Verification and Confirmation Verifiability Criterion of Meaning According to the
verifiability criterion of meaning, a statement is
cognitively meaningful only if it is either verifiable by
empirical observation or is an
analytic truth (i.e. true by virtue of its own
meaning or its own
logical form).
Cognitive meaningfulness was defined variably: possessing
truth value; or corresponding to a possible state of affairs; or intelligible or understandable as are scientific statements. Other types of meaning—for instance, emotive, expressive or figurative—were dismissed from further review.
Metaphysics,
theology, as well as much of
ethics and
aesthetics failed this criterion, and so were found cognitively meaningless and only
emotively meaningful (though, notably, Schlick considered ethical and aesthetic statements cognitively meaningful). Ethics and aesthetics were considered subjective preferences, while theology and metaphysics contained "pseudostatements" that were neither true nor false. Thus, logical positivism indirectly asserted
Hume's law, the principle that
factual statements cannot justify
evaluative statements, and that the two are separated by an unbridgeable gap.
A. J. Ayer's
Language, Truth and Logic (1936) presented an extreme version of this principle—the
boo/hooray doctrine—whereby all evaluative judgments are merely emotional reactions.
Revisions to the criterion Logical positivists in the Vienna Circle recognised quickly that the verifiability criterion was too restrictive. In his 1936 and 1937 papers,
Testability and Meaning,
Carnap proposed
confirmation in place of verification, determining that, though universal laws cannot be verified, they can be confirmed. The formulation of what eventually came to be called the "criterion of cognitive significance", stemming from this research, took three decades (Hempel 1950, Carnap 1956, Carnap 1961). In his 1936 book,
Language, Truth and Logic,
A. J. Ayer distinguished
strong and
weak verification. He stipulated that, "A proposition is said to be verifiable, in the strong sense of the term, if, and only if, its truth could be conclusively established by experience", but is verifiable in the weak sense "if it is possible for experience to render it probable". He would add that, "no proposition, other than a
tautology, can possibly be anything more than a probable
hypothesis". Thus, he would conclude that all are open to weak verification.
Analytic-synthetic distinction In
theories of justification,
a priori statements are those that can be known independently of
observation, contrasting with
a posteriori statements, which are dependent on observation. Statements may also be categorised into
analytic and
synthetic: Analytic statements are true by virtue of their own
meaning or their own
logical form, therefore are
tautologies that are true by
necessity but uninformative about the world. Synthetic statements, in comparison, are
contingent propositions that refer to a state of facts concerning the world.
David Hume proposed an unambiguous distinction between analytic and synthetic, categorising knowledge exclusively as either "relations of ideas" (which are
a priori, analytic and
abstract) or "matters of fact and real existence" (
a posteriori, synthetic and
concrete), a classification referred to as
Hume's fork.
Immanuel Kant identified a further category of knowledge:
Synthetic a priori statements, which are informative about the world, but known without observation. This principle is encapsulated in Kant's
transcendental idealism, which attributes the mind a constructive role in
phenomena whereby
intuitive truths—including synthetic
a priori conceptions of
space and
time—function as an interpretative filter for an observer's experience of the world. His thesis would serve to rescue
Newton's law of universal gravitation from Hume's
problem of induction by determining
uniformity of nature to be in the category of
a priori knowledge. The Vienna Circle rejected Kant's conception of synthetic
a priori knowledge given its incompatibility with the
verifiability criterion. Yet, they adopted the Kantian position of defining mathematics and logic—ordinarily considered synthetic truths—as
a priori.
Carnap's solution to this discrepancy would be to reinterpret logical truths as tautologies, redefining logic as analytic, building upon theoretical foundations established in
Wittgenstein's
Tractatus. Mathematics, in turn, would be reduced to logic through the
logicist approach proposed by
Gottlob Frege. In effect, Carnap's reconstruction of analyticity expounded Hume's fork, affirming its analytic-synthetic distinction. This would be critically important in rendering the verification principle compatible with mathematics and logic.
Observation-theory distinction Carnap devoted much of his career to the cornerstone
doctrine of
rational reconstruction, whereby scientific theories can be formalised into
predicate logic and the components of a theory categorised into
observation terms and
theoretical terms. Observation terms are specified by direct observation and thus assumed to have fixed empirical definitions, whereas theoretical terms refer to the
unobservables of a theory, including
abstract conceptions such as
mathematical formulas. The two categories of
primitive terms would be interconnected in meaning via a
deductive interpretative framework, referred to as
correspondence rules. Early in his research, Carnap postulated that correspondence rules could be used to define theoretical terms from observation terms, contending that scientific knowledge could be unified by
reducing theoretical laws to "protocol sentences" grounded in observable facts. He would soon abandon this model of reconstruction, suggesting instead that theoretical terms could be defined implicitly by the
axioms of a theory. Furthermore, that observation terms could, in some cases, garner meaning from theoretical terms via correspondence rules. Here, definition is said to be 'implicit' in that the axioms serve to exclude those interpretations that falsify the theory. Thus, axioms define theoretical terms indirectly by restricting the set of possible interpretations to those that are true interpretations. Rational reconstruction is sometimes referred to as the
received view or
syntactic view of theories in the context of subsequent work by
Carl Hempel,
Ernest Nagel and
Herbert Feigl. Carnap's early anti-metaphysical works employed Russell's
theory of types. Like Russell, Carnap envisioned a universal language that could reconstruct mathematics and thereby encode physics. Yet
Kurt Gödel's
incompleteness theorem showed this to be impossible, except in trivial cases, and
Alfred Tarski's
undefinability theorem finally undermined all hopes of reducing mathematics to logic. Thus, a universal language failed to stem from Carnap's 1934 work
Logische Syntax der Sprache (
Logical Syntax of Language). Still, some logical positivists, including
Carl Hempel, continued support of logicism. ==Philosophy of science==