that those rules have to be presupposed in order to explain our understanding of 'speech-acts'. These Rules lie in the differentiating combinatorial-features of a compositional meaning-theorems within a compositional meaning-theory. The Axioms show how the particulars can be put in combination to make a sentence interpretive for another speaker.

Second Question: What are the particulars, i.e. which are the smallest parts out of which the meaning of a sentence given the combinatorial rules can be reconstructed?

Proposals:

1) Semantical Primitives
2) Words
3) Speech-Acts

where 1) and 3) are context-sensitive but are easier to 'grasp' because 2) contains demonstratives and 'objects' alike, for whom Reference has to be given in order to make them somehow contribute to meaning, apart from context-sensitive use.
but it also seems to me that 1) and 3) make the finding of 'exact' Axioms pretty hard if not impossible, but maybe there I just didn't have a good look at the proposals made.
But still, we know that there is logical structure underlying language (think of particles of negation) and that understanding of it contributes a great deal to correct interpretation.
And then we may further ask where this logical structure comes from and how we come to conceive similarities or differences in nature. There we have the problems with the Universals and Salience.

Ja?

Kirk Ludwig

Let me say a bit about how I have been using the term 'interpretive'. To explain it, I want to compare it to my use of 'translational'. I use 'translational' in connection with axioms or T-theorems of a truth theory. Let me give examples of both.

First, a T-theorem for a language without context sensitive expressions, say the language of mathematics.

'II + II = IV' is true in L iff 2 + 2 = 4

I call this a translational theorem if and only if 'II + II = IV' in L translates '2 + 2 = 4' in English (the language of the theorem in this case). Tarski's Convention T says a truth definition (axiomatic truth theory) is adequate only if it entails a translational T-theorem for each sentences of the object language (the language the theory is a truth theory for).

An axiom for such a theory, for example,

A pair of things, x and y, are such that '=' is true of them in L iff x is identical with y

is translational if and only if '=' in L translates 'is identical with' in English.

Convention A, applied to a theory for a context insensitive language would require that all the axioms be translational (I have not give a full accounting of how it would look but only indicated the basic idea with one type of axiom).

Now, when we turn to a context sensitive language, we cannot require the theorems or axioms be translational. A theorem for 'Je suis faime' for example would look like this.

For any speaker s, and time t, 'Je suis faime' is true in French taken as if spoken by s at t iff s is hungry at t.

But here 'Je suis faime' does not translate 's is hungry at t' because the latter has variables in it and no expression that means the same as 'I'.

But it does spell out what the meaning of a particular utterance of it is relative to a particular speaker and time. So I say the theorem is interpretive, rather than translational. And this is then in effect a technical term.

More precisely and more generally, we can say that a theorem

S is true in L taken as if spoken by s at t iff p

is interpretive if the corresponding M theorem is true:

(M) For any speaker s, for any time t, S means in L taken as if spoken by s at t that p

Then for axioms I intend a similar interpretation. So for 'faime' we would have

For any x, for any speaker s, for any time t, 'est faime' is true of x taken relative to s at t iff x is hungry at t.

and this is interpretive iff

For any x, for any speaker s, for any time t, 'est faime' means as applied to x and taken relative to s at t that x is hungry at t.

Now, the issue that Miguel raised (I think your first question is more directed to that than to the question that Benjamin raised) was not whether the axioms of a truth theory considered as an object talked about by a meaning theory can be considered interpretive. He was suggesting that for one to use the truth theory for the intended purpose of coming to understand sentences in the object language one would have to understand the language in which it was stated. And that is something I agree with. And he was suggested that the knowledge I had said was sufficient for that was not. And I think he has a point. For there is something I had been thinking was to be included but which what I said I think does not secure, and that has to do with the way the grammar of the language of the truth theory is to be laid out. For I was supposing it would provide in effect a analysis of sentence structure in terms of semantical categories like noun phrase, verb phrase, verb, adverb, adjective, noun, determiner, connnective, quantifier, and the like, so that from knowing what the axioms mean as stated in a language we understand one by one, we would be in a position to associate terms in the language we knew with terms in the language of the truth theory, and so come to see in fact how it in turn was to be taken as showing what object language expressions mean.

But Miguel's deeper worry had to do with whether having to have knowledge of one language for the theory to do its work would undermine its ability to explain how competence works generally. I argued in the previous post that it did not because we are not modeling the speaker's competence in how the theorist comes to be in possession of knowledge sufficient to understand the language. What we want by this requirement is to reveal what the rules are that that govern or are expressed in the speaker's competence in the language.

For the second question, the answer is #1, by definition. And then which expressions are semantical primitives depends on the language. Speech acts would not be relevant here because these are not linguistic expressions. We use sentences to perform speech acts, but we can perform speech acts without using sentences as well. For example, if someone asks me if I want to go to the latest Bond movie and I put on an exaggerated expression of boredom, I have answered the question, and so performed a speech act, but not by uttering a sentence. Words are sometimes semantical primtives and sometimes not. 'or' is a semantical primitive. It has no subunits which are semantically significant. On the other hand, 'walked' is not semantically primitive because it is the combination of two expressions to which rules attach independently, 'walk'+ 'ed'. Roughly, it works like this. 'walk' really has the form 'walk(x,t)' where 'x' takes as values things that can walk and 't' takes times as values. Then 'ed' adds a quantifier: '[there is a time t such that t lies in the past of now]'. We put them together to get 'walked' = '[there is a time t such that t lies in the past of now][walk(x,t)]. Inflection for case likewise involves a semantical rule attaching to something smaller than a word.

So, it all depends on the workings of the language in question. Chinese, for example, does not use inflection for tense but always auxiliaries. So it would be like: walks today/walks tomorrow/ walks past/ walks future/ etc.

While sometimes it is not obvious how to formulate axioms for certain words, there is nothing intractable in principle about doing so. It is a matter of making use of all the information we can gather about how we use them with other words to form sentences we use for performing speech acts of various kinds. And this is a matter of finding patterns, and distinguishing between those that express semantical rules and those that express other aspects of usage (some patterns, for example, emerge because we are generally polite--it is not a matter of the meaning of 'like' that people almost always say they like the gifts that people give them, no matter how hideous they may be).

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TMD Handouts

  • Handout #1
    The Role of a Truth Theory in a Meaning Theory
  • Handout #2
    Objections and Challenges to Truth-theoretic Semantics Met
  • Handout #3
    What is Radical Interpretation?
  • Handout #4
    The Impossibility of Radical Interpretation
  • Handout #5
    Metaphysics and Epistemology: radically different conceptual schemes, impossibility of massive error, first person authority, inscrutability of reference.
  • Handout #6
    Are There Any A Priori Arguments for Radical Interpretation?