19: On Propositions in which the Verbs 'Begin' and 'Cease' OccurEvery
On Propositions with 'Begin' and 'Cease'
It should also be noted that 'except' is never taken diminu- 'tively unless it is added to a numerical term or to a term which designates some whole. However, when it is taken diminutively and added to a numerical term, then it is asserted not that the predicate is denied of that to which the expression 'except' is added, but rather that it is denied of the subject. For example, by means of 'Ten except five is five' it is asserted not that five is removed from five but that five is removed from ten. Similarly, by means of such a proposition it is not asserted that the predicate inheres in that to which the expression 'except' is added. For example, by means of 'Ten except four is six' it is not asserted that four is six, but rather that six is left after four is taken away. And the same holds for other such cases. These remarks about exceptive propositions should suffice for the present.
19: On Propositions in which the Verbs 'Begin' and 'Cease' Occur Every proposition in which either of the verbs 'begin' or 'cease' occurs has two exponents, since each such proposition is equivalent to a conjunctive proposition. Now some writers assign exponents in different ways with respect to different kinds of things. Hence, they claim that such propositions should be expounded in one way with respect to successive entities and in another way with respect to enduring entities.'
But although this could be so insofar as the intentions of those who use these terms are concerned, still it does not seem very reasonable.
Therefore, I claim that the propositions in question have the same exponents with respect to any kind of entity, but that the exponents of a proposition in which 'begin' occurs are different
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'God beatifies everyone whom he now beatifies and God did not immediately before this beatify everyone whom he now beatifies'— and in this sense the proposition is true. The other sense is this:
'God beatifies everyone whom he now beatifies and he did not immediately before this beatify anyone whom he now beatifies'— and in this sense the proposition is false. Exactly the same can be said of the proposition 'God begins to punish everyone whom he now punishes'. Propositions such as the following should be treated in a similar way: 'Peter begins to be like Paul in a certain respect', assuming that each is first an unbeliever and later becomes a believer.' In that case 'Peter begins to be like Paul in a certain respect' can be conceded without qualification, since he is now for the first time like Paul in a certain respect and before this he was not like Paul in that respect. Nevertheless, 'Peter begins to be similar to Paul' is, strictly speaking, false, since he was similar to Paul before this. Still, this proposition can be understood improperly to have this sense: 'Peter is similar to Paul, and he was not similar to Paul with respect to a certain quality, with respect to which he is now similar to him'.
And so it is clear that a proposition in which the verb 'begin' occurs has two exponents and, as a result, is equivalent to a conjunctive proposition.
In the same way, a proposition in which the verb 'cease' occurs has two exponents. One exponent is a present-tense affirmative proposition and the other is a future-tense negative proposition—
On Propositions with 'Begin' and 'Cease' not just any one, but one in which the phrase 'will not be suchand-such immediately after this' is added. For example, 'Socrates ceases to be white' has these exponents: 'Socrates is white' and 'Immediately after this he will not be white'. And just as it was said, with respect to propositions in which the verb 'begin' occurs, that sometimes such propositions can be distinguished as amphibolous, since they can be taken either properly or improperly, so too many propositions in which the verb 'cease' occurs can be distinguished as amphibolous, since they can be taken either properly or improperly.
With regard to the supposition of the terms in such propositions it should be noted that the subject of such a proposition supposits in the same way that it does in the corresponding proposition which does not contain 'begin' or 'cease'. However, there is a difficulty with respect to the supposition of the predicate.
It should be claimed that the predicate in a universal affirmative proposition of this type has merely confused supposition, since it is not possible to descend either conjunctively or disjunctively. For this does not follow: 'Every man ceases to be white; therefore every man ceases to be this white thing or every man ceases to be that white thing'. Nor, consequently, is it possible to descend conjunctively. Similarly, in a universal negative proposition of this.type the predicate has confused and distributive supposition, while in a non-universal proposition it has determinate supposition.
Still, two things must be taken into account at this point. The first is that both determinate supposition and confused and distributive supposition are of two types. One type occurs when it is possible to descend to the things for which the term supposits— or is able to supposit—by means of demonstrative pronouns alone.
For example, in the proposition 'A man is running' the term 'man' supposits for this man and that one, and so on for the others.
And this follows correctly: 'A man is running; therefore this is running', referring to this man, 'or that is running', referring to that man, and so on for the others. However, sometimes it is possible to descend not by means of demonstrative pronouns alone but only by means of demonstrative pronouns taken with the common term under which the descensus is supposed to occur.
On Propositions with 'Begin' and 'Cease'
Now the predicate of a proposition in which 'begin' or 'cease' occurs does not have determinate supposition of the first type.
For this does not follow: 'Socrates begins to be white; therefore Socrates begins to be this or begins to be that', no matter what is referred to. For if Socrates changes from being black to being white, then 'Socrates begins to be white' is true, even though, no matter what is referred to, the proposition 'Socrates begins to be this' is false. For the second of the following propositions is false:
'Socrates is this' and 'Socrates was not this before'. Rather, the predicate supposits determinately in the second way. For this is valid: 'Socrates begins to be white; therefore he begins to be this white thing or he begins to be that white thing', and so on for the others. Hence, 'Socrates begins to be this white thing', referting to Socrates, is true, since Socrates is now this white thing and he was never previously this white thing.
But this is not valid: 'Socrates begins to be this white thing; therefore he begins to be this', always referring to the same thing. Rather, this is a fallacy of a figure of speech, committed by confusing 'quale quid' with 'hoc aliquid'.* For there is frequently a fallacy of a figure of speech in such cases when one argues from some connotative term—whether it is the whole predicate or is taken with a demonstrative pronoun—to a demonstrative pronoun taken by itself.
Now someone might object that 'this' and 'this white thing', referring to the same thing, are interchangeable and that, therefore, an inference from one to the other is valid. It should be replied that the rule 'There is a valid consequence from one of two interchangeable terms to the other' has many counterin- © stances, specifically, when the terms do not supposit personally, and also sometimes when some syncategorematic expression is added to the verb. For example, this does not follow: 'A man is per se in the second mode risible; therefore a man is per se in the second mode a man'.® It is especially true, however, that the rule does not hold with respect to many past-tense and futuretense propositions when the interchangeable terms in question are interchangeable at present but not interchangeable without qualification. This is the case with the two terms 'this' and 'this white thing', for when the thing in question is not white, the two terms are not interchangeable.
On Propositions with 'Begin' and 'Cease'
Second, it should be noted that sometimes determinate supposition is such that it is possible to descend to the inferiors and, conversely, it is possible to ascend from the inferiors—but sometimes this is not so. Hence, this follows: 'A man is running; therefore this man is running or that man is running', and so on for the others. And, conversely, this follows: 'This man is running; therefore a man is running'. But this is not always the case with a term suppositing determinately in the predicate position in a proposition containing 'begin' or 'cease'. Hence, this is valid:
'Socrates begins to be this colored thing; therefore he begins to be white or black', and so on for the others. But the converse does not follow. For this does not follow: 'Socrates begins to be white; therefore he begins to be colored'. The reason for this is that the negative exponent of the antecedent does not entail the negative exponent of the consequent. For this does not follow: 'Socrates was not white; therefore Socrates was not colored'.
And it is a general rule that when the antecedent and consequent have exponents, then if an exponent of the consequent does not follow from some exponent of the antecedent, the inference involving the antecedent and consequent is not valid.
From what has been said one can gather that the consequence from an inferior to a superior with respect to the verb 'begin' or 'cease' is not valid, just as this is not valid: 'Socrates begins to be white; therefore Socrates begins to be colored'. Similarly, this does not follow: 'The Son of God begins to be a man; therefore the Son of God begins to be some thing'. Nor is an argument such as this valid: 'Every man is some thing; the Son of God begins to be a man; therefore the Son of God begins to be some thing'.
Rather, this is a fallacy of accident. For just as there is always a fallacy of accident when in the first figure the major premise is affirmative and the minor negative, so too there is always a fallacy of accident when in the first figure the major premise is affirmative and the minor premise has some negative exponent. For example, this is invalid: 'Every man is an animal; only what is risible is a man; therefore only what is risible is an animal'. But this is the case with the argument proposed above, for the minor premise, 'The Son of God begins to be a man', has this negative exponent: 'The Son of God was not a man immediately before this'. Therefore, in such an argument there is a fallacy of accident.