1: On the Classification of Propositions in General
1: On the Classification of Propositions in General Now that something has been said about terms, we must discuss propositions. First, some classifications should be given; second, we should see what is necessary and sufficient for the truth of propositions; and, third, we must examine carefully some things concerning the conversion of propositions.
Concerning the first point it should be noted that one way to divide propositions is into categorical propositions and hypothetical propositions. A categorical proposition has a subject, predicate, and copula, and it does not include more than one such proposition. A hypothetical proposition is one which is composed of more than one categorical proposition. According to the usual view hypotheticals are divided into five species: conjunctive, disjunctive, conditional, causal, and temporal.
A conjunctive proposition is one which is composed of two or more propositions—either categoricals or hypotheticals, or one categorical and the other hypothetical—joined by the conjunction
'and'. An example of the first is 'Socrates is running and Plato is debating'. An example of the second is 'If Socrates exists, an animal exists, and Socrates is running and Plato is debating'. An example of the third is 'If a man is running, an animal is running, and Socrates is debating'. But since these last two types are rarely used, I intend to talk only about conjunctive propositions of the first type, namely, those which are composed of two categoricals.
A disjunctive proposition is composed of two or more propositions joined by the conjunction 'or'.
A conditional proposition is one composed of two or more propositions joined by the conjunction 'if', as in 'If Socrates is running, an animal is running' or 'A man exists if Socrates exists'.
For it does not matter whether the conjunction in question is placed before the first proposition or between the propositions.
A causal proposition is one composed of two or more propositions joined by the conjunction 'since', as in 'Since a man is tunning, a man is moving'.
On the Classification of Propositions in General A temporal proposition is one composed of two propositions joined by some temporal adverb, as in "When Socrates is running,
Plato is debating' and, similarly, 'While Socrates is running, John is a man', and so on for the others.
Another way of dividing propositions is into non-modal (de inesse)' propositions and propositions de modo or modal propositions.
A modal proposition is one in which a modal term occurs.
A non-modal proposition is one without a modal term.
All the best thinkers seem to agree that there are only four modes, namely, 'necessary', 'impossible', 'contingent', and 'possible'. The reason is that the Philosopher did not mention more modes, nor did he specify more modes in the Prior Analytics when he treated the conversion of such propositions and the syllogisms composed of them." Nevertheless, since he did not deny that there are other modes, it can be said, speaking more generally, that there are more modes which make propositions modal than these four.
On this point it should be noted that a proposition is called modal because of the addition of a mode to the proposition.
But not any mode is sufficient to make a proposition modal.
Rather, it is necessary that the mode be predicable of a whole proposition. Therefore, properly speaking, the mode of a proposition is, as it were, truly predicable of the proposition itself.
And it is in virtue of such a mode or the adverbial form of such a predicable—if it has an adverbial form—or its verbal form that a proposition is said to be modal. But there are more such modes than the four mentioned above. For just as one proposition is necessary, another impossible, another possible, another contingent, so too one proposition is true, another false, another known, another not known, another spoken, another written, another thought, another believed, another opined, another doubted, etc. Therefore, just as a proposition is called modal in which the mode 'possible' or 'necessary' or 'contingent' or 'impossible' or the adverbial form of any of them occurs, so too a proposition in which one of the above mentioned modes occurs can just as reasonably be called modal. Thus, just as 'That every man is an animal is necessary' and 'Every man is necessarily an animal' are modal propositions, so too are 'That every man is an animal is known' and 'Every man is known to be an animal' and On the Classification ofPropositions in General propositions such as 'That every man is an animal is true'—and so on for the others.
If someone should ask why the Philosopher did not deal with these propositions, it should be replied that the Philosopher, striving for brevity, did not want to treat these propositions extensively, for what he said about the others can be applied to these.
Now in what follows it will become clear in what way many things which were said about the other modal propositions can be applied to these.?
A third way to divide categorical propositions is into those which are equivalent to hypothetical propositions—even though they are categoricals—and those which are not equivalent to hypothetical propositions. Exceptives, exclusives, reduplicatives, and certain others are propositions of the first kind. In fact, whenever a concrete term in the first mode* is the subject or predicate, the proposition in question is equivalent to a hypothetical proposition, as will become clear. Some examples of propositions of the second kind are 'An angel is a substance', 'God exists', 'God is the Father', etc.
Another division is this: some propositions are universal, some particular, some indefinite, and some singular. A universal proposition is one whose subject is a common term determined by a universal sign—whether the proposition is affirmative or negative— as in 'Every man is running', 'No man is running', 'Both of them are running', and so on. A particular proposition is one whose subject is a common term determined bya particular sign, e.g.
'Some man is running', 'A certain man is running', and so on.
An indefinite proposition is one whose subject is a common term without either a universal or a particular sign, e.g. 'A man is an animal', 'An animal is running', and so on. A singular proposition is one whose subject is the proper name of something, or a demonstrative pronoun, or a demonstrative pronoun with a common term. An.example,of the first is 'Socrates is running'; an example of the second is 'He is running', pointing to someone; an example of the third is 'This man is an animal'.
Nevertheless, with respect to many propositions one may be uncertain as to what their quantity is. The following are examples:
(1) 'They are running'.® On the Classification of Propositions in General (2) 'One of the two is running'.
(3) Likewise, a part of a conjunctive proposition in which the subject is some relative pronoun, as in 'Socrates is running and he is debating'.
(4) Similarly, propositions such as 'It is not the case that every man is running', 'It is not the case that no man is an animal', and so on.
(5) Likewise, propositions such as 'Man is a species', 'Animal is a genus', "Man is in the nominative case', and so on.
(6) Similarly, propositions such as 'God creates', 'God generates', 'God is the Father and the Son and the Holy Spirit'.
(1) To the first of these it should be said that 'They are running' is a singular proposition, since such a demonstrative pronoun supposits for specific things.
Now someone might claim that it is never proper to add a universal sign to a singular proposition. Hence, just as 'Every Socrates is running' is not well-formed, neither is 'Every that is an animal' or 'Every he is running'. But it is proper to say 'All these are running'. Therefore, the proposition 'They are running' is not singular.
It should be replied that according to the common way of speaking it is proper to add such a sign to a plural term, even if the latter is a demonstrative pronoun—although perhaps, strictly speaking, such a sign should not be added, since 'They are running' and 'Ali these are running' are totally equipollent. If the latter is proper, then nothing more is conveyed by the one that by the other. Still, just as sometimes the same expression is repeated within the same subject or predicate for some particular reason, so too a universal sign is added to a plural pronoun for the sake of greater expression or emphasis or for some other such reason—although, literally and properly speaking, it should not be so added.
(2) To the second it should be said that 'One of the two is Tunning' is an indefinite proposition, just as 'Both of them are running' is universal. For a universal sign like this, which distributes over only two things, can be added to a plural pronoun and render a proposition universal. And thus what was said earlier, namely, that a proposition whose subject is a demonstrative pronoun is singular, should be understood to apply when that pronoun is in the nominative case. However, when it is in an On the Classification of Propositions in General oblique case the proposition need not be singular, but can be universal or indefinite. And, in the same way, when it is said that a proposition whose subject is a common term with a universal sign is a universal proposition, it should be understood that a proposition is also universal when sucha sign is added to a pronoun in the genitive case. Therefore, propositions such as these are universal: 'Both of them are running', 'Each of them is a man', and so on. Likewise, propositions such as the following are particular:
'Some of them are mnning' and 'Some of them are animals'. For the particular sign is added to a pronoun in the genitive plural and the sign itself is in the nominative case.
(3) To the next one it should be said that whena relative pronoun has as its antecedent a discrete name it renders the proposition singular. When it has as its antecedent a common name it renders the proposition indefinite. Thus, in 'Socrates is running and he is debating'—if it is properly formed—the second part of the conjunctive is singular. But the second part of the conjunctive proposition 'A man is running and he is debating' is indefinite, since the relative supposits for the same thing or things that its antecedent supposits for. Therefore, whether the proposition is singular or indefinite depends on whether the antecedent of the relative term is a discrete or proper name or a common name.
(4) To the fourth it should be said that propositions like 'It is not the case that every man is running' and 'It is not the case that no man is an animal' are particular, since the negation precedes the universal sign. Therefore, when it is said that a particular proposition is one whose subject is a common term, etc., the following should be added:
. unless a negation precedes the particular sign; and a proposition is particular when its subject is a common term with a universal sign preceded by a negation." Hence, propositions such as these are particular: 'It is not the case that every man is running' and 'It is not the case that no man is an animal'. And propositions such as these are universal: 'It is not the case that some man is running' and 'It is not the case that a certain man is not running' and so on.
(5) To the fifth uncertain case: with respect to propositions like 'Man is a species', 'Animal is a genus', and 'Man is in the nominative case'—and, in general, with respect to any proposition in which a term supposits simply or materially—it can be said
On the Classification of Propositions in General arbitrarily, as it were, either that they are singular or that they are indefinite. For this depends more on how one decides to use the terms 'singular proposition' and 'indefinite proposition' than on any substantive issue.
Hence, if one wishes to say that a proposition whose subject is a common term without a sign and without a preceding negation is always indefinite, then he should say that all propositions like those in question are indefinite. On the other hand, if one wants to use these terms in another way, then he should say something else. For he should say that it is not sufficient that the subject be a common term of this sort, but that it is necessary to add that such a common term is suppositing personally.
And in that case all propositions in which terms supposit simply or materially are singular.
(6) Almost the same thing holds for the last uncertain case.
For if one wants to call every proposition in which the subject is a term predicable of two or more really distinct supposita an indefinite proposition, then he should say that propositions like
'God creates', 'God generates', etc., are indefinite. The reason for this is that 'God' is a term predicable of more than one suppositum. On the other hand, if one wants to say that a proposition is not indefinite unless the common term may be predicated of several supposita which are not simply one thing, then he should say that 'God creates' and other propositions of this sort are singular and not indefinite.
Therefore, it should be said that a universal proposition is (a) one in which the subject is a common term determined by a universal sign and not preceded by a negation—this is needed because of propositions like 'It is not the case that every man is tunning' and 'It is not the case that no man is an animal'; or (b) one in which the subject is a common term without a universal sign but with a preceding negation—this is needed because of propositions like 'It is not the case that some man is running' and 'It is not the case that a man is an animal', which are universal; or (c) one in which the subject is a demonstrative pronoun in the genitive plural with a universal sign but with no preceding negation—this is needed because of propositions like 'Both of them are running' and 'Each of them is-a man'; or (d) one in which the subject is a relative pronoun whose antecedent has
On the Classification of Propositions in General confused and distributive supposition—this is needed because of propositions like "Every man is running and he is debating', since the second part of the conjunctive is universal in the same way that the first part is. And according to one view it should be added that such a common term is suppositing personally.
Hence, on that opinion the following are not universal: 'Every man is a common term with a universal sign' and "Every man is composed of a common term and a universal sign'. But one who holds this opinion must concede that, strictly speaking, numerically the same proposition is universal and singular, because in numerically the same proposition the same term can supposit simply (or materially) and personally. If the term supposits simply or materially, the proposition will be singular. If it supposits personally, the proposition will be universal. For example, assume that I Lave two respondents and that to one of them I specify that when I utter the proposition 'Every man is a common term determined by a universal sign',
I want the expression 'every man' to supposit materially. In that case he would concede that the proposition is singular. To the other, let us assume,
I specify that I want the subject to supposit personally. In that case he would concede that the proposition is universal. So in the posited circumstances a single proposition is uttered, and yet one person, responding correctly, will say that it is singular, and the other will say that it is universal. Consequently, a single proposition will be singular and universal. But this is no more inappropriate than saying that numerically the same proposition is known and not known because it is known by one person and not known by another. In the same way, one who holds the opinion under discussion should concede, strictly speaking, that numerically the same proposition is true and false, necessary and impossible, and that the same syllogism is demonstrative and yet sophistical and incorrect in form.
But what should be said about these cases will become clear in what follows.
From what has been said one can easily tell which propositions are universal, which are indefinite, and which are singular.
A sixth division of propositions can be made. For some propositions are present-tense, e.g. 'A man is an animal', 'A man is running', etc.; some are past-tense, e.g. 'Socrates was a man', 'Soc-