For all their analogies with Wittgensteinian doctrine, Carnap’s views go far beyond Wittgenstein’s in one essential respect: Even though logic and the whole range of what cannot be said were, for Wittgenstein, incapable of truth or falsehood, there was nonetheless a sense in which that odd type of information was responsible to an independent reality, however otherworldy it might be. Carnap’s’ principle of tolerance completely obliterated this dimension of Wittgenstein’s thought, and to the extent that it succeeded, it displays an understanding of linguistic frameworks as entirely constitutive of meanings rather than as obliquely reflecting an independently given “essence of the world”. (Coffa, 1991, p. 326)
To understand Carnap’s formulation of linguistic frameworks it is required to take full cognisance of his resistance to any ontological views about facts which might ground these linguistic frameworks. ‘Facts which ground…’ are the sorts of facts which extend to the truth conditions for a claim about, in this case, the existence or non-existence of linguistic frameworks. ‘Facts which ground...(X)’, in this sense, form part of a justification for a claim about (X). Carnap insists that a semantic theory which incorporates the notion of linguistic frameworks should not depend on presuppositions about the existence or non- existence of objective facts to support linguistic frameworks.
Carnap assumes that linguistic communication happens in two ways: firstly, we communicate effectively by using symbols of a given language according to the rules we have for using them and then, secondly, we do the aforementioned as well as denote something in the world when doing so. Linguistic
communication does not always entail the second step, but always entails the first. So, rules for use are always part of effective communication. But because the way in which we speak is often so ingrained in
23 Of course, what has been written by both Carnap and Quine and their many followers and students about truth by convention is not a little. It is also of deep interest to me. This section, however, gives a brief overview for the purpose of being further explained in sections later in thesis where I give more detailed descriptions and also engage philosophically (argumentatively) with this polemic.
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our behaviour it is sometimes hard for us to tell when we are saying things about the world, i.e.
denoting, and when we are simply correctly using the rules we have created for speaking about it (Stafford, 2005). But, one might wonder, how can these two events come apart when the chief purpose of linguistic communication is surely to say things about the world?
For Carnap, there is a difference because when we adopt rules for how we should use terms it does not necessarily mean that there is an object in the world which is associated with the term or to which it makes reference. For example the term ‘10’; there is a rule for how we use it, in fact there are many, but following such rules does not secure a referent for ‘10’. Similarly, there is not necessarily an object in the world which is associated with the word ‘quark’ or ‘electron’. Similarly, there might be no such object or state of affairs to which ‘X is entailed by Y’ refers to, because it is not possible to locate a relationship of entailment among parts of the empirical world. Hume taught us this. Yet, there are rules which stipulate how we use these terms correctly.
To be clear, there are rules for the use of all words, for those which we know the comparatively unproblematic referents of, such as ‘chair’, and for those which we do not. So, the distinction is not between referring and non-referring words. The distinction is between the rules for use (of all words and symbols, such as the symbols of logic and mathematics) and the linguistic ‘event’ of referencing, which only sometimes occurs.
For Carnap, the distinction between language which we know references the world and language which constitutes the rules for how we use certain ‘symbols’, whether these symbols happen to refer or not, is at the foundation of an account of analytic truth (Stafford, 2005). He argues that there are two types of languages which ‘service’ these distinct linguistic needs. Both such languages are part of any linguistic framework (Stafford, 2005). For instance, the linguistic framework of physics will consist of sentences which express rules of use, thus enabling communication among physicists, and sentences which
express rules for use as well as facts about the world (i.e. they refer). Carnap, like Frege, realises that not all language is effective (in communication) because it is fact tracking or truth stating. Some language works very well despite it doing neither of the above. This means that a good semantic theory should be able to give an explanation of this, without assuming that the only outcome of linguistic activity is stating true or false claims about the world, even if it might be the case that this is the goal of speakers.
Since we know that natural language emerged as a means of enabling humans to effectively communicate with each other, and not as a means of “finding truth” or any other such modern abstraction, it is
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reassuring to find a theory that places its emphasis on linguistic convenience rather than on a search for deep metaphysical insights. (Stafford, 2005)
How does Carnap divide languages into those which are fact stating and those which simply state the rules we have for correctly using the terms of any given linguistic framework? This division happens within the linguistic framework and is also formulated by the linguistic framework.
A linguistic framework is not a natural language like English or Zulu. It is a ‘language’ like that of physics, organic chemistry, propositional logic or Christianity. A linguistic framework consists of a metalanguage as well as an object language (Ebbs, 2011, pp. 197, 199), or “thing language” (Stafford, 2005). The metalanguage part of a linguistic framework contains all the rules for how to use the lexicon of that language; variables and constants, if there are both. Such rules must always be explicitly formulated definitions (Ebbs, 2011, p. 198). The metalanguage of, for instance, an axiomatised system within physics contains the definitions24 for all the terms of that axiomatised system. Definitions which all belong to one framework bear on each other. The more definitions that are added to the metalanguage of a particular linguistic framework, the more constrained physicists are in how they use such definitions and infer meaning from them (Bohnert, 1963, p. 420).
It is a well-known fact of axiomatics that as one adds postulates or other strictures to a system, the range of possible interpretations or realizations is, in general, progressively cut down, and this would be essentially the force at work here. The system of metalanguages, the tightly interwoven net of definitions of both empirical and logical terms makes misinterpretation increasingly unlikely the more the learner follows out its implications and interrelations. (Bohnert, 1963, p. 420)
The object language of a linguistic framework contains two distinct sets of sentences: one which is the set of sentences which state facts about the real world and the other which state the conclusions from logical or deductive processes. The first set of sentences in the object language employs terms which are defined within the metalanguage, but which make reference to parts of reality. Or at least it is treated as if it does but sometimes, in fact, doesn’t (Bohnert, 1963, p. 410). Such sentences which are part of the object language are therefore fact bearing and truth-apt (if truth is correspondence to the world) and are always justified or known, if known at all, a posteriori or empirically (Bohnert, 1963, p. 409).
24 The distinction between explicit and implicit definitions is discussed in Part 2, section 2 and Part 3.
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But an object language can also contain sentences which are derived, inferred or deduced from definitions which are part of the metalanguage. Consequently, one says that deductively inferred sentences in an object language are logically derived.
Carnap proposes that we replace the vague sentence ‘the truth of logical statements is based
solely on their logical structure and on the meaning of their terms’ with a syntactical definition of logical truth (analyticity) for sentences of an object language-system LS, stated in a metalanguage MLS: a sentence s of a (non-contradictory) language LS is logically true (analytic) if and only if s is a special sort of syntactical consequence in LS of the empty set of sentences of LS. (Ebbs, 2011, p. 199)
If sentences are logically derived they are not justified a posteriori. All definitional sentences in an object language derived in this way are logically true and because of this they are justified a priori. All factual sentences in an object language are justified empirically, or a posteriori. For Carnap there is no
particular worry that the supposed conventions which comprise a metalanguage, and which then further serve to give rise to analytic sentences in object languages, also are in need of definitions themselves.
This would then require another metalanguage. And so on (Ebbs, 2011, p. 210). For some, such as for Quine (to be discussed shortly), the regress which is implied by making something like a metalanguage responsible for meaning, as opposed to meaning being accounted for by referencing to the world, is a further reason to reject the possibility of knowledge which is not empirical. Carnap does not share Quine’s concern. For Carnap, whether or not there is a distinction between a priori and a posteriori knowledge was not the point and furthermore it was a confused (metaphysical) question. The point of postulating the distinction is simply that it seems like a good way for scientifically minded philosophers to organise their thoughts about knowledge. The aim, of course, was to avoid ‘letting through’ factual claims which are not justified empirically.
[Carnap’s] goal was not to solve the traditional problem of how it is possible for us to have a priori knowledge, but to reject that problem, which he regarded as confused, and focus instead on specifying linguistic frameworks within which it is clear which sentences are to count as ‘L-true’ and which ones are to be evaluated only on the basis of empirical observations. (Ebbs, 2011, p. 212)
The set of sentences which is the object language of a linguistic framework and are fact stating are synthetic sentences, or are synthetically true, if true. The set of sentences which is the part of the object language, but are logical deductions or inferences are analytic sentences, or analytically true. On the other hand, all sentences which are part of a metalanguage are analytic. This means that analytic
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sentences are found in object languages, but no synthetic sentences form part of a metalanguage. In metalanguages all sentences express constructed or created rules or conventions for the use of specified lexicon. All analytic sentences, whether part of the metalanguage or object language are logical truths.
This is because they are either conventions which have been invented (i.e. in the metalanguage) using other conventions/definitions about the meanings of terms, or they are the results of logical inference or deduction (i.e. in the object language). In the former case they are tautological constructs and in the second they are logical conclusions (Ebbs, 2011, p. 199). Either way they are logical truths. Analytic sentences are not factual and synthetic ones are.
But, even though the distinction between fact bearing and non-fact bearing sentences occurs in the object language, the rules for saying where and when the distinction is drawn are formulated within the metalanguage. This is why they are metalinguistic. Such rules might be the “evidential rules” for either analytic or synthetic truths, respectively called L-rules (logical rules) or P-rules (physical rules) (Friedman, 1988, pp. 87, 89). These rules are not part of the object language itself. This means that such rules are also invented conventions, according to Carnap, and say things about the object language, such as where and how to draw the distinction between analytic and synthetic sentences.
Carnap equates the logical truths of a linguistic system with the analytic ones, and he stresses that ‘The analytic–synthetic distinction can be drawn always and only with respect to a language-system, i.e., a language organized according to explicitly formulated rules, not with respect to a historically given natural language’ (Carnap 1952a, p. 432). (Ebbs, 2011, p. 197)
Frege speaks similarly about the distinction between sentences “in the system” and sentences “about the system”.
This step was taken in principle by Frege in his inclusion of precise formation rules specifying the
admissible sentence structures in the system of Grundgesetze, and drawing his sharp distinction between sentences in the system (object language) and sentences about the system (in the metalanguage).
(Bohnert, 1963, p. 409)
It seems to me impossible to not take seriously the analytic-synthetic distinction in an account of Carnap’s linguistic frameworks. This is because it is a function of the non-factual sentences of the metalanguage of a linguistic framework which says what the criteria are for distinguishing logical truths from factual truths in the object language. We’ll now see why it is also the case that analytic truth is
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explicated in terms of linguistic frameworks. And if this appears worryingly circular already, this is explained shortly.