Abstract of Logic, Book 1 · Chapter 5
CHAP. V. Of Quantity.
Ax. 1. AN Accident is a being inherent in a Subſtance.
That is, ſo as that it can no ways exiſt ſeparate from it. Hence follows, that,
I. An Accident cannot exiſt without a Subject.
II. Cannot paſs from one Subject to another.
III. Cannot inhere in another Accident. Of which more is to be philoſophiz'd in the Metaphyſicks.
Ax. 2. Quantity is an Accident which hath by it ſelf Part out of Part.
In which three things are attributed to Quantity: 1ſt. To have Parts; and therefore God, Angels, Human Souls, Points, Unites, &c. are neither Quantity, nor Parts of Quantity, becauſe not conſiſting of Parts. 2dly. To have Part out of Part; that is, to have Parts not in Eſſence only, but alſo in Scite and Space different: For there are two kinds of Parts: Some together, and mutually penetrating each the other; as Matter and Form: Others not, but are different in Scite, as Head, Breaſt, Body, Limbs, &c. And ſuch as theſe are requir'd in Quantity. I ſaid Part out of Part, rather than Parts, becauſe Quantity may have but two, as in the Number Two. 3dly. To have Part out of Part by it ſelf. Becauſe a Corporeal Subſtance, and every Accident inhering in it, hath Part out of Part; but by reaſon of Quantity, not by it ſelf: But, Quantity, as Magnitude, and Number, and Time, have Part out of Part, and that by themſelves.
Ax. 3. Quantity is either continu'd or diſcrete.
Ax. 4. Continu'd is that whoſe Parts are connected together by one common Term.
Ax. 5. Diſcrete, whoſe Parts are not connected by one common Term, and is nothing elſe but Number.
Number uſes to be divided into Number numbering, and Number numbred. Number numbering is nothing elſe but Number in the Abſtract, or a Collection of Unities it ſelf, as two, three, &c. Number numbred is only Number in the concrete, or the things that are to be numbred, as Two Men, Three Horſes, &c.
Ax. 6. Quantity continu'd, is either Magnitude or Time.
Ax. 7. Magnitude is a Permanent Quantity.
Ax. 8. Time a Fluent.
Ax. 9. Its Term is a Moment, or foreign.
That Quantity is ſaid to be permanent which conſiſts of Parts having a Poſition amongſt themſelves, or whoſe Parts exiſt together, and of which each may be ſhewn, where ſeated, and to which of the other Parts it ſticks or coheres. But the Parts of Magnitude exiſt together, and each of them may be ſhewn where it is ſeated, and to which of the other Parts it coheres. But the Parts of Time have no Scite, becauſe they conſiſt in a continual Flux. Nor have the Parts of Number any Poſition, becauſe they are no where ſeated, neither do they cohere. Yet the Parts both of Time and Number have an Order amongſt themſelves, by which ſome are before others, &c.
Ax. 10. Magnitude is either a Line, or a Superficies, or a Body.
Ax. 11. A Line is a Magnitude one way diviſible.
Ax. 12. Its Term is a Point.
Ax. 13. A Superficies is a Magnitude, and two ways diviſible.
Ax. 14. Its Term is a Line.
Ax. 15. A Body is a Magnitude three ways diviſible.
Ax. 16. Its Term is a Superficies.
Ax. 17. A Term is an Extremity or Bound.
A Line is ſaid to be one way diviſible, becauſe it is a meer Length without Breadth or Depth, as an Ell, a Furlong, a Mile. A Superficies two, becauſe Length and Breadth, without Depth; as an Acre of Land. A Body three; that is, into Length, Breadth, and Thickneſs; as a Cube, a Sphere, &c. For altho' a Body elſewhere ſignifies a Subſtance compos'd of Matter and Form, yet in this place it denotes nothing elſe, but Magnitude or Quantity every way diviſible in the Abſtract.
Nor are we yet to imagine a Longitude is to be found without Breadth, or a Breadth without Thickneſs: For theſe things are not really ſeparate, but diſtinct only in the Mind.
Ax. 18. To Superficies is reduc'd Place.
Place is the next Superficies of the Body containing, as the next Superficies of the Cask is the place of Wine, &c.
Ax. 19. The Notes of Quantity are theſe Three: Firſt, Quantity has not its Contrary.
That is, By it ſelf: For if Quantity be ſaid to be contrary to Quantity, it is becauſe of its Quality adjoined; as when the Winter Seaſon is ſaid to be contrary to the Summer, becauſe of the Cold and Heat.
Ax. 20. Secondly, Quantity receives not more and leſs.
That is, Is not intended or remitted; but it is extended and contracted.
Ax. 21. Thirdly, Things are ſaid by Quantity to be equal or unequal.
I. For Equality and Inequality are Relations agreeing to things on the account of Quantity.
II. Hitherto of Quantity, properly ſo call'd, which, becauſe contain'd in this one Category, is wont to be call'd Praedicamental. There is alſo another Quantity improperly ſo call'd, which conſiſts not in the Extenſion of Parts, but in the Perfection and Vertue of every thing. Hence uſes it to be call'd, The Quantity of Perfection, and Quantity of Vertue. For the Eſſential Perfections of Things and Vertues are compos'd of divers Degrees, as, the Quantity of a Heap or Mole of ſeveral Parts. This, becauſe diffus'd almoſt through all the Categories, uſes to be call'd a Tranſcendental Quantity.
III. To theſe may be added the Precepts which Ariſtotle gives us, Book IV. of his Metaphyſicks, Cap. 13. Of Quantities, ſays he, ſome are by themſelves, others by Accident. Thoſe are ſaid to be Quantities by themſelves, in whoſe Definition is put Quantity. And theſe are either Quantities, foreign, that is, according to their Eſſence, as Line, Superficies, and thoſe other things which we have before-mention'd: Or foreign, that is, Affections of thoſe things which may be call'd Quantities according to their Eſſence, as Multum, Parum, Magnum, Parvum; that is, Much, Little, Great, Small, &c. And the like if taken foreign, that is, abſolutely. For if foreign, that is, compared one with another, they belong to the Category of Relation.
IV. Quantities by Accident are ſaid two ways, Firſt, thoſe which are ſaid to be Quantities upon the account of the Quantity in which they are, whether extended with the extenſion of the Subject, as, Whiteneſs in the Wall; Or not, as, Muſick in a Man. Secondly, Thoſe whoſe Diviſibility ariſes from the Diviſibility of other things, as that of Motion, &c.