Note 274 — Chapter IX

It has been argued that, starting from the categorical form, we cannot pass to the conditional, if the subject of the proposition is a simple term. The basis of this argument is that the antecedent of a conditional requires two terms, and that in the case supposed these are not provided by the categorical. Thus, Miss Jones (Elements of Logic, p. 112) takes the example, “All lions are quadrupeds.” It will not do, she says, to reduce this to the form, “If any creatures are lions, they are quadrupeds,” since this involves the introduction of a new term, and passing back again to the categorical form, we should have “All creatures which are lions are quadrupeds,” a proposition not equivalent to our original proposition. If, however, “creature” is regarded as part of the connotation of “lion,” there is no reason for refusing to allow that the two propositions are equivalent to one another. Similarly, in any concrete instance, by taking some part of the connotation of the subject of our categorical proposition, we can obtain the additional term required for its reduction to the conditional form. Where we are dealing with purely symbolic expressions, and this particular solution of the difficulty is not open to us, we may have recourse to the all-embracing term “anything,” such a proposition as All S is P being reduced to the form If anything is S it is P.