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This function maps from posi- tions to the code numbers of the symbols occurring at that position. At this level it is not yet possible to make any empirical claims.


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Until correspondence rules have been provided there is no way to determine the truth value of any descriptive claim. Physical Syntax is an extension of Ax- iomatic Syntax in which the only factual claims that can be made concern which symbols appear where. A truth predicate, for a language that makes factual claims about things other than symbols, could therefore not be part of Physical Syntax, and a fortiori could not be part of the less expressive branches of syntax either.

That Carnap sees the science of syntax as exclusively concerned with symbols is the reason he does not think it can include the truth predicate. Creath concludes that Carnap had no good reason for claiming that truth is not a logical notion. Of course truth is not syntactical in this sense, but the question is why should philosophy be restricted to syntax in so narrow a way. Creath , p. Given that Carnap restricts philosophy to the syntax of language, Creath is right to assert this illegitimately excludes concepts that can both be made perfectly clear and turn out to be fruitful.

This captures what Carnap himself came to see under the influence of Tarski. But the examples Creath gives far from prove his point. What one needs to do is to show that an indeterminate sentence can be constructed out of the expression in question and other purely logical vocabulary. We have seen, contra Oberdan, that it was not a fear of infinite hierar- chies of languages which prevented Carnap from giving a definition of a truth predicate.

We saw, contra Coffa, that it was not that a verificationist bias led Carnap to consider only definitions which allow one to identify instances.

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However, as Creath rightly observes, restricting philosophy to syntax in this sense is illegitimately restrictive. If Carnap had realized earlier that a definition of contingent truth was not intractable, that it did not involve providing a theory of meaning for the entire language, then he would have seen that his restriction of philosophy to the syntax of language, in the sense presented above, was too narrow. In fact, after being shown by Tarski that a tractable definition of truth is possible, this is ex- actly what he does.

Carnap agrees with Russell and Wittgenstein that the axiom of infinity is not purely logical, given its strong existential commitments. Carnap believes, however, that he can avoid making such changes. He interprets the variables of level 0 as ranging over coordinates rather than objects. Thus, the existence of no object is implied by either Languages I or II. Carnap writes: In our Languages I and II, the matter is quite different owing to the fact that they are not name-languages but coordinate languages. The expressions of type 0 here designate not objects but positions.

The Axiom of Infinity [. But the doubts previously mentioned [doubts concerning the apparent empirical content of existence state- ments] are not relevant here. For here, those sentences only mean, respectively, that for every position there is an immediately succeeding one, and that at least one position exists. But whether or not there are objects to be found at these positions is not stated.

However, this move cannot work. But if a language asserts the existence of infinitely many members of the domain, then whether or not they are designated in some systematic way has nothing to do with the strength of the existential commitments of this assertion. That Carnap means that variables of level-0 range over spatial positions is clear from the above quote, since it would not make sense for an object to occupy a position if the positions in question were merely positions in an abstract series.

Carnap appeals to his distinction between formal and material modes of speech to respond to this worry. The distinction between the formal and material modes of speech is supposed to solve two problems: the problem of reference and the problem of universal words. The former problem was inherited from the Vienna Circle and their distaste for talk of the relation between language and the world. Carnap, at the time of Syntax, thought that the notion of reference was so vague perhaps even mystical that a sufficient clarification was an unlikely prospect.

So all talk of reference must be eliminated from a scientific philosophy. According to Wittgenstein, what cannot be expressed merely by the use of a variable that ranges over the natural numbers as opposed to employing a predicate that applies to all natural numbers ought not be expressed at all. Notice that the first contains a universal word, and the second involves reference.

He calls such sentences pseudo-object sen- tences because there are equivalent statements that concern only linguistic expressions.

Kant's Antinomies

Questions concerning the relation of lin- guistic expressions and reality e. The first part is that positions are not objects. However, it is certainly not the case that all con- tentful assertions about the physical world are concerned with objects in the ordinary sense of that term.

So the assertion that there are positions might be as problematic as the assertion that there are objects. There are two reasons for this. First, in the formal mode there is simply no such thing as reference. Carnap could have had the variables of level 0 range over abstract objects, things-in-themselves or platonic forms.

So long as the assertions in which they figure are interpreted in the formal mode, there is no question that reference to these entities is being made. Carnap has therefore not addressed Wittgenstein concerns. The above criticism proceeds on the assumption that Carnap meant his coordinates to stand for spatial positions.

On this reading the entities of level-0 stand for an abstract series of positions. So let us now turn to the treatment of abstract objects in Syntax. How- ever, a certain aversion to abstract objects can be detected in Syntax. In discussing this distinc- tion, only empirical sciences are discussed mathematics is not mentioned until later.

However, the same is true of the second statement. The property of being an odd and of course also even numeral is clearly something that could be defined in Pure Syntax. In fact, for any analytic sentence of the object language, a similar trans- lation will be possible. That mathematics is a system of pseudo-propositions is not a conclusion that Carnap would have wished to draw. Thus Carnap did not have a consistent view regarding the status of mathematical statements and mathematical objects. Even if the objects of level-0 are interpreted as abstract objects, there is no satisfactory answer in Syntax to the ontological worries that Carnap considers.

Thus, it must be concluded that Syntax is completely deficient in providing an answer to the problems of ontology that it raises. His elaborate dance around the question of the ontological im- plications of the axiom of infinity can be seen as nothing but a failure.

After his adoption of semantics his views on ontology are unqualifiedly improved. Rather than being founded on vague intuitions, his ontological views are grounded on principles that were always central to his philo- sophical outlook. Carnap believes an explication is successful if it fulfills four conditions. Second, the explicans must be similar to the explicandum that is, in general, but not necessarily universally, the analyzed notion and the unanalyzed notion should apply to the same cases.

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Third, explication should be as simple as possible. Finally, the explication must ultimately prove fruitful.

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Un- less Carnap is willing to abandon one or more of these three ideas the view of ESO is unavoidable. By contrast, Ricketts suggests that Carnap was mistaken to adopt se- mantics. One reason he gives for this is that semantics leads Carnap to require a notion of logical truth beyond provability i. As we have seen, the view of Syntax already requires a notion of analyticity that goes beyond provability. In fact, it is one of the central goals of Syntax to articulate such a notion.

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Second, the main purpose of the passage is to reject psychologism. Finally, Carnap is not saying that properties really are real; he is making informal remarks to motivate the adoption of a language. In order for this to be successful it does not have to be the case that objects really do have properties; it is sufficient that it not be nonsensical to use such a language. Goldfarb gives other arguments for why Carnap was mistaken to have adopted semantics. The first is that analyses should be capable of convey- ing an understanding of the language to a layperson.

Carnap thought that it was an important task to show how the meanings of the vocabulary of theoretical physics depend on the meanings of terms of the observation language.

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Goldfarb believes that by considering only semantic metalan- guages, Carnap is closing off all but trivial explanations of the meaning of the theoretical vocabulary. As is well known, the Ramsey sentence is formed by taking the conjunction of all the axioms of a theory and replacing all distinct theoretical terms by distinct variables of the appro- priate type and then existentially quantifying over these variables.


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Ramsey showed that given a theory T and its Ramsey sentence R, any sentence of the observation language derivable from T is also derivable from R. Carnap ad- vocates adding definitions to the metalanguage that differentiate between two types of truths. A sentence is by definition an analytic truth if it is a consequence of the Carnap sentence, and it is called a synthetic truth if it is not analytic but a consequence of the Ramsey and Carnap sentences.

In short, the Carnap sentence fixes the meaning of theoretical terms and displays the relation between theoretical and observational vocabulary. This axiom allows the introduction of a new constant into the language. Take a metalanguage in which only the observational predicates are primitive. In other words, ti is defined as some definite but arbitrarily chosen entity that is related to other definite but arbitrarily chosen entities in such a manner that the Ramsey sentence is satisfied.

I have outlined the account here not to argue that it is correct but to demonstrate that a nontrivial explanation of the meaning of theoretical terms and their relations to observational vocabulary is possible within the framework of semantic metalanguages. The relationship between theoretical and observational vocabulary can be demonstrated both in metalaguages that contain the theoretical predicates as primitives and in languages that do not contain them as primitive.