95. Examine the doctrine that a judgment can properly be denied only by another judgment of the same type. Illustrate by reference to (a) universal judgments, (b) particular judgments (c) disjunctive judgments, (d) apodeictic judgments. [K.]
CHAPTER IV.
IMMEDIATE INFERENCES.[122]
[122] In this chapter we concern ourselves mainly with the traditional scheme of propositions, and except where an explicit statement is made to the contrary we proceed on the assumption that each class represented by a simple term exists in the universe of discourse, while at the same time it does not exhaust that universe. This assumption appears to have been made implicitly in the traditional treatment of logic.
96. The Conversion of Categorical Propositions.—By conversion, in a broad sense, is meant a change in the position of the terms of a proposition.[123] Logic, however, is concerned with conversion only in so far as the truth of the new proposition obtained by the process is a legitimate inference from the truth of the original proposition. For example, the change from All S is P to All P is S is not a legitimate logical conversion, since the truth of the latter proposition does not follow from the truth of the former. In other words, logical conversion is a case of immediate inference, which may be defined as the inference of a proposition from a single other proposition.[124]
[123] Ueberweg (Logic, § 84) defines conversion thus. Compare also De Morgan, Formal Logic, p. 58. In geometry, all equiangular triangles are equilateral would be regarded as the converse of all equilateral triangles are equiangular. In this sense of the term conversion, which is its ordinary non-technical sense, we may say—as we frequently do say—“Yes, such and such a proposition is true; but its converse is not true.”
[124] In discussing immediate inferences we “pursue the content of an enunciated judgment into its relations to judgments not yet uttered” (Lotze). Instead of “immediate inferences” Professor Bain prefers to speak of “equivalent propositional forms.” It will be found, however, that the new propositions obtained by immediate inference are not always equivalent to the original proposition, e.g., in conversion per accidens. Miss Jones suggests the term eduction as a synonym for immediate inference (General Logic, p. 79); and she then distinguishes between eversions and transversions, an eversion being an eduction from categorical form to categorical, or from hypothetical to hypothetical, &c., and transversion an eduction from categorical form to conditional, or from conditional to categorical, &c. For the present we shall be concerned with eversions only.
127 The simplest form of logical conversion, and that which is understood in logic when we speak of conversion without further qualification, may be defined as a process of immediate inference in which from a given proposition we infer another, having the predicate of the original proposition for subject, and its subject for predicate. Thus, given a proposition having S for its subject and P for its predicate, our object in the process of conversion is to obtain by immediate inference a new proposition having P for its subject and S for its predicate. The original proposition may be called the convertend, and the inferred proposition the converse.
The process will be valid if the two following rules are observed:
(1) The converse must be the same in quality as the convertend (Rule of Quality);
(2) No term must be distributed in the converse unless it was distributed in the convertend (Rule of Distribution).