30: On Hypothetical Propositions and their Properties
On Hypothetical Propositions And perhaps the reason why the Philosopher did not devote a special tract to such propositions and their propoerties and conversions was this: from what should be known about de necessario, de contingenti, de possibili, and de impossibili propositions~and a few others—one can easily discern what should be said of other modal propositions and their properties. Still, ignorance of these things, just like ignorance of other propositions and their properties, leads many modem thinkers to make mistakes and to be caught up in confusions in theology and in the other particular sciences, both speculative and practical.
Moreover, in order to clarify the conversion of all modal propositions, it should be noted that modal propositions in the sense of division and their equivalents are commonly converted just like non-modal propositions in which some adverbial determination is added to the verb. For in these latter propositions the adverbial determination or its equivalent should not be added to the composition in the same way in the proposition to be converted and in the proposition into which it.is converted. Rather, in the consequent such a determination should be placed only in the subject position, as has been pointed out.? In the same way, in the consequent the mode should be placed totally in the subject position, as has been illustrated by the examples.
30: On Hypothetical Propositions and their Properties Now that categorical propositions and their properties have been briefly treated, a few things should be said about hypothetical propositions and their properties.
It should first be noted that a proposition is called hypothetical when it is composed of two or more categorical propositions joined by some adverb or conjunction. Not only is it possible for a single adverb or a single conjunction to join the categorical
On Hypothetical Propositions propositions and form a hypothetical proposition, but it is also possible for several conjunctions and adverbs to do so—and sometimes one or more adverbs plus one or more conjunctions can combine to form a hypothetical proposition. Hence, the following is a hypothetical proposition: 'Socrates is running or Plato or John'. And so is this: 'If a man is running an animal is running, and Plato is debating'. Accordingly, some hypothetical propositions are composed of more than two categorical propositions.
However, it could simply be stipulated that a proposition is not hypothetical when it contains both an adverb and a conjunction—or two conjunctions—which normally form hypothetical propositions of different types. And the same can be said about adverbs.
Second, it should be noted that hypothetical propositions are assigned to five species, namely, conditional, conjunctive, disjunctive, causal, and temporal.
But it seems that there are other hypothetical propositions besides these. For every proposition, true or false, which is composed of two categoricals, is a hypothetical proposition. But there are many propositions of this sort besides those named above.
Therefore, etc. The major premise is sufficiently obvious. The minor is clear, for the following proposition is of the requisite form: 'Socrates is running where Plato is debating'.
However, it should be noted that although there are many hypothetical propositions besides the ones named above, still there are many which seem to be different from those named above but which should be reduced to the latter. For example,
'Socrates philosophizes, lest he be ignorant' is a causal proposition. For it is equivalent to this: 'Since Socrates does not want to be ignorant, Socrates philosophizes'. And so it is with many other propositions.