18 Mar 2009

Vergauwen, A Metalogical Theory of Reference, 1.4 Must There Still Be Truth? Physicalism in Semantics

by Corry Shores
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Roger Vergauwen

A Metalogical Theory of Reference: Realism and Essentialism in Semantics

Chapter 1.4 Must There Still Be Truth? Physicalism in Semantics

Previously we uncovered the paradoxes that result when
1) we use a more powerful metalanguage to express the meanings of a lesser powerful object language. (recall that "power" is the capacity to express a quantity of meanings. The more power, the more meanings a language can express. So we use metalanguages to express the meanings of more restricted object languages.)
2) we use the 'truth predicate' is true in our metalanguage to define sentences in our object language. Such truth definitions would take the general form:

The sentence X is true (in L) if and only if p.

3) our object language also has the truth predicate is true.

As a result, we found that we may obtain such paradoxical truth definitions as:

"This sentence is false" is true if and only if that sentence is false.

Tarksi's conclusion is that the object language must not be able to express things about the meaning of the metalanguage. So he thought that the object language cannot contain any semantic notions whatsoever.

Recall that we wanted to build up larger sentences compositionally from smaller ones, but that we could not then arrive at quantified sentences. Tarski's solution involved the notion ofsatisfaction. So when we have a sentence that cannot be given a truth value, because it has a free variable, we can really only say that an object satisfies it. We cannot really say that some object makes it true. So his formulation was:

an object a satisfies the sentential function "X" if and only if p.

Here, p results when we replace the variable(s) in X with object(s) a. Thus for example,
an object a satisfies the sentential function 'x is green' if and only if a is green.

But this satisfaction formulation does not guarantee that that we will omit every semantic notion. What we want to say instead is that a predicate applies to objects, not so much that they semantically satisfy its meaning. So we will reformulate it as

An adequate definition of 'satisfaction-in-L' must contain (in the metalanguage) all the instances of the following scheme:

"P(x1 . . . Xn) is satisfied by the series (objects) a1 . . . an if and only if P(a1 . . . an), in which P is a (complex) predicate."

So the predicate "is green" applies to grass. But applicability is only possible if the word "grass"refers to a green thing. So applies is also a semantic term.

Vergauwen points-out this is no solid objection. For, if we strictly delineate the difference between the object language and the metalanguage, we will not obtain any contradiction. We later will discuss a model-theoretic semantics based on Tarski's truth definitions. And there we will also find that there are problems only in restricted cases.

What Vergauwen wonders instead is why would the objecters want a semantic theory that does not contain any semantic notions? Tarski's explanation is that if we did have semantic notions, then we could not also maintain science's physicalism, which is the idea that everything in science can be reduced to physics. In physicalism, primitive reference becomes a physical fact: "physicalism in semantics implies that for each acceptable predicate (primitive or complex) there is an equivalency with a predicate which contains terms from physics alone."
Physicalism is opposed to semanticalism, which says that there are "irreducibly semantic facts." According to the semanticalist theory, semantic phenomena, such as "Schnee" refers to snow, are primitive facts.

And we find that Tarski may not have even succeeded at providing a reference theory forphysicalism. We find this for example in Tarski's theory of names. We know that "Belgium" names a country. So the country Belgium satisfies the name "Belgium." Hence we have the name "Belgium," and we have many countries that are candidates. But in this case there is one country that satisfies the requirements for that name. However, there are many possibilities. There is Germany, for example too. So it is not really a physical fact that the name "Belgium" refers to Belgium. Physics cannot explain this reference relation between the two.

The person who offers this critique is Field. He wants still a physicalistic reference theory. He proposes that we use the empirical sciences to see how physical causes lead to our brains referring to certain objects by certain names.

Vergauwen objects. Field's proposal would do away with the notion of truth. He would rather we say something like "'Belgium' refers to Belgium if and only if "Belgium" relates to Belgium according to a psychological cause that lead-to us joining the two referentially." So we might make the following formulation for reference:

x refers to y if and only if x stands in the relation R to y.

We see that we may define R in scientific terms that can be verified by scientific experimentation, all without recourse to semantic concepts. However, Vergauwen notes, science still needs to know what the sentence "relates according to a psychological cause" means. Otherwise they could not conduct their experiment. Yet this would require using a Tarskiantheory of truth. But then we would need to define truth and reference using these very same notions, which will produce a circularity.

So we see that there is a general problem of using a truth theory to fashion a semantic theory of reference to real external objects. The notion of "satisfaction" does not clarify for us the relation between reality and language. It seems at first, then, that we cannot explain the concept of truth using a truth-semantics, and also that physicalist reductions of the concept of truth just push the problem to a higher level.

Vergauwen agrees with Field's suggestion that we cannot glue language to reality from the outside. If we do not have the notions of truth and primitive reference, we lose the organizationalprinciples of our internal conceptual schemes. If we cannot glue reality to language beginning from the outside, Vergauwen wonders if we may do so from the inside by means of a theory of truth or meaning. We might then construct a realistic semantics. Vergauwen turns now to this possibility.

Vergauwen, Roger. A Metalogical Theory of Reference: Realism and Essentialism in Semantics. London: University Press of America, 1993.

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