Logic - Deductive and Inductive by Carveth Read
page 86 of 478 (17%)
page 86 of 478 (17%)
![]() | ![]() |
|
have the same subject whilst the predicates are contrary or
contradictory terms. If, then, the disjunctive _A is either B or C_ (_B_ and _C_ being contraries) implies that both alternatives cannot be true, it can only be adequately rendered in hypotheticals by the two forms--(1) _If A is B, it is not C_, and (2)_If A is not B, it is C_. But if the disjunctive _A is either B or C_ (_B_ and _C_ not being contraries) implies that both may be true, it will be adequately translated into a hypothetical by the single form, _If A is not B, it is C_. We cannot translate it into--_If A is B, it is not C_, for, by our supposition, if '_A is B_' is true, it does not follow that '_A is C_' must be false. Logicians are also divided in opinion as to the function of the hypothetical form. Some think it expresses doubt; for the consequent depends on the antecedent, and the antecedent, introduced by 'if,' may or may not be realised, as in _If the sky is clear, the night is cold_: whether the sky is, or is not, clear being supposed to be uncertain. And we have seen that some hypothetical propositions seem designed to draw attention to such uncertainty, as--_If there is a resisting medium in space_, etc. But other Logicians lay stress upon the connection of the clauses as the important matter: the statement is, they say, that the consequent may be inferred from the antecedent. Some even declare that it is given as a necessary inference; and on this ground Sigwart rejects particular hypotheticals, such as _Sometimes when A is B, C is D_; for if it happens only sometimes the connexion cannot be necessary. Indeed, it cannot even be probably inferred without further grounds. But this is also true whenever the antecedent and consequent are concerned with different matter. For example, _If the soul is simple, it is indestructible_. How do you know that? Because _Every simple substance |
|