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# Posterior Analytics

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Posterior Analytics translated by G. R. G. Mure

Numbered in terms of chapters.

71a - 73b

Aristotle starts by explaining what his object of inquiry is. He mentions scientific knowledge, but not what we mean by scientific knowledge like knowledge about biology or physics. He's talking about demonstrations and arguments using prior knowledge to acquire new knowledge. I'm not going to get into the nuance of the word here, other than to say that by science he basically means demonstrating conclusions about things which are necessarily the case. So, this probably leaves out things about imagination, possibility, intuition, and so on.

1 - You can know what a right triangle is, and you can know that what you are looking at is a right triangle. The difference is that you need to investigate the triangle you are looking at to know that it is a right triangle. This seems problematic when we think about right triangles that exist but we are unaware of. Do we then not know what all right triangles are? Do we only talk about right triangles in terms of the right triangles we have seen and nothing else? If the only prime numbers you know about are the ones you memorized, and you don't have a rule to calculate prime numbers, then in what sense do you actually know what a prime number is? Anyway, you can know about things universally, like how you know that the concept right triangle refers to all right triangles, including those you have not observed and those that have yet to exist.

2 - Premises must ultimately rest on a premise that meets the following criteria: true, primary, immediate, better known than the conclusion, and prior to the conclusion.

You probably can use the ideas 'better known than the conclusion' and 'immediate' for figuring out first principles of a field. He doesn't mention sense perception or what this ultimate grounding is, but finding what is better known than the conclusion would be a process of reduction to sense perception in the Oist sense of reduction. Aristotle specifically mentions that by prior, he means prior in terms of man's knowledge (epistemologically prior), not metaphysically prior.

3 - Circular demonstration (proving in a circle) is impossible - except when the attributes imply each other. So you could prove in a circle about mind and body, because they imply each other.

Edited by Eiuol
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73b - 75a

4 -

'True in every instance of its subject'
Also true at all times, that is, time is abstracted away.

Essential
Characteristics that compose a subject's definition, and are necessarily the case. This is in contrast to characteristics that aren't necessarily in a subject. Even and odd both belong to number, so they are both essential to number. Brown and spotted can both belong to dog, but dogs are not necessarily brown and spotted. This is not the same sense of 'essential' as Rand.

Commensurable universal
An essential that can be shown to belong to any random instance of the subject and the subject is the first one that the attribute can belong to. This is close to what Rand meant by essential as far as I can tell, although defined differently. Not only does the characteristic apply to the particulars you have enumerated, but any instance that could be offered.

In later chapters the translator talks about necessary and contingent facts. I see no reason for such a translation because the dichotomy didn't even exist during Aristotle's time. He is talking about when characteristics are necessarily part of the subject, or when 2 or more events are causally connected.

5 - There are certain times when we fall into error about commensurable universals.

When the subject is an individual or there is no universal about the individuals. Multiple individuals without a universal is probably simply anything that can't be united, like circles and dogs.

When multiple subjects belong to different species and have a universal, but no name yet exists for the universal.

When the subject is taken as a whole, but in reality it is only a part of a larger whole.

Edited by Eiuol
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75b - 78b

6 - Demonstrative knowledge rests on basic truths.

7 - You can't demonstrate from one genus to another except in certain cases. This sounds like saying you can't demonstrate by changing the context of your abstractions. Geometry can't prove anything of lines except the characteristics they possess in virtue of their genus. You could demonstrate other things about lines with other genera.

8 - Aristotle says that if the premises proceed from commensurable universals, then the conclusion is eternally true - not perishable. You could interpret this as all things possessing a platonic sort of universal. But given the context, I'm quite sure "eternally true" means for Aristotle that the truth of the conclusion doesn't change, that is, the truth of it doesn't go away at some point in the future. If the essential of man is rational thought, and if it is true, it will remain so qua essential.

10 - If a teacher does not demonstrate a provable assumption to a pupil, then to the pupil, the assumption is a hypothesis.

11 - Law of excluded middle

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78b - 82b

13 - Knowledge of the fact is when you know something is the case or exists as an observation (such as birds fly) but don't know why. Knowledge of the reasoned fact is when you know why something is the case (one reason birds fly is that they have evolved to do so).

Aristotle basically says that knowledge of the reasoned fact is the domain of the respective expert. It's interesting to note that he acknowledges that math concerns itself with forms (based on all my reading so far, it is best to interpret "forms" as "concepts") but not anything empirical, so can't say anything about "knowledge of the fact". Math might be able to explain why some things are the case, however. This can be done in combination with other fields that are more connected to the empirical. Aristotle says you could combine optics and math for example.

14 - "all A belong to all B, all B belong to all C, therefore all A belong to C" is the most scientific logical figure.

18 - Here Aristotle is very clear about the importance of sense perception. He explicitly says that it is impossible to grasp universals without induction, and that induction requires sense perception.

19 - Can you do descend from the highest abstractions all the way down to particulars infinitely? Can you ascend from particulars to the highest abstractions infinitely?

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82b - 84b

22

Predicates that signify substances (concrete individuals) are either identical with the subject or species of the predicate. Predicates that don't signify substances are accidents or coincidences. Here Aristotle explicitly rejects Plato's Forms as relevant. He calls them sound without sense, which makes me think of a parrot that doesn't know it says. In this context it sounds like he's criticizing as if it's obvious that Forms are disconnected from concretes. It sounds like attention but I think it's another example of how these texts are used as teaching tools. It's a good place to transition into criticizing Plato if he wanted to in a lesson.

If we know the consequent in a demonstration only through the antecedent (the premises), and if there is nothing better than knowledge, then the series going down must terminate somewhere if there is scientific knowledge of the consequent. If it doesn't terminate, then you can't acquire scientific knowledge through demonstration. Basically, if you could go on forever, there would be an infinite number of things to possibly demonstrate. If there are infinite things to possibly demonstrate, then there can be no determinate definition. The best you could do in this case is pick an arbitrary cutoff point in terms of your premises and treat that as a hypothesis. But this can't demonstrate what is necessarily the case about a subject.

The series when going downward must terminate in a substance. Aristotle does not mean terminating in the smallest part of a substance, but terminating the individual whole. If that same series goes upward, it must then terminate somewhere, because if it went on infinitely, there would be infinite attributes in a definition - but infinite attributes can't apply to a single subject. I think by definition he means all the essential elements (elements that are necessarily part of something by nature) of something.

Edited by Eiuol
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84b - 87b

23 - there are a finite number of terms between the conclusion and the subject. You can condense everything between the subject and the conclusion, until the remaining premise is immediate. In particular, the premise of the subject becomes single. This would be a basic unit. This also sounds like reduction in the Oist sense, which is also a type of demonstration.

24 -

Aristotle presents an argument that demonstration of particulars is better than demonstration of universals. It revolves around saying that universals don't touch reality as much as particulars, and more likely to mislead. I think he is presenting a reasonable argument, maybe even his own devils advocate argument, because it is such a clear rejection of Platonic forms. Basically: "abstractions are further from reality, so isn't demonstrating them inferior in all cases?"

Demonstration of the commensurable universal it is actually the best because it could say the most about reality. The extent of what it covers (multiple individuals), and how it is predicated of the subject by that subject's very nature, will provide a great sum of knowledge that isn't detached from reality anyway. This makes sense, because if the best arguments had to do with concrete particulars, that would be a concrete bound mentality. But conceptual thinking, and thinking with the essentials of concepts, is best for human thinking.

29 - How many ways can you prove a conclusion?

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87b-90b

31 - The mere act of perception cannot provide scientific knowledge. You cannot see commensurable universals directly.

Not clear if he thinks there are exceptions. He mentioned eliciting the universal from an act of perception. Maybe he means when you already possess knowledge of the universal?

32 - 2 kinds of fundamental truth: from premises of a demonstration, from subject-genus

33 - the object of scientific knowledge and opinion can be about the same. The difference comes in with how you apprehend the object. You can have a true opinion that doesn't qualify as knowledge in the sense that an opinion that man is animal means that you think man is not necessarily animal and animal is anonessential (not part of the nature of man) element to man, while knowledge that man is animal means that you think that animal is an essential element in man.

Book II

1 -
Is the connection between an attribute and a thing a fact?
Why is there a connection?
Does the thing exist?
What is the nature of the thing?

2 - Why there is a connection and what is the nature of the thing both essentially ask "What is the middle term?" At least when the connection is determined to exist or the thing exists.

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90b - 93b

3 - Not all definable things are demonstrable. Not all demonstrable things are definable.

Definition reveals the essential nature, it is of the essential nature of something. Demonstration reveals whether an attribute that attaches to a subject, it demonstrates a connection.

5 - Continually dividing - the method of division - does not provide an inference, as it doesn't demonstrate. It cannot answer why, since there is no middle term.

7 - If definition can prove the essential nature of the thing, can it also prove that the thing exists? It can't, because definition and demonstration are about different types of things, and existing is not a genus (and therefore can't be an essence).

A demonstration can't prove that a particular name has to mean any particular thing.

8 - Aristotle says he will start again and think about which conclusion so far are soun. So anything incomplete before or seeming to imply something else is only because he is working through everything. It really does seem like he's getting at how a definition should properly be of essentials, but not something that proves or demonstrates.

You cannot apprehend the reason for a fact before apprehending that a fact exists. You cannot apprehend the essence of something before apprehending that it exists. You might accidentally be aware of a thing through an element in its character, like the blockage of light during an eclipse, but this doesn't count as knowledge because you still don't know what the element is of in the first place. (This sounds similar to when Rand mentions implicit knowledge).

You can't deduce essential nature, but through deduction you can exhibit essential nature. Yet he concludes that the essential nature that has a cause distinct from itself can't be known without demonstration, and it cannot be demonstrated? Something doesn't make sense to me.

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93b - 100b

10 - A definition is: an indemonstrable statement of essential nature, or a syllogism of essential nature (the difference is grammatical form), or the conclusion of a demonstration that has given essential nature.

11 - One version of the 4 causes, but not the commonly mentioned version. It seems to be missing material cause, and "antecedent which necessitates a consequence" replaces it. Aristotle seems to me cases where causes are linear as opposed to simultaneous or complementary. A cause can both exist for an end as well as by necessity. A cause might also only be for an end, like why people build houses.

12 - Further ideas about temporality in relation to causes.

Processes are divisible, events are indivisible and atomic. Past events and present processes are not contiguous. Aristotle says that a process contains an infinity of past events. But I don't understand how if a process contains an infinity of past events, that it wouldn't be contiguous? In any case, the issue might be translation, and Aristotle recognizes that this explanation is not good enough because he says he will talk more about it later (he might be offering a response to his ideas).

13 -

This section basically describes what we would consider epistemology about the way concepts are related to each other.

Aristotle talks about a method to tracing predicated elements that contain or involve the definable form. I understand this to mean finding what are in fact the essential elements of a subject that are put into its definition. Even more simply, the method of how to properly define something.

He talks about attributes that apply to the subject and has wide application, but doesn't extend beyond the genus. This sounds equivalent to the CCD. Hue applies to red, but also green, and in fact all colors - the genus. These are the kind of attributes we need to think about.

Further he says that if you're writing a book about a subject generically as a whole (a general handbook about a subject), you should divide the genus into species, then find the definition with the help of what I called the CCD. After that, examine the differentiae.

Divisions are not primary. But dividing from something more general to something more specific will guarantee that the general category will contain everything more specific.

Find what elements a set of individuals in a species have in common. Repeat this, but for a different species in the same genus. Keep going until you find a particular identity, and can create a formula for that identity, that is, the definition. But! If you reach several formulas, you have to do more work. Or at least, you are defining more than one thing actually. Although this still is far from scientific experimentation, Aristotle clearly advocates for examining specific individuals of multiple species and finding out what they do.

14 - Collect common characters that you observe. Sometimes, though, the common character has no specific name.

17 - Effects may have more than one cause, but not when the subjects are the same species.

19 - If you possess scientific knowledge from birth, it would mean that you possess apprehensions more accurate than demonstration and fail to notice those apprehensions. If you need to acquire those apprehensions, you would need to do so with pre-existing knowledge (but you don't have the apprehension in the first place of any knowledge!). So, there must be some capacity, because we still manage to apprehend things, but it can't necessarily be superior then developed states like scientific knowledge.

Aristotle explains this capacity by reasoning from animals in general. Because of sense perception, all animals have a discriminatory capacity. To the extent that sense impression does not persist, the animal doesn't "know" anything beyond the simple act of perceiving. If the sense impression persists, and repeated enough, it becomes memory. When memories repeat enough, they become experiences; memories becoming experiences is possible for those with the power of systematizing. Essentially, Aristotle is saying that the capacity and basis for our ability to possess scientific knowledge through demonstration is built up from the capacity of sense perception. He is giving a biological explanation.

The content of sense perception is universal? This is unclear. Then again, Aristotle literally says his statement will be unclear.

He says that intuition is always true. I doubt that he means intuition in this context the way we mean it.

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On 7/20/2021 at 6:49 PM, Eiuol said:

93b - 100b

. . .

19 - If you possess scientific knowledge from birth, it would mean that you possess apprehensions more accurate than demonstration and fail to notice those apprehensions. If you need to acquire those apprehensions, you would need to do so with pre-existing knowledge (but you don't have the apprehension in the first place of any knowledge!). So, there must be some capacity, because we still manage to apprehend things, but it can't necessarily be superior then developed states like scientific knowledge.

Aristotle explains this capacity by reasoning from animals in general. Because of sense perception, all animals have a discriminatory capacity. To the extent that sense impression does not persist, the animal doesn't "know" anything beyond the simple act of perceiving. If the sense impression persists, and repeated enough, it becomes memory. When memories repeat enough, they become experiences; memories becoming experiences is possible for those with the power of systematizing. Essentially, Aristotle is saying that the capacity and basis for our ability to possess scientific knowledge through demonstration is built up from the capacity of sense perception. He is giving a biological explanation.

The content of sense perception is universal? This is unclear. Then again, Aristotle literally says his statement will be unclear.

He says that intuition is always true. I doubt that he means intuition in this context the way we mean it.

Eiuol, I thought the following might be good to mention here.

On 4/18/2020 at 4:40 PM, Boydstun said:

. . .

I want to close the present installment by noting the change in translation of APo. II 19 by Barnes concerning the traditional intuition in intuitive induction. The older translation relied upon by Peikoff 1964, 66, reads: “From these considerations it follows that there will be no scientific [i.e. deductive] knowledge of the primary premises, and since except intuition nothing can be truer than scientific knowledge, it will be intuition that apprehends the primary premises” (APo. 100b10–12). Barnes final translation reads: “Hence there will not be understanding of the principles; and since nothing apart from comprehension can be truer than understanding, there will be comprehension of the principles” (APo. 100b10–12). In the Barnes translation, scientific knowledge has become understanding; primary principles have become principles; and intuition has become comprehension. Each of these differences is significant, and Barnes argues for them. On the last of those three alterations in translation, Barnes argues against the traditional English of nous into intuition. He remarks in part:

"The commentators translate nous by 'intuition'. The word 'intuition' is a term of art; when it has a determinate sense (and does not merely stand for knowing we know not how), it implies a sort of mental 'vision'; intuition is mental sight; intuited truths are just 'seen' to be true; intuiting that P is coming to know that P without any ratiocination and without using sense-perception—it is 'seeing' that P. The term 'intuition' has a hallowed connection with B 19; indeed, the classical distinction between 'intuitive' and 'demonstrative' knowledge, which is common property to rationalists and empiricists, derives ultimately from this chapter." (1992, 267)

Barnes argues that induction factors into Aristotle’s answers on whether we have innate knowledge of indemonstrable principles that are starting-points of demonstrations and, if not, how knowledge of such principles is acquired. He argues that nous is answer to a different question of Aristotle’s: what is our state that knows those principles? Under Barnes picture, Aristotle has us in the state Barnes calls understanding when we know theorems and has us in the state nous, which Barnes calls comprehension, in our knowledge of indemonstrable principles. “Understanding is not a means of acquiring knowledge. Nor, then, is nous. / . . . ‘Intuition’ will not do as a translation for nous; for intuition is precisely a faculty or means of gaining knowledge. Hence in my translation I abandon ‘intuition’ and use instead the colourless word ‘comprehension’" (268).

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7 hours ago, Boydstun said:

scientific knowledge has become understanding

This is strange to me because Aristotle's clear that scientific knowledge is a narrow form of knowledge that you arrive at through deduction and demonstration from already known knowledge. I don't understand translators sometimes, their choices often seem to drop context or make Aristotle's terms considerably more abstract than they actually are.

7 hours ago, Boydstun said:

it implies a sort of mental 'vision'; intuition is mental sight; intuited truths are just 'seen' to be true

I really think the best translation is "mental vision". There is no need to use an English term with widely different connotations and origins. Mental vision is even more "colorless" than the word comprehension because it captures the context better whenever he uses the term nous. It seems to imply a mental focus, an awareness, not in the form of propositions, a way to engage the world mentally, the way the soul (life) has contact with reality most generally.

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