Daily notes on Aristotle's corpus

[Eiuol]

Every day I am reading Aristotle. I'm not going through his corpus sequentially necessarily, but I am going to read all of it. My objective for doing this reading is to 1) understand philosophy from an approach before centuries of confusions and rationalizations, and 2) gain a wider understanding of Rand as a modern Aristotelian.

My notes are generally consist of points that I found particularly interesting and worth committing to memory, and not obvious (some points are absolutely essential but pretty obvious to anyone well-versed in Objectivism and philosophy in general, so I don't write them down). They are not appropriate as study guides, although they should be good if you want to mine Aristotle for ideas. There is a lot I am taking note of mentally, so a lot of this is nothing more than a record of ideas, a sort of diary. Feel free to post questions about what a read.

[Eiuol]

Prior Analytics translated by Robin Smith

47b - 52b 

Notes are listed in terms of the chapter they reference.

33 - Sometimes Aristotle uses proper names. It seems that many scholars think that this is a generic term or as the concept 'man'. I'm thinking that most likely it references a student of his, and probably should stand for a particular, that is, a substance (a concrete individual). Aristotle talks of a "musical Mikkalos" in a deduction, but the deduction isn't quite clear. It is an example of evidence that Aristotle is presenting much of his philosophy in a pedagogical way - perhaps that doing philosophy is active through discussion with students, where writing is a tool of illustration rather than the main content.

33 - When deducing, be careful with how the different premises relate to each other. Resemblance between 2 premises can cause error.

34 - Poorly set out terms cause error. Try substituting to avoid that.

44 - One cannot deduce below assumptions, that is, there will not be a deduction if one goes below the assumptions.

44 - deductions work when one agrees that they will accept the conclusion. Deduction through impossibility requires no agreement to this. 

Because of all the spatial descriptions of the different deductions and figures, and throughout the text, I suspect that everything written down should ultimately be presented visually in a geometric way. Writing it down makes it seem like a transcription by a student, hence the seeming errors or strange grammatical constructions that would be even unusual for Aristotle. Or, it was for Aristotle's own use simply to get a quick glance at how to explain his reasoning.

[Doug Morris]

10 hours ago, Eiuol said:

44 - One cannot deduce below assumptions, that is, there will not be a deduction if one goes below the assumptions.

 

Can you clarify?

[Eiuol]

I mean that you cannot deduce anything about which an assumption is predicated on. If one assumption is that dolphins are mammals, then the deduction from there cannot demonstrate that in fact dolphins are mammals.

[Eiuol]

This is Book 2.

53a - 63b

One general theme here is deducing truth through falsehood, basically what - from a modern perspective - we understand to be valid but unsound arguments where the premises are false.

5 - Aristotle mentions proving in a circle. I'm not sure if he is saying that this is a fallacious way of thinking, or if it is simply a type of deduction. He mentions proving in both directions: A to B to C, C to B to A. I think this could have to do with distinct concepts that are nonetheless aspects of the same thing on the same level of abstraction. This would be a unity. You could deduce that virtue belongs to flourishing, and that flourishing belongs to virtue. I don't know if he had this sort of thing in mind.

15 - Contraries are related to universals ('to every' is the contrary of 'not to every'). Opposites are related to particulars ('to some' is the opposite of 'not to some' even though not belonging to some implies also belonging to some).

16 - You cannot prove a thing through itself. If you could, everything could be known through itself. Furthermore, Aristotle seems to be saying that for a deduction or proof to exist, the conclusion must be falsifiable. This makes sense, considering that we can't prove that existence exist. It is not even possible to conclude that existence does not exist. It is not falsifiable. Of course, we could always argue if the particular premise is falsifiable in the first place.

17 - 

Birds are vertebrates.

The earth is round.

Therefore, trees are rocks.

Clearly the conclusion is false, despite the truth of the premises. It is also a badly formed argument. But Aristotle asks why it is that "the falsehood does not follow" is true. Is it because if you take out one premise, the conclusion is still false? Or is it because in reality, the conclusion is false regardless of if these particular premises are true or not? It's a question about his own system of logic.

Edited July 7, 2021 by Eiuol

[Doug Morris]

21 hours ago, Eiuol said:

He mentions proving in both directions: A to B to C, C to B to A.

I don't know whether this has anything to do with what Aristotle was getting at.  In math, we often prove that A and C are equivalent by proving the two directions separately.  We might go A to B to C and C to B to A, or A to B to C and C to D to A.  In many cases one direction is easier than the other.

22 hours ago, Eiuol said:

'to some' is the opposite of 'not to some'

In what sense?  In English, the negation of a statement containing "to some" would substitute "not to any".

[Eiuol]

3 hours ago, Doug Morris said:

I don't know whether this has anything to do with what Aristotle was getting at.

Basically, it would be taking a conclusion and also using it as a premise.

3 hours ago, Doug Morris said:

In English, the negation of a statement containing "to some" would substitute "not to any".

He says what you say here elsewhere, sure. But in this part I'm not totally clear why he stated things differently. Here he is simply adding "not" to the statement "to some". I wonder if he made a distinction between opposite statements and opposite premises that I didn't notice. The important point is that contraries involve universals, opposites do not. And by the way, universals here refer to secondary substances (aspects said of something else, which we might call abstractions, or you might want to call it a predication of concretes) that apply "to every" of something.

Edited July 8, 2021 by Eiuol

[Eiuol]

66a - 69a

19 - Aristotle mentions the problems of using the same premise twice in a deduction. It's not a proper deduction. It's interesting though that he mentions this in the context of a debate. He makes it a point to say that if you are on the offensive, you could use the same premise twice in a deceptive way. It's a particularly easy way to manipulate seems to be the point of doing it here - probably very useful for interrogation scenarios where you make it sound like you have a convincing argument that you know something secret even if in reality you don't have enough evidence.

21 - Sometimes it's hard to tell when someone is making a bad deduction in comparison to mistaking that one premise belongs to another. This isn't really what Aristotle was saying here at all, but it's what he made me think about.

23 - Deduction through induction. He has in mind going from A, then to C, then to B (the middle term). This is in contrast to the usual A to B (the middle term) to C. It still doesn't seem like he means deduction here in the sense he has been using the word. It might be a translation thing. Aristotle reminds us that with inductions, C is made up of all individuals of a certain kind. It just sounds like a formal way to describe induction through his system, so he might just mean deduction as a type of argument in his system. He is still talking about (in my estimation)  using some set of facts about an individual and then generalizing.

[Doug Morris]

Would Aristotle object to the following proof that 0 times any number x is 0?

(I will use * to indicate multiplication.)

0 * x = (0 + 0) * x because 0 is the additive identity element.

(0 + 0) * x = 0 * x + 0 * x by the distributive law.

0 * x = 0 * x + 0 * x because = is transitive.

0 * x + -(0 * x) = (0 * x + 0 * x) + -(0 * x)  because equals added to equals give equals.

(0 * x + 0 * x) + -(0 * x) = 0 * x + (0 * x + -(0 * x)) because addition is associative.

0 * x + -(0 * x) = 0 * x + (0 * x + -(0 * x)) because = is transitive (first of two premises used twice).

0 = 0 * x + 0 by definition of the unary operator -.

0 = 0 * x because 0 is the additive identity element (second of two premises used twice).

[StrictlyLogical]

 

6 hours ago, Doug Morris said:

Would Aristotle object to the following proof that 0 times any number x is 0?

(I will use * to indicate multiplication.)

0 * x = (0 + 0) * x because 0 is the additive identity element.

(0 + 0) * x = 0 * x + 0 * x by the distributive law.

0 * x = 0 * x + 0 * x because = is transitive.

0 * x + -(0 * x) = (0 * x + 0 * x) + -(0 * x)  because equals added to equals give equals.

(0 * x + 0 * x) + -(0 * x) = 0 * x + (0 * x + -(0 * x)) because addition is associative.

0 * x + -(0 * x) = 0 * x + (0 * x + -(0 * x)) because = is transitive (first of two premises used twice).

0 = 0 * x + 0 by definition of the unary operator -.

0 = 0 * x because 0 is the additive identity element (second of two premises used twice).

I'm not sure you have connected each step in this hypothetical "proof".

 

How about this [taking K as the additive identity element: K = (K + K)]

So

K*x = (K + K)*x

       = K*x + K*x

       = 2*K*x

Using the unitary operator "-"

K*x - K*x = 2K*x - K*x

or

0 = K*x

for any x.

 

 

[Eiuol]

8 hours ago, Doug Morris said:

Would Aristotle object to the following proof that 0 times any number x is 0?

Prior Analytics isn't about proper argumentation, it's concerned with Aristotle's formal system of logic and how deductions are formed within that system. I avoid the word syllogism because apparently (according to translation notes) the meaning of that term has been distorted after centuries of translations such that we associate in English the word syllogism with a specific type of deduction, even though Aristotle was actually only referring to arguments within his deductive system. Topics and Rhetoric deal with the way arguments are used. 

Also, in your example, you used a rule twice, you didn't use a premise twice. In this case, a premise would be an entire line in what you wrote out. After I read the translator's notes, apparently I misunderstood. I'm still a little unclear (this is not unique to me simply as a student of Aristotle, even Aristotle experts find Prior Analytics difficult to interpret because it is such an ambiguous text). But I think he was saying using a shared premise twice. Let me explain:

A > B

B > C

B > D

A > D

So sometimes it might appear that C leads to D, whether it be due to deception or error. Again though, I might be misunderstanding.

17 hours ago, Eiuol said:

 It still doesn't seem like he means deduction here in the sense he has been using the word. It might be a translation thing.

It's interesting that the translator says that the ancient Greek word epagogee is traditionally translated as induction because in Latin people translated it as inductio. Apparently that Greek word means "to lead into" or "bring in". It is probably better to think of the term induction here as reaching conclusions about a genus from a species. 

2 hours ago, StrictlyLogical said:

I'm not sure you have connected each step in this hypothetical "proof".

I'm trying to reserve these threads here for questions and discussion about my particular readings on Aristotle. But, I want to point out that from a modern perspective, there are often better and more efficient ways to express logical statements than Aristotle. Boolean logic for instance helps things a lot, as does the idea of operators. For better or worse, Aristotle system would work like Doug's example, even though your reply is definitely a better deduction. Fortunately, he takes his system as one that can develop over time.

[Eiuol]

On 7/8/2021 at 1:49 PM, Doug Morris said:

In what sense?  In English, the negation of a statement containing "to some" would substitute "not to any".

Some clarification and answers to my own questions:

Contraries are about universal premises, premises about "every".

Opposites are about other types of pairs, that is, ['to some' and 'to no'] and ['to some' and 'not to some']. It captures the different ways people might say 'to some'; Aristotle always seems careful to point out when language might be ambiguous.

69a - 70b

This is the end of the book. More readings will be in new threads.

24 - Aristotle formally treats using examples as a type of deduction in his system. He says it is similar to deduction through induction, because although it generalizes, it doesn't involve every particular related to the premise (to translate to Oist context, this would be a generalization that doesn't involve every instance of a concept or premise). It seems like he's talking about demonstrating similarities as a supplemental method or something more related to using premises that you aren't completely sure of yet.

27 -

Signs are like symptoms, in the sense that a fever is a result of the flu, and feeling hot is a result of a fever, therefore feeling hot is a sign of the flu. But other diseases might have that same sign. 

This is the example Aristotle uses. Suppose the following:

A = courage
B = large extremities
C = lion

B belongs to every C, but also other animals.
Every A belongs to every C, but no other animals.

In this way, B would be a sign. Notice that large extremities is shared by both A and C.

[Eiuol]

One final note is that I realize some things I have written here are inconsistent or incomplete, or not phrased perfectly. This is because my focus is on learning and amending my understanding as I say more. I expect to make lots of mistakes.

[Eiuol]

On 7/7/2021 at 2:56 PM, Eiuol said:

I mean that you cannot deduce anything about which an assumption is predicated on. If one assumption is that dolphins are mammals, then the deduction from there cannot demonstrate that in fact dolphins are mammals.

Fixed because the first sentence actually makes my point more unclear.

[Eiuol]

On 7/9/2021 at 12:39 AM, Eiuol said:

23 - Deduction through induction. He has in mind going from A, then to C, then to B (the middle term). This is in contrast to the usual A to B (the middle term) to C. It still doesn't seem like he means deduction here in the sense he has been using the word. It might be a translation thing. Aristotle reminds us that with inductions, C is made up of all individuals of a certain kind. It just sounds like a formal way to describe induction through his system, so he might just mean deduction as a type of argument in his system. He is still talking about (in my estimation)  using some set of facts about an individual and then generalizing.

https://inductivequest.blogspot.com/2009/10/aristotles-view-of-induction-summary.html

This is further support for how this section is not talking about induction as we understand it. In this instance, "induction" is "leading to" and is a form of deduction.