Page 274 - Encyclopedia of Philosophy of Language

Language and Logic
Aristotle's method is cast in the form of a natural deduction system. Corcoran convincinglyshows that Aristotle's proofs can be read as objects generated by an underlying logical calculus which does not pre- suppose propositional logic.
An insightful logical assessment of Aristotle's achievements and program is embodied in Lear (1980), while Westerstahl (1990) offers an analysis of Aristotle's theories from the point of view of the gen- eralized quantifier analysis of natural language quantification.
See also: Aristotle and the Stoics.
In making plans, in evaluating actions, in justifying beliefs as well as in theorizing,hypotheticalsituations or deliberate counterfactual possibilities are fre- quently considered. Conditionals directly reflect this ability to reason about alternative situations. They consist of two constituents, the first of which is called the 'protasis' or 'antecedent' and the second the 'apod- osis' or 'consequent.' The antecedent expresseswhat is hypothetically (counterfactually, possibly,...) so, while the consequent states what, given this condition, will be (would have been, might be,...) the case. See examples (1-2):
1. Conditional Markers
If Shakespeare didn't write Hamlet, someone else did.
(D
Every language has some way of forming conditional sentences. Descriptive studies of the range of forms used by native speakers to express conditionals show that these forms can be substantially different from the if-then construction, which is prototypical for English. There are even languages in which there is no clear prototypical construction at all. In Chinese, for example, most conditional sentences have the form of a conjunction, and their conditionality has to be read off from the context. In Latin, by contrast, the si unambiguously marks conditionality. In Classical Arabic there are two prototypes: in for expressing indicative conditionals, and law for counterfactual conditionals. A still more elaborate system can be found in Classical Greek in which even the degree of hypotheticality is sharply characterized. Although in English the if-then is the clear-cut mark of con- ditionality, neither the if, nor the then is necessary; Tell him a joke, and he will laugh expresses the same conditional as does If you tell him ajoke, he will laugh. And in the sentence No cure,nopay mere juxtaposition suffices to enforce a conditional reading.
On the other hand, the occurrence of syntactic mar- kers of conditionality is not a sufficient reason for conditionality either. A sentence like I paid you back, if you remember is generally considered not to be a real conditional sentence; for here the speaker is com- mitted to asserting the consequent outright—not if something else is so.
The question as to the various means by which native speakers express conditionals is of considerable interest not only to the descriptive, but also to the historical studies of conditionals. In the latter tra-
If Shakespeare hadn't written Hamlet, (2) someone else would have.
This pair of examples illustrates the contrast between indicative conditionals and counterfactuals. The first conditional (1) is obviously true. Given that the play Hamlet does in fact exist, and given the way plays come into existence, somebody must have written it. If not Shakespeare—and the use of the indicative sug- gests that we have to reckon with this possibility—it must have been somebody else. The use of the plu- perfect in (2), however, strongly suggests that Shake- speare did in fact write Hamlet. And it is very difficult to give up this idea, as the antecedent of this coun- terfactual invites one to do, without giving up the idea that it was written at all. So, (2) seems downright false. This article is confined to general properties of conditional sentences and theories of indicative con- ditionals, and mentions counterfactuals only occasionally.
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Bibliography
Aristotle 1928 The Works of Aristotle Translated into English, Ross W D (ed.), vol. 1. Oxford University Press, Oxford
Corcoran J 1974 Aristotle's natural deduction system. In: Corcoran J (ed.) Ancient Logic and its Modern Interpret- ations. Reidel, Dordrecht
Lear J 1980 Aristotle and Logical Theory. Cambridge Uni- versity Press, Cambridge
Lukasiewicz J 1957 Aristotle's Syllogistic, 2nd edn. Oxford University Press, Oxford
Westerstaohl D 1990 Aristotelian syllogisms and generalized quantification. Studio Logica XLVIII
Conditionals F. Veltraan