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Atque haec de communibus axiomatis affectionibus, spe∣cies sequuntur.
VVE have hitherto heard of whatsoever is 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 to an axiom in general: for though 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, and 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 belong
onely to the rules of Art, yet because they may be sim∣ple or composite axioms, ergo, they are generally to be taught to them both: the judgment moreover of such axioms was prima verissimaque scientia. Prima, because that was first, and per se true, and most true, because all other deducts do so far forth approve themselves true, as they agree to the first, and these first rules are few, therefore they come nearest to God who is but one, and are next to his wisdom: o∣thers, which are deducts, may be many, and they come next to the first rules: we have among us a distin∣ction of doctrine and use, doctrina is properly the first rule of Art, and use is the application thereof, or the special deducts gathered from the first. Others I find take doctrina for the first part of Divinity, and Use for the special practice of a rule of Art, but they are deceived, and speak improperly: and all the rules that Kickerman saith are wanting in Ramus, are no∣thing but the practice of a rule, that is 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, and they are infinite. As posita causa ponitur effectum, this ariseth from the definition of causa, and it is onely true, where the cause is brought as a third ar∣gument in a syllogism, and otherwise we have no use of it, and having handled all that is general to an axiom, now we come to the species, Atque haec de com∣munibus, &c. This is a transition not from one part of an axiom to another, for those things that we heard of before touching an axiom, are but adjuncts to an axiom, therefore must not be severed from their subject: but because these have taken up two Chap∣ters, and so continued the doctrine of axioma long, why we may have forgotten our selves, thinking we have heard of the species already? no, saith Ramus, we come but now to the species.
Disposition we heard did dispose arguments ei∣ther firstly, or at the second hand, in an axiom they are disposed either one with one, or one with more, or more with more; if one be disposed with one, so that there be but two sides, as it were playing at two hand ruffe, then it is a simple axiom: and from this simple disposition of the arguments, it is called sim∣plex, compositum contra: so that this double disposi∣tion of arguments makes this distribution, whereas affirmatum, negatum, and the other adjuncts before, rather looked at the band, then at the disposition of the arguments: so that axiomatica dispositio is simplex in respect of the simple disposition of the arguments that are disposed therein.
Simplex is first, because there cannot be a compo∣site axiom, but there will be a simple axiom, and the composite is as it were a manifold simple.
He defines it from the band, not that it ariseth from thence, but because a verb fals out to tie an axi∣om to one.
For Invention did handle arguments severally, but in axioms they are laid together with a cyment or verb.
Object. Why doth he call it a verb? we have not heard of Grammar yet, doth he mean that verb which is taught there?
Answ. No: but his meaning is, that the parts of this axiom are tied together by that which if it be ut∣tered is a verb: so that verbum here is a metonimy of the adjunct from the subject, verb being put for
that whose name will be a verb. If a man would lay bricks with bricks, to have them hold together, he must have morter; and if he would fasten two peices of wood together, he must have a nail, or a pin of wood: for as the morter is to the bricks, and the nail or pin to the wood, such is this vinculum here spoken of to the arguments.
He cals it vinculum, because the vinculum holdeth the arguments together in a kind of composition: imitating God therein, who hath tied things in nature with an affection: and indeed to speak the truth, it springs from the affection that is between the two ar∣guments disposed.
Before we heard in an axiom, that affirmatum was Quando vinculum ejus affirmatur, negatum contra: why then a simple axiom having the band affirmed must be affirmed & contra: so that this is nothing but a spe∣cial application to this kind of axiom, of that which was before taught generally to all axioms: and that which is special here is, that it is the verbum that is denied or affirmed, which was vinculum before: and this commendation indeed is chiefly for contradicti∣on: for if there be contradiction here, the verb must be affirmed, and denyed: ut ignis urit: ignis est antece∣d••ns, urit consequens: here he cals the argument go∣ing before the verb antecedens, and the argument fol∣lowing the verb, consequens: others call them sub∣jectum, and praedicatum, but he is not pleased with their names, because subjectum is properly an argu∣ment in invention, therefore if it should be used here, it would breed confusion: and not onely subjects
and predicates are disposed here, but all other argu∣ments, therefore he rather keepeth the general terms shewing so much: again, they are fitter, because here we are in disposition, ergo, there must be an argument to go before the vinculum, and another to so low. Now we use these terms also in a composite axiom, but they are more proper here. The Aristotelians used their terms subjectum and praedicatum onely in a sim∣ple axiom, for they had no composite axioms, but a connex, as we shall hear afterward.
Prima by nature, not otherwise, because we can∣not make a composite axiom of more arguments with more, but there will be more lines: here in a sim∣ple axiom there is but one line, and in a syllogisme there will be a triangle, the demonstration may be this.
A simple axiom.
A composite of one to more
A composite of more to more.
A Syllogisme.
Ramus doth commorari in telling us the use of a simple axiom, and he tels us all arguments may be disposed therein, but plenae comparationes, and
Plenae distributiones, for so he means, else homo est animal is a distribution, and yet a simple axiom: but otherwise these will evermore be a composite axiom.
Not but that consentanea may be denied, and dissen∣tanea affirmed, for we heard before that the same axi∣om might be affirmed and denied, but thus they ought to be disposed, consentanea affirmando, dissentanea ne∣gando: now here by consentanea he doth not mean onely causa, effectum, subjectum and adjunctum, but also those that do arise from them, even all that may any way agree: as in like sort by dissentanea he means also all them that do arise from them, or that do any way disagree: but here we are to know, that this is not any rule of Art, but onely a commoration, ap∣plying that here in special, which he taught before. Now this disposition is easie: but here sometime the band, and the consequent part grammatically uttered will be the same, as ignis urit: now we come to the affections of a simple axiom, which belong not to a composite.
This is a distribution of the subject into the ad∣juncts, and though a composite axiom may be gene∣ral, or special, yet there we do not look after it: so that composite axiomes in a syllogisme may make a simple syllogism, being considered not as composite, but as the arguments are simply disposed.
This term comes of genus, not that this axiom con∣sists alwayes of those arguments genus and species; but he means that commune which we hear of in
Grammar, and yet notwithstanding the antecedent part may be common, and the axiom may be proper, ergo, he rather keeps that term generale, then commune, though it be a hard trope. Now in a general axiom we are to observe these three things, first an antece∣dent that is common, secondly, a common consequent, thirdly, a general attribution of them, for else it might be a special axiom: so that generality and speciality belong to an axiom, and are not to be sought for in the doctrine of arguments.
He is careful to teach us contradiction, because there is a mean matter, because there is no dispute where there is no contradiction, ergo, he teacheth us the contradiction of a simple axiom, and now of a ge∣neral axiom which will not alwayes divide truth and falshood, sed contingentium utraque pars, &c. that is, when we contradict a general by a general.
Why saith he non contingentium? because these non contingentia are such as fall out, peradventure impossibilia, as in this example. Omne animal est ra∣tionale, nullum animal est rationalia, he could not well call them necessaria, nor possibilia, because they may be denied, whereas an impossible axiom should be affirmed.
It is called axioma speciale, not in respect it hath a species alwayes disposed in it with a genus, but in re∣spect it is more special than the general quando conse∣quens, &c. Consequens indeed is the chiefest part in
an axiom, and is commonly the argument that is brought to argue: not the antecedent, he doth not say consequens commune: because it may be either common, or proper, it is no matter whether of them it be.
Omni and non omni are contradictory, now omnis dicitur de tribus ad minimum, saith the Schools, ergo, if omnis be given generally to all in a general axiom, then non omnis may be given to one, as it is a special axiom: omnis indeed is the sign of a general axiom, but where it cannot be had, there the axiom is special: non omni, that is to the antecedent that cannot have omnis put before it.
Attribuitur, in an affirmed axiom, it may seem that there is attributio: but in a denied axiom rather ab∣negation: but attribuitur both here and in a general axiom must be taken more generally for the same that disponitur is, whether it be by way of affirmation or negation.
So that if our contradiction with any body be a special axiom, then we may be assured, that the one part is false, and that there is contradiction in it.
Particulare doth intimate a common, for nothing can be parted but a common, and it is so called, be∣cause though the antecedent be common, yet it takes but part of it.
Here is a fault in the print, for if it should be com∣muni, because the consequent (as we heard before)
may be common or proper: but the antecedent must be common; but here is a particularis attributio. Now a general axiom is before a special, because it is more large. Homo est doctus is a particular axiom, for antecedens is common, now it differs from a gene∣ral, first in that a general must have a common con∣sequens, this may have a common or proper; second∣ly, a general must have a general attribution, this is a particular one.
Therefore in like sort generali axiomati specialiter contradicitur, and then dividit verum a falso, for con∣tradict a general by a particular, and it will divide truth and falshood; so that a general axiom hath a double contradiction, one when we contradict a ge∣neral by a general, and another when we contradict a general by a particular.
This axiom doth require first a consequent be it proper or common: secondly a proper antecedent: thirdly an attributio. Now he means by proprium, not that the antecedent should always be a proper name, for an axiom of genus and species may make a proper axiom.