Classical harmony.
Alan Weir · Notre Dame Journal of Formal Logic · 1986
A standard metaphor used in explaining the notion of a valid argument is that the conclusion of such an argument is contained in the premises.Now if the conclusion is contained in any very direct sense then the argument will lack epistemic value; it will not be of use in persuading someone to accept the conclusion who does not already do so but does accept the premises (cf.[2], pp.3OOff).The classical logician has a fairly straightforward reply to this dilemma: the conclusion is only contained in the premises in the sense that it is true in any situation in which all of the premises are true.Since this fact may not be at all evident, deductive argument, in establishing it, is epistemically useful.For such a logician, then, validity is a semantical notion characterizable independently of the epistemic notions, such as that of proof, which are used as tests for it.Now this classical conception has come under a great deal of attack, especially from those who subscribe to the Wittgensteinian slogan that meaning is use and interpret it as requiring that all ingredients of meaning can be made manifest in our use of sentences, especially in teaching or communicating their senses, for it is often claimed that classical bivalent semantics, in ascribing truth values to sentences regardless of whether these values are discoverable, violates this requirement.Alternative conceptions of truth are then advanced which, by tying it closely to proof, justification, or a similar epistemic concept, enable one to explicate validity in a way more in keeping with the above interpretation of the Wittgensteinian slogan.The most radical proposal is to eschew entirely an appeal to the concept of truth in explications of validity and rely purely on proof-theoretic notions.It is clear that if one is to do so, one must discriminate among purported proofs; otherwise any and every proof-system, including trivial ones in which every formula is a theorem (such as Prior's infamous system for his connective "tonk" [7]), will be equally acceptable as explications of the concept of validity.