Sunday, December 13, 2009
Conditional Propositions
Two main premises of Analytical Logic are, first, that every well-formed Proposition is either True or False, and not both; and, second that the Truth-Value , i. e. True or False, of a compound Proposition is a function of the Truth-Values of its constituent Propositions. One continued irritant to Analytical Logicians is the problem of the Valuation of Conditional Propositions, i. e. 'If A, then B'. For, for example, 'If John resides in Boston, then John resides in Massachusetts' is True according to Analytical Logic, and to the layman seems to involve cogent reasoning. But that Truth does not depend on the Truth-Value of its constituent Propositions, i. e. the reasoning still seems cogent even if John is in fact a resident of Worcester MA, in which case 'John resides in Boston' is False, and 'John resides in Massachusetts' is True; or even if John actually resides in Hartford CT, making both the antecedent and the consequent False. The effort to resolve this problem has become a cottage industry in Analytic Philosophy, and the general aversion to jettisoning those two main premises of the Logic excludes the suggestion that in Conditional Propositions, the constituents are neither True nor False. For, as Husserl might put it, the 'If' suspends the Actuality of the Proposition, meaning that it suspends any question of correspondance between the suspended Propositions and the actual world. Now, within the suspension, 'True' could denote a coherence between the Propositions, e. g. Boston is in Massachusetts, but the coherence notion of 'Truth' is at odds with the correspondance notion of 'Truth' that determines whether e. g. 'John resides in Boston' is True. But, even if Analytical Logic were to rely on a hybrid notion of Truth, internal coherence does not restore Truth-Value to each of the suspended constituent Propositions. Evolvemental Logic regards the problem as irresolvable, because it regards Conditional Propositions as fundamentally practical, in which case they do not refer to Actuality, and, so, not merely do they have no Truth-Value, in the correspondance sense of the term, but the very question of Truth, in this sense, is inapplicable them. Analytic Logic's appropriation of Conditionality suppresses, but does eliminate, this inapplicability.
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