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29. CONTRARIETY AND CAUSALITY IN HUME Hume's notion of contrariety ranks among the most obscure in his theory of relations. To make matters worse, the puzzling account of contrariety he offers can be shown inconsistent in the following way. The Treatise (T69-82) divides all relations into two disjoint classes - one class containing relations of knowledge (in the strict sense) ascertained by the mere comparison of ideas, the other containing those of probability or 'uncertain knowledge' requiring 'experience' or empirical evidence. Causality is the paradigm of a probability relation - contrariety falls into the class of knowledge relations. Thus unlike causality the discovery of a contrary relation appears to require no experience. Yet in direct contradiction Hume claims that with the exception of existence and non-existence (which are singled out for special attention) , all knowledge of contrary relations demands experience: no two ideas are in themselves contrary , except those of existence and non-existence.... All other objects, such as fire and water, heat, and cold, are only found to be contrary from experience , and from the contrariety of their 'causes ' or effects ' . (T15) The charge of inconsistency appears inevitable. However, I shall argue that Hume escapes by implicitly operating with two distinct concepts of contrariety: one (which I shall term "logical contrariety") a relation of knowledge, the other (to be called "empirical contrariety") reducible to a peculiar type of causal relation, and therefore a probability relation. To adduce independent grounds for this claim I demonstrate that acceptance of these two concepts is essential if we are to explain why Hume finds 2 it important to place the following restriction on contra- 30. riety (hereafter, R): properly speaking no objects are contrary to each other, but existence an (y exists) . And (4) can hardly be said to represent a form of contrariety between existent and non-existent objects. (Indeed paradox of material implication aside, (4) is an analysis of "x causes y".) Therefore to hold R and still maintain some sense of contrariety between existent and non-existent objects, Hume must restrict contrariety to logical contrariety . 32. Hume's own remarks bear out my claim. In the Treatise he recognizes that restricting contrariety to existence and non-existence means treating it as contradiction : the flattest of all contradictions ... (is) ... that 'tis possible for the same thing both to be and not to be. (T19, my emphasis.) . . . with contrariety ... No one can once doubt but existence and non-existence destroy each other, and are perfectly incompatible and contrary. (T70) And in the Enquiries he interchanges the terms 'contrary' and 'negation' : The contrary of every matter of fact is still possible ; because it can never imply a contradiction ... (EU25) ... No negation of a fact can involve a contradiction. (EU164) This usage indicates that if ? is (logically) contrary to q, ? is -q, the negation of q. In this case the conjunction of ? and q spells the contradiction (q & -q) . The definition of logical contrariety we adopt is the same as the definition of contradiction specialized to existential sentences, so we need not state it. It is sufficient to give as a paradigm the following contradiction: (5)(Mars exists) & - (Mars exists) . Here it is the existence of Mars that is logically contrary to the non-existence of Mars and therefore the contrariety restriction R is satisfied. Again it is only the existence and non-existence of the same object that is logically contrary. Empirical contrariety is most clearly defined in terms of the Lewis counterfactual G=>, where 1O' is a monadic predicate, 'e.' and 'e.' represent distinct arbitrary events, and "0(e)" means "event e occurs": 33. 5 Here it is not the existence and non-existence or occurrence (EC) e. is empirically contrary to e. iff 0(e.) D=> ~0(e.)." and non-occurrence of distinct events that gives rise to contrariety. Rather it is the existence or occurrence of one event that is empirically contrary to the existence or occurrence of another. To establish Hume's motivation for framing the condition R in such a way as to identify contrariety with contradiction, I now turn to examine the epistemological ground of the difference between empirical and logical contrariety . The ontological distinction between empirical...


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