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Burnyeat, "Aristotle on Understanding Knowledge"

Burnyeat, "Aristotle on Understanding Knowledge" in Berti

I.
The PA does two things:
1) provides a theory of the structure of science; the conditions for a proposition to belong to a body of systematic knowledge;
2) gives an account of the cognitive state of an individual who has mastered a body of systematic knowledge.

Aristotle first gives an account of the cognitive state of epistasthai (knowing the cause and necessity) and then draws the second conclusion about the objects of episteme.

"Because episteme involves grasping the demonstration of necessary conclusions, it is grounded epistemologically on the premises of that demonstration" (99).

Aristotle is concerned with one's cognitive state with regard to particular propositions (rather than who branches) because he distinguishes between unqualified episteme with respect to a theorem of science from various qualified versions of episteme in relation to the same theorem. (100)

What should we make of the distinction between qualified and unqualified episteme?
* qualified is still episteme, just not the favored kind.
**How should we make sense of this? Demonstration from archai is only one form of proper justification; something can have justification without deductive demonstration. (See A2, A5, and A13 for places where Aristotle recognizes this distinction.)

"In other words, Aristotle both knows and emphasizes that his requirement that demonstration proceed from first principles is not a requirement of justification but of scientific explanation." (101)

(NOTE: missing pp 102&3)

"In the PA, episteme is coordinate with epistasthai and denotes either a cognitive state or the body of knowledge he has mastered" (105).

In A2, Aristotle says that epistasthai is ordinarily conceived that: "x epistatai y iff (a) x gignoskei the explanation of y is and (b) x gignoskei that y cannot be otherwise than it is."

This fits our conception of UNDERSTANDING much better than it fits the concept of knowledge. This isn't to say that we can't use the term 'knowledge', but we have in mind the sense of the word when we say 'he has knowledge of mononucleosis' rather than 'he has knowledge of where is car keys are'.

"Aristotle is analyzing a cognitive state which is achieved by knowing explanations, and whether he is currently calling it episteasthai or gignoskein the corresponding term for that philosohical state in philosophical English is 'understand'" (107).

II.
Episteme is of what cannot be otherwise.

"If Aristotle is making a claim about understanding, hiw point will be that understanding depends on explanation and what gets explained in the sciences...which general regularities and connections: lawlike regularities in the modern jargon, necessary connections in Aristotle's" (109).

Doesn't Aristotle also talk of things that happen "for the most part" and wouldn't this be the law-like regularities?

Burnyeat references the EN here. The quote from the EN is as follows: "Clearly then practical wisdom is a virtue and not a skill. And sicne there are two parts of the soul that possess reason, it will be in virtue of one of them, namely, that which forms beliefs, both beliefs and practical wisdom being concerned with what cannot be otherwise. (EN 6.5, 1140b)."

One can apply the explanation of a recurring type of phenomenon to a particular instance of it; but this results in accidental episteme, not episteme haplos.

Scientific explanation is at first an explanation of laws rather than an explanation of particular events.

When Aristotle says that knowledge is of what cannot be otherwise, he's commenting that understanding is constituted by knowing the explanation of necessary conditions in nature.

The considerations make more sense as considerations about explanation than considerations about knowledge or certainty.
1) because epistasthai involves explanation that Aristotle insists on the characteristics of the principles (true, primitive, etc)
2) necessary premises is a requirement of explanatoriness.

Burnyeat points to A6 for this. I don't see it here, though. What A says is that if he apodeiktihe episteme comes about, you need necessary principles. Does Burnyeat want to say that apodeixis = explanation?

Aristotle's most substantial claim (at a.6, 74b26ff) is that "to explain the holding of a conclusion that is necessary one must demonstrate it through a necessary middle term" (110).

To understand a theorem you must understand
1) that it is necessary
2) WHY it is necessary (it is necessary because it id demonstrable from prior principles which are necessary, and those prior principles are necessary because they are per se predications expressing a definitional connection)

It sounds weird to say one understands THAT something unless the sort of understanding you're talking about is semantic understanding.

In B.6, although the details aren't clear, "it seems fair to say that he is trying to give substance to the idea that the fundamental predications of a science ought to be self-explanatory. (ie they're not merely immediate (no explanation via a middle term) but actually explain themselves).

Aristotle is looking for substantive knowledge of a thing's essence in a scientific definition.

The man who achieves unqualified episteme is a man for whom every "why?" question in a given domain has been given an appropriate answer. His grasp is:
1) systematic and
2) synoptic
In that everything in the domain is explained in light of first principles which explain themselves.

Aristotle has a vision of complete understanding which supports his claim that one can only have episteme of what is universal, necessary, and everlasting.

Aristotle is not saying that we can't KNOW that accidental states of affairs obtain; it's just that accidental knowledge falls outside the reach of systematic explanation and understanding.

There is no episteme through perception of particular things because explanation requires generality and this is beyond the scope of explanation. Perception DOES yield knowledge, though. (gnosis, not episteme)

If we understand episteme as justified true belief, then Aristotle presents a very skeptical view. If we take it as understanding, then the restrictions he places upon it are intelligible.

III.

Aristotle doesn't appeal to concepts like evidence, certainty, and justification.

"This is reason, of course, for disavowing the once prevalent idea that the PA advocates demonstration as a method of scientific discovery". Rather, demonstration is a method of teaching facts already won. It is not how you discover facts but how you should present and impart them.

But it is bad pedagogy to lead a pupil straight to archai and then launch into a remorseless chain of syllogisms.

How do we make sense of the PA as good pedagogy, then?

Consider again the distinction between knowledge and understanding.
* When you teach by imparting KNOWLEDGE, you will include evidence and justification in your teaching.
* When you teach via imparting UNDERSTANDING of knowledge that pupils already have or understanding of a science with which they are already acquainted in an unsystematic way, one does this by unifying things, putting them into a systematic framework.

Think of this education (put forward in the PA) as an advanced graduate level course, not an introductory course.

IV.

Does this account of Aristotle's pedegogical philosophy improve the claims of demonstration?
*it depends on whether we agree on certain philosophical questions regarding understanding.

The key to understanding (for Aristotle) is demonstration and the sort of demonstration that Aristotle has in mind is demonstrations of the form Barbara (AAA. AaB, BaC, therefore AaC)

Even if we grant that understanding can be gained from relating and organzing bits of knowledge, it doesn't follow that understanding is to be sought from putting knowledge into ARISTOTLE'S mould (ie syllogisms and demonstrations).

The extent to which we doubt understanding is the fruit of axiomitization is the extent to which we doubt that demonstration is the method in which to impart understanding.

"A teacher can sensibly aspire to conduct Aristotelian demonstrations if it is right to claim that, where we can achieve full axiomitization will provide us with a completed structure of explanation which should be the idea fulfillment of a common conception of understanding" (126).

"For Aristotle, an axiomatic system isn't just a preferred ordering of humanly constructed knowledge, but a mapping of the structure of the real" (126).

V.

In A2, A. says that it is a requirement of episteme that one know and be convinced of the first principles. Can't this be so I can know and be convinced of the demonstrated conclusions?

Explanation, being prior to what it explains, is more knowable and familiar in the order of nature, and is thereby more believable and convincing.

The relationship between the knowable (familiar) and the convincing is important.

Aristotle makes a distinction between what is more knowable in the order of nature nad what is more knowable to us.

Demonstration produces gnonai...but this gignoskein is knowledge as a grasp of what is knowable by nature.

So we can constrast knowledge with and knowledge without full understanding.

You can have knowledge and even have put things together in an orderly way and STILL not have mastered them because you lack intellectual practice and familiarity. (in EN VI and VII, ee B. pp 129-30).

Aristotle didn't see a problem transforming inductive belief into knowledge (gnosis) but he thought that this isn't yet understanding. To get understanding we need more familiarity, more dialectical practice, intellectual habituation.

The archai are knowable in themselves, etc; when one has propositions we knows on inductive grounds which are convincing and knowable in themselves, one need just become fully familiar with them and convinced. This conviction and understanding is nous. (132)

PA Alpha, chapter 6

PA Book 1 chapter 6

The central claim of this chapter is that P is demonstrated through necessary principles.

1. If demonstrative understanding proceeds from necessary principles; and
2) if whatever holds of an object in itself is necessary, then
3) demonstrative deduction will proceed from certain items of this sort (ie necessary items)...because everything holds either incidentally or in this way (presumably through demonstrative deduction)

We must argue like this or posit as a principle that demonstration is necessary. "for from truths you can deduce without demonstrating, but from necessities you cannot deduce without demonstrating."

There is evidence for this idea that demonstration proceeds from necessity because we say that the premises aren't necessary if we think it possible for them to be otherwise.

A further argument in favor of the idea that demonstration must proceed from necessities is as follows:
1) if in a case of demonstration, someone who doesn't possess an account of the reason why doesn't have understanding; and
2) if it might be A holds of C by necessity but B (the middle term through which this is demonstrated) do not hold from necessity, then
3) he doesn't know the reason why.

If I 'demonstrate' the necessary proposition AaC from non-necessary premises, then I don't know why AaC and thus do not understand AaC

If premises are contingent, then AaC can't hold because of them.

This seems to indicate that the way to come to understand the reason why comes via demonstration with necessary truths. Hopefully later he'll give an account of how demonstrations act as a proper way to come to know the reason why. Or why the results of demonstration are considered accounts of the reason why.

It's also interesting to note the idea that understanding does not come about without having an account of the reason why.

If someone does not know something now
1) although he has an account,
2) the account is preserved (ie the person is alive)
3) the object is preserved (the truth; p is true at t1 and at t2)
4) he has not forgotten
Then he didn't know it earlier.

A presupposition apparent in (3) is that a proposition (P) might change its truth value between t1 and t2.

Would this be for things that happen for the most part? Necessary truths can't change their truth value, surely.

But the middle term might perish (be false) if it isn't necessary.

But because the person is preserved, and the object is preserved, he will possess an account, and yet he doesn't have knowledge, and therefore he didn't have knowledge earlier.
* even if this hasn't occurred, it can (because the middle term might perish) and so one can't have knowledge in these conditions.

Even if a conclusion holds of necessity, the middle term need not because you can deduce a necessary truth from non-necessary truths (in the same way you can deduce a truth from non-truths).
*BUT when the middle term holds from necessity, the conclusion also holds from necessity (like a conclusion from true propositions is always true).

Since understanding from demonstration must hold from necessity, your demonstration must proceed from a middle term which is necessary. Otherwise you will understand neither the reason why nor that it is necessary for it to be the case.

Of incidentals which do not hold of things in themselves, there isn't demonstrative understanding because you can't prove the conclusion from necessity (because it is possible for the incidental to be otherwise).

One might wonder why one would even ask about incidentals if it isn't necessary for the conclusion to hold.

For any argument of the form P so necessarily Q will be good since NO argument of that form will be good, where Q is not necessary.

We should ask these questions NOT because the conclusion will be necessary because of the points proposed in the question but rather because it is necessary for anyone who accepts the proposals to state the conclusion (truly).

Since whatever holds of something in itself and as such holds of it by necessity, it is clear that demonstrations must proceed from such items (in itself & by necessity). This is true because what is incidental doesn't hold necessarily and so you don't know necessarily that the conclusion holds (even if it is always the case)...because you will not understand in itself
1) that it holds in itself, nor
2) why it holds

PA Alpha, chapter 5

PA Book 1, chapter 5

We often make mistakes. What we try to approve does not hold primitively and universally, even though we think we are proving it universally and primitively.

We make mistakes:
1) when there is nothing higher we can take apart from a particular case;
2) when there is something higher, but it is nameless and covers objects of different forms
3) when the proof applies to something that is a partial whole

Example of 1: If the only triangles we were aware of were isosceles, we might believe 2R held universally of the isosceles because we have no concept of triangle.

Example of 2: Aristotle is referring to a universal mathematics - an allusion to Eudoxian generalization.

Example of 3: If we observe that all perpendiculars are parallel and we wrongly inter that this is what we demonstrate.

When do you not know universally but do know simpliciter?
* you would know simpliciter if it was the same thing to be a triangle and be equilateral. But if it is different and if something holds of them as a triangle, then you don't know it.

To what does the demonstration apply universally?
* to the first item after the removal of which it doesn't hold.
-- for example, 2R holds of a bronze triangle. When 'bronze' is removed, it is still a triangle. But when 'figure' is removed, it is no longer a triangle.

But 'figure' and 'limit' aren't the first (item after the removal of which...), rather triangle is the first.

'first' means first terms after whose abstraction R fails to hold. The thing that holds first holds primitively; so the abstraction colds primitively of 'triangle'.

PA Alpha, chapter 4

I found this to be a nearly incomprehensible chapter. The notes below barely make sense, Barnes' commentary, while helpful, was also baffling (although I doubt Barnes is at fault here). This is something I need to go back to at a future date when I might have a better idea of what is going on.

PA, Alpha, Chapter 4

Because it is impossible for understanding simpliciter to be otherwise, demonstrative understanding will be necessary.

A demonstration is a deduction which proceeds from necessities. SO we must see what kind of items demonstrations proceed from..

We must define three things:
1) 'of every case'
2) 'in itself'
3) 'universally'

Something holds of every case if it does not hold in some cases and not in others, nor at some times and not at others.
* for example, if 'animal' holds of every man then if this is true to call this a man, it is true to call him an animal, and if he is now he also was previously.

Something holds in itself if it holds in it what it is.
* for example, the line of triangles or points of lines. (The essence of a triangle comes from the lines.)
If what it holds in itself inheres in the account which shows what it is, there is an account which specifies the specific thing it is.
* for example, 'straight' and 'curves' both hold of lines; 'even' and 'odd' both hold of numbers.

Aristotle gives four ways A can hold of B 'in itself'. The first two:
1) A holds of B in itself = df 'A holds of B and A inheres in the definition of B'
ex: animal holds of man in itself
2) A holds of B in itself = df 'A holds of B and B inheres in the definition of A'
ex: mortal holds of animal (good example?)

Barnes then talks of I-predication. A proposition is an I-predication if
a) it is of the form 'Every B is an A' and
b) it is true in virtue of the fact that A holds of B in itself.
The proposition is an I1 proposition if 'in itself' is taken in sense 1 (above) and a proposition is an I2 proposition if 'in itself' is taken in sense 2 (above).

Certain items are not said of some other underlying subject. Things that aren't said of an underlying subject are called things in themselves.

A. distinguishes things that exist in themselves (independently) with things that exist incidentally.

A distinction between natural and unnatural predications. If 'x is y' is a natural predication, then
1) 'x is y' doesn't entail something else is Y and happens to be X
2) X is not ontologically dependent on anything else, and
3) x is an independently identifiable subject of change

Another way to describe that something holds 'in itself' is to say that what holds of something because of itself holds of it in itself.
* for example, if something died while being sacrificed, it died in the sacrifice since it died because of being sacrificed and it was not incidental that it died while being sacrificed.

This involves a connection between events

When something is understandable simpliciter and is said to hold of things in themselves either by
1) inhering in what is predicated or
2) being inhered in
then it holds of them because of themselves and from necessity. This is because it is not possible for them not to hold
1) either simpliciter or
2) as regards the opposites.

A. is referring to I1 and I2 predications. When A. says that "A holds of B simpliciter" he is talking of I2 predication, and when he refers to "as regards the opposites" he refers to I2 predications.

'Universal' is defined as what holds of every case in itself and as such.

Something holds universally when it is proves of an arbitrary and primitive case.

The definition of 'universal 'has three components:
1) 'of every case'
2) 'in itself', and
3) 'as such' (qua)

A holds B as such iff there is no term C which explains why A holds of B; iff AaB is immediate.

Being an I-predication and holding as such are logically equivalent.

reread Barnes' summary of the chapter on pp 120-2. Are there any articles that might make this a bit more clear?

PA Alpha, chapter 3

PA Chapter 3

Some people think that because you must know the primatives in order to have a demonstration (and thereby have understanding) that
1) there is no understanding, or
2) there are demonstrations of everything.
Neither of these is correct.

The first group claims that we're led back ad infinitum. It is impossible to survey infinitely many things. But if there is a stop in the chain then the principles are unknowable because there is no demonstration (and the only kind of understanding comes from demonstration). SO, because you cannot know primatives, then you cannot know what proceeds from them simpliciter, and you can thereby only posit as supposition that they are the case.

The second group agrees about understanding but says that all things can be demonstrated because demonstrations can proceed in a circle or reciprocally.

Aristotle asserts not all knowledge is demonstrative. Indemonstrable understanding is possible for immediate items. This must be so because
1) if you must understand the items which are prior;
2) and these items are the things from which the demonstration proceeds, then
3) things must come to a stop
4) and these immediates must be undemonstrable

There is not only understanding but some principle (arche^n) of understanding by which we know the definitions.

At 100b15 Aristotle says that the principle of understanding is the nous or comprehension by which we have knowledge of the principles.

There are three arguments that claim that it is impossible to demonstrate simpliciter in a circle if demonstration must proceed from what is prior and more familiar.
1) because it is impossible for something to be prior and posterior at the same time...except in different ways, ways that induction makes familiar. In this case (where it is prior in one sense (in relation to us) and posterior in another (simpliciter)), knowing simpliciter will not be properly defined; it will be ambiguous or it is not demonstration simpliciter.

2) those who advocate circularity say nothing more than if A is the case then A is the case, and it is easy to prove anything this way.

3) Circular reasoning is only possible for items which follow one another. So even if it is possible, it is only possible for objects counterpredicted (convertible propositions). There are very few counterpredicted items in demonstrations, and so it is impossible to say demonstrations may be reciprocal and thus there can be demonstrations of everything.

PA Alpha, chapter 2

AP Book 2

We think we understand something simpliciter when we think we know of the explanation (because of which the object holds) that it is the explanation and that it is not possible to be otherwise.

Therefore, if there is understanding simpliciter of something, it is impossible for it to be otherwise.

The definiendum is understanding simpliciter
The definiens contains two conjuncts
1) to do with the explanation (aitia, to dioti, to dia ti)
2) to do with necessity

To give the aitia for something is to say why it is the case.

The first conjunct of the definiens of understanding:
1) a understands x only if a knows that y is the explanation of x
The second conjunct of the definiens is ambiguous. it is either:
2a) a understands x only if x cannot be otherwise
2b) a understands x only if a knows that x cannot be otherwise.
(Barnes goes for 2b)

These two (necessary) conditions for understanding are jointly sufficient. So we get a definition for understanding simpliciter:
a understands x = df a knows that y is the explanation for x and a knows that x cannot be otherwise

Note how restrictive 2b is - it only allows knowledge of necessary matters. Even Aristotle seems to want (at times) to broaden the notion of episteme to matters which hold only for the most part.

There may be another type of understanding (see Barnes' discussion of this). For now we'll assert that we know things through demonstration.
Demonstration = scientific deduction
Scientific deduction = a deduction by possessing which we understand something

Demonstrative understanding must proceed from items which are
1) true
2) primitive
3) immediate
4) more familiar than
5) prior to
6) explanatory

True because you can't understand what is not the case.
Primitive and indemonstrable because otherwise you would not understand unless you possess a demonstration of these things

Primitive: there is no Q prior to P...there is no Q from which knowledge of P must be derived. Indemonstrable: needing no demonstration. This does not imply that it is immediate because there may be a vaild but non-demonstrative syllogism concluding to P

Explanatory because we only understand something when we know its explanation

If the only knowledge necessary for having a demonstration of P is knowledge of the principles from which P is deducible, then the principles must contain the explanation of P.

Prior (and more familiar) because they are explanatory and we already know them (not only in the sense of grasping them but of knowing they are the case)

Priority is knowledge; knowledge that Q requires knowledge that P but not vice versa. A. treats familiarity the same as priority.

Immediate: to lack a middle term. A syllogistic proposition AxC is immediate iff there is no term B distinct from A and C such that AxB, BxC |-- AxC is a syllogism.

These characteristics concentrate on the implication of the explanatory conjunct of the definiens (see above); the implication of the necessity definiens will be taken up in A4.

The six characteristics are divisible into two groups:
1) absolute features of demonstration
2) relative features of demonstration

The six features characterize principles or axioms of a demonstrative science.

Things are prior and more familiar in two ways:
1) in relation to us (items nearer to perception)
2) simpliciter (items further away; most universal)

A principle of a demonstration is an immediate proposition.
* a proposition is immediate if there is no other proposition prior to it.

A proposition is one part of a contradictory pair.
* A bit further on, A says that a statement is also one part of a contradictory pair. A contradictory pair is a pair of opposites between which there is nothing.

If there is nothing 'between' P & Q then there is no third possibility apart from P or Q.

A proposition is:
* dialectical if it assumes either part (of the contradictory pair) indifferently
* demonstrative if it determinately assumes one part because it is true

Types of immediate deductive principles:
posit: it can't be proved but need not be grasped by anyone who is to learn anything
axiom: it must be grasped by anyone who is gong to learn anything

A posit which
* assumes either of the parts of a contradictory pair (that something is or that something is not), is a SUPPOSITION
* does not assume this is a DEFINITION

Aristotle use the phrases 'common axiom' as well as 'axiom' to mean the same thing. It is called a common axiom because it is shared with more than one science.

We should take suppositions to be exclusively existential propositions.

A. should have said that there are two kinds of posits:
1) that something is (supposition)
2) what something is (definition)

I need to read up on posits. It looks like a vexed subject.

Because
1) you must be convinced about some object and know it insofar as you have a demonstration
AND 2) given that there is a deduction that these items are the case; then you must
3) already know the primatives (all or some)
4) know them better

"Hence if we know and are convinced of something because of the primatives, then we know and are convinced of them better, since it is because of them that we know and are convinced of the posterior items."

Anyone who is going to have understanding through a demonstration must
1) not only get to know the principles better than what is being proved but
2) there must be no item more convincing or familiar among the opposites of the principles from which a deduction of contrary error may proceed.
Why? Because anyone who understands anything simpliciter must be incapable of changing is mind (and if 2, then he might well change his mind).

look back at Barnes' analysis of this argument.

PA Alpha, chapter 1

AP, book 1

(Note: I wrote up a summary of this before...but because I put down the AP a while ago and have just now picked it back up, I want to work through the text from the very beginning. So this will be a bit repetitive, although certainly has some new/differently thought about stuff.)

All teaching and learning proceed from preexisting knowledge.

Deductive and inductive arguments effect their teaching in similar ways.
* Deductive: assuming items that we are presumed to grasp.
* Inductive: proving something universal by way of the fact that the particular cases are plain.

There are two ways that we must already have knowledge:
1) we must already believe that they are
2) we must grasp what the items spoken about are.

Knowledge is of two sorts.
1) knowledge of propositions (that x is)
2) knowledge of terms (what x means)

(Barnes says: the knowledge presupposed by a teacher is of two sorts..." I don't get this reference to a teacher - perhaps it is looking back to 71a5(6?) where A. says that both deductive and inductive arguments "effect their teaching through what we already know"?)

It is possible to acquire knowledge when you get knowledge of some things earlier and you get knowledge of the others at the same time.

So if I learn that Sophie is a mammal by inference from the following premises:
1) all cats are mammals and
2) Sophie is a cat
Then though I must already know that all cats are mammals, I may learn that Sophie is a mammal and that Sophie is a cat at the same time.

Note: A. doesn't say that we learn the premise as we learn the conclusion but rather as we are being led to the conclusion.

Before you are led to a conclusion (before being given a deduction), you should be said to understand it in one way (universally) but not understand it in another way (simpliciter; haplos). (Because if you don't know there is such a thing (simpliciter) how would you know it has two angles (simpliciter)?

Read more about knowledge simpliciter/episteme haplos. It's hard to get my mind around right now.)

Barnes: Universal knowledge is knowledge of things like 'all triangles have three angles' but perhaps not particular knowledge (about this triangle).

We should not be convinced by folks who make assumptions about every number or triangle simpliciter, not about everything of which they know it is a triangle or a number.

(For example, you might say, all triangles have three angles. Someone would then present you with a triangle that you had never seen before. They would then say that because you have not seen all triangles, you can't possibly know that all triangles have three angles...your knowledge of that claim is limited to the triangles that you've seen. Aristotle says this is baloney - you have universal knowledge even if you don't have particular knowledge.)

Nothing prevents us from understanding in one sense and being ignorant in another.

Back again

OK...new semester and renewed need to study for this exam. I'm working my way through the Posterior Analytics. As noted in a previous entry, the translation and commentary I'm using is by Jonathan Barnes. Because Barnes' commentary is so extensive (and excellent), I decided that I need a way to distinguish his commentary from my questions and notes...so I've created two different styles of blockquotes. The box with a white background will have notes from Barnes' commentary and the box with the blue background will have my own notes and comments. Hopefully this will make everything a bit clearer.

PA Alpha, chapter 1

I'm not sure, going into this, how I'm going to best go through it. My guess is that I'll go through it slowly, outlining (as I've done thus far) and asking questions. I'll also be looking back at Barnes' commentary (the PA is 74 pages, the commentary is almost 200 pages. That should be an indication of something, I think.) throughout. And, if the time it took me to get through chapter 1 is an indication, this is going to be very slow going.

(This is a close paraphrase to direct quotation at times. I only wish I knew it well enough to be able to explain it on my own.)

Chapter 1

All learning and teaching come from pre-existing knowledge. This is also the case with deduction and induction, they effect their teaching through things already known.
Deduction: assuming items which we are presumed to grasp
Induction: proving something universal because the particular instances are clear

There are two ways in which one must already have knowledge:
1) we must already believe that they are (that x is)
2) we must grasp what the items spoken about are (what the term 'x' means)
(For some things, we must know both things. For example, when we say something about a triangle we must know what it means and 'that it is')

(COMMENTARY: knowledge presupposed by a teacher is of two sorts: 1) knowledge of propositions; 2) knowledge of terms)

"It is possible to acquire knowledge when you have acquired knowledge of some items earlier and get knowledge of others at the very same time" (71a17)
(COMMENTARY: "If at t I learn that a is F by inference from the two premisses that a is G and that everything G is F, then I must have known before t that everything G is F, but I may learn that a is G "at the very same time" as I learn that a is F.")

For example, consider the following argument:
1) Every triangle has two R
2) This figure in the semi-circle is a triangle
3) This figure in the semi-circle has two R
Thus I have to have known (1) before time t, but I might learn both that the figure in the semi-circle is a triangle and that the figure in the semi-circle has two R.

In some cases, learning occurs in this way (what way? in the way (2) is learned? In the way (3) is learned?) and the last term doesn't become known through the middle term. This happens when the items are particulars and aren't said of any underlying subject.

Once you deduce the conclusion, you can be said to know the conclusion in one way and not in another...namely, you know the conclusion universally (all triangles have 2R but you don't know the conclusion simpliciter (haplos)

(COMMENTARY : Barnes reconstructs this sort of scenario:
(1) b knows that everything G is F
(2) a is G
(3) b does not know that there is such a thing as a
(4) (we can thus conclude that) b does not know that a is F
(5) b knows that a is F (from 1 and 2)

The knowledge in (4) is knowledge simpliciter. This is an ordinary knowledge claim.
The knowledge in (5) is knowledge universally. (Although maybe we want to claim that it is (1) that is universal knowledge and not (5).))

Thus, if someone will go up to you and say that do you know that a pair is even, and you say that it is, and then they show you a pair that you've never considered before, you can say that you knew that the pair was even (ie university) even if you didn't know that that pair was even simpliciter (because you'd never considered the pair before). We can claim this sort of knowledge because we assume it holds for every case.

It is only absurd to say that you are learning something in the same sense in which you already know it. (You can learn it in one sense even if you know it in another.)

Barnes' introduction to the Posterior Analytics

Before moving on to practical knowledge, I'm going to spend a bit of time coming to grips with theoretical knowledge. Thus, I'm going to be spending the next several entries working through the Posterior Analytics. I'll be relying on Barnes' translation (2nd ed.) and notes and thus any quotes that I make will come from that translation and edition.

To start with, though, I want to work through Barnes' own introduction to the work and make notes of things that seem interesting and noteworthy:

I

Book A

Book A does not lay out a scientific methodology...or indeed any sort of methodology that one is directed to follow. Instead it concerns itself with how we are to organize and arrange the results of our research.

"it's aim is to say how we may collect into an intelligible whole the scientist's various discoveries - how we may so arrange the facts that their interrelations, and in particular their explanations, may best be revealed and grasped." (xii)

Demonstration is meant to organize what is already discovered, not discover things previously unknown.

I can see how this works with the first principles, given how Aristotle says that they're discovered. How does this work for the principles/conclusions derived from demonstration? Will these already be known prior to putting them into such form? It seems at least possible that one could discover new things via the method of demonstration. Although perhaps this isn't really the point...A. might not deny that you can learn things via demonstration, but still insist that it's primary purpose isn't discovery but the organization of things you've already discovered.

The essential thesis of book A: the sciences are properly expounded in axiomatic form. (Aristotle wanted to do this with every branch of knowledge.) The axiomatization must be formalized in a well-defined language.

The influence of Plato and his dialectic?

Was mathematics already axiomatized at this point, or was Euclid the one that axiomatized mathematics? (This ties back, too, with the idea that Plato wanted knowledge to be modeled after mathematics...)

Book B.

"The axioms of any science...must be (or at least include) definitions or statements of essence; and its main burden is to ask how these definitions are to be elicited and exhibited." (xiii)

"the essence of a kind K is that characteristic, or set of characteristics, of members of K upon which any other properties they have as members of K depend." (Me: ??!) It's sort of like the underlying structure upon which we explain other, more superficial, characteristics or properties.
-- this just assumes that in all things there are some properties that are explanatorily basic and others that are explanatorily derivative.

Like having a shape of a certain kind, colors in a certain configuration, etc as primary properties and it being beautiful as a derivative property?

Other notes

The Posterior Analytics was written when Aristotle was still teaching at the Academy and thus much of the material stems from/is tailored to concerns in the Academy at the time (which also means that what is just baffling to us might be absolutely apparent to that audience).

II

The Analytics shouldn't be seen as a chronological succession (one before the other) but rather as twin contributions to the same lecture course. Although the Posterior Analytics does presuppose the syllogistic reasoning put forward in the Prior Analytics.

These were very much a work in progress, a series of lecture notes that were treated as such by Aristotle, and so it doesn't really make sense to say one is 'written' before the other.

The Posterior Analytics depends on syllogistic reasoning...which is both a serious accomplishment and a problem.
1) Aristotle created a logic that is rigorous and elegant
2) Syllogism is only a fragment of logic (and this shows in the Posterior Analytics itself...Some of Aristotle's scientific and mathematic examples don't work all that well on the schema as he's presented it.

Fundamentals of syllogistic:

"Syllogistic is a series of relations that hold between syllogistic propositions."

A syllogistic proposition is of the form AxB where A and B are terms (A=predicate and B=subject) and x is one of four syllogistic relations (a, e, i, o)

SO AaB is a universal affirmation proposition (Every B is an A). Aristotle expresses such propositions in one of the following ways:
* A holds of every B
* A is said of every B
* A is predicated of every B
* A follows every B

AeB is a universal negative (No B is an A)

AiB is a particular affirmative (Some B is A)

AoB is a particular negative (Some B is not A)

The most important relations that hold between these various propositions are:

the Laws of Conversion:
(AeB -| |- BeA ; AiB -| |- BiA; AaB |- BiA)

The Laws of Subalternation:
(AaB |- AiB; AeB |- AoB)

A mood is an ordered sequence of three syllogistic propositions:
The first two propositions have one term in common; the third proposition conjoins the other two terms (the 'extremes').
There are three arrangements of premise pairs that define the syllogistic figures:
(I: AxB, BxC), (II: MxN, MxX), (III: PxR, SxR).

There are 192 moods of which Aristotle accepts 14 as valid argument forms.

An example of this? All men are mortals, Socrates is a man (would this be a case of AiB?), Socrates is a mortal. (?) Perhaps Every cat is a mammal, every mammal bears live young, therefore every cat bears live young?

The fourteen valid arguments have traditional names and the three vowels of each name give in order the syllogistic relations of the mood:
(I)
bArbArA
cElArEnt
dArII
fErIO

(II)
cEsArE
cAmEstrEs
fEstInO
bArOcO

(III)
dArAptI
fElAptOn
dIsAmIs
dAtIsI
bOcArdO
fErIsOn

SO Barbara = AaB, BaC |- AaC
and Celarent would be AeB, BaC |- AeC

Aristotle also uses modal notions of 'necessarily' and 'possibly'. A demonstration is a species of modal syllogism...all of the propositions are necessary. Barbara is the paradigm demonstrative mood. So the paradigm demonstrative mood will be: ☐AaB, ☐BaC |- ☐AaC

A demonstrative science is one that can be displayed through demonstrations.

Supplementary Notes

"A Pst is primarily concerned to investigate how the various facts and theories which practising scientists discover or construct should be systematically organized and intelligibly presented. The connection with teaching is this: in so far as a teacher is concerned to transmit a body of knowledge, he will best do so by preseinting it in a form in which its organization and explanatory coherence are intelligibly revealed." (xix)

Barnes' introduction to the Posterior Analytics

Before moving on to practical knowledge, I'm going to spend a bit of time coming to grips with theoretical knowledge. Thus, I'm going to be spending the next several entries working through the Posterior Analytics. I'll be relying on Barnes' translation (2nd ed.) and notes and thus any quotes that I make will come from that translation and edition.

To start with, though, I want to work through Barnes' own introduction to the work and make notes of things that seem interesting and noteworthy:

I

Book A

Book A does not lay out a scientific methodology...or indeed any sort of methodology that one is directed to follow. Instead it concerns itself with how we are to organize and arrange the results of our research.

"it's aim is to say how we may collect into an intelligible whole the scientist's various discoveries - how we may so arrange the facts that their interrelations, and in particular their explanations, may best be revealed and grasped." (xii)

Demonstration is meant to organize what is already discovered, not discover things previously unknown.

I can see how this works with the first principles, given how Aristotle says that they're discovered. How does this work for the principles/conclusions derived from demonstration? Will these already be known prior to putting them into such form? It seems at least possible that one could discover new things via the method of demonstration. Although perhaps this isn't really the point...A. might not deny that you can learn things via demonstration, but still insist that it's primary purpose isn't discovery but the organization of things you've already discovered.

The essential thesis of book A: the sciences are properly expounded in axiomatic form. (Aristotle wanted to do this with every branch of knowledge.) The axiomatization must be formalized in a well-defined language.

The influence of Plato and his dialectic?

Was mathematics already axiomatized at this point, or was Euclid the one that axiomatized mathematics? (This ties back, too, with the idea that Plato wanted knowledge to be modeled after mathematics...)

Book B.

"The axioms of any science...must be (or at least include) definitions or statements of essence; and its main burden is to ask how these definitions are to be elicited and exhibited." (xiii)

"the essence of a kind K is that characteristic, or set of characteristics, of members of K upon which any other properties they have as members of K depend." (Me: ??!) It's sort of like the underlying structure upon which we explain other, more superficial, characteristics or properties.
-- this just assumes that in all things there are some properties that are explanatorily basic and others that are explanatorily derivative.

Like having a shape of a certain kind, colors in a certain configuration, etc as primary properties and it being beautiful as a derivative property?

Other notes

The Posterior Analytics was written when Aristotle was still teaching at the Academy and thus much of the material stems from/is tailored to concerns in the Academy at the time (which also means that what is just baffling to us might be absolutely apparent to that audience).

II

The Analytics shouldn't be seen as a chronological succession (one before the other) but rather as twin contributions to the same lecture course. Although the Posterior Analytics does presuppose the syllogistic reasoning put forward in the Prior Analytics.

These were very much a work in progress, a series of lecture notes that were treated as such by Aristotle, and so it doesn't really make sense to say one is 'written' before the other.

The Posterior Analytics depends on syllogistic reasoning...which is both a serious accomplishment and a problem.
1) Aristotle created a logic that is rigorous and elegant
2) Syllogism is only a fragment of logic (and this shows in the Posterior Analytics itself...Some of Aristotle's scientific and mathematic examples don't work all that well on the schema as he's presented it.

Fundamentals of syllogistic:

"Syllogistic is a series of relations that hold between syllogistic propositions."

A syllogistic proposition is of the form AxB where A and B are terms (A=predicate and B=subject) and x is one of four syllogistic relations (a, e, i, o)

SO AaB is a universal affirmation proposition (Every B is an A). Aristotle expresses such propositions in one of the following ways:
* A holds of every B
* A is said of every B
* A is predicated of every B
* A follows every B

AeB is a universal negative (No B is an A)

AiB is a particular affirmative (Some B is A)

AoB is a particular negative (Some B is not A)

The most important relations that hold between these various propositions are:

the Laws of Conversion:
(AeB -| |- BeA ; AiB -| |- BiA; AaB |- BiA)

The Laws of Subalternation:
(AaB |- AiB; AeB |- AoB)

A mood is an ordered sequence of three syllogistic propositions:
The first two propositions have one term in common; the third proposition conjoins the other two terms (the 'extremes').
There are three arrangements of premise pairs that define the syllogistic figures:
(I: AxB, BxC), (II: MxN, MxX), (III: PxR, SxR).

There are 192 moods of which Aristotle accepts 14 as valid argument forms.

An example of this? All men are mortals, Socrates is a man (would this be a case of AiB?), Socrates is a mortal. (?) Perhaps Every cat is a mammal, every mammal bears live young, therefore every cat bears live young?

The fourteen valid arguments have traditional names and the three vowels of each name give in order the syllogistic relations of the mood:
(I)
bArbArA
cElArEnt
dArII
fErIO

(II)
cEsArE
cAmEstrEs
fEstInO
bArOcO

(III)
dArAptI
fElAptOn
dIsAmIs
dAtIsI
bOcArdO
fErIsOn

SO Barbara = AaB, BaC |- AaC
and Celarent would be AeB, BaC |- AeC

Aristotle also uses modal notions of 'necessarily' and 'possibly'. A demonstration is a species of modal syllogism...all of the propositions are necessary. Barbara is the paradigm demonstrative mood. So the paradigm demonstrative mood will be: ☐AaB, ☐BaC |- ☐AaC

A demonstrative science is one that can be displayed through demonstrations.

Supplementary Notes

"A Pst is primarily concerned to investigate how the various facts and theories which practising scientists discover or construct should be systematically organized and intelligibly presented. The connection with teaching is this: in so far as a teacher is concerned to transmit a body of knowledge, he will best do so by preseinting it in a form in which its organization and explanatory coherence are intelligibly revealed." (xix)

Questions from the reading group:

Met with the reading group on Wednesday and we talked about the first part of Taylor's paper (the bit on theoretical knowledge). Rather than jump into practical knowledge, we're going to stick with theoretical knowledge for the time being and look at the Posterior Analytics and one or two articles whose aim is to make the PA comprehensible.

A few questions were raised at the reading group, that I wanted to add here...for further reference and so, hopefully, some sort of answer can be gotten for them over the course of studying:

1) What does a first principle look like? What's a paradigm instance of a first principle?

2) Do the different branches of knowledge/science (astronomy, biology, physics, etc) have drastically different first principles? Are there some principles that unify the sciences?

3) Will the first principles differ based upon which of the four causes one is giving an explanation of? (Aristotle says that there are four causes, each of those four causes acts as a way to explain some phenomenon, an aim of demonstration is to provide explanations, thus will the principles that structure those (four) different kinds of explanation differ drastically from one another?)

Taylor, part 3

This has been sitting on my computer for a few days now...I just didn't get around to posting it. That's it for the Taylor article. I'm planning to move onto the Nicomachean Ethics book 6 and then the Posterior Analytics.

---

Taylor, “Aristotle’s Epistemology”, part 3. Aristotle’s Theory of Perception

Any capacity is defined in terms of the nature of its actualization. (For ex: musical ability is defined in terms of being able to play music.) SO the capacity to perceive must also be defined in terms of its actualizations.

(ME: Basically quoting for a bit. Can't figure out a way to properly paraphrase this...)
Aristotle gives an account of the nature of sight (one sort of perceptual ability):
1) That which is capable of perception is potentially what the object of the sense is actually.
2) Perception is a sort of alteration in that which is capable of perceiving: it is acted on by the object of perception, so as to become what the object is actually.
3) The sense or the sense organ receives sensible forms without their matter
4) The actualization of the sense and the actualization of its object are one and the same, but their being is different
5) The sense judges or discriminates its proper objects
6) It is impossible to be mistaken regarding the proper objects of any sense
7) When we perceive by any sense, we perceive that we perceive.

The objects of sense are colors, sounds, tastes, etc (not houses, trees, people, etc) If I see Socrates, I see him only incidentally, I see the colors, sounds, etc essentially.

The senses are capacities to register their appropriate objects, (1) - (3) give a theory of the nature of this registering. According to (1) and (2) the perceptual qualities act on the organs so as to make the organs what the qualities are actually. (3) describes this abstractly.

This is a physiological process...the visible mechanism becomes colored, etc. ("In every case where A acts on B, A actually possesses certain character F, and acts on B by causing B to become F" (140).) This isn't a purely physiological process, though, because the sense organ discriminates the perceptual qualities (see proposition 5). The discrimination is perception. Further, the individual perceives that he perceives. "The physiological changes constituting the operations of the embodied sense-faculties are processes in which the percipient becomes aware of the sensible qualities of external things" (138).

(4) and (6) are both central to Aristotle's claims regarding perception being a source of knowledge. (4) ensures objectivity of what the senses discriminate and (6) ensures the reliability essential to a source of knowledge.

There is an open question of how strong Aristotle's claim in (6) should be taken. We might want to say that because sense organs are designed for discrimination of their particular objects (sight, sound, taste, etc), in normal conditions the perception is correct...we might say that this claim only holds 'for the most part'.

Might we see this as a prototype of perception as a criterion of truth? Although one might have to claim that for it to be a proper sort of criterion of truth it must be true all the time and not just for the most part. This is much more like the Epicurean account of epistemology, at least, than I thought. (Although the Epicureans were atomists, and so their account of perception is going to be drastically different than Aristotle's).

We can understand (4) thusly: "Given any object O and any sensible quality S, if O possesses S, then, when O is not activating any sense-organ appropriate for the registering of S, O possesses S potentially; O possesses S actually when and only when O activates some sense-organ appropriate for the registering of S" (139). A bell struck when no one is within earshot does not actually sound, but sounds only potentially; the bell only actually sounds when the sound is heard.

((1)-(3)) and (4) are incompatible with one another...because in (1)-(3) the faculty is seen as passive, but in (4) we see the claim that the object exists only potentially prior to the act of perception, there is no sense in which the object acts on the faculty and not vice versa.

We see motivation for why Aristotle would posit both (1)-(3) and (4) (although incompatible). (1) - (3) describe a causal theory of perception...one acquires sensory information via the causal agency of the world. (4) is a sort of realism about the objects of the senses. But the nature of a given color or taste, etc is that it is the content of a perceptual act. So the objective feature is what is realized in the perceptual act and all that is 'out there' prior to the act is potentiality.

(Taylor talks about a potential solution to this problem in an approach advocated by the Atomists and why Aristotle rejected this explanation. I'm skipping over a summary of this.)

We can see how, then, Aristotle's theory of perception provides a foundationalist account of the justification of knowledge. Knowledge is founded on perception and perception is guaranteed to be veridical (at least for the most part) given that the faculties of perception are designed to register their proper objects. This doesn't provide sufficient foundation for theoretical and practical knowledge. Indirect perception plays a role in scientific theories but Aristotle says that these are phainomena.

--
That's it for the Taylor article. I'll be starting in on the primary literature now...I'll begin with EN book 6 and then move onto the Posterior Analytics.