The Second Part of Logick

    Wherein is considered the nature of a proposition it’s kinds and affections

    Cap. 1. of Judgement or Proposition its Definition &c.

    In the Preceeding part we considered the simple notions of things, and discussed the natures and properties thereof, it follows that we compare them, one with the other, and explain how they agree and disagree among themselves, which is to affirm or deny, and in one generall name is termed to Judge.

    This judgement is otherwise termed Proposition, and from what hath been already said, it is manifest that Proposition is a certain sentence declaring something true, or false;—which manifests 2 things.

    1. That there must be two terms, The one that of which something is affirmed or denyed, which is called the subject; The other, that which is affirmed or denyed, which is called the predicate, or attribute.

    2. That these 2 terms be conjoyned or separated by the mind; for otherwise this would be simple perception or apprehension, which is the first operation of the mind and consequently belongs to the first part of Logick.

    These two terms are conjoyned or separated by the verb substantive [est] which is termed the copula or vinculum of the Proposition, because the 2 parts are connected there by: when the verb is solitary, it betokens affirmation, when it hath the particle [non] annexed to it, then it betokens negation.

    Although it is necessary that every proposition consist of these 3 things, yet may a proposition be fully contained in 2 words, or in one.

    Men for the Compendiousness of Speech have found out very many words which signifie both the affirmation, i.e. that which the verb substantive denotes and the attribute, or something which is predicated, of this number are all those verbs which are called substantives: Thus Deus existit, i.e. est existins. Deus amat homines, i.e. est amans homines:16 solitary (as when I say cogito, Ergò Sum) ceases to be purely substantive; because then the most general of Attributes [ens] is annexed to it, for ergò sum here is just as much as ergò sum ens, or ergò sum aliquid.

    Among the Latines one word may constitute a Proposition, since it may Include in it besides the copula both a subject and a predicate; Thus veni, vidi, vici, do constitute 3 entire axioms or propositions; and the latine word (sum) contains as much in it as ego sum ens17 where both the subject and predicate are proposed and connected by the vinculum or copula [sum].

    Cap. 2d: Of a Proposition it’s division.

    A Proposition may divers ways be distinquished, according to the different considerations which it may pass under, for if not consider it as to it’s substance, it may be divided into simple & complex; if we consider it as to it’s quality, it may be divided into true and false; affirmative and negative; and if it be considered as to it’s quantity, we may then divide it into universal, Particular and singular, all which considerations we shall pass on Proposition and distribute it according to each respectively.

    If we respect the substance of proposition, or consider it as genus, it may be divided (as we said before) into simple & compound.

    A simple proposition is that which besides the copula consists only of one subject and one predicate, thus if I assert that man is an Animal, the subject is one viz. man; the predicate is likewise one viz Animal.

    A simple proposition is either purely simple or complex.

    A Proposition purely simple or incomplex is a proposition which contains in it besides the copula nothing but an incomplex subject and predicate: as in the forementioned instance, man is an Animal.

    A complex proposition is a proposition which contains in it besides the copula a subject and predicate one of which at least is a complex term including another proposition in it which we may term an Incident proposition.

    This incident proposition, when it falls on the matter of the main proposition (for sometimes it falls on the form thereof, as we shall see afterwards) is part of the subject or predicate conjoyn’d there with by the pronoun (qui) the nature whereof is so to knit many propositions as that they will all grow into one propositon: Thus when our Saviour saith, ille, qui facit, voluntatem patris mei qui in coelis est, regnum coelorum possidebit,18 the subject of that proposition contains two other propositions which are conjoyn’d by the pronoun qui, and so made parts of one subject; otherwise then when I say, bona et mala à deo proveniunt,19 for they I make truly two subjects, since I was well say, as mala as bona, that it does provenires à Deo.

    And it is all one whether we deliver these propositions by noun adjectives or participles without any verb and pronoun, or by a verb and pronoun, since it is the same thing to say, Deus invisibilis creavit mundum visibilum, as to say Deus qui est invisibilis creavit mundum qui est visibilis; for in either expressions it is not primarily asserted Deum esse Invisibilem, or mundum esse visibilem,20 but these two things supposed or taken for 2 propositions which were before asserted, we now only affirm hunc Deum Creasse hunc mundum.

    These complex propositions are of 2 sorts since the complexion (if I may so term it) may fall either on the matter of the proposition, i.e. on that subject or predicate, or each, or on the form; i.e. the verb.

    The complexion falls on the subject when the subject is the complex term; as Deus qui est invisibilis Creavit mundum.

    Beatus ille qui procul negotiis,

    utprisca gens mortalium,

    paterna rura bobus exercet suis

    Solutus omni Fanore.21

    In this last proposition the verb [est] is understood, beatus is predicated, all the rest is subjected.

    The complexion falls on the predicate, when the predicate is the complex term; as here, Deus creavit mundum qui est visibilis.

    Sum pius Æneas fama super æthera notus.

    The complexion falls both on the subject and on the predicate, when each is a complex term: as in this proposition, potentes qui pauper es opprimunt à Deo punientur, qui oppressorum protector est.22 Also in this,

    ille ego qui quondam gracili modulatus avenâ

    Carmen et egressus Sylvis, vicina coegi

    ut quamvis avido parerent arva colono:

    gratum opus agricolis; at nunc horrentia martis

    arma virumq cano Trojæ qui primus ab oris

    Italiam fato profugus, lavinaq venit

    Littora.23

    Here, the 3 first verses with half of the 4th are the subject of the proposition, the remainder is the predicate, the affirmation being included in the verb cano.

    These are 3 ways whereby propositions may be complex in respect of their matter, i.e. either of their subject or predicate.

    The complexion is said to respect the form or copula, when an incident proposition or term conjoyn’d with a proposition affects it’s form, i.e. the affirmation or negation noted by the verb (est) as, when I say, ego assero terram esse rotundam, ego assero, is an incident proposition and part of the main proposition; yet is it evident that it neither affects the subject nor the predicate, because it changes nothing in them, they being conceived after no other manner then they would have been had I only said, Terra est rotunda; so that the incident proposition here falls only on the affirmation which may be expressed two ways, viz: either by the verb (est) as it is ordinarily, or more expressly by the verb (assero).

    After the same manner it is in these forms of speech, nego; verum est, non est verum, also when to a proposition there is conjoyned a reason propping and supporting the proposed assertion; as here, Rationes Astronomicæ convincunt Solem esse terrâ multò majorem: For the first part of the proposition is only the ground of the affirmation:24

    But here we must note that of these propositions there are some which have an ambiguous sense and ought to be understood diversly according to the different intention of the speaker: for if I should say, omnes Philosophi docent res graves spontè deor sumferri;25 and my intent should be only to show, that heavy bodies naturally tend downwards, then the first part of the proposition will be only incident; but if on the contrary I should propose this as the opinion of Philosophers not approving of it, then this first part will be the principal proposition and the remainder only a part of the predicate; for so I should not affirm that heavy things naturally tend downwards, but only that all Philosophers do teach this doctrine: nor is it difficult to understand, that these two modes of this proposition to be understood do so change it, that two different propositions may be made, having 2 different significations; but it may evidently appear from what follows in which sense such a proposition ought to be understood; for if to the forementioned proposition (for example sake) I should subjoyn, sed lapides sunt res graves ergò sponte deor sum feruntur.26 It would thence be evident that I gave the first signification to it, and that the first part was only incident; Whereas on the contrary, if I should thus assume, sed hoc est falsum; ergò evenire potest ut omnes Philosophi doceant id quod est falsum,27 it is thence manifest that I gave the second signification to it, i.e. the first part will be the principal proposition and second will be only part of the predicate.

    Among complex propositions whose copula, not subject or predicate, is affected by a complex term, Philosophers have especially noted those which they have called modal, bee: the affirmation or negation in those is modyfied by one of the 4 modes: They are Possibilis, contingens, impossibilis, necessarius; and because every mode may be either affirmed or denied, as est possibile, non est possibile, and likewise joyned either with an affirmative or negative proposition, as Terra est rotunda; Terra non est rotunda, every mode may have 4 propositions, and all the modes together, sixteen.28

    Cap. 3. Of the nature of incident Propositions, which constitute a part of complex Propositions.

    Before we proceed to compound Propositions, it will not be amisse to propose some farther considerations concerning the nature of incident propositions which are parts of the subject and predicates in Propositions complex according to their matter.

    1. It was said that those are termed incident Propositions, whose subject is the pronoun Qui; as here, homines qui sunt creati ad cognoscendum et amandum deum; or, homines qui sunt pii; the term homines being taken away, that which remains is the incident proposition:29

    But here we must call to mind what we proposed in the 7th chapt of the forementioned part, (Page. 28) how that Additaments of complex terms are of 2 sorts; The first, which may be termed simply explicative, being, when the Additament does no ways change the Idea of the term, or when nothing is added which does not agree to the term in it’s full extension; as in the first example, homines qui sunt creati ad cognoscendum et amandum Deum.

    The Second, which we called determinative, being, when the Additament does not agree to the term in it’s full extension but restrains and determines the signification thereof; as in the second example, homines qui sunt pii:—whence it follows, that the pronoun is somtimes explicative, somtimes determinative.

    Now we are to note, that when the pronoun is explicative, the predicate of the incident proposition is affirmed of the subject to which the pronoun is referred (althô it happens only incidently in respect of the whole proposition) so that the subject it self may be put in the place of the pronoun, as we may see in the first example, for instead of saying homines qui sunt creati ad cognoscendum et amandum, we might have said homines sunt creati ad cognoscendum et amandum Deum.

    But if the pronoun is determinative, the predicate of the incident proposition is not properly affirmed of the subject to which the pronoun is related; for if as to this proposition, homines qui sunt pii, sunt misrecordes?30 I should put in the place of, Qui, homines, and say homines sunt pii, there would be a false proposition, for so men quatenus men31 would be said to be pious, which is not true, but in the other proposition homines qui sunt pii, sunt misrecordes, neither all men in generall, nor any men in particular are said to be pii; but the mind from an Idea of man and an Idea of piety joyn’d together, frames a total Idea; to which it Judges that the Idea of misrecordia does belong: and so the mind in the incident proposition only Judges expressly that the Idea of piety may consist with the Idea of man which Idea’s it may thence consider as united, and examine together what may agree to them from this union.

    2. We may note that propositions are somtimes found doubly or trebly complex, since they may consist of many members; every one of which maybe complex by it self: in such propositions, the incident propositions may also be many and of a different kind since in these the pronoun may be determinative, in those it may be explicative, as in this example, doctrina qua collocat summum bonum in voluptate corporis, quæ fuit tradita ab Epicuro, est indigna Philosophe.32 Indigna Philosophe is the predicate of this Proposition, the rest is the subject which is a complex term including 2 incident propositions the first whereof has a determinative Pronoun, the second and explicative pronoun for it’s subject.

    3. And lastly we may note, that to know the nature of propositions and to find out whether the pronoun in the incident propositions be determinative or explicative, we must mind more the sense then the words of the speaker.

    for complex terms occurr somtimes which seem to be incomplex or at {least} not only complex, as really they are, because part of the signification is only in the mind of the speaker, and so is understood and not expressed as appears from what was Cap. 7. part. 1. where it was hinted that nothing is more usual in common discourse than to signifye singular things by genericall words.

    Cap. 4. Of a Compound Proposition and the Species thereof.

    A compound proposition is a proposition whose either subject or predicate is (at {least}) 2 fold. It has 2 sorts; one, when the composition is expressed; The other, when the composition lies hid; called exponibilis.

    We may divide propositions of the first kind into 6 species; viz. copulative and disjunct; conditional and causal; Relative and discrete.

    Of Copulative Propositions

    Those are called copulative propositions which have more subjects or predicates connected by an affirmative or negative conjunction; i.e. per et, nee: for non or nec do act the same thing in these propositions which et does, if the negation be transferred from the nouns to the verb; as when I say, Scientia et divitiæ non faciunt beatum; here I do as fully couple Scientiam & divitias as I should, had I said Scientia et divitiæ faciunt hominem vanum.33

    Copulatives may be divided into 3 sorts.

    1. 1. When more subjects do occur: as here mors et vita sunt in manibus linguæ.
    2. 2. when there are more predicates: as here, homo habet vitam et rationem.
    3. 3. When there are more both subjects and predicates: as here, homo et angelus, existunt, et sunt creati.34

    ¶ Note, that the verity of these propositions does depend on the truth of both parts; for if I should say Fides et bona opera sunt ad salutem necessaria,35 the proposition would not be true unless each were necessary unto salvation; according to which, if I should say, fides et divitia sunt necessariæ ad salutem, the proposition would be false althô faith is necessary and that reason is because riches are not necessary.

    of Disjunct Propositions.

    Disjunct propositions are such propositions as contain in them a disjunct conjunction: as, Amicitia pares aut accipit, aut facit.36

    The verity of these propositions ariseth from a necessary opposition of the parts which admitts no tertium.

    Of Conditional Propositions.

    Conditional propositions are such whose parts are united by that conditional particle [si]. The former part wherein the condition is found, is called the Antecedent, the latter part the consequent:—Si anima est Spiritualis, this is the antecedent, erit et Immortalis, this is the consequent: This consequence is sometimes mediate and somtimes Immediate: mediate when there is nothing in the terms which conjoynes the 2 parts: as here, Si terra stataria est, sol movetur:—Si Deus est Justus, mali punientur.37 these consequences are good but yet not Immediate; bec: the parts having no common term are connected only by that which is in the mind and is not uttered, immediate, when the 2 parts are conjoyn’d by a common term, as here, Si mors est transitus ad vitam meliorem, mors est expectibilis.38—Vid. page 89. 90. cui tit Ars cogitandi.

    Here the truth of the propositions is not looked at, but only the truth of the consequence; for althô each part be false, yet if the consequence be legitimate, the proposition as conditional is to be accounted true, as here, si voluntas creata potest Impedire re voluntas Dei absoluta effectum. Sortiatur, Deus non est omnipotens.39

    Of causal propositions.

    Causal propositions are such which contain 2 propositions connected by those causal conjunctions, Quia, or ut.

    Væ divitibus, quia in hoc mundo reaperunt consolationem suam: Tolluntur in Altum, et lapsu graviors ruant:—Possunt, quia posse videntur. &c:40

    To these propositions are reduced those which are called reduplicatives: as,

    Homines quatenus homines sunt rationales;

    Reges in quantum reges soli Deo subsunt.41

    In order to the verity of these propositions it is requisite that one part be the cause of the other; hence it behooves each part to be true, for that which is false neither is nor can be a cause, yet each part may be true and yet false as causal. Thus a man may be unhappy and born under such a sign and yet his unhappiness not be because he was born under that sign:

    Of Relatives.

    Relative propositions are such which contain any comparison or relation.

    ubi est Thesaurus, ibi est cor:

    Qualis vita, Talis mors.

    Tanti es, quantum habes.42

    The truth of these propositions depends on the accuracy and goodness of the comparison or relation.

    Of discretes

    Discretive propositions are such in which there are divers Judgments, and this variety is noted by the particles, (sed, tamen,43 of the like nature.)

    fortuna opes auferre, non animum potest.

    et mihi res, non me, rebus submittere conor.

    cælum non animum mutant qui trans mars currunt.44

    The verity of these propositions depends on {the truth} of both parts and of the discretion used, for althô [each] part be true yet the proposition would be absurd, if there should be no opposition between the parts, as if I should say Judas erat fur et latro et tamen ægre tulit quid Maria Magdalæna unguenta pretiosa in christum dominum effuderit.45

    The second sort of compound propositions is such whose composition is more hidden: These may be reduced to 4 species. Viz: Exclusives, Exceptives, comparatives, Inceptives and desitives, of which we may read in Ars cogitandi, page 92 &c cap 8. p. 2d46

    Cap. 5. of A Proposition as to it’s quality & quantity:

    A Proposition with respect to it’s quality may be divided:

    1. 1. Into true & false.47

      A true proposition is that which pronounces concerning a thing, as it is: as when I say, Terra est rotunda, the proposition is true, because I assert that of the earth which does agree to it; Viz. a sphærical figure.

      A false proposition is that which pronounces concerning a thing otherwise then it is; as when I say, homo est animal irrationale.

      The same proposition cannot be true and false together, for thus there would be 2 contradictories which is most absurd.

      If it be objected, that this copulative proposition, Cladius et Theophilus astra contemplantur, is both true and false, because one of them does the other does not contemplate the starrs; The answer is most ready from what we before said concerning copulative propositions, viz. that their verity does depend on the truth of each part.

    2. 2. into affirmative and negative.

      An affirmative proposition is that wherein the subject and adjunct are conjoyn’d or do agree: as when we say, homo est animal, the proposition is affirmative bec: the predicate [Animal] is said to agree with the subject [homo]

      A negative proposition is that wherein the subjt &, attribute are disjoyn’d or do disagree, as in this proposition, homo non est brutum.

      The manner of the English speech differs from the Latine way as to this point, for [non est] in the latine tongue is the phrase of negation; whereas when we would deny, we do not say [It not is so] but still put the adverb after the verb, saying [it is not so]. Therefore to know whether the english proposition wherein [not] is contained, be affirmative or negative, we must consider whether, the adverb [not] bejoyned in signification with the verb or copula, or whether it be separated therefrom; if the adverb be joyn’d with the copula, then [is not] is as it were but one word and denotes only negation, if it be separated from the copula and joyned with the predicate, it then makes the predicate an indefinite term and so leaves the proposition affirmative, as thô there was no [not] in the proposition; as in this instance,

    Man is not—a stone: is neg:

    Man is—not a stone: is affirm:48

    And thus much concerning the quality of a Proposition.

    1. A Proposition with respect to it’s quantity may be divided (according to the difference of terms) into universal, particular and singular.
    2. An universal proposition is that whose subjt, as a common term, is prefaced with an universal sign; such as all—being affirmative; and no—being negative; for the term no includes in it negation besides universality: no man—all men—&c:
    3. A particular proposition, is when a common term, is limited by that determining sign or note [some] Whether it affirms, as here, aliquis amans est miser, or denies; as here, aliquis aulicus non est justus.
    4. A singular proposition is that, whose subjt is an individuum determined either by name, as when I say Aristotle is the prince of philosophers; or by sign, as when I say hic vel ille homo est Justus.49
    5. As for those propositions which are called Indefinite (viz. Such which have an universal term for their subject but note either of universality or particularity prefixed to that term, as here homo est animal, as to these propositions, I say) they are evermore to be accounted universal in disputes, and when used in common discourse or found among authors, they are to be accounted universal or particular propositions according to what the matter will allow, so that we need not constitute them as a fourth head of propositions.
    6. Althô a singular proposition does differ from an universal, in that whereas the subjt of an universal is a common term, of a singular, an individual term, yet it has a greater affinity with an universal then with a particular, because the subject in as much as it is singular is necessarily taken according to it’s full extension which is the cheif thing that is essential to an universal proposition, for though a proposition may be universal it signifies little whether the extension does comprehend more or fewer things, so that if it comprehends all that belong to the terms hence singular propositions in disputes are accounted universals: Therefore all propositions may be reduced to 4 kinds, being noted for the memory sake by the 4 vowels, a. e. i. o.
    7. A universal affirmative, as—omnis vitiosus est servus.
    8. E universal negative, as—nullus vitiosus est beatus.
    9. I particular affirmative, as—aliquis vitiosus est dives.
    10. O particular negative, as—aliquis vitiosus non est dives.50
    11. And that they may be kept the more firmly in our memories they are proposed to us in this latine distich.

    Asserit A, negat E, verum generaliter ambo

    Asserit I, negat O, Sed particulariter ambo.51

    Cap. 6. of the Opposition of Propositions having the same subjects and predicates.

    Among Propositions which have the same subject and likewise predicate, some are termed subalternates, some contraries, some subcontraries and others contradictories.

    Subalternates are such as agree in quality and differ in quantity, as, omnis circulus est figura—Quidam circulus est figura. These subalternates prove somtimes to be both true, and somtimes to be both false. True—as some circle is a figure, every circle is a figure, false—as some circle is a triangle; every circle is a triangle.

    Contraries are 2 universal propositions of a different quality: As, omnis homo est opulentus—nullus homo est opulentus.52

    These may both be false, but cannot both be true.

    Subcontraries are 2 particular propositions of a different quality: as, quidam homo est medicus,—quidam homo non est medicus.

    These may be both true, as, aliquis homo est Justus,—aliquis homo non est Justus, but cannot both be false; for if it be false,—aliquem hominem esse justum, it will necessarily be true, nullum hominem esse justum, bee: this proposition is contradictory to the former.

    Contradictories are 2 propositions which differ both in quantity and quality, which causes opposition in the highest degree as,—omnis homo est animal—Quidam homo non est animal. These cannot be both true nor yet both false.

    Some term the opposition an affection of propositions, and annex to it 2 more Viz. Equivalence and conversion, and accordingly do define

    Equivalence to be a reconciling these opposites by inserting the negative particle [non]

    Conversion is a changing of the subject & predicate the same quality remaining:—but it is enough that we have mentioned these things and therefore we here conclude this sixth and last chapter of the second part and passe hence to our Third part of Logick.