ART. I. -- NATURE OF JUDGMENT.
28. Judgment is the second operation of the intellect, by which it predicates the agreement or disagreement of the attribute with the subject.{1} -- By simple apprehension the intellect perceives the subject and attribute separately; but after this operation it compares them, and affirms or denies their agreement, that is, it forms a judgment. The intellect, by this second operation, perfects the first, which is initial and imperfect.
The chief division of judgments is that based on their nature, and embraces the two classes of a priori and a posteriori judgments.
An a priori judgment is one in which the agreement or disagreement of the ideas compared is necessary, and either is manifest or can beeome so from their mere consideration; as, "God is infinite."
An a posteriori judgment is one in which the agreement or disagreement of the ideas compared is not necessary, and can be known from experience alone; as, "Columbus discovered America."
A priori judgments are also called necessary, analytical, pure, metaphysical, absolute. A posteriori judgments are styled contingent, synthetical, empirical, physical, hypothetical.
29. The a priori synthetical judgment of Kant must be rejected. -- In his "Critique of Pure Reason," Kant lays down this third kind of judgment, the a priori synthetical. He holds rightly that all a priori or analytical judgments must fulfil three conditions: 1. The attribute must be included in the subject; 2. It must be necessary; 3. It must be universal. But he further maintains that such judgments as, "Every effect must have a cause," or "7 and 5 are 12," are wanting in the first condition. Now, every judgment implies the perception by the mind of the identity or diversity of the ideas compared. This identity or diversity can be apprehended either from the consideration of the ideas, and in this case the judgment is a priori or analytical; or from some extrinsic source, i.e., experience, and then the judgment is a posteriori or synthetical. Between these there is, therefore, no middle. Moreover, if the second and third conditions are fulfilled, evidently the first must also be fulfilled, since from it the other two result.
ART. II. -- THE PROPOSITION AND ITS ELEMENTS.{2}
30. A proposition is the expression of a judgment in words spoken or written. The elements of a proposition may be reduced to two, noun and verb. -- A proposition, as being the expression of a judgment, must contain as many terms as the judgment. But the judgment is composed of three elements: subject, attribute, and copula. To these three elements of the judgment correspond the three elements of the proposition: two terms, which express the subject and predicate or attribute, and the copula, which unites them. The subject is generally a noun, the attribute an adjective; the copula is a verb. The copula is called a verb, because the word (verbum) of our mind is not complete without a judgment, and judgment is formally constituted only by the copula. The verb "to be" is explicitly or implicitly the copula in every judgment and proposition, because by it identity of subject and attribute, or want of identity, is expressed, and every proposition predicates one or the other. The terms constitute the matter of the proposition; the copula, which gives being to the proposition, is its form.
The verb "to be," or the copula, is often contained in the predicate, as "I love God," which is equivalent to "I am loving God."{3}
Besides the noun and the verb, Grammar recognizes other parts of speech, as the pronoun, adverb, conjunction, etc.; but Logic is not concerned with these terms, because they do not constitute an essential element of the proposition, and because they serve only to represent, modify, or connect nouns or verbs.
ART. III. -- DIVISION OF PROPOSITIONS.
31. The division of propositions is the same as that of judgments. Hence a proposition is simple or compound according to the nature of the judgment expressed. A simple proposition is either simple incomplex or simple complex. -- A proposition being regarded in logic simply as the expression of a judgment, there are as many kinds of propositions as of judgments. But a judgment is simple or compound: simple when the relation is established between only one subject and one attribute; compound when there are several subjects or several attributes. When a judgment is simple, the attribute or the subject may be absolutely simple, or simple by reason of the connection between the parts which compose it; in the first case, the judgment is simple incomplex or categorical; as, "God is good:" in the second, it is simple complex; as, "He who loves not his neighbor, whom he sees, does not love God, whom he does not see." Propositions, then, considered logically, are simple or compound. Grammarians who consider in propositions chiefly the words of which they consist, divide them into simple, complex, and compound; but Logic is not concerned with these divisions, since it contemplates propositions solely in their relation with thought.
32. A categorical proposition, considered in respect to its quantity, is universal, particular, or singular, definite or indefinite; in respect to its quality, it is affirmative, negative, or infinitating; in respect to the mode or manner in which it asserts that the predicate belongs to the subject, it is modal. -- A categorical proposition may be divided in the same manner as the judgment which it expresses. Hence according to its quantity, that is, according to the extension of its subject, it is universal if the subject is universal; as, "All men are mortal:" particular if the subject is particular; as, "Some men are just;" singular if the subject expresses oniy one individual determinately; as, "Peter is just." A proposition may sometimes appear universal without in reality being so; as, "Men are deceptive." Propositions are called indefinite{4} when the subject is not affected by a determinate sign; as, "The Americans are enterprising;" and definite when the subject is affected by a determinate sign; as, "Some men are deceptive."
According to its quality, that is, according to the affirmation or negation indicated by the copula, a proposition is affirmative; as, "God is good:" or negative; as, "The soul is not mortal." If the negation does not affect the copula, but the predicate, the proposition is then said to be infinitating; as, "The human soul is not-mortal."
A proposition is absolute when it merely affirms the agreement or disagreement of subject and attribute; as, "God is just:" it is modal when it expresses the mode or manner in which the attribute is predicated of the subject; as "God is necessarily just." The attribute may be predicated of the subject according to four modes: necessary, contingent, possible, and impossible. There are, then, four kinds of modal proposition: as, "Man is necessarily rational;" "Man may be good;" "Man can be bad;" "Man cannot be an angel." The truth of a modal proposition depends on the mode according to which the attribute is predicated of the subject; thus the proposition, "Man is necessarily bad," is false.{5}
33. A compound proposition is either explicit or implicit. An explicit compound proposition is copulative, causal, adversative, relative, or hypothetical. A hypothetical proposition is conditional, disjunctive, or conjunctive. An implicit or exponible compound proposition is exclusive, exceptive, comparative, or reduplicative. -- A compound proposition consists of several propositions expressing several judgments which make but one by virtue of some logical bond established between them; as, "If you are good, you will be rewarded." The truth of a compound proposition depends not upon each of the judgments, but upon the connection between them; as, "If the soul is material, it is not immortal." A compound proposition is copulative when it has several categorical propositions united by the conjunction and or the like, expressed or understood; as, "Time and Truth are friends."
It is causal when it states the reason why the antecedent contains the consequent, by means of the particle because or a word of similar import; as, "He is proud, because he is rich."
It is adversative when it expresses some opposition between its members, by means of the particles but, nevertheless, etc.; as, "Virtue is persecuted, but it will be rewarded."
It is relative when it expresses some similitude between the propositions that compose it; as, "As life is, so death shall be."
It is hypothetical when it states something not absolutely, but with the proviso that something else be verified; as, "If you love me, you are my disciple."
A hypothetical proposition is conditional when, by means of the particle if, it unites two categorical propositions, one of which contains the reason or condition of the other; as, "If you will live piously, you will suffer persecution." The proposition that contains the reason is called the antecedent, the other is the consequent. When the several component members of a hypothetical proposition are united by the particles either -- or, or by or only, the proposition is disjunctive; as, "It is either day or night." But when a hypothetical proposition denies that two or more predicates can be affirmed of the same subject at the same time, it is conjunctive; as, "No man can serve both God and Mammon."
Besides these compound propositions proper, there are others really compound, though apparently categorical, and called exponibles. They are of four kinds: exclusive, exceptive, comparative, and reduplicative. The first is affected by an exclusive particle, as only, alone, or the like; as, "Virtue alone is praiseworthy;" and is expounded by the compound proposition: "Virtue is praiseworthy; nothing else is praiseworthy." The second is affected by an exceptive particle, besides, except; as, "All is lost except honor;" which is expounded thus: "Honor is not lost; all else is lost." The third is affected by a comparative particle, expressed or implied; as, "Gentleness effects more than violence;" which is equivalent to: "Gentleness effects something; violence effects something; the effect of gentleness is greater than that of violence." The fourth is a proposition whose subject is affected by a particle which repeats it, inasmuch as, as such, etc.; as, "Fire, inasmuch as it is fire, burns;" which is equivalent to this: "Fire burns, because such is its nature."
34. The propositions forming a compound proposition may be all principal, or some principal and others incidental. -- A compound proposition contains several independent judgments which may be expressed in several propositions; as, "Patience and meekness are virtues;" "Charity is meek and patient." That a compound proposition be true, all the parts which compose it must be true; thus the proposition, "Men and angels are mortal," is false.
A compound proposition may be resolved into several grammatical propositions either co-ordinate, i.e., simply in juxtaposition, as in the foregoing example, or into propositions some of which are principal and others incidental and explicative; as, "Sin, detested by God, sullies the soul;" which is equivalent to the two independent judgments, "Sin is detested by God," and "Sin sullies the soul." If the propositions joined to the principal one are restrictive, the whole proposition is not compound but simple.
ART. IV. -- PROPERTIES OF PROPOSITIONS.
35. There are three properties of propositions: opposition, conversion, and equipollence.
36. Opposition is the affirmation and negation of the same thing in the same respect.
37. Opposition is twofold, contradictory and contrary. -- Contradictory opposition is the repugnance between two propositions, one being universal and the other particular, or both being singular. Contrary opposition is the repugnance between two universal propositions.
Some recognize what is called Subcontrary opposition, which holds between two opposite particular propositions; but this is not true opposition, since the subjects of the two propositions may express different things. Still less can we consider as opposition that which is called Subaltern, and which holds between two affirmative or two negative propositions, the one being universal and the other particular. In this case there is no opposition, since there is no affirmation and negation of one and the same thing in one and the same respect. Of the four propositions: "All men are wise," "No man is wise," "Some men are wise," "Some men are not wise," the first and second are contraries; the first and fourth, the second and third, contradictories; the third and fourth, subcontraries; the first and third, the second and fourth, subalterns.
Representing the universal affirmative proposition by A, the universal negative by E, the particular affirmative by I, and the particular negative by 0, we have the following diagram:
38. Neither contrary nor contradictory propositions can both be true, for one of the contraries or contradictories affirms what the other contrary or contradictory denies.
Of two contradictories one must be true and the other false, since each affirms or denies just enough to make the other false.
Contraries can both be false in contingent matter, because one not only affirms what the other denies, but states its extreme opposite.
Subcontraries can both be true, but cannot both be false, for then their contradictories would be true, and thus two contrary propositions would be true.
Subalterns can both be true or both false in necessary matter; as, "All men are mortal, Some men are mortal;" "All bodies are infinite, Some bodies are infinite;" or one may be true and the other false in contingent matter; as, "All men are rich, Some men are rich."
39. Equipollence is the reduction of a proposition to another equivalent in meaning. -- Two propositions, though apparently different, may have the same meaning; as, "Every man is a rational animal; No man is not a rational animal." These two propositions are said to be equipollent.
40. When the subject of a proposition is affected by a negation, the proposition becomes equivalent to its contradictory; as, "All men are wise; Not all (some) men are wise, and therefore, Some men are not wise."
When the predicate of a proposition is affected by a negation, the proposition becomes equivalent to its contrary; as, "All men are wise; All men are not wise, or, No man is wise."
When the predicate of a particular proposition is affected by a negation, the proposition becomes equivalent to its subcontrary; "Some men are wise; Some men are not-wise, or Some men are not wise."
When both subject and predicate of a proposition are affected by a negation, the proposition becomes equivalent to its subaltern; "All men are wise: Not-all men are not-wise, or Some men are wise. " -- These rules result from what has been said concerning the nature and rules of opposite propositions.
41. Conversion is that change in a proposition by which, without altering its truth, the predicate is made the subject, and the subject the predicate. -- The proposition to be converted is called the convertend; the proposition resulting from conversion, the converse.
42. Conversion is simple, per accidens, or by contraposition. -- The conversion is simple when, the predicate being made the subject, the proposition retains its quantity; as, "No man is a plant; No plant is man."
It is per accidens, when, the predicate being made the subject, the proposition changes its quantity; as, "The Americans are men; Some men are Americans."
It is by contraposition when, the predicate being made the subject, finite terms are changed into infinitating; as, "All men are animals; All not-animals are not-men; Only animals are men."
In effecting a conversion, the quality of the proposition must not be changed, otherwise there would be no conversion, but simply opposition. -- The following are the rules for conversion: Universal negative propositions and particular affirmatives are converted simply; as, "No man is an angel; No angel is a man.".
Universal affirmative propositions and universal negatives are converted per accidens; as, "All men are mortal, Some mortals are men."
Particular negative and universal affirmative propositions are converted by contraposition, that is, by obverting or infinitating the proposition, and then converting simply; as, "Some men are not just; Some unjust beings are not not-men; Some unjust beings are men."{6}
{1} Or with St Thomas That action of the intellect by which it compounds or divides by affirming or denying.
{2} As Logic has to do with mental operations and their signs only in so far as they contain or express truth or falsity, so of all the kinds of sentence of which the grammarian treats, it is concerned with the declarative alone. This kind of sentence is called in logic a proposition.
{3} The use of the term predicate in Logic must be carefully distinguished from its use in Grammar. In logic the attribute never includes the copula. Moreover, the copula, as the formal element of the judgment, must be in the present tense, indicative mood. Hence such propositions as, "The Martyrs suffered for the Faith," must he resolved into the equivalent, "The Martyrs are persons who suffered for the Faith."
{4} A singular proposition is the most limited case of the particular proposition. An indefinite proposition is universal or particular according as it expresses a necessary or a contingent truth.
{5} The mode always affects the copula in true modal propositions. They are always capable of being reduced to another proposition of which the word or words expressing the mode is the predicate. Thus, Man can be bad is equivalent to "That man be bad is possible."
{6} The rules of conversion are expressed in the mnemonic couplet:
Simpliciter fEcI convertitur, EvA per accid (ens),
Ast O per contrap(ositionem). Sic fit couversio tota.
The capital letters in the words fEcI and EvA of the first line and O of the second line stand for the different kinds of proposition to be converted, as explained on page 26.