This lesson is from Bachhuber, Andrew H., S.J. 1957. "Chapter 14: Kinds of Propositions," An Introduction to Logic. New York: Appleton-Century-Crofts, Inc. Pp. 281-91.
We have already treated of several kinds of propositions. In Chapter 3 we gave a thorough explanation of the attributive proposition, of the division of propositions into affirmative and negative, and of the division into singular, particular, and universal (A, E, I, and O). We also mentioned the divisions into true and false and into existential and non-existential. In Chapter 8, as a prerequisite to the study of the hypothetical syllogism, we explained three kinds of hypothetical propositions—that is, the conditional proposition, the dis junctive proposition, and the conjunctive proposition. Finally, when we took up the enthymeme, we gave a partial explanation of causal propositions (“because ...,” “since ..., for ... ). To avoid over¬ burdening ourselves with terminology that was not a prerequisite to the study of inference, we postponed the treatment of the other kinds of propositions to the present chapter.
That is necessary which is and cannot not be. That is contingent which is but can cease to be. Propositions are necessary or contingent, depending on whether the truth they express is a necessary truth or a contingent truth. This division of propositions is based on the special character of their thought content and not on their logical form.
a. Necessary Proposition
A necessary proposition expresses a necessary truth. It does not state a mere fact but expresses a truth that cannot be other than it is. The propositions “A triangle is a plane figure bounded by three straight lines” and “Man is a rational animal” are necessary propositions. A triangle that is not a plane figure bounded by three straight lines, as well as a man that is not a rational animal, is conceptually repugnant and therefore absolutely impossible. The proposition “A man is not a stone” is also a necessary proposition, since both a man that is a stone and a stone that is a man are impossible.
Every attributive proposition whose predicate is the genus, species, or property (in the strict sense) of the subject is a necessary proposition.
Notice that we cannot have philosophical demonstration unless we have necessary propositions as premises. As much as possible, science aims at attaining to necessary truths that are expressed in necessary propositions.
b. Contingent Proposition
A contingent proposition expresses a contingent truth. It states a mere fact—that is, it states something that is but could be, or could have been, other than it is. “Socrates sits” is a contingent proposition. Of course, on the supposition that Socrates is sitting, he cannot be simultaneously not sitting; but there is no conceptual repugnance in Socrates’s not sitting. Every attributive proposition whose predicate is a logical accident of the subject is a contingent proposition.
The proposition A triangle is a figure” is a necessary proposition; not to be a figure is conceptually repugnant to a triangle. Still, in this proposition, no mention is made of the necessity—or the necessary mode—with which to be a figure belongs to a triangle. In the proposition “It is necessary that a triangle is a figure,” however, not only is “figure” attributed to “triangle,” but the necessity—or the necessary mode—with which a triangle is a figure is also expressed.
On the basis of whether or not the manner, or mode, with which the copula unites the subject and predicate (or with which the simple or qualified existence of a subject is posited, or relations among member propositions are asserted) is expressed, propositions are either absolute or modal. “A triangle is a figure is an absolute proposition. “It is necessary that a triangle be a figure” is a modal proposition.
There are four modes. They are necessity, contingency, possibility, and impossibility. We shall define them in their concrete adjectival forms.
That is NECESSARY which is and cannot not be.
That is CONTINGENT which is but can cease to be.
That is POSSIBLE which is not but can be.
That is IMPOSSIBLE which is not and cannot be.
Sometimes "possible" is used in a broader sense so as to include what is as well as what is not but can be.
a. Absolute Proposition
An absolute proposition (as opposed to a modal proposition) merely makes an assertion without stating whether what is asserted is necessary, contingent, possible, or impossible. An attributive proposition is absolute if it merely affirms or denies an attribute of a subject (“A dog is an animal” and “A dog is not a cat ). An existential proposition is absolute if it merely posits or^sublates the existence of its subject (“God exists” and Troy is not ).
b. Modal Proposition
A modal proposition not only makes an assertion but also states whether what is asserted is necessary, contingent, possible, or impossible.
The mode must state whether the objective relationship of the subject and predicate (or of the subject to existence) is necessary, contingent, possible, or impossible. The proposition “The ship sails swiftly” is not a modal proposition; “swiftly” belongs to the predicate itself, and does not express a relationship of the predicate to the subject. The proposition “It is certainly true” is also not a modal proposition, since “certainly” expresses the state of mind of the speaker rather than the objective relationship of “it” and “true.”
The following are modal propositions. Notice the different ways in which the mode is expressed.
God exists necessarily.
That Socrates sits is contingent.
It is possible that men are living on Mars.
It is impossible that any square be a circle.
A modal proposition has two parts, the dictum and the mode. The dictum is the part that affirms or denies an attribute of a subject, or that posits or sublates the existence of a subject. The dicta of the examples given above are: “God exists,” “Socrates sits,” “Men are living on Mars,” and “Any square is a circle.” The dictum can be singular, particular, universal, or indeterminate, just as the corresponding absolute propositions.
The mode is the part that states whether the dictum is necessary, contingent, possible, or impossible. The mode can be expressed by an adverb (“necessarily,” “contingently,” “possibly,” “impossibly”), by a clause ( It is necessary that..., and so on), and sometimes by a verb (“I can ...”).
Necessity and impossibility are the universal modes, since what is necessary always takes place and what is impossible never takes place. For this reason, the modes expressing necessity and impossibility are construed as A and E respectively.
Possibility and contingency are the particular modes. Modal propositions expressing possibility are construed as I propositions, since they are the contradictories of those expressing impossibility, which are E. Those expressing contingency are construed as O propositions, since they are the contradictories of those expressing necessity, which are A.
c. Opposition of Modal Propositions
The nature of modal propositions will be made more clear if we consider the traditional square of opposition of modal propositions.
To refute the proposition “It is necessary that every man eat”(A), all you have to prove is that some man eats contingently—which is the same as proving that it is not necessary that every man eat or that it is possible for some man not to eat. The relationships of modal propositions towards one another are so obvious from a consideration of the square that it is not necessary to call attention to them in detail.
Before we explain the nature of compound propositions, we shall say a few words about simple propositions, because the former are best understood by contrasting them with the latter.
The propositions “God exists” and “A dog is an animal” are simple propositions. The first merely posits the existence of a subject; the second affirms an attribute of a subject. Notice that in both of these propositions our assent is expressed by the verb—by “exists” in the first, and by “is” in the second.
There are other propositions in which our assent is expressed by conjunctions, adverbs, and so on, as in the proposition “If the sun is shining, then it is day. In this proposition our assent is expressed by if ..., then ..., and bears directly on the relationship of the first clause (the if clause) to the second clause (the “then” clause).
Propositions of this sort are compound propositions. Compound propositions, then, consist of at least two clauses; and in compound propositions our assent is expressed by conjunctions, adverbs, and so on, that indicate the relationship of the clauses towards one another.
Hypothetical propositions (that is, conditional, disjunctive, and conjunctive propositions) are compound. You will recall that we studied them before we took up the hypothetical syllogism. The causal propositions (“because ...” propositions) mentioned in connection with the enthymeme are also compound propositions. In the present section we shall give a brief account—which will be little more than a catalog--of some other kinds of compound propositions.
The main division of compound propositions is into those that are openly compound and those that are occultly compound.
a. Openly Compound Propositions
A proposition is openly, or formally, compound if the plurality of clauses (exclusive of those that are merely parts of a complex term) is stated explicitly. There are several kinds. Some of these kinds have occultly compound variants.
1) COPULATIVE PROPOSITIONS. Copulative propositions are compound propositions that have two or more subjects, or predicates, or both, which are joined together by and, both ... and, “neither... nor,” and so on. The following is a copulative proposition that is openly, or formally, compound: Peter was martyred in Rome, and Paul was martyred in Rome.” The same truth can be expressed in an occultly compound proposition “Both Peter and Paul were martyred in Rome.” “Neither wealth nor honors can make you happy” is likewise an occultly compound copulative proposition; it can be resolved into the openly compound proposition, “Wealth cannot make you happy, and honors cannot make you happy.”
A copulative proposition is true if its every member is true; it is false if any member is false. The contradictory of a copulative proposition is a disjunctive in the broad sense. Thus, the contradictory of “Both Jimmy and Johnny are naughty boys” is “Either Jimmy is not a naughty boy, or Johnny is not a naughty boy (or neither is a naughty boy).” It can also be expressed: “Jimmy and Johnny are not both naughty boys.” The contrary, however, of “Both Jimmy and Johnny are naughty boys” is “Neither Jimmy nor Johnny is a naughty boy.”
2) ADVERSATIVE PROPOSITION. An adversative proposition is similar to a copulative proposition in that it has two or more subjects, or predicates, or both, which are joined together into a compound proposition. It differs from a copulative in that it also expresses a contrast of clauses by the use of conjunctions such as “but,” “although,” “nevertheless,” “still,” and so on. The clause introduced by the adversative conjunction is an assertion of something other than what you would expect to follow from, or to accompany, the other clause.
An adversative proposition is often a denial of the corresponding inferential, or illative, proposition. Let us examine the following example: “He is an American Indian but does not have black eyes.” You would expect that he would have black eyes as a consequent of being an American Indian. The use of an adversative conjunction suggests what is included in the parentheses: “He is an American Indian (and therefore you would expect him to have black eyes), but he does not have black eyes.”
For an adversative proposition to be true, each of the clauses must be true when it is taken by itself, and there must also be some kind of contrast between them. Thus, the example “He is an American Indian but does not have black eyes” is true if he is an American Indian and if he does not have black eyes, since you would expect an American Indian to have black eyes as a consequent of his being an American Indian. But the proposition “It is a razor but sharp” is not true even if the thing referred to is a razor and also is sharp. The reason for this is that there is no contrast between a thing’s being a razor and its being sharp; sharpness is an attribute you would expect a razor to have.
3) CAUSAL PROPOSITION. A causal proposition is a compound proposition whose clauses are joined by the causal conjunctions “because, since, “for,” and so on. The clause introduced by the causal conjunction must state the cause, reason, occasion, or explanation, of what is asserted in the other clause. Sometimes it states the cause, occasion, or reason of the thing itself, as in the proposition "He is wearing a cast because he broke his arm.” Sometimes it states the reason for our knowledge of the thing, as in the proposition “He must have broken his arm because he is wearing a cast.”
For a causal proposition to be true, each of its members must be true when it is taken by itself, and the clause introduced by the causal conjunction must actually state the cause, reason, occasion, or explanation, either of what is asserted in the other clause or of our knowledge of it. Thus, the proposition “Abraham Lincoln was elected president because he was a very tall man” is false although he was elected president and also was a very tall man; it is false because his being a very tall man was not the cause, occasion, and so on, either of his being elected president or of our knowledge of his election to the presidency.
Enthymemes, as we have seen, are frequently expressed by causal propositions.
4) INFERENTIAL PROPOSITION. An inferential (illative, or rational) proposition is a compound proposition whose clauses are joined by the conjunctions “therefore,” “for this reason,” “and so,” and so on. As the name “inferential” suggests, an inferential proposition states an inference; the clause introduced by the inferential conjunction (“therefore,” and so on) is the consequent, and the other clause is the antecedent.
For an inferential proposition to be true, each clause must be true when it is taken by itself, and the sequence expressed by the inferential conjunction must be valid.
Enthymemes, as we have seen, are frequently expressed in inferential propositions.
b. Occultly Compound Propositions
A proposition is occultly, or virtually, compound if it explicitly states only one clause (exclusive of clauses that are parts of terms) but implies one or more other clauses through the use of words such as “only,” “except,” “as such,” and so on.
These propositions are called exponibles because they can be “exposed,” or resolved, into two or more clauses by fully stating the clause that is implied by the word such as “only,” and so on. There are several kinds.
1) EXCLUSIVE PROPOSITION. An exclusive proposition is an occultly compound proposition in which a word like “only,” “alone,” and so on, implies an entire clause. Sometimes the word “only” excludes the predicate from everything else than the subject, as in the proposition “Only citizens are voters.” Here the word “only” restricts the applicability of “voter” to “citizens” and excludes “voter” from everything besides “citizens.” Hence, this proposition can be exposed to “Non-citizens are not voters; (at least some) citizens are voters.” The proposition “Only citizens are voters” is a sort of contrapositive of the A proposition “All voters are citizens” (notice the interchange of the subject and predicate) and, at least as far as its logical form is concerned, is perfectly equivalent to it. (Recall what was said about the equivalence of various logical forms when we studied conversion, obversion, and contraposition.)
Notice that the proposition “Only some houses are white” is different from the proposition given above. In this proposition the word “only” is affixed to the quantifier “some,” not to “houses.” Hence, this proposition does not mean that all white things are houses. This proposition is exposed to “Some houses are white, and some houses are not white.”
2) EXCEPTIVE PROPOSITION. An exceptive proposition is an occultly compound proposition in which the subject term is restricted in its application by words such as “except,” “save,” “but,” and so on. Notice that exceptive propositions are often equivalent to exclusive propositions. Thus, the exceptive proposition “None but (save, except) citizens are voters” is equivalent to the exclusive proposition “Only citizens are voters,” and both of these propositions are exposed to “Non-citizens are not voters; (at least some) citizens are voters.” The proposition “None but citizens are voters” is likewise equivalent to the A proposition “All voters are citizens.”
3) INCEPTIVE AND DESITIVE PROPOSITIONS. Inceptive propositions express the beginning of a thing, action, or state. Desitive propositions express the ending of a thing, action, or state. Akin to these are propositions expressing continuance in being or action; but such propositions have no special name.
“He began to smoke last month” is an inceptive proposition. It is exposed as follows: “He did not smoke before last month; he did smoke and continued to do so last month.”
“He gave up smoking” is a desitive proposition. It is exposed as follows: “He did smoke; then (for a while) he did not smoke.”
The fallacy of many questions is frequently incurred by proposing a question in the form of an inceptive or desitive proposition; for instance, “Have you finally begun to behave yourself?,” “Have you stopped beating your wife?,” and “How long will you continue that nonsense?”
4) REDUPLICATIVE PROPOSITION. A reduplicative proposition is an occultly compound proposition that expresses the special aspect of the subject by reason of which the predicate belongs to it. It does this by words such as “as,” “as such,” “in so far as,” “inasmuch as,” and so on. “As logicians, we are concerned with the transition from data to conclusion; but, as rational beings, we are concerned with the attainment of truth” is a reduplicative proposition.
A reduplicative proposition is true if the proposition would be true without the reduplication and if, besides that, the reduplicated formality is the reason why the predicate belongs to the subject. The proposition “As a swimmer, he plays the trombone well” is false, even if he is a swimmer and does play the trombone well, because his being a swimmer is not the reason for his playing the trombone well.
5) COMPARATIVE PROPOSITION. A comparative proposition is an occultly compound proposition in which we compare the way an attribute is present in one subject with the way it is present in another; for instance, “John is bigger than James.” This proposition can be exposed to “John has size; James has size; the size of John is greater than the size of James.”