Aristotel - Druga Analitika - Sadržaj 1. Knjige Na Engleskom

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ARISTOTLENOTES ONPOSTERIOR ANALYTICS (I.1-10)

By Dr. Dave YountMesa Community College

May 2013

Introduction

The following are detailed notes of AristotlesPosterior Analytics(Book I, chapters 1-14, and Book II, ch.19), which were part of a Summer Project Grant, approved by the Maricopa County Community CollegeDistrict. I would like to thank them for allowing me to spend time and effort on this research.

Please be aware that in what follows, these are actual sentences of Aristotles text in some cases, but thisis not the whole text. More importantly, I have deletedmany unnecessary words, phrases, sentences, and/orexamples (when 3 would suffice), and addedchapter headings (that should be very helpful), numbers, underlining,italicizing, and so on, to make the text easier to understand. I have also added any notes or objections I mayhave thought about along the way, which are underlined and highlighted in blue. I have also moved hisexamples nearer to when he describes a principle (sometimes he says, e.g., X is Y and not-Y and then gives anexample of not-Y for several sentences, until finally getting to an example of Y; I moved the example to make itmore easily accessible).

In addition, these notes are in no way to be thought of as being a substitute for reading all of thePosteriorAnalyticsfor oneself; these notes are merely what I thought was most important, and put into a form that I couldmore easily understand.

Lastly, despite all these disclaimers, I do sincerely hope that these notes are of some value to the reader.

Posterior AnalyticsBOOK I, Chs. 1-14

1 All Teaching/Learning Comes from Knowledge that Already Exists; Two Kinds of Awareness;(71a-b). All teaching and all intellectual learning come about from already existing knowledge. Mathematicalsciences (and every other art) are acquired in this way. Arguments (deductive and inductive) proceed in this way;

both produce their teaching through what we are already aware of (deductive arguments get their premises asfrom men who grasp them; inductive arguments prove the universal through the particular's being clear). [Andrhetorical arguments also persuade in the same way either through examples (induction) or throughenthymemes (deduction).]

It is necessary to be already aware of things in two ways: (1) of some things we must already believe thatthey are (e.g. of the fact that everything is either affirmed or denied truly, one must believe that it is); and (2) ofsome we must grasp what the thing said is (e.g. of the triangle, that it signifies this). Of others, we must bealready aware of both (1) and (2) (e.g. of the unit, both what it signifies and that it is).

You can become familiar by already being familiar with some things but gaining knowledge of the others

at the very same time (i.e. of whatever happens to be under the universal of which you have knowledge). E.g.,that every triangle has angles equal to two right angles was already known; but one can discover that there is a

triangle in the semicircle here at the same time as the induction.Before the induction or a deduction, in a way you know and in a way you do not. If you did not know ifa triangle is simpliciter[= in itself], how did you know that it has two right angles simpliciter? You know it

universally[DY: Does Aristotle meant that you know the kind of thing a triangle is (since that is what a universalis, for him)? I am not sure what universally means here, exactly.] but not simpliciter. (Otherwise the puzzle intheMenowill result; for you will learn either nothing or what you know.)

One should not attempt to solve it this way: Do you (or don't you) know of every pair that it is even?

When you say, Yes, they bring forward some pair that you didnt think was a pair or that it was even. Theysolve it by denying that people know of every pair that it is even, but only of anything of which they know that itis a pair. But they know what they have demonstration of and which they have their premises of; and they gotthem not about everything of which they know that it is a triangle or that it is a number, but of every number


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and triangle simpliciter. For no proposition of such a type is assumed (that what you know to be a number orwhat you know to be rectilinear), but they are assumed as holding of every case. [DY: Is holding of every casethe universal knowledge he mentioned above?]

Nothing prevents one from in a sense knowledge and in a sense being ignorant of what one is learning;what is absurd is not that you should know in some sense what you are learning, but that you should know it in

the way and sense in which you are learning it.

2 Knowledge Simpliciter; Knowledge through Demonstration; Definitions of Proposition,Dialectical, Contradiction, Posit, Axiom, Supposition, and Definition Itself; Must Be Aware ofthe True Premises of a Demonstration and More Certain of Them Than the Conclusion (71b-72b). We know a thing simpliciterwhenever we think we are aware both that the explanation because of which the objecisis its explanation, and that it cannot be otherwise. (Those who do not know think they are themselves in such

a state, and those who do know actually are.)We do know through demonstration. By demonstrationI mean a scientific deduction; and by

scientific I mean one in virtue of which, by having it, we know something.If knowledge is as we posited, demonstrative knowledge necessarily depends on things [starting

points/premises] that are true, primitive, immediate, more familiar than, prior to, and explanatory of theconclusion (in this way the principles will also be appropriate to what is being proved). There will be deduction

even without these conditions, but there will not be demonstration; for it will not produce knowledge.The premises must be true because one cannot know what is not the case (e.g. that the diagonal is

commensurate). They must depend on what is primitive and non-demonstrable because otherwise you will notknow if you do not have a demonstration of them; to know that of which there is a demonstration non-accidentally is to have a demonstration. They must be (a) explanatory (we only know when we know theexplanation), (b) more familiar, and (c) prior (if they are explanatory, and we are already aware of them not onlygrasping but also knowing that they are).

Things are prior in two ways (by nature and in relation to us) and more familiar in two ways (morefamiliar and more familiar to us). Prior and more familiar in relation to us is what is nearer to perception; priorand more familiar simpliciteris what is further away. What is most universal is furthest away, and the particularsare nearest; and these are opposite to each other.

Depending on things that are primitive is depending on appropriate principles; the same thing isprimitive and a principle. A principle of a demonstrationis an immediate proposition (one to which thereis no other prior). A propositionis the one part of a contradiction (one thing said of one); it is dialecticalif itassumes indifferently either part, and demonstrativeif it determinately assumes the one that is true. (Astatement is either part of a contradiction.) A contradictionis an opposition that excludes any intermediate ofitself; and a contradiction contains (i) an affirmation (saying something ofsomething), and (ii) a denial (sayingsomethingfromsomething).

A positis an immediate deductive principle if one cannot prove it but it is not necessary for anyone whois to learn anything to grasp it; an axiomis an immediate deductive principle that is necessary for anyone whois going to learn anything whatever to grasp. A suppositionis a posit that assumes either of the parts of acontradiction (that something is or that something is not). A definition is a posit that assumes neither part of a

contradiction. [A definition is a posit (for the arithmetician posits that a unit is what is quantitatively indivisible)but not a supposition (for what a unit is and that a unit is are not the same).]

Since one should both be convinced of and know the object by having a deductive demonstration, andsince this is the case when the premises of the deduction are true, one must already be aware of the primitives(either all or some of them) and be better aware of them. If we know and are convinced because of theprimitives, we both know and are convinced of them better, since it is because of them that we know and areconvinced of what is posterior.

It is not possible to be better convinced than one is of what one knows, of what one in fact neither knowsnor is more happily disposed toward than if one in fact knew. But this will result if someone who is convincedbecause of a demonstration is not already aware of the primitives, because it is necessary to be better convincedof the principles (either all or some of them) than of the conclusion.


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Moreover, there must be no other thing more convincing to him or more familiar among the oppositesof the principles on which a deduction of the contrary error may depend (ifanyone who knows simplicitermust beunpersuadable).

3 All Knowledge is Not Demonstrative; Knowledge Immediates is Non-Demonstrable; It isImpossible to Demonstrate SimpliciterCircularly and so Demonstrate Everything (72b-73a).

Neither of the following views is either true or necessary: (1) Because one must know the primitives, there is no

knowledge at all; (2) There is knowledge, but there are demonstrations of everything.Those holding (1) claim that we are led back ad infinitumon the grounds that we would not know what is

posterior because of what is prior if there are no primitives (they are correct, since it is impossible to go throughinfinitely many things). If it comes to a stop and there are principles, they say that these are unknowable sincethere is no demonstration of them, which knowledge requires; but if one cannot know the primitives, neither canthe inferences or conclusions be understood simpliciteror properly (except on the supposition that they are thecase).

The other party (2) agrees that knowledge occurs only through demonstration and exists. But they arguethat nothing prevents there being demonstration of everything, since demonstration can come about in a circleand reciprocally.

But wesay that all knowledge is not demonstrative; knowledge the immediates/priors is non-

demonstrable, and necessarily so, because if it is necessary to know the things which are prior and on which thedemonstration depends, and it comes to a stop at some time, it is necessary for these immediates to be non-demonstrable. (There is not only knowledge but also some principle of knowledge by which we become familiar

with the definitions.)Against (2), it is impossible to demonstrate simpliciterin a circle, if demonstration must depend on what is

prior and more familiar; it is impossible for the same things at the same time to be prior and posterior to thesame things, unless one is so in another way (i.e. one in relation to us, the other simpliciter), which inductionmakes familiar. But if so, knowing simpliciterwill not have been properly defined, but will be twofold. Or is the

other demonstration not demonstration simpliciterin that it comes from what is more familiar to us?Against (2) too, they only say that A is the case if A is the case; it is easy to prove everything in this way.

It is clear that this results if we posit three terms: whenever if A is the case, of necessity B is, and if this then C,

then if A is the case C will be the case. Thus given that if A is the case it is necessary that B is, and if this is thatA is (that is what being circular is), let A be C: so to say that if B is the case A is, is to say that C is, and this

implies that if A is the case C is. But C is the same as A. So those who assert that demonstration is circular saynothing but that if A is the case A is the case.

Moreover, even this is impossible except in the case of things that follow one another, as properties do.Now if a single thing (= no term or posit is posited) is laid down, it is never necessary that anything else shouldbe the case. Now if A follows B and C, and these follow one another and A, in this way it is possible to prove allthe postulates reciprocally in the first figure, as was proved in the account of deduction. But one cannot provecircularly things that are not counter-predicated; so, since there are few such things in demonstrations, it is bothempty and impossible to say that demonstration is reciprocal and that because of this there can bedemonstration of everything.

4 Demonstration is Deduction from What is Necessary; Definitions of Holding in Every Case,In Itself, and Universally (73a-74a). Since it is impossible for the object of knowledge simpliciterto be

otherwise, the object of demonstrative knowledge will be necessary. So demonstration is deduction from what isnecessary. So we must grasp on what (sort of) things demonstrations depend. Let us define what we mean by (1)holding of every case, (2) in itself, and (3) universally.

(1) Something holds of every case if it holds in all cases and at all times (e.g. if animal holds of every man,then if it is true to call this a man, it is true to call him an animal too; and if he is now the one, he is the othertoo; and the same goes if there is a point in every line). Evidence: when asked if something holds of every case,we try to find objections with exceptional cases or times.


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(2) One thing belongs to another in itself only if (a) it belongs to it in what it is[e.g. line to triangle andpoint to line (their substance depends on these and they belong in the account which says what they are)] and (b)the things it belongs tothemselves belong in the account which makes clear what it is (e.g. straight belongs to lineand so does curved; odd and even to number; prime and composite; equilateral and oblong; and for all thesethere belongs in the definition line (in the first case), and number (in the others). [Things that dont satisfy

conditions (a) and (b) are accidental (e.g. musical or white to animal).]What is not said of some other underlying subject (i.e., a substance or whatever signifies some this) is

just what it is without being something else, and are things in themselves; accidentals are those that are said ofan underlying subject.

In another way what belongs to something because ofitself belongs to it initself, and what does not

belong because ofitself is accidental (e.g. if it got lighter out when he was walking, that was accidental; for it wasnot because of his walking that it got lighter out). But if something belongs to something else because ofitself,then it belongs to it initself (e.g. if something died while being sacrificed, it died inthe sacrifice since it diedbecause ofbeing sacrificed, and it was not accidental that it died while being sacrificed).

So regarding what is understandable simpliciter, whatever is said to belong to things in themselves in the

sense of inhering in the predicates or of being inhered in, holds both because ofthemselves andfromnecessity. Itis impossible for them not to belong, either simpliciteror as regards the opposites (e.g. straight or crooked to line,and odd or even to number). For the contrary is either a privation or a contradiction in the same genus (e.g.

even is what is not odd among numbers, in so far as it follows). So if it is necessary to affirm or deny, it isnecessary too for what belongs in itself to belong.

(3) Universal is whatever belongs to something both of every case, in itself, and as such. So whatever isuniversal belongs from necessity to its objects. [To belong in itself and as such are the same thing e.g. pointand straight belong to line in itself (for they belong to it as line), and two right angles belong to triangle astriangle (for the triangle is in itself equal to two right angles).]

Something holds universally whenever it is proved of a chance case and primitively [e.g. having two rightangles neither holds universally of figure (e.g. the quadrangle is a figure but it does not have angles equal to tworight angles), and a chance isosceles does have angles equal to two right angles, but not primitively the triangleis prior.

5 Mistakes in Proving Which does Not Belong Primitively and Universally; KnowledgeSimpliciter(74a-b). We often make mistakes when what is being proveddoes not belong primitively and

universally in the way in which it seemsto be being proved (universally and primitively). We make this errorwhen either (1) we cannot grasp anything higher apart from the particular, or (2) we can but it is nameless forobjects different in sort, or (3) the thing proved is in fact a whole that is a part of something else.

If someone were to prove that right angles do not meet, the demonstration would seem to hold of thisbecause of its holding of all right angles. But this demonstration would not hold, if it comes about because theyare equal in any way at all.

If there were no triangles other than the isosceles, having two right angles would seem to belong to it asisosceles.

Perhaps proportion alternates for things as numbers, as lines, as solids, and as times (proportion used to

be proved separately but is now proved in all cases at once by a single demonstration). Because all these things(numbers, lengths, times, solids) do not constitute a single named item and differ in sort from one another,proportion used to be taken separately. But now it is proved universally; for it did not belong to things as lines oras numbers, but as this that they suppose to belong universally.

Thus, even if you prove of each triangle either by one or more demonstrations that each (equilateral,scalene, and isosceles) has two right angles, you do not yet know of the triangle that it has two right angles, orthe same of triangle universally (not even if there is no other triangle apart from these). For you do not know itof the triangle as triangle, nor even of every triangle.

So when do you not know universally, and when do you know simpliciter? You would know simpliciterif itwere the same thing to be a triangle and to be equilateral (either for each or for all). But if it is not the same butdifferent, and it belongs as triangle, you do not know. Does it belong as triangle or as isosceles? When does it


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belong in virtue of this as primitive? Of what does the demonstration hold universally? Whenever afterabstraction it belongs primitively (e.g. two right angles will belong to bronze isosceles triangle, but also whenbeing bronze and being isosceles have been abstracted but not when figure or limit have been abstracted). Iftriangle (e.g.), it is in virtue of this that it also belongs to the others, and it is of this that the demonstration holdsuniversally.

6 Demonstrative Knowledge Depends on Necessary Principles; The Middle Term of a

Demonstration Must be Necessary; No Demonstrative Knowledge of Accidentals (74b-75a). Ifdemonstrative knowledge depends on necessary principles (what one knows cannot be otherwise), and whatbelongs to the objects in themselves is necessary, demonstrative deduction will depend on necessary principles;everything belongs either in this way or accidentally, and what is accidental is not necessary.

Given the above, and positing as a principle that demonstration is necessary and that if something hasbeen demonstrated it cannot be otherwise, the deduction must depend on necessities. From truths one candeduce without demonstrating, but from necessities one cannot deduce without demonstrating; this is preciselythe mark of demonstration.

Evidence: we bring our objections against those who think they are demonstrating by saying that it is notnecessary (because it is absolutely possible for it to be otherwise, or at least for the sake of argument).

Those people who think they get their principles correctly if the proposition is reputable and true (e.g.

sophists who assume that to know is to have knowledge) are silly. [DY OBJ: It is silly for someone to think thatto know is to have knowledge? We need an explanation of that example from Aristotle or an Aristotelian.] It isnot what is reputable or notthat is a principle, but what is primitive in the genus about which the proof is; and not every

truth is appropriate.More evidence that the deduction must depend on necessities: if, when there is a demonstration, a man

who has not got an account of the reason why does not have knowledge, and if it might be that A belongs to Cfrom necessity but that B (the middle term through which it was demonstrated) does not hold from necessity,then he does not know the reason why. For it is possible for B not to be the case, whereas the conclusion is

necessary.If someone does not know now, though he has got the account and is preserved, and the object is

preserved, and he has not forgotten, then he did not know earlier either: the middle term might perish if it is not

necessary; so that though, by himself and the object being preserved, he will have the account, yet he does notknow. So he did not know earlier either. If it has not perished but it is possible for it to perish, the result would

be capable of occurring and possible; but it is impossible to know when in such a state. [DY: FYI, this is notlikeSchrodingers Cat (click hereor here), because in the SC case, the cat at one point both is and is notdead, whichAristotle would deny.]

When the conclusion is from necessity, nothing prevents the middle term through which it was provedfrom being non-necessary; one can deduce a necessity from a non-necessity, just as one can deduce a truth fromnon-truths. But when the middle term is from necessity, the conclusion too is from necessity, just as from truthsit is always true (e.g. let A be said of B from necessity, and this of C; then A belongs to C from necessity). Butwhen the conclusion is not necessary, the middle term cannot be necessary either (e.g. A belong to C not fromnecessity, but to B and B to C from necessity, then A will belong to C from necessity too; but it was not

supposed to).Since if a man knows demonstratively, it must belong from necessity, he must have his demonstrationthrough a middle term that is necessary too; or else he will not know either why or that it is necessary for that tobe the case, but either he will think but not know it (if he believes to be necessary what is not necessary) or hewill not even think it (equally whether he knows the fact through middle terms or the reason why actuallythrough immediates).

There is no demonstrative knowledge of accidentals.Since in each kind what belongs to something in itself and as such belongs to it from necessity, scientific

demonstrations are about what belongs to (and depends on) things in themselves. What is accidental is notnecessary, so you do not necessarily know why the conclusion holds not even if it should always be the case butnot in itself (e.g. deductions through signs). You will not know in itself something that holds in itself; nor will you


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know why it holds, because to know why is to know through the explanation. So the middle term must belongto the third, and the first to the middle, because ofitself.

7 One cannot Prove Something by Crossing from Another Genus; Conclusions, Axioms, andGenera in Demonstrations; Demonstrations Always Include the Genus of the Conclusion; WhatDifferent Sciences Cannot Prove about Other Sciences (75a-b). One cannot prove anything by

crossing from another genus (e.g. something geometrical by arithmetic). [DY OBJ: Why not? I cant prove

geometrically of a triangle that a2+b2= c2, by squaring and adding the numbers using arithmetic?] There arethree things in demonstrations: (1) conclusion(what is being demonstrated, or what belongs to some genus in

itself); (2) axioms(the things on which the demonstration depends); and (3) the underlying genus of which thedemonstration makes clear the attributes and what is accidental to it in itself.

The axioms may be the same; but of things whose genus is different (e.g. arithmetic and geometry), onecannot apply arithmetical demonstrations to the accidentals of magnitudes (unless they are numbers).

Arithmetical (and other) demonstrations always include the genus of the conclusion; so the genus must

be the same, either simpliciteror in some respect, if the demonstration is going to cross. [DY: Crossing is notclear, given the first sentence of this chapter.] Otherwise, it is impossible: it is necessary for the extreme and themiddle terms to come from the same genus (if they do not belong in themselves, they will be accidentals).

One cannot prove by geometry that there is a single science of opposites, nor even that two cubes make

a cube; nor can one prove by any other science the theorems of a different one, except when they are relatedsuch that the one is under the other (e.g. optics to geometry, and harmonics to arithmetic). Nor can one proveby geometry anything that belongs to lines not as lines and as from their proper principles (e.g. whether thestraight line is the most beautiful of lines or whether it is contrarily related to the circumference); that belongs tothem not as their proper genus but as something common.

8 A Demonstration Must Have an Eternal Conclusion; No Demonstration of Perishable Things(e.g. Eclipses) (75b). If a demonstrative deduction (or simpliciter) depends on universal propositions, it is

necessary for its conclusion to be eternal too. There is no demonstration or knowledge simpliciterof perishablethings, but only accidentally, because it does not hold of them universally, but at some time and in some way.

In such a demonstration, it is necessary for the one proposition to be non-universal (because its subjects

will sometimes be and sometimes not be) and perishable (because when it is, the conclusion will be too), so onecannot deduce universally, but only that it holds now.

The same goes for definitions, since a definition is either a principle of demonstration or a demonstrationdiffering in position or a sort of conclusion of a demonstration.

Demonstrations and sciences of things that come about often (e.g. eclipses) clearly hold always in so faras they are of such-and-such a thing, but are particular in so far as they do not hold always.

9 Demonstrations must Proceed from Principles that Belong to a Thing As That Thing;Knowing (Non-)Accidentally; It is Difficult to be Aware when One Knows or Not (75b-76a). Since

one cannot demonstrate anything except from its own principles if what is being proved belongs to it as that thing,knowledge is not this(if a thing is proved from what is true and non-demonstrable and immediate). [DY: I think,

but am not sure, that the phrase knowledge is not this = knowledge is not a demonstration of things that comeabout often (without being absolutely true or holding always). Moreover, it is puzzling if he is saying thatknowledge is not of something essential of a substance, or that demonstrations are not proved from what is true,non-demonstrable, and immediate he states that premises of a demonstration have precisely thesecharacteristics.] Such arguments prove in virtue of a common feature that will also belong to something else;that is why the arguments also apply to other things not of the same kind. So you do not know it as that thingbut

accidentally; otherwise the demonstration would not apply to another genus too.We know a thing non-accidentally when we know it in virtue of that in virtue of which[DY: the genus, I

believe, or the principles] it belongs, from the principles of that thing as that thing (e.g. we know having anglesequal to two right angles when we know it in virtue of the principles of that thing). So if that too belongs in itself

to what it belongs to, it is necessary for the middle to be in the same genus.


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If this is not so, then the theorems proved as harmonical theorems are proved through arithmetic. Suchthings are proved in the same way, but they differ; the fact falls under a different science (for the underlyinggenus is different), but the reason under the higher science under which fall the attributes that belong inthemselves [DY: is the same?]. So one cannot demonstrate anything simpliciterexcept from its own principles.But the principles of these sciences have the common feature.

If this is true, one cannot demonstrate the proper principles of anything; those will be principles ofeverything, and knowledge of them will be sovereign over everything. You know better if you know from the

higher explanations; you know from what is prior when you know from unexplainable explanations [DY: TheTredennick/Forster translation has it when he knows it from causes which are themselves uncaused.Maybe that helps.!]. So if you know better and best, that knowledge too will be better and best. But

demonstration does not apply to another genus (except, as has been said, geometrical demonstrations apply tomechanical or optical demonstrations, and arithmetical to harmonical).

It is difficult to be aware of whether one knows or not: It is difficult to be aware of whether we knowfrom the principles of a thing or not (and that is what knowing is). We think we know if we have a deductionfrom some true and primitive propositions. But that is not so, but it must be of the same genus as the primitives.

[DY OBJ: This really undercuts his view of knowledge, because according to Aristotle, we need to knowtheprinciples are true; and we need to knowthat the conclusion is eternal; we cant just guess if the conclusioncannot be otherwise. And hes already stated above that we know the premises by non-demonstrable knowledge

so how can we knowthat?]

10 We must Assume Principles in Each Genus Exist; Things Proper to Each Science and ThingsCommon Used in Demonstrative Sciences; Three Things Demonstrative Sciences Deal With;Suppositions v. Postulates; the Geometer Does Not Suppose Falsehoods (76a-77a). It is notpossible to prove that principles in each genus exist. Both what the primitives and what the things dependent onthem signify is assumed; but that they are must be assumed for the principles and proved for the rest (e.g. wemust assume what a unit or what straight and triangle signify, and that the unit and magnitude are; but we mustprove that the others are).

Some things they use in demonstrative sciences areproperto each science and others common(by analogy,since things are useful insofar as they bear on the genus under the science): proper(e.g. that a line is such and

such, and straight so and so); and common(e.g. that if equals are taken from equals, the remainders are equal).But each of these is sufficient insofar as it bears on the genus; it will produce the same result even if it is notassumed as holding of everything but only for the case of magnitudes (or, for the arithmetician, for numbers).

Proper too are the things that are assumed to be, about which the science considers what belongs tothem in themselves (e.g. arithmetic is about units, and geometry is about points and lines). They assume these to

be andto be this. As to what are attributes of these in themselves, they assume what each signifies (e.g. arithmeticassumes what odd or even or quadrangle or cube signifies, and geometry what irrational or inflection or vergingsignifies and they prove that they are, through the common items and from what has been demonstrated;astronomy proceeds in the same way).

Every demonstrative science deals with three things: (1) what it posits to be(these form the genus of what itconsiders the attributes that belong to it in itself); (2) the common axioms, the primitives from which it demonstrates;

and (3) the attributes, of which it assumes what each signifies. Nothing prevents some sciences from overlookingsome of these, e.g. from not supposing that its genus is, if it is evident that it is it is not equally clear thatnumber is and that hot and cold are, and from not assuming what the attributes signify just as in the case ofthe common items it does not assume what to take equals from equals signifies, because it is familiar. So thereare by nature these three things, that about which the science proves, what it proves, and the things from whichit proves.

What necessarily is the case because of itself and necessarily seems to be the case is not a suppositionor a postulate. Demonstration is not addressed to external argument (but to argument in the soul) sincededuction is not either. One can always object to external argument, but not always to internal argument.

Whatever a man assumes without proving it himself though it is provable (e.g. if he assumes somethingthat seems to be the case to the learner), he supposes it(and it is a supposition not simpliciterbut only in


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relation to the learner); but if he assumes the same thing when there is either no opinion present in the learneror actually a contrary one present, hepostulates it. (A postulate is what is contrary to the opinion of thelearner, which though it is demonstrable is assumed and used without being proved).

Terms are not suppositions (they are not said to be or not be anything), but suppositions are among thepropositions, whereas one need only grasp the terms; and suppositions are propositions such that, if they are thecase, then by them the conclusion comes about.

The geometer does not suppose falsehoods (as some say); my opponents state that one should not use a

falsehood but that the geometer speaks falsely when he says that the line that is not a foot long is a foot long orthat the drawn line that is not straight is straight. But the geometer does not conclude anything from there being

this line that he himself has described, but from the conclusion that is made clear through them. [DY OBJ: Andis this not something separate and apart from this particular line? Then why can Aristotle not accept that Formsexist, or, how has Aristotle not separated the universal, as he accuses Plato of doing?]

Every postulate and supposition is either universal or particular; but terms are neither of these.

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