# VERIFICATION

The term "verification" concerns statements or theories. Since a theory can be formulated as a conjunction of hypotheses, and therefore as a single statement, the considerations pertaining to statements are also valid for theories. This article considers only the case of statements. In a strict sense, to verify a statement is to recognize its truth. But in the current theory of verification, the term is used in a broader sense: to verify a statement is to test its truth-value. A statement is said to be verifiable if a method can be given for its verification, at least in principle. The theory of verification concerns statements only in their cognitive meaning. And it has been developed only for purely logical and empirical statements (i.e., statements belonging to the empirical sciences). In the case of metaphysical statements, the conditions of their truth coincide with the validity of the methods that are used to establish them (e.g., metaphysical inference or reflexive analysis).

Logical statements. Purely logical statements are statements whose truth-value depends not on the content but only on the form, and more exactly on the meaning of the logical constants they contain. In the frame of a formalized language (for which the notion of consequence is defined), a statement is formally (or logically) true, or analytic, if it is a consequence of every class of statements; it is formally (or logically) false if every statement is a consequence of it. A tautology is a formally true statement containing only propositional connectives. The problem of verification for purely logical statements is the logical problem of decision. It can be solved for tautologies, but it cannot be solved, in the general case, for statements containing quantifiers (see logic, symbolic).

Empirical statements and confirmation. The verification of an empirical statement can be direct or indirect. Direct verification is a confrontation between a statement and empirical observation. A statement P is indirectly verified as follows: from this statement, in conjunction with other statements that are already verified or analytic, a consequence C is deduced that can be directly verified. The falsification of a statement amounts to the verification of its negation. If C is verified, it cannot be concluded that P is true. If C is falsified, according to the case, either P or some other nonanalytic premise in the deduction is to be rejected. An empirical statement can thus never be considered as true or false in a definitive manner; it must always be treated as a hypothesis. (Even a directly verifiable statement can be treated in this manner to the extent that it admits of indirect verification.) It is therefore preferable to speak of confirmation rather than verification.

The confirmation of a statement is a test procedure accompanied by the specification of the conditions under which, according to the result obtained, this statement is considered as scientifically accepted or rejected. Confirmation may be direct or indirect. An empirical statement can never be considered as accepted or rejected in a definitive manner; it has only a certain degree of confirmation. Different criteria have been proposed to characterize this concept: probability, falsification of rival hypothesis, simplicity, and syntactical or metrical expression. The theory of confirmation is still in the process of development.

Verification and meaning. The concept of verification has been used by modern empiricism as a criterion of meaning: a statement is meaningful if and only if it is directly or indirectly verifiable. According to this criterion, metaphysical statements are meaningless. The verifiability criterion of meaningfulness has been criticized by many empiricists, and alternative criteria have been proposedfor example, translatability into an empiricist language or inclusion in a system that is partially interpretable in observational terms. C. G. Hempel has pointed out that the notion of cognitive significance can perhaps be attributed only to systems considered as wholes and that "cognitive significance in a system is a matter of degree."

The search for an empiricist criterion of meaning is linked with the empiricist principle according to which a statement has cognitive meaning only if it is logically true or false, or capable, at least potentially, of being tested by experiential evidence. And this principle in turn is based on the epistemological assumption that the only sources of knowledge are sense intuition and analysis. An abstractionist theory of concepts seems to be more apt to give account of the procedures of science; it is in any case indispensable, together with a theory of analogy, to found the possibility of metaphysics.

Bibliography: a. pap, An Introduction to the Philosophy of Science (Glencoe, Ill. 1962). c. g. hempel, "The Concept of Cognitive Significance: A Reconsideration," Proceedings of the American Academy of Arts and Sciences 80 (1951) 6177.

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