Page 306 - Encyclopedia of Philosophy of Language

Language and Logic
charged would (at least in part) explain the car's not starting.
By extension from the physical—or causal—cases, it is possible to define various other kinds of necessary and sufficient condition—including nomic and con- ceptual ones. For example, it appears to be a necess- ary, but not sufficient, condition of speaking a sentencethatthesubjectutterwords.Inthisexample, there is a claimed conceptual connection between speaking and uttering. Likewise, in the conceptual analysis of memory, that it is of the past seems to be a necessary condition for something's being a memory.
That a ball is red is a logically necessary condition of its being red and made of vinyl (and the latter is a logically sufficient condition of its being red). This is so because of the deductive relation between:
The ball is red and made of vinyl (2) and:
Perhaps in this case, the truth-functional account of necessary and sufficient conditions comes as close to being acceptable as it is ever likely to. Even so, counter- intuitive consequences obtrude. For instance, any logically true sentence would now be a necessary con- dition of every sentence (for example, anything of the form 'p v ~ p' is a logical truth, and so the conditional 'q-»•(Pv~p)'isthereforetruenomatterwhatsen- tence 'q' represents). Classical logicians may be pre- pared to accept this kind of result as a corollary of the so-called 'paradoxes of material implication.'
See also: Deviant Logics; Entailment; Relevant Logic.
Bibliography
Anderson A R, Belnap N 1975 Entailment the Logic of Relevance and Necessity. Princeton UniversityPress, Prin- ceton, NJ
Wilson I R 1979 Explanatory and inferential conditionals. Philosophical Studies 35:269-78
The ball is red.
(3)
Philosophers have long supposed that certain prop- ositions are not merely true but necessarily true: they could not possibly be false. The search for such prop- ositions and attempts to explain the source of their necessity have occupied a central place in the history of philosophy. Many of the great problems of phil- osophy may be formulated in terms of the modal concepts of necessity, contingency, and possibility. Aristotle's problem of the open future is the problem whether, if it is true that something is going to happen, them it must happen. Hume's problem of causation is the problem of whether an event E can have an effect which in some sense must occur, given the occurrence of E. Kant's problem of free will is the problem of whether in a world governed by laws of nature there is any sense in which agents can act otherwise than they do. Examples may be multiplied. In con- temporary philosophy, the analysis of modal concepts themselves has also flourished, hand in hand with a revived interest in such central issues in modal meta- physics (Kripke 1980; Lewis 1986a; Van Inwagen 1983). Both the analytical and the metaphysical aspects of the debate are discussed.
1. Varieties of Necessity
As the problems of Aristotle, Hume, and Kant make plain, there is more than one notion of necessity. Some
notions are epistemic, such as the notion of what is implied by what we know, but the concern here is not with epistemic concepts. The most important non- epistemic notions are these, from least to most con- strained: (a) (narrow) logical necessity; (b) mathematical necessity; (c) metaphysical necessity (sometimes called 'broadly logical necessity'); and (d) physical necessity. Logical necessity belongs to the validities of logic, mathematical necessity belongs to the truths of mathematics, metaphysical necessity to the truths of metaphysics, and physical necessity to laws of nature.
Three questions may be raised about each type of necessity: (i) how does that type of necessity relate to the others, and in particular, is it 'reducible' to any of the others?, (ii) what are specific examples of prop- ositions which are necessities of that type?, and (tii) wherein lies the source of the type of necessity in question? For example, with regard to (i), the logicist movement in philosophy of mathematics was con- cerned to show that mathematical truth reduces to logical truth, a thesis which has as a corollary that mathematical necessity reduces to logical necessity. With regard to (ii), there has been considerable recent discussion of certain putative metaphysical necessities (Kripke 1980; Putnam 1975). And with regard to (iii), the problem of the source of necessity has prompted
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Necessity G.Forbes