The “logical” dimension of positivism

The “logical” dimension of positivism

The main novelty of the Vienna Circle consists in its use of the logic developed by Frege and Russell for the study of scientific problems. The conception of philosophy is thus radically modified, to focus on epistemology and the philosophy of science: all the rest would be only false problems for which no scientific solution can be expected. Philosophy should be the “logic of science”, i.e. examine scientific theories, and draw out their logical relationships. It must show how the language of observation constituted by the “protocol propositions”, or “observational statements”, provides the premises on which one can deduce the scientific propositions, or theoretical ones, properly so called.

The verificationist theory of meaning

Science, for its part, would be threatened by metaphysics, a simple myth comparable to poetry. Carnap will say of the metaphysician that he is “a musician without musical talent”. According to positivism, most metaphysical statements are neither true nor false: they are only “nonsense” (Unsinnig), insofar as they are neither analytical statements nor empirical synthetic statements and therefore verifiable by recourse to experience, and that finally the existence, affirmed by Kant, of a priori synthetic judgments is denied. With the shift from positivism to logical positivism, the critique of metaphysics shifted from a critique of its methods and theses to a critique of its meaning itself.

Logic will therefore be used here to distinguish meaning from nonsense: the verificationist theory of meaning is used as a criterion. The meaning of a proposition is reduced to its cognitive meaning, in other words to its truth value: a proposition which is neither true nor false is, according to the Vienna Circle, devoid of meaning. It is in this sense that positivism affirms that poetic or metaphysical statements are statements about language, and not about the world: they have no truth value, which depends on a correspondence with empirical facts.

According to verificationist theory, the logical meaning of a statement indeed depends on the possibility of its empirical verification: “the meaning of a statement is the method of its verification” (Carnap). According to positivism, statements are divided into analytical statements (the propositions of logic and mathematics, reducible to tautologies) and synthetic statements, which constitute the empirical sciences. Analytic statements tell nothing about the world, and are true in the meaning of the terms that compose them (thus, “all single people are unmarried”). They are sinnlos and not unsinnig propositions: not “absurd”, but “meaningless”. The logical reductionism of Frege and Russell would then show, by reducing the statements of mathematics to mathematical logic, that the latter are made up of tautologies. By rallying to Wittgenstein, Russell thus abandons his position of 1903 (in Principles of Mathematics), where he considered that Kant had been right, in the Critique of Pure Reason, to qualify mathematics as “synthetic”, but that he should also have accorded this status to logical statements.

For a synthetic statement to have meaning, it must therefore relate to an observable empirical fact. If it is not verifiable by experiment, then it is either pseudo-science or metaphysics. Thus a proposition that “there is a God” is neither true nor false, but simply meaningless, being unverifiable. Logical empiricism thus divides the statements of scientific theories into “logical expressions” and “descriptive expressions”: logical expressions bring together logical connectors and quantifiers, and are shared by all sciences, while descriptive expressions are specific to each science (e.g. the concept of “force”, “electron” or “molecule”). The descriptive terms themselves are divided into “observational language” and “theoretical language”: observational language refers to publicly observable entities (i.e. observable to naked sight, e.g. a “chair”), while that theoretical language includes terms for unobservable (or more difficult to observe, such as a “proton”) entities.

From this distinction between observational descriptive statements and theoretical descriptive statements, verificationist theory of meaning comes to posit that “a statement has cognitive meaning (i.e., makes a true or false assertion) if and only if it is not analytical or contradictory and if it is logically deducible from a finite class of observable statements.”

Translate theoretical vocabulary into observational vocabulary

Consistent with the distinction among descriptive statements between observational and theoretical statements, positivists attempt to “translate the theoretical vocabulary into the observational vocabulary”, since only the latter can provide empirical support for knowledge. In The Logic of Modern Physics (1927), Percy Williams Bridgman, future Nobel Prize in physics and supporter of operationism, asserted that it was possible to achieve such a full translation. Likewise, Ernst Mach, before him, and Rudolf Carnap, in Der Logische Aufbau der Welt (1928), thought that such a reduction to observational vocabulary was possible.

But in 1936-1937, Carnap shows the failure of this program, in an article entitled Testability and Meaning. Take the statement “A body is soluble if and only if when immersed in water it dissolves”, which translates into observational terms the theoretical concept of “solubility”. The antecedent (a body is soluble) is true even when the antecedent of the second proposition is false: in other words, every body is soluble until it is immersed in water. Carnap then proposes to use statements of “reduction”, for example “If a body is placed in water (at time t), then this body is soluble if and only if it dissolves (at instant t). Carnap therefore reverses the logical connectives: the biconditional (if and only if) takes the place of the conditional. But this reduction statement is weaker than the definition in observational terms: it only partially specifies the meaning of “soluble”.

Positivists will then distinguish, among mature, axiomatizable scientific theories, between the theoretical vocabulary, made up of axioms or postulates, and theorems derived from these, and observational predictions, formulated using terms from the vocabulary observational, these being attached to it by a system of “correspondence rules” (Carnap and Nagel; Reichenbach speak of “coordinating definitions”; FP Ramsey and Campbell of “dictionary”, and Hempel of “interpretive system”) .

The emotivism of Alfred Ayer

Alfred Ayer thus criticized, for this reason, the idealism of the British philosopher F.H. Bradley, in his book Language, Truth, and Logic (1936), which popularized the theses of logical positivism in the Anglo-Saxon world. The verificationist criterion was also intended to be used in the sciences, to hunt down the metaphysical statements that were still present there. Ayer also defended a meta-ethical conception qualified as emotivist in this work, which is opposed to all moral cognitivism: since moral values ​​cannot be the subject of logical propositions, it is not possible, according to him, to argue rationally in matters of morality.

The instrumental design of scientific theories

Moreover, the Vienna Circle shares an instrumental conception of scientific theories: these must make it possible to make observable predictions, and not to explain reality, that is to say to give representations (true or false) of reality.

Logic status

On the other hand, the status of logic is not unanimous in the Vienna Circle, and has been subject to changing views. Schlick defends a conception, close to Wittgenstein, which makes logic an activity and not a theory. Since logic cannot say anything sensible, it only has the role of giving clarifications on scientific propositions. Therefore, the verificationist theory of truth, which is supposed to distinguish meaning from nonsense, would itself be nonsense.

Carnap defends an opposite view of logic. Admittedly, logic does not speak of the objects of the world, but it is indeed a theory, it establishes the syntax of scientific propositions. It is possible to talk about discourse without getting lost in metaphysics. But if in 1934, Carnap affirms, in the Logical Syntax of Language, that it is possible to distinguish in a language the sentences endowed with meaning from the absurd sentences (Unsinnig) with the help of a simple “purely syntactic formal analysis”, he recognizes in Introduction to Semantics (1942), written after the work of Tarski, “the necessity of resorting to semantic concepts (such as those of reference and truth) to determine the cognitive status of the utterances of a language”.

In 1934, the syntactic, logical analysis of Carnap enabled him to reformulate in the “formal idiom” the sentences of the “material idiom”, which enabled him to show, according to him, that certain metaphysical statements are not absurd, but “give the illusion of conveying information about the world”. He then joins Wittgenstein’s thesis in the Tractatus logico-philosophicus, which radically distinguishes science from philosophy: philosophical statements, when they are not absurd, do not relate to the world, but to language: they express a preference for a linguistic framework.

Critique of logical empiricism

In The Logic of Scientific Discovery, Karl Popper criticized the use of the verificationist criterion as a criterion of scientific demarcation, distinguishing between what is science and what is not. For him, a theory (and not a statement) is scientific only if it is refutable.

Quine, in the Two Dogmas of Empiricism, attacks more radically the theses of logical empiricism. He attacks the idea that one can make a clear distinction between synthetic statements, bearing on “facts”, and analytical statements, true in an a priori and necessary way, by virtue of the only rules of logic. For him, the notion of analytical statement is poorly defined.

The second “dogma of empiricism” according to Quine, that of the reductionism of all statements to statements about sensations (the “protocol” or “observational statements”) is not tenable. Quine defends a holistic approach: the experiment cannot invalidate a particular statement, but brings into play the whole of the theory, the experimenter having the free choice to modify the statements he wants (whether they are “observational” or “theoretical”) in order to fit his theory to experience. Therefore, he suggests that logic can also to a certain extent, and in the last instance, be revised, like any statement of fact. Unlike Carnap, who believed in the existence of a priori true analytic statements, Quine thinks that no true statement, even a priori, is irrefutable. He puts forward that even Euclidean geometry has been replaced by a non-Euclidean geometry, and that nothing prevents, a priori, to affirm that classical logic could not be replaced by another logic.

Another criticism, focusing on the dichotomy established by Carnap between “observational statements” and “theoretical statements”, as well as on Carnap’s hope to construct a formal, precise language, without going through imprecise, “pre-scientists”, was elaborated by Hilary Putnam, in an article titled “What theories are not”. This is based on two main points:

• “observational statements” refer not only to publicly observable things, but also to unobservable entities; conversely, there are theoretical terms which designate observable things;
• the interpretation of an experiment does not concern only “observational statements”, but also “theoretical statements”: justification, in science, is carried out in all possible directions; observational statements are justified by theoretical statements and vice versa.

Includes texts translated and adapted from Wikipedia