We haven't had an Aristotle thread in a while. Some things people were talking about in the past:1.) Is 'one' a number? How and why did so many Greek philosophers deny that it was?2.) How were Aristotle's criticisms of Platonic Forms perhaps misguided?3.) What is Aristotle's position on determinism?4.) Is Alexander's influential nature/essence distinction a correct interpretation of Meta 7-8?5.) Does Aristotle's God think Forms after all?I'll start off by shilling for position I've argued for in other threads - Aristotle's God is not thinking "all that is intelligible" but simply himself. One of the main theses of the Metaphysics is that universal concepts cannot be prior to sensibles and exist apart from them *at all*, whether in an intellect or not. To say 'why not in the divine intellect?' is to misunderstand the nature of Aristotle's divine intellect, which is absolutely simple. He never once says that it thinks anything but itself, and this because it is totally one and 'has no contrary' (DA 3.6 or 7) - not in the way that any substance has no contrary, but in that there is no potency in it or passing from one to another (clear from the context). But there ARE intermediaries below it - the other unmoved movers who move the other spheres stand in an ordering as first and second, as he says in Meta 12. Also in De Caelo 2 he talks about the higher spheres are 'better' than the lower ones and uses this to explain diversity of orbits. It's not possible for them to be equal in species, but they have to be like numbers, with a first, a second, and so on. The differentiation of these subordinate movers would seem to be degrees of actuality, with the higher ones being closest to the first principle - that's a traditional reading that's not explicitly formed anywhere, but it seems like the only way they could possibly be distinguished.It's a big deal imo because this is emanationism. When an ultimate good creates the less good simply by the power of its goodness and the desire of the lesser for it, that's all the Neoplatonists ever mean when they talk about emanation. So a huge feature of Neoplatonism is arguably more prominent in Aristotle than it is in Plato - Aristotle's cosmos involves a series of progressively-inferior emanations going back to an ultimate God, just like Plotinus. When Plotinus criticizes Aristotle's first principle, he's really criticizing Alexander's understanding that it is thinking all that is intelligible (hence complex, hence not really a first principle). (Aristotle never once says this btw). And when Plotinus describes his own first principle, he admits that it in a way 'is', that it in a way is 'substantiality', that it 'comprehends' itself in a hyperintellectual manner, that it loves and wills itself without any differentiation, that it is in a way activity - it's the same God as Aristotle is proposing and the daylight between them is exaggerated. Or is it? What do YOU say??
>>239035081 semantics2 they weren't3 he was a determinist4 no5 he doesn't think anything because he doesn't existthere I solved your faggy thread
>>23903520NTA but kill yourself for making that low effort retard post
Let me save everyone else, including OP, the trouble>>23903520retardThere, now no one has any reason to reply to this clearly bad faith faggot again in the thread. Be on the lookout for him and ignore him.
>>239035201) One is not a number because it's a principle of number. It's not logically possible for unity and plurality to be on the same level.2.) It's misguided because it assumes a Form is the same as the essence of an individual and/or a hypostasized concept. His arguments against Forms all assume that they're just sensible essence writ large, but this is clearly not the case in Plato (consider the Living Animal). It's like all his knowledge of the theory of Forms comes from the Phaedo, honestly.3.) He wasn't a determinist where human action is concerned. When it came to inanimate events, he was more interested in the distinction of eternal essence and accident than determined/not, but seems to have accepted per accidens determinism of natural processes.4.) No. The primary essence is the essence of the individual, while the universal essence we think comes from individuals. Universal truths are eternally true because the universe is caused by God, but not in the Platonic or Alexandrian sense that there is an actual Intellect thinking everything true.5.) No, see OP. Aristotle's God, like Plato's Good or Plotinus' One, is prior to Forms or eternal truths.
>>23903540>denies Aristotle believes in eternal essences, then says Aristotle believed in eternal essences
>>23903540The principle of number is measurement, not the unit. You can't explain a number through only a unit. You have to explain the relationship between the unit and the hypothetical quantity, which then makes the number intelligible. >but one is not a number because I'm fixed on the need for a multitudeOne is a number because it is the unit measured against itself or against an equivalent. There are always a multitude being compared. >Aristotle wouldn't be a big fan of something like one being seen as twoThen I suppose you wouldn't be a fan of the end of Physics Bk1, where he explains why the principles of nature could either be two or three. They're at least two because unity and opposites are two principles, but then opposites could always imply two principles in themselves. Yet each principle would be meaningless without the other principle. So it could be 2 total principles or 3 total principles depending on how you "slice" it. Yet the logic still stands in a similar way. >measurement being a principle of number is completely un-AristotelianThen explain why Aristotle uses number as the stand-in for measure when Aristotle explains his philosophy of time: time is the number of motion in regards to the before and after.
>>23903553They're real they just don't exist. How could the idea of copper cause copper to come to be?
Greek philosophers were, almost by definition, not very competent mathematicians. That’s why they did philosophy. If you want to read Greek mathematicians though there are plenty of very bright ones. The first philosopher who knew his shit when it came to math was Descartes (possibly Pythagoras too but we don’t have his work), and it is no surprise he completely differed from prior philosophers and basically reinvented the discipline
>>23903580Fractally wrong on every account. Descartes and the Early Moderns launched a two-pronged attack on the clarity of thought, butchering both mathematics and philosophy in the pursuit of wealth, power, and pleasure.
>>23903583You probably don’t know anything about mathematics either but Aristotle’s natural philosophy was objectively wrong on many counts, and this was heavily revised to significant success by the thinkers you accuse of butchering it. His mathematical contributions were of course nonexistent
>>23903587I guarantee that you know absolutely fuckall about Aristotelian philosophy, and that you've spent many fruitless years consuming and regurgitating memes about Aristotle instead of reading the primary text, and you confuse your ignorance for knowledge. I'm not playing these retard games with you.
>>23903595Sure I do, I think his contributions to logic (which has been superseded)and literary theory are worthwhile.
>>23903601You haven't read anything by Aristotle nor can you articulate why you think such-and-such principle or thinking is outdated (example: most of Aristotle's Physics has nothing to do with experimental science). Your opinion is worthless to me. Kick rocks faggot.
>>23903560I think I remember you from the last thread. Were you the guy talking about time as a number? Because he forestalls your interpretation openly in Physics 4 - time isn't a number in that way. I was annoyed that you kept repeating it even after I pointed it out to you. OK this is my only response - I don't think you'll ever accept that I'm right because you're too stubborn/full of yourself, but it will be maybe helpful for other more sincere students of Aristotle.>The principle of number is measurement, not the unit. Very basic logical error here. Measurement is an idea that's common to many genera, but in the case of number the measure is the unit. Reminds me of the other thread when you were so mixed up on the difference between 'one' in general and the 'unit' of number.>You can't explain a number through only a unit. Correct, number is a plurality of units.>You have to explain the relationship between the unit and the hypothetical quantity, which then makes the number intelligible.Again, the answer is measure. One is a measure for numbers and 'produces' them by measuring them and saying how many they are. You're thinking "oh but the number IS many! So how can the one be prior to the many if number requires the many, not the one?" It's prior because the many can't exist without one but vice versa one can, and because one is its measure. Asking for an 'explanation' of the 'relationship' between unity and plurality would be like asking for an explanation of the relation between between the plucked string and the sound, and then on being told that one produced the other, demanded that we account for the relationship. Aristotle says that this sort of thinking is typical of uneducated people - they can't distinguish first principles from secondary ones. Nor, FWIW, is this a pointless debate, because one is not a number in the same way that God is not in a genus.>One is a number because it is the unit measured against itself or against an equivalentIt's not measured against itself, I tried to explain this to you in the last thread but it was clearly in one ear out the other. Just because you see a monad and recognize it as such and say 'it is one' does not mean it has been measured - measuring involves dividing into parts, as Aristotle discusses. (1/2)
>There are always a multitude being compared.There's no multitude in a thing's being one by definition. You're confusing the plurality of thought/object of thought with unity itself - a gross error.>Then I suppose you wouldn't be a fan of the end of Physics Bk1, where he explains why the principles of nature could either be two or three.He's talking about how they're two in one way and three in another, not how two could be three. Another risible error.>Then explain why Aristotle uses number as the stand-in for measure when Aristotle explains his philosophy of time: time is the number of motion in regards to the before and after."Number is [so called] in two ways: we call number both (a) that which is counted and countable, and (b) that by which we count. Time is that which is counted and not that by which we count. (That by which we count is different from that which is counted.)" (Physics 4.11)Look at that it's right there, just like I said. Time is not a number in the way that numbers are numbers and it is not a measure in the way the one or unit is the measure of numbers.Btw>The smallest number, in the strict sense of the word 'number', is two. (Physics 4.12)Lol. The most annoying part of making these threads is having to spend so much time swatting away pseuds.
>>23903580Discussing the nature of number isn't proper to mathematics but metaphysics and lots of philosophers were also mathematicians, including Aristotle.
>>23903604Not him but you're the one who is in the wrong. By shortening things down into various forms of algebraic notation, Descartes, Leibniz etc provided "relief for the imagination", and consequently "clarity of thought", exactly the opposite of what you've just claimed. You then tried (and failed) to wriggle out of your error by making things about Aristotle, except the train of thought started with Descartes/early moderns. The other guy is also correct that Descartes knew what he was doing when it came to math. Post another childish retort.Why is a mere change/invention in notation so important, and cognitively non-trivial? To get away from writing tedious shit like "If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in multitude, then, whatever multiple one of the magnitudes is of one, that multiple also will all be of all."
>>23903615>>23903618Don't worry, I'll cut your haughtiness down to size.>Measurement is an idea that's common to many generaWhat genera is measurement common to, specifically in a way that it is not also common to number? Name them. In fact, I'll up the ante for you. What are you trying to logically define or isolate with the concept of number? >Reminds me of the other thread when you were so mixed up on the difference between 'one' in general and the 'unit' of number.That's a dishonest way of not only framing the problem but also recalling a previous conversation where you clearly failed to make your opinion. Doubly worse because Aristotle recognizes the problem that being implies unity. >Again, the answer is measure.See, you already agree with me that the principle of number is measure. As in, what is the basis of number, what makes number intelligible, etc. And lest we get bogged down in a second round of semantics, tell me what Greek terms Aristotle uses for the concept "principle"? It's certainly not principle, since that would be Latin. >One is a measure for numbers and 'produces' them by measuring them and saying how many they areWhat is produced when you measure something and you only find the equal or the lonesome? Furthermore, would the product after you measure in this case be an answer to the question "how many?" >There's no multitude in a thing's being one by definition.Now you can't decide on whether a unit can be measured against itself or whether it necessarily requires another. >He's talking about how they're two in one way and three in another, not how two could be three. Another risible error.You're waffling about. Aristotle clearly comes to the conclusion at the end that there is no decisive way to count these principles because it could be either way, logically-speaking. >"Number is [so called] in two ways: we call number both (a) that which is counted and countable, and (b) that by which we count. Time is that which is counted and not that by which we count. (That by which we count is different from that which is counted.)" (Physics 4.11)... He's clearly emphasizing the principle of measure in numbers. What you are doing is begging the question, hard by neglecting the obvious component of measurement in counting.
>>23903634>Not him but you're the one who is in the wrong. By shortening things down into various forms of algebraic notation, Descartes, Leibniz etc provided "relief for the imagination", and consequently "clarity of thought", exactly the opposite of what you've just claimed. You then tried (and failed) to wriggle out of your error by making things about Aristotle, except the train of thought started with Descartes/early moderns.This is the kind of statement made by someone who's never looked at, say, Maxwell's or Newton's equations and asked what physical meaning the in-between operations that derive them amount to. The equations seem to "work", but they're not clear with respect to what they're supposed to be clear about, the things of nature. All they did was make it easier to treat totally different magnitudes as arithmetically calculable.
>>23903634>By shortening things down into various forms of algebraic notation, Descartes, Leibniz etc provided "relief for the imagination"Because if you write a symbol down, that automatically makes the referent a legitimate concept, right? If anything, the early moderns have expanded fictional thinking in a field that should have no use for it while they struggled to grasp the first principles that govern math (and FAILED utterly in thinking their way out of the mess). >You then tried (and failed) to wriggle out of your error by making things about Aristotle, except the train of thought started with Descartes/early moderns.Are you braindead? This THREAD is about Aristotle. Where did you blow in from? Retardville? >To get away from writing tedious shit like "If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in multitude, then, whatever multiple one of the magnitudes is of one, that multiple also will all be of all."This is like talking to a kid who doesn't want to eat his vegetables.
>>23903657The childish retort, as expected, and right on cue. I accept your concession. Type in caps some more.>>23903650The initial presentation of any system of notation entails a prose treatment in natural language, ideally explaining why things are the way that they are. When done properly, this solves what you've complained of. The point is that keeping everything in natural language ultimately becomes obfuscatory.
>>23903671>whoa... I acted like a retard, so he called me a retard>that means I win and I don't have to explain myselfRedditpost some more.
>>23903690Any posts not about Aristotle are redditposts desu.I've found a couple of features in Plotinus that are distinctly 'modern' and also reflect the true opinion of Aristotle or derive from it. One is that sense is a cognitive process that comes from within ourselves, so we don't really perceive things 'as they are' but only so far as we can perceive them. Aristotle doesn't quite say this but he does say that perception is an activity of the perceiver, and a thing is only perceptible if it's perceived, and I've always read him as holding the same view.Another is Plotinus' denial that when we acquire science of a subject our intellect has actually 'become' an eternal Form. He's clear that the Form causes the science but isn't the same as it - i.e. your understanding of biology isn't the same thing as the principles of life themselves. Aristotle never quite says this either but it is implicit in his understanding of essence (and learning too). To truly know all of an essence you'd have to know all of its essential qualities - everything about it. But we're not even in a position to know that much about many sensibles because of their complexity. And Aquinas also upholds this idea. But I've run into people here and elsewhere who think that the understanding mind 'becomes form' in the sense that it is the intelligible in itself, when really it is it qua intelligible to us dianoetically.
I am constantly told that Aristotle significantly differs from platonism (or neoplatonism, which is the same thing). I can't, for the life of me, understand why this is so. I'm talking about people who apparently know their stuff, not normies who think Plato defended the existence of forms as perfect exemplars (maybe even outside of Intellect), and that Aristotle refuted him with the third man argument. (this is of course of a gross caricature)To make matters more complicated, there is a growing trend (Perl, Gerson) of reaffirming the neoplatonic/boethian position that Aristotle was simply discussing different matters but that if he were to be made coherent regarding the higher matters, he would be a platonist as well. Modern thomists (who are the main exponents of Aristotle nowadays as far as I can tell) also tend to downplay the differences.Anyway, if anyone has a good, accessible book (or a bunch of selected writings) that show where the differences lie, without caricaturing either side, it would greatly interest me.
In the work, 'De interpretatione': How is it that the negation of>'every is just'is>'not every man is just'(which makes sense to me), but the negation of>'every man recovers'(where the subject is the same) is>'every man does not recover'rather than>'not every man recovers'? How does dropping the copula change the nature of the subject? (Chapter 8, I think.) I can see the parallel that the copula-less statements change in form in the same way as Socrates is white--Socrates is not white, but I don't understand why 'every man' is 'taken universally', as Aristotle says, when there is a copula vs. behaves like the subject 'Socrates' in 'Socrates is white' when there isn't as copula.
>>23903746>How is it that the negation of>>'every is just'>is>>'not every man is just'I mean:How is it that the negation of>'every man is just'is>'not every man is just'
>>23903736Aristotle is like the Bible, there are different schools of interpretation that are at least partly motivated by the biases of different readers. That isn't to say one of them isn't right, or more right than the others.Whether Aristotle 'differs from Plato' depends on what you mean by differ. Seen by one angle, they are obviously of one 'haeresis'. In Meta 1 Aristotle even seems to class himself with Plato as a 'modern' thinker. What makes him 'modern' is that he sees first principles as being non-sensible, and his denial of materialism. And Plato is all over Aristotle even when not named, he's obviously a huge influence.But I'm sure Aristotle would not have seen himself as a Platonist because he constantly attacks Plato. To me it's obvious that they're different - they disagree about matter, on the method of finding definitions, on whether there are intelligible Forms, on whether Unity is the first principle, on the faculties of the soul, the nature of the soul, the immortality of the soul, how creation occurred, epistemology, politics. Many, many things. He might be close enough to Plato to be profitably used by later Platonists but I bet he'd be offended if you called him a Platonist lol. He saw Platonists as fundamentally misguided about Forms, positing beings that were impossible, crudely 'duplicating' the perishable world in the imperishable world, overly addicted to abstract theorizing without observation, etc.
>>23903756The logical structure's the same in either case. What's strictly being negated in 'not every man is just' is the 'is', by analysis it's 'every man not-is just'. The reason is that if you don't deny the verb it's not a true contradictory.
>>23903782I was talking about the opposing statements: >Every man recovers.>Every man does not recover.My question was why is the negation of the first>Every man does not recover.and not>Not every man recovers.When the negation of the statement>Every man is just.is>Not every man is just.and not>Every man is not just.It must be something to do with the copula, right? It looks like its absence changes the nature of the subject. (The subject being 'Every man'.)
>>23903966Yeah I'm saying they're synonymous. Every man is not just means exactly the same thing as not every man is just, for Aristotle. The classical square of opposition is really: all x is b vs all x not-is b; all x not-is not-b vs all x is not-b, you see this in the way his tables progress among other places. And then all x is not-b becomes no x is b (tho really no x is b is a broader idea since it includes the possibility of there being no x at all, but either sense is obv in different ways contrary to all x is b). And if you have a verb not a copula, well replace is b with the verb in the analysis. The words "not every man is just" and "every man does not recover" are different, the logical structure is the same. The words don't matter much because Aristotle is looking forward toward his theory of syllogism and demonstration in which one 'term' could be a complex idea. But regardless of the words it is, structurally and in the abstract, always 'all a is b' and 'all a not-is b' as contradictories.
>>23903768>He saw Platonists as fundamentally misguided about Forms, positing beings that were impossible, crudely 'duplicating' the perishable world in the imperishable worldThat's the weird thing. To me Plato's view seem to be exactly Plotinus' (and probably Ammonius') views, in that the crude idea of form as distinct objects or perfect exemplars is explicitly denied. What is present is intellect, but to be sure there really can be no talk of "dogness" as some entity standing on its own for instance, apart from the manifestation of an actual dog in the discursive realm.And so the "aristotelian" objections on the topic of forms really do seem to refute a doctrine that was never held by anyone. On the other hand, he did know Plato for like 20 years, though apparently he was not among his closest students. I don't know what to think of it. It seems to me unthinkable that he would be so highly regarded yet so mistaken, but then again, there are many scholars (Findlay is the only one I can think of right now) who seem to think it's that simple. We also now pretty much know (and I think there is less resistance on this point because it's not a very consequential debate, historically) that he grossly misunderstood Anaxagoras' views. So I really don't know what to make of him.
>>23904017Yeah it is a puzzle, he seems to systematically read Plato in the most retarded way possible. The way I see it there are a few viable hypotheses:1.) The Asshole - Aristotle just hated Plato for whatever reason and interpreted his works uncharitably on purpose. In particular he had no patience for metaphor and seems to interpret both the dialogues and the unwritten doctrines in an almost willfully unimaginative way.2.) The Dullard - Aristotle was so in love with his own ideas that he lost perspective and had trouble understanding the philosophy of others. It's just hard for me to believe that someone as smart as Aristotle would have been deceived in that way so thoroughly.3.) The Schizo - Aristotle really was a crypto-Platonist all along, and his criticisms are supposed to point you toward a true interpretation of the dialogues. He took Plato's theories about philosophical composition to heart and his own work is as if 'in dialogue' with Plato. It's the sort of thing you might want to believe but it is pretty schizo, like any esoteric reading. Not only does Aristotle reject Plato he sees himself as one of many Academics that did so including Speusippus. Hard to spin that in a way that works with the schizo hypothesis.None of the three makes sense really. to imagine him being so nasty as to misrepresent his opponents, hard to imagine him as too dumb to understand the dialogues as well as a high school kid could, hard to imagine him playing 4-D badminton quite that hard as to pretend to disagree. I do think he self-consciously rejects metaphor/myth/subtlety in the dialogues, though, and that's part of it. He talks about that in De Caelo when the question of the 'metaphorical generation' of the heavens in the Timaeus comes up. I think another factor may be Plato's own refusal to explain himself. The 'unwritten doctrine' as in the lecture On the Good was cryptic. Aristotle talks about Academics arguing about the interpretation of the dialogues which suggests Plato didn't explain them. Maybe Aristotle's understanding of the Forms was influenced by what garden variety Academics were theorizing about them more than exegesis of the dialogues themselves - he often refers to "them". And maybe many of the Academics didn't understand Plato particularly well, either, because Plato never clearly explained himself.
>>23904048(cont'd)Or I could put it like this - there is plenty of evidence for Aristotle's simplistic two-world interpretation of Plato even if it's ultimately wrong. And even today people come away from Plato with that reading. So maybe I shouldn't say a high school kid could read him right.
Plotinus' analysis is that Aristotle was a foolish and unvirtuous, his mind was always directed at things of sense and he could never understand what was beyond sense (can't remember sauce but it's there somewhere, he doesn't actually call him foolish/wicked but it's implied). There's open irony here because this is exactly what Aristotle accuses the Platonism of doing - making the imperishable like the perishable by positing Forms of sensibles. It comes down to Aristotle rejecting that thought and predication depended on intelligible beings that were prior to and corresponded with sensibles. There's just no need for this, in his eyes, and the Good can produce without a world of Forms or a being that is actualizing Forms by thinking them etc. Plotinus would say 'if the intelligible ground of the substance was simply part of the composite it would cease to exist just like the sensible form ceases to exist.' It doesn't make metaphysical sense, for example, for the idea of the shoe in the cobbler to exist along with and within the individual shoe, rather than being prior to it. And art imitates nature. Plotinus would also say of course that these intelligibles must be altogether in an intellect and that this intellect is not the first, but that'd take more arguments.
>>23904048I have seen 1) argued for, yes (though it is uncharitable)The idea seems to be that he was mad he got passed over as Plato's successor. I wouldn't say I can believe that sort of thing either.As I said, I have never read Aristotle except the passages that pertain to his mistreatment of Anaxagoras, so I can only speculate.However I can say that there is definitely something, among aristotelians, about hating anything that resembles mysticism. It is pretty obvious that the principle is not something that can be said, but a lot of aristotelians seem to be sort of midwitted in that way, and to think the discursive is all there is. This is something that made Nicholas of Cusa's life extremely difficult, for instance, it led to him calling aristotelians a sect and being quite pessimistic about the chances of them "rejecting Aristotle and leaping higher".So maybe this was a tendency Aristotle himself had, idk. After all, I vaguely recall a passage from him in which he said that asserting the One made no sense because it was not empirically knowable, or something along those lines. It's possible that, like his heirs, he just felt frustrated that it was not possible to put clear words on the One, and so he rejected it. (Despite the fairly obvious argument, now associated with Plotinus, that what he calls Being/Intellect can't be first)As to the ever-enduring caricature of platonism that is taught everywhere, I'm pretty sure it has to do with the fact that Plato and Plotinus could not be read up until like the renaissance, at which point their image had already suffered greatly. It is sort of ironic that christian philosophy should have turned to Aristotle, as from what I gather his philosophy seems pretty hard to reconcile with christian thought, and at least I know for sure that platonism is a very natural fit.Funny story, I recently heard from a young thomist priest that Aquinas had "read and refuted Plotinus" and that people should stop wasting their time on platonism. Of course Aquinas could not have read any text of Plotinus', as he did not know greek and basically no translation (or greek texts, afaik) were available in 13th century western Europe. But yeah, this is the sort of headcanon people have about platonism, apparently.
>>23903624Pure mathematics is a kind of metaphysicsAristotle was not a mathematician
>>23904229Why are so many people eager to argue about words but hardly anyone can argue about ideas? Metaphysics studies the highest principles that stand behind all reality including math. Math might deal with reality at a high level of abstraction and in that sense be 'metaphysics' in a loose sense, but it is not metaphysics and doesn't consider properly metaphysical questions. For example, metaphysics considers contrariety and privation in general, while mathematics only considers them as they apply to math.As for Aristotle not being a mathematician - he deals with mathematical subjects all the time, like the nature of infinity and limits. He laid the ground for modern calculus.
>>23904253>Why are so many people eager to argue about words but hardly anyone can argue about ideas?Makes people feel smart.It is not very common to see philosophical discussion not devolve into a comparison of "isms" and debates about who said what.To borrow a phrase from Plotinus, many of these people might be scholars, but they are definitely not philosophers.
Maybe Aristotle believed in something that was always perceiving access to a universal
>>23903615>>23903618>>23903645not to get involved in the catfight, but how does "principle" fit into Aristotle's logic and metaphysics? Like, what words does he use here, and how does it fit into Aristotle's system? Is it like an arche (the basis of demonstration)? Is it like a form/essence of a substance? I ask because the topic is about the being of number, and I can't tell if principle is meant as in a formal cause or as in an un-demonstratable axiom. Maybe there's a "structural" intersection between Aristotle's logic and his ontology here?
>>23903583Nta, but is there a book/ source for that..I'm generally interested in this?
>>23905776They don't have nearly the same polemic to it, but Jacob Klein's Greek Mathematical Thought and the Origin of Algebra and Edwin Burtt's Foundations of Metaphysical Sciences are good reads for this idea. Husserl, Heidegger, Guenon, Thomists, etc., all play around with this idea in their unique ways.
>>23903580"Let no one ignorant of geometry enter"
>>23905776>>23905789Morris Kline too
bump
>>23905789Thank you, will look this up, I've been thinking about Descartes, Kepler, Leibniz and Newton and the mechanization of the natural world and its laws, banishing away the animistic principles. The rise of materialism.
>>23903618>>23903634>>23903645>>23905499I was interested in this question and looked at the beginning of Metaphysics and parts of Physics, and it seems like the word "principle" is often used as the translation of either "arche" or "aitia." Aristotle often uses them interchangeably. I reckon that "arche" is akin to a special kind of non-demonstrable cause. I'm by no means an expert though. I'd like to know if this matches with more of Aristotle's corpus, in particular: the rest of Metaphysics, the rest of Physics, Posterior Analytics (this is especially interesting), etc. Also, would the four causes count as arche? Hopefully somebody else can chime in.
>>23907656IIRC, Aristotle uses the term "axiom" in Posterior Analytics. But this is not to be confused with the modern term, e.g. "What are your axioms?" Axioms are not arbitrary and they are not subjective. They are the finest and noblest principles from which all conclusions descend.
>>23907656>>23907723Check out 1006a-b in Metaphysics. Aristotle situates axioms with the study of what is most universal, the first substance, the first principles, etc. and even makes the distinction that separates the philosopher from the mathematician is that the mathematician cares less about the axioms and more about what follows from them. Furthermore, philosophers know the "principles" (archai) of genera. Causes as in aitia are not used here, but it wouldn't surprise me if archai, axiomata, and aitiai (of a certain "highest" kind, ἀκροτάτας αἰτίας) are largely triangulating around the same concept.
can't let this thread go until somebody engages with something one last time :(
