Aristotle's Metaphysics

"The whole is more than the sum of its parts"

Aristotle thought empty vacuous matter united with natures, combining to be objects in the world. So things are part material part spiritual. But the spiritual natures were tailored made for matter, to be instantiated. Thus there is the finite world. Then there is his Prime Mover(s). Besides the finite world and the divine, Aristotle thought nothing existed. So maybe math for him was true only in our minds. Unless he would say the Prime Mover(s) guaranteed the truth of them

Also important is that Aristotle thought God or Gods were ahead of instead of behind Aristotle's eternal universe. His God acted as a final cause instead of an efficient cause. This may have some relation to the distinction between this Greek philosophy and Christianity, and to Truth as seen by Aristotle

Quoting DS1517

I've read some of Aristotle but I'm no expert. I am wondering what an Aristotelian response might be to abstract objects such as the principles and axioms of mathematics? Are those pure abstractions to an Aristotelian?

As you may know, Aristotle was an immanent realist, not a Platonic realist. He regarded mathematical objects as an aspect of the world that could be investigated (albeit in a more abstract sense), not as existing apart from it (in the sense of Plato's Forms which he rejected).

Aristot. Met. 13.1078a:The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does.

There is no afterlife for Aristotle. Just an eternal succession of temporal states. All things must pass away he thought, except God or Gods who were in the never reached future. So it's an interesting question if Aristotle thought mathematics was true because of matter or true in itself

Reply to Andrew M

I think that is correct. Aristotle believed that mathematical properties are immanent within concrete objects. I'm wondering how he would account for the laws of logic and the principles of mathematics that make geometry and math possible in the first place? I'm guessing they are just abstractions of concrete objects or fundamental principles of being?

Quoting DS1517

I've read some of Aristotle but I'm no expert. I am wondering what an Aristotelian response might be to abstract objects such as the principles and axioms of mathematics? Are those pure abstractions to an Aristotelian?

James Franklin is your man.

Reply to Wayfarer Thank you for sharing that. I found the article very helpful. Some Platonists accuse Aristotle of laying the groundwork for nominalism. I don't think it is fair to accuse Aristotle of nominalism. Are there other good Aristotelian responses to nominalism?

Quoting DS1517

Thank you for sharing that. I found the article very helpful. Some Platonists accuse Aristotle of laying the groundwork for nominalism. I don't think it is fair to accuse Aristotle of nominalism. Are there other good Aristotelian responses to nominalism?

You're welcome. (Actually decades ago I was manager of a University computer store, and Jim Franklin was one of my customers!)

Have a listen to a couple of minutes of this lecture starting from where I've bookmarked it. 'Thinking as a universalising activity....literally, you could not think if materialism was true' :clap: . When we recognise kinds, types, species, they're all essentially manifestations of form. I think this is a reference to the famous passage in De Anima about the 'active intellect', the faculty which grasps 'the forms' and is able to reason on that basis.



(If you don't know Lloyd Gerson, by the way, he's probably one of the leading academics in Platonist studies. That lecture he's reading is Platonism vs Naturalism.)

Nominalism proper only took root with William of Ockham, Francis Bacon, and others, in medieval times. I believe that the debate between scholastic realists (who accepted the reality of forms) and the nominalists was a watershed in Western thinking. The nominalists - precursors of later scientific empiricism - won the day, and, as is said, 'history is written by the victors'. So much so that in this particular matter, that it is very hard for us moderns to even understand what the argument was about. But the upshot was, in my view, that with the victory of nominalism, the possibility of a real metaphysic was lost, as this depends on there being degrees of reality, which neither nominalism nor later empiricism can accomodate.

Quoting DS1517

I think that is correct. Aristotle believed that mathematical properties are immanent within concrete objects. I'm wondering how he would account for the laws of logic and the principles of mathematics that make geometry and math possible in the first place? I'm guessing they are just abstractions of concrete objects or fundamental principles of being?

To take the law of non-contradiction as an example, Aristotle regards it as a fundamental principle of being ("It is not possible for the same thing at the same time both to belong and not belong to the same thing in the same respect" - Met. 1005b19-20). That distinguishes his view (immanent realism) from both Platonism (that the LNC exists in separation from being) and Nominalism (that the LNC is just a law of thought).

Excellent. Thank you so much for all the helpful comments. I really appreciate it.

Another thought ... Perhaps a Platonic objection but I was wondering what you thought. From an Aristotelian perspective, if I could destroy all the circular objects in the world, would I have successfully destroyed the essence of circularity? What might an Aristotelian response be? (I've read Aristotle but I can't remember if he addresses this question.)

Thanks again for the help!

Reply to Wayfarer Thank you! That is very interesting and enlightening.

Reply to Andrew M Yes, that makes sense. Thanks!

Quoting DS1517

Another thought ... Perhaps a Platonic objection but I was wondering what you thought. From an Aristotelian perspective, if I could destroy all the circular objects in the world, would I have successfully destroyed the essence of circularity? What might an Aristotelian response be? (I've read Aristotle but I can't remember if he addresses this question.)

I think demonstrating the potential for circular objects is sufficient to ground mathematical circles. And since mathematical circles can be considered in separation from circular objects anyway (see the earlier Aristotle quote), the contingency of circular objects has no effect on mathematical practice.

Absent a demonstrable grounding, circles might be regarded as mysterious or dubious, just as negative numbers and complex numbers have been in the past before constructive visualizations were found for them.

Reply to DS1517

I think that it should be kept in mind that mathematical principles are not the same kind of thing that mathematical objects (i.e. triangles or numbers) are. Same with logic. Whatever principles (or laws or axioms or posits) are, which is not at all clear as is usually the case with Aristotle, they do not seem to be treated or function similarly to "proper" abstract objects. For example, it is usually said that such axioms, laws or principles are intuitively or naturally grasped and they have to be grasped in order to be able to know anything. They are also said to be unprovable or indemonstrable, yet indubitable. Instead of "objects" or "things", these principles seem to be more like relations between such "objects" or "things". The debate around principles such as PNC seems to be whether Aristotle takes them to be metaphysical or just logical/mathematical.

When it comes to the way Aristotle thinks of universals I find it useful to think about it from the POV of "priority". It's usually accepted that Aristotle recognises different senses of priority. For example, priority in definition/account, priority in time, priority in nature and substance. A common view is that, according to Aristotle, universals have definitional priority compared to substances, but concrete objects are prior in nature and substance compared to universals. There's much literature around this and it gets really complicated really fast, but I think that the following quote from Stephen Menn's The Aim and the Argument of Aristotle's Metaphysics illustrates neatly the nuances between the platonic, the aristotelean and the nominalist approaches. The issue of priority is also discussed in terms of ways of existing, but it's also related to the issue of archai. Contra Plato and the the Pythagoreans, Aristotle argues that universals cannot be archai, that is to say, the cause of all being.

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Quoting Andrew M

As you may know, Aristotle was an immanent realist, not a Platonic realist. He regarded mathematical objects as an aspect of the world that could be investigated (albeit in a more abstract sense), not as existing apart from it (in the sense of Plato's Forms which he rejected).

The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does. — Aristot. Met. 13.1078a

As I understand it, the essence or universal of circularity is in the circular object, because for Aristotle, concrete objects demonstrate mathematical properties (weight, volume, extension, etc.) The essence of circularity is not floating around in a Platonic heaven somewhere.

I think it is correct to say that Aristotle believed we could understand mathematics in a more abstract sense, as mathematics and logic are derived from being and particular objects. He also mentions in the Posterior Analytics that the mind is so constituted that we can apprehend and understand these more abstract principles. The above quote from Aristotle's Metaphysics seems to indicate that he didn't think mathematics exists in the same way other things exist (which I think is intuitively correct). However, does that make Aristotle a conceptualist or nominalist? (I know conceptualism and nominalism are later philosophical phenomena. However, I had a professor tell me that Aristotle laid the intellectual foundation for nominalism and I'm trying to figure out for myself if that is really true.)

Thanks again for all your insight and help. I know I have a lot more to learn about this!

Quoting DS1517

As I understand it, the essence or universal of circularity is in the circular object, because for Aristotle, concrete objects demonstrate mathematical properties (weight, volume, extension, etc.) The essence of circularity is not floating around in a Platonic heaven somewhere.

Not object, but concept. Such a concept doesn’t exist anywhere but in a mind, but it is nevertheless the same for all who think. I think the big underlying difficulty in our thinking about this, is that we are ‘born and bred naturalist’, in that we can only conceive of reality in terms of what exists in space and time. Whereas concepts such as geometrical forms, and even natural numbers, are not locatable in terms of space and time. That is the sense in which they are ‘transcendent’ to space and time.

I am not a fan of Edward Feser in all respects, but some of his Blog posts are very good. Have a read of Think, McFly, Think

Quoting DS1517

The above quote from Aristotle's Metaphysics seems to indicate that he didn't think mathematics exists in the same way other things exist (which I think is intuitively correct). However, does that make Aristotle a conceptualist or nominalist?

Important point, and a contested point, in that almost nobody else on this forum will agree with it: that numbers, universals, and so on, don’t exist in the same way that the objects of experience do.

Nearly everyone will object that things either exist or not, and that it is unintelligible to say that some categories of things exist in a different sense to some others. But I think in Platonic philosophy generally, and in this context this includes Aristotelianism, there is an at least implicit conception of what is called the ‘intelligible object’, whose existence is purely intellectual, but which is real in own right; even, in some sense, of a higher degree or domain of reality than the objects of common sense. The reason that is controversial, is that modern culture tends overwhelmingly towards some form of philosophical materialism, which holds that ultimately only material objects or forms of matter and energy exist. It holds that intelligible objects such as concepts are the activities of brains, and that brains are physical, thereby grounding such things as abstractions in ostensibly physical (i.e. neurophysiological) processes generally shaped by evolutionary development.

So, it’s not really just a coincidence that the typical advocates of Platonism in modern culture turn out to be Catholic, on the whole, because Aristotelian philosophy offers a model of dualism, called hylomorphism (matter-form dualism) which accommodates a broadly Platonist philosophy (see, for instance, Peter Kreeft's Youtube lecture series on Platonism.) Whereas the majority view is that only one half of the Cartesian dualism of mind and body, namely, body, has any ultimate reality. What is mental or intellectual is in some sense either subjective or socially constructed but possessed of no inherent reality.

As I say, mine is a minority view on this forum, as I’ve never been able to accept the premisses of scientific materialism, but that is the way I see it.

Would Aristotle say geometry is true because of matter or because of the Prime Mover?

Quoting Wayfarer

Not object, but concept. Such a concept doesn’t exist anywhere but in a mind

Not according to Aristotle. From the point of view of Aristotle, that's nominalism; closer to Lycophron's thesis than to his own.

Quoting Wayfarer

But I think in Platonic philosophy generally, and in this context this includes Aristotelianism, there is an at least implicit conception of what is called the ‘intelligible object’, whose existence is purely intellectual, but which is real in own right

Again, that's not what Aristotle says. Universals' existence is certainly not "purely intellectual" according to him. It might be true of "Aristotelianism" though, who knows.

Quoting Two

Not according to Aristotle. From the point of view of Aristotle, that's nominalism; closer to Lycophron's thesis than to his own.

How does nominalism account for the nature of concepts, then? Isn't it the case that, according to nominalism, concepts (and the like) are simply names given to like things? Did you perchance glance at the Feser blog post I linked to about it?

For the sake of clarity, then, an edited passage from Ed Feser, with my comments on it:

[quote=Feser]As Aristotelians and Thomists use the term, intellect is that faculty by which we grasp abstract concepts (like the concepts man and mortal), put them together into judgments (like the judgment that all men are mortal), and reason logically from one judgment to another (as when we reason from all men are mortal and Socrates is a man to the conclusion that Socrates is mortal). It is to be distinguished from imagination, the faculty by which we form mental images (such as a visual mental image of what your mother looks like, an auditory mental image of what your favorite song sounds like, a gustatory mental image of what pizza tastes like, and so forth); and from sensation, the faculty by which we perceive the goings on in the external material world and the internal world of the body (such as a visual experience of the computer in front of you, the auditory experience of the cars passing by on the street outside your window, the awareness you have of the position of your legs, etc.).

That intellectual activity -- thought in the strictest sense of the term -- is irreducible to sensation and imagination is a thesis that unites Platonists, Aristotelians, and rationalists of either the ancient Parmenidean sort or the modern Cartesian sort. [/quote]

I would say, that what Feser designates 'thought', I would designate 'reason' or 'judgement', and that what he designates 'intellect' is clearly descended from the Greek term nous.

He gives some examples:

[quote=Feser]First, the concepts that are the constituents of intellectual activity are universal while mental images and sensations are always essentially particular (hence the remark by Gerson above, paraphrasing Aristotle, that 'reason is a universalising activity'). Any mental image I can form of a man is always going to be of a man of a particular sort -- tall, short, fat, thin, blonde, redheaded, bald, or what have you. It will fit at most many men, but not all. But my concept man applies to every single man without exception. Or to use my stock example, any mental image I can form of a triangle will be an image of an isosceles , scalene, or equilateral triangle, of a black, blue, or green triangle, etc. But the abstract concept triangularity applies to all triangles without exception. And so forth.

Second, mental images are always to some extent vague or indeterminate, while concepts are at least often precise and determinate. To use Descartes’ famous example, a mental image of a chiliagon (a 1,000-sided figure) cannot be clearly distinguished from a mental image of a 1,002-sided figure, or even from a mental image of a circle. But the concept of a chiliagon is clearly distinct from the concept of a 1,002-sided figure or the concept of a circle. I cannot clearly differentiate a mental image of a crowd of one million people from a mental image of a crowd of 900,000 people. But the intellect easily understands the difference between the concept of a crowd of one million people and the concept of a crowd of 900,000 people. And so on.[/quote]

Reply to Wayfarer

Depends on the specific branch of nominalism. The whole talk of nominalism is already steps away from Aristotle, it's parasitic to his work. I referred to it because I found it paradoxical that you want to argue against the idea that Aristotle was a "nominalist", yet what you ascribe to him (by way of "Aristotelianism" or "Platonism"), is closer to ancient "nominalists" like Lycophron. What's important is what Aristotle says about the way universals exist and nowhere does he say that universals exist "purely intellectually", as far as I know. That's one of the theses he argues against. I guess you're taking as a given that the matter in which we come to know, grasp or understand something, inevitably leads to how it's supposed to exist, i.e. if we know universals through the intellect, then universals exist in a purely intellectual manner. That's not what Aristotle says though. Neither the logic nor the conclusion makes justice to him. Even talk about knowing universals through the intellect can't be taken seriously as an interpretation of Aristotle, since it discounts numerous distinctions both regarding "universals" and the "intellect".

I skimmed through Feser's article. It's not about Aristotle's discussion of various ways of existing. It's entirely free of it. It's also free of any substantial discussion of various ways of existing simpliciter. For example, the part that you quoted only refers to various human faculties. There's no reference (let alone argument), to the various ways things exist. I'm somewhat familiar with Feser's work: I've read multiple blog articles in the past. Nothing scholarly in them, it's mostly cultural commentary (aka polemics). I would never recommend them to someone who wants to understand Aristotle. I've also read his introduction to scholastic metaphysics and his book on Aquinas. Better than his blog, still in no way a sound recommendation for someone who wants to understand Aristotle (or Aquinas for that matter).

In my first post I linked a few quotes from Stephen Menn's draft of "The Aim and the Argument of Aristotle's Metaphysics" - that's what I consider Aristotelian scholarship. Some related books and articles that I consider worth reading on this and related subjects (irrespective of the interpretation they provide):

Aristotle on the Many Senses of Being and The Question of Seperation -- Stephen Menn

Priority in Aristotle's Metaphysics -- Michail Peramatzis

The Priority in Being of Energeia -- Jonathan Beere

Ontological Priority and Grounding in Aristotle's Categories -- Riin Sirkel

Reply to Two thanks, good references, and I shall read them. //edit//although as often with these papers, knowledge of ancient greek is assumed, which poses a rather high bar to entry. Several are behind academic paywalls, and the last one returns an error. But thanks all the same.//

I'm very encouraged by the first sentence in the first reference, to whit, 'Aristotle thinks that serious philosophical errors have been made, from Parmenides down to his own day, as a result of failing to draw distinctions between different senses of "being". '

Quoting Two

What's important is what Aristotle says about the way universals exist and nowhere does he say that universals exist "purely intellectually", as far as I know.

I am the very first to admit the scanty nature of my knowledge of Aristotle and indeed the classics generally. But there's a very interesting concept in Aristotle that, as you appear to be so well versed in the matter, perhaps you like to comment on. This is that in Aristotle's hylomorphic dualism knowledge comprises a union of both sensory and intellectual elements, whereby the sense detect the material substance, but the intellect detect the form. The senses receive the material form, but the intellect perceives the intelligible form:

Everything in the cosmic universe is composed of matter and form. Everything is concrete and individual. Hence the forms of cosmic entities must also be concrete and individual. Now, the process of knowledge is immediately concerned with the separation of form from matter, since a thing is known precisely because its form is received in the knower. But, whatever is received is in the recipient according to the mode of being that the recipient possesses. If, then, the senses are material powers, they receive the forms of objects in a material manner; and if the intellect is an immaterial power, it receives the forms of objects in an immaterial manner. This means that in the case of sense knowledge, the form is still encompassed with the concrete characters which make it particular; and that, in the case of intellectual knowledge, the form is disengaged from all such characters. To understand is to free form completely from matter.

Moreover, if the proper knowledge of the senses is of accidents, through forms that are individualized, the proper knowledge of intellect is of essences, through forms that are universalized.

From Thomistic Psychology: A Philosophical Analysis of the Nature of Man, by Robert E. Brennan, O.P.; Macmillan Co., 1941.

So, this lends to support to the 'intelligible' nature of universals - they're the 'intelligible forms' that the mind discerns in order to understand what a thing is.

Quoting Wayfarer

they're the 'intelligible forms' that the mind discerns in order to understand what a thing is.

How would you say that the "mind" does this (as far as Aristotle is concerned)?

Reply to Two Have a look at the Gerson video above - it’s been bookmarked to the passage about this point.

Reply to Wayfarer It doesn't seem to be bookmarked, it starts from the beginning.

Reply to DS1517

Have you considered Aristotle's metaphysics viz time?

"It can be said that the world of mathematics exists in an eternal present, a state in which neither the past nor the future have any meaning; there is no significance to the questions of what came before, or of what will happen next... Within the sphere of mathematics, the moment of time is always 0. In other words, time has neither meaning nor significance within mathematical operations."

https://www.oxfordscholarship.com/view/10.1093/0199247900.001.0001/acprof-9780199247905

http://www.torahscience.org/mathematics/time1.html

And of course the so-called infamous Aristotelian paradoxes of same:

In his first published work Hegel, after the the preface and introduction, immediately starts expounding on the "paradox" of time. I personally don't see the problem. The present merely moves forward constantly within metaphysical nothing. Time exists but past doesnt. The future doesn't exist except as a present. So I don't see a true paradox. Whether the present is in our heads or outside i don't find to be a fruitful topic of discussion.

I don't see a problem with nominalism either. Are two men more similar or dissimilar? That's the only aspect in which the question has meaning. Feser is an idiot. He insists he can prove God exists separate from us and the wheat hylomorphism thing. When asked to prove it he makes up a bunch of empty categories. He is also arrogant

Quoting Gregory

personally don't see the problem. The present merely moves forward constantly within metaphysical nothing. Time exists but past doesnt. The future doesn't exist except as a present. So I don't see a true paradox. Whether the present is in our heads or outside i don't find to be a fruitful topic of discussion.

Gregory!

Just a few things to wet your whistle both related to metaphysics and logical impossibility.

- how does our sense perception perceive time?
- do time zones (East v. West) present paradox? (Can I re-live lost time traveling west to east?)
-is eternity time or time eternity?
- is time subordinate to change or is change subordinate to time? (Does change affect time or does time affect change.)
-how thick is present time? (When I cognize about that question, I need the past/future to answer the question.) What then constitutes present.
-is mathematics a timeless truth?
-do clocks measure time or change?
-does mathematics have biological survival value?

Just a few things to consider :smile:

Reply to Two

This is the relevant passage:

Aristotle, in De Anima, argued that thinking in general (which includes knowledge as one kind of thinking) cannot be a property of a body; it cannot, as he put it, 'be blended with a body'. This is because in thinking, the intelligible object or form is present in the intellect, and thinking itself is the identification of the intellect with this intelligible. Among other things, this means that you could not think if materialism is true… . Thinking is not something that is, in principle, like sensing or perceiving; this is because thinking is a universalising activity. This is what this means: when you think, you see - mentally see - a form which could not, in principle, be identical with a particular - including a particular neurological element, a circuit, or a state of a circuit, or a synapse, and so on. This is so because the object of thinking is universal, or the mind is operating universally.

….the fact that in thinking, your mind is identical with the form that it thinks, means (for Aristotle and for all Platonists) that since the form 'thought' is detached from matter, 'mind' is immaterial too.

Lloyd Gerson, Platonism vs Naturalism, 39:00

emphasis added.

The written lecture is here, the passage above p. 16.

Reply to 3017amen

Thanks for the post. I think change is what we experience and Time is a mystical idea we have. With mystical things they are kinda outside us and kinda within, and they are near impossible to analyze. I don't think matter cannot think. Thomists, being poor at philosophy, think they can fully understand what matter is and delineate what it can do. I don't know what survival skills we have because of our ability to think about philosophy. Maybe it simply keeps our mental juices flowing. And I don't know about timeless truth. Eternity doesn't exist outside a black hole though. Nominalism, nevertheless, is not an evil philosophy. Two humans are very similar. They have differences as well. What more is needed to understand humans? Why must we posit two principles in them (matter and form)? Why not one principle for each human and each human being very similar (which is obvious)? The mentality of Feser and company boils down to a psychology that has to categorize in a certain way. I believe they are far from wiasom. Thanks again for the post!

From the linked article:

Aristotelian realism stands in a difficult relationship with naturalism, the project of showing that all of the world and human knowledge can be explained in terms of physics, biology and neuroscience. If mathematical properties are realised in the physical world and capable of being perceived, then mathematics can seem no more inexplicable than colour perception, which surely can be explained in naturalist terms. On the other hand, Aristotelians agree with Platonists that the mathematical grasp of necessities is mysterious. What is necessary is true in all possible worlds, but how can perception see into other possible worlds? The scholastics, the Aristotelian Catholic philosophers of the Middle Ages, were so impressed with the mind’s grasp of necessary truths as to conclude that the intellect was immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.

I have long thought that the so-called "possible worlds" are just worlds we can coherently imagine. Our ability to imagine, and our senses of logic, quantity, proportion and so on are inherent in us, in our very structures, just as logic, quantity and proportion are inherent in the physical structures we observe.

So the challenge to build an "artificial intelligence system" would be to build an entity that is able to imagine. If the ability to imagine has evolved over countless aeons, then the challenge to create an entity which can imagine would seem to be as difficult to meet as the challenge to create complex life from scratch.

I think Aristotle was wrong to believe the universe could be eternal. You would have to say, if he was right, that there could have been an infinite number of cats who lived, for example. I think the whole idea is irrational. Potentiality slipped into actuality by its nature, and Time began. Or change, if you will.

Quoting DS1517

As I understand it, the essence or universal of circularity is in the circular object, because for Aristotle, concrete objects demonstrate mathematical properties (weight, volume, extension, etc.) The essence of circularity is not floating around in a Platonic heaven somewhere.

Yes, Plato conceived of Forms in a separate and prior realm. Whereas Aristotle conceived of form in the world itself (per hylomorphism), neither prior to nor separate from it.

Occam took exception to the Scholastic tendency (partly influenced by Neoplatonism) to multiply and reify forms (hence Occam's Razor). Whereas for Aristotle, a wheel is circular, but that circularity is not a separate entity. It is instead a characteristic of the wheel that can be abstracted and considered separately, even though it is not actually separate. Which then leads to your question below...

Quoting DS1517

I think it is correct to say that Aristotle believed we could understand mathematics in a more abstract sense, as mathematics and logic are derived from being and particular objects. He also mentions in the Posterior Analytics that the mind is so constituted that we can apprehend and understand these more abstract principles. The above quote from Aristotle's Metaphysics seems to indicate that he didn't think mathematics exists in the same way other things exist (which I think is intuitively correct). However, does that make Aristotle a conceptualist or nominalist? (I know conceptualism and nominalism are later philosophical phenomena. However, I had a professor tell me that Aristotle laid the intellectual foundation for nominalism and I'm trying to figure out for myself if that is really true.)

The difference is that Occam conceived of form as not in the world but in the mind, as concepts or as names for perceived similarities. But for Aristotle, the wheel is circular independent of human thought or language.

The difference between each of these philosophical positions is the relation between matter and form.

A triangle cannot be separated from its angles. Matter and form don't exist though as a triangle exists with its angles. Aristotle was trying to make a dualistic distinction in objects. It's completely ad hoc. Why not three principles in an object instead of two? Why not five. A chair is just a chair. There is nothing universal about it. Thinking about universals is just a psychological state

"How do you put on a shirt of empty sky"

Quoting Andrew M

for Aristotle, the wheel is circular independent of human thought or language.

key point. It is real independently of any particular mind, but can only be grasped by a rational intellect. See Augustine on Intelligible Objects (foot of page).

Quoting Andrew M

The difference is that Occam conceived of form as not in the world but in the mind, as concepts or as names for perceived similarities.

This essay contains a deep analysis of Ockham's criticism of scholastic realism and its momentous consequences for Western thought.

Imo Augustine was dead wrong, as dead wrong as he is dead. The contingent is not inferior to the necessary because life is the best it can be (if we make it so). The necessary is just potentiality. The changeless (a black hole?) is not superior to the mutable. I don't think he was wise, I don't think he was smart, I don't like him and I think he was a nerd.

Aristotle, in De Anima, argued that thinking in general (which includes knowledge as one kind of thinking) cannot be a property of a body; it cannot, as he put it, 'be blended with a body'.

This then means that there are different kinds of thinking. Which do you think these are and how do they differ? Also, do you think that Aristotle draws any distinctions when it comes to knowledge? For example, is our knowledge always already complete or can there be incomplete knowledge?

Quoting Wayfarer

for Aristotle, the wheel is circular independent of human thought or language.
— Andrew M

key point. It is real independently of any particular mind, but can only be grasped by a rational intellect. See Augustine on Intelligible Objects (foot of page).

It takes a human being to understand that a wheel is circular. OK. It implies that the world is intelligible, which Aristotle held. It doesn't imply a prior and separate Platonic realm.

Quoting Wayfarer

This essay contains a deep analysis of Ockham's criticism of scholastic realism and its momentous consequences for Western thought.

The author spends a lot of time referencing Aquinas and other Scholastics, and none referencing Aristotle. Consider the author's take on formal cause:

"The existence of the form 'sight' by which the eye sees" and "fire warms by informing objects with its heat."

That is the kind of verbiage and muddled thinking that Occam was right to reject.

I agree with you that Nominalism is mistaken. But in this case I think it's necessary to clear the ground and take a fresh look at the original Aristotle.

Quoting Two

This then means that there are different kinds of thinking. Which do you think these are and how do they differ?

More than two. Remember the analogy of the divided line - there are gradations of knowledge from 'mere opinion' upwards to noesis. (Galileo was to seize on Plato's 'dianoia' with enormous consequence.)

I think the key point about Gerson's paraphrase of De Anima, is that when the intellect (nous) knows an intelligible, it does so by something like a process of identification - as in the example he gives, 'equals less equals are equal'. There's a kind of apodictic certainty inherent in such rational truths which are absent from judgements about sensible objects; they are seen, as it were, with the 'eye of reason' which is immediate, whereas sensory knowledge is by nature mediated. My feeling is that the ancients still had a 'distrust of the senses' whereas modern culture with its emphasis on naturalism, regards sensory experience as the sine qua non of knowledge (which after all is the basis of empiricism). The knowledge of mathematical and 'formal' truths constituted an insight into the real nature of things, whereas (the ancients would say), moderns have an exceedingly high regard for normality.

Remember also that Platonism sets the bar very high for what constitutes 'knowledge'. Again from my inexpert understanding, many of the dialogues about this question conclude with aporia or various hypotheses none of which are conclusive. But the general drift is that the uneducated person, the hoi polloi, don't possess real knowledge all, it can only be won by the arduous exercise of reason. (There are parallels with the Eastern concept of 'vidya' as 'true knowledge' although in the Greek philosophers, there's much more emphasis on mathematics and reason, as Russell remarks in HWP.)

At any rate, without going too far into all these digressions, the notion of 'matter' and 'form' provides a solution, in that 'matter' is said to be intrinsically inchoate and therefore unintelligible until it receives form (as a seal is impressed on wax). Matter itself is unintelligible in this picture. In Aquinas' rendering of hylomorphic dualism:

If, then, the senses are material powers, they receive the forms of objects in a material manner; and if the intellect is an immaterial power, it receives the forms of objects in an immaterial manner. This means that in the case of sense knowledge, the form is still encompassed with the concrete characters which make it particular; and that, in the case of intellectual knowledge, the form is disengaged from all such characters. 'To understand' is to free form completely from matter.

This is at least an echo of the 'contemplation of the Forms'.

Quoting Andrew M

"The existence of the form 'sight' by which the eye sees" and "fire warms by informing objects with its heat."

That is the kind of verbiage and muddled thinking that Occam was right to reject.

Ah, but in context it makes an important point. Ockam says of Aquinas' 'inherence theory of predication' (Aquinas' account of universals) that it:

requires, in addition to all the beings about which I can form true propositions, a whole new set of beings, namely, the natures or forms, which verify any true proposition about those beings. For Ockham, this proliferation of objects was the ground for grave objection. In Ockham’s judgment, it is at best a meaningless play of language, and at worst an irresponsible complication of our theorizing, to insist that “the column is to the right by to-the-rightness, God is creating by creation, is good by goodness, just by justice, mighty by might, an accident inheres by inherence, a subject is subjected by subjection, the apt is apt by aptitude, a chimaera is nothing by nothingness, a blind person is blind by blindness, a body is mobile by mobility, and so on for other, innumerable cases.” Why should we “multiply beings according to the multiplicity of terms”? This is, for Ockham, “the root of many errors in philosophy: to want it to be such that, to a distinct word there always correspond a distinct significate, so that there is as much distinction between the things signified as between the nouns or words that signify.”

You can see here the reasoning that was to become known as 'Ockham's razor'.

However, says Hotschild, what this doesn't see is that there is not a 1:1 relationship between 'forms' and their manifestations:

among all the kinds of forms which can be signified by terms, according to Aquinas, there is no one uniform way in which they exist. The existence of the form “sight,” by which the eye sees, may be some positive presence in the nature of things (which biologists can describe in terms of the qualities of a healthy eye that gives it the power to see), but the existence of the form blindness in the blind eye need be nothing more than the nonexistence of sight ? the 'form' of blindness is a privation of the form of sight and so not really an additional form at all. In general, distinguishing and qualifying the different ways there can “be” a form present in a thing goes a long way toward alleviating the apparent profligacy of the realist account of words signifying forms. Arguably such qualification of modes of being, and not theological discourse, is the real theoretical crux of Aquinas’s views on the “analogy of being.”

Aquinas’s famous thesis of the unicity of substantial forms is an example of another strategy: linguistically I may posit diverse forms (humanity, animality, bodiliness) to account for Socrates being a man, an animal, and a body, but according to Aquinas there is in reality just one substantial form (Socrates’ soul) which is responsible for causing Socrates to be a man, an animal, and a body. In this and other cases, ontological commitment can be reduced by identifying in reality what, on the semantic level, are treated as diverse forms.

Hothschild goes on to argue, and this is the crux of the essay in my opinion, that

[quote=Joshua Hothschild]A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.

In short, the appeal to forms or natures does not just help account for the possibility of trustworthy access to facts, it makes possible a notion of wisdom, traditionally conceived as an ordering grasp of reality.

The absence of this sense manifests in the pervasive attitude that the Universe is 'irrational' or 'purposeless' which underlies the modernist outlook.

Quoting Andrew M

I think it's necessary to clear the ground and take a fresh look at the original Aristotle.

The scholastics adopted Aristotle to their purposes, no doubt. But at least they retained him. Philosophy since Galileo has tended to through Aristotle out with the bathwater of geocentrism. I think the reason Aristotle is making a comeback, is because the notion of formal and final cause is indispensable to any mature philosophy.

Reply to Wayfarer

Hey, that's all good, but my question was about the kinds of thinking in Aristotle and whether Aristotle's philosophy allows for incomplete knowledge or if it's already always complete. I don't feel that there was an answer to these questions in your post. This is because...

a. The fact that Aristotle might also believed in gradations of knowledge does not mean that he believed in the exact same theory that Plato's analogy points to. Also, that particular question was about the kinds of thinking, not knowledge. There might be gradations of knowledge but Gerson distinguished between knowledge (as a kind of thinking) and other kinds of thinking. Which are these other kinds of thinking (which aren't necessarily kinds of knowledge)?

b. Again, the question was about Aristotle, not Plato, the Ancients in general or Aquinas. All these might share some doctrines but their theories are not necessarily the same top to bottom; unless this is what you're arguing for of course (but if this is so, let's first focus on what Aristotle says). Furthermore, the question wasn't really related to perception or to a possible apodictic nature of rational truths. It was about the possibility of incompleteness of our knowledge, whatever knowledge is. For example, is a geometer's knowledge of his science already complete from the get go or is this completeness achieved with time? The accuracy of the knowledge he has gained at anyone point is not the issue here, I'm just asking if he knows from the start all that there is to know. Also, taking a non-science example, do we, as regular people, know all there is to know from the start according to your understanding of Aristotle?

Reply to Two well, those are very interesting questions, and I would have to read up a lot more to begin to answer them. As you can see, my approach is eclectic and thematic, I'm exploring certain themes as they manifest in the history of ideas. But as to whether Aristotle thought that knowledge could be 'complete' - well, it's obviously a deep question. I think 'true knowledge' is what Aristotle thought comprises 'wisdom' where he says e.g. in the Nichomachean ethics:

Scientific Knowledge is a mode of conception dealing with universals and things that are of necessity; and demonstrated truths and all scientific knowledge?since this involves reasoning are derived from first principles. Consequently the first principles from which scientific truths are derived cannot themselves be reached by Science*; nor yet are they apprehended by Art, nor by Prudence. To be matter of Scientific Knowledge a truth must be demonstrated by deduction from other truths; while Art and Prudence are concerned only with things that admit of variation. Nor is Wisdom the knowledge of first principles either : for the philosopher has to arrive at some things by demonstration.

If then the qualities whereby we attain truth,3 and are never led into falsehood, whether about things invariable or things variable, are scientific Knowledge, Prudence, Wisdom, and Intelligence, and if the quality which enables us to apprehend first principles cannot be any one among three of these, namely Scientific Knowledge, Prudence, and Wisdom, it remains that first principles must be apprehended by Intelligence/

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0054%3Abook%3D6%3Achapter%3D6

* this is because, I think, they must be assumed, they're the axioms that enquiry starts with, but are not themselves capable of being proven. (For some reason, this brings Godel to mind. )
Also

Hence it is clear that Wisdom must be the most perfect of the modes of knowledge. [3] The wise man therefore must not only know the conclusions that follow from his first principles, but also have a true conception of those principles themselves. Hence Wisdom must be a combination of Intelligence and Scientific Knowledge: it must be a consummated knowledge of the most exalted objects.

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0054%3Abook%3D6%3Achapter%3D7

However, I have the idea that Aristotle's notion of scientific knowledge might be incommensurable with the modern conception, because it is based on a metaphysics which has largely been rejected in the modern world. Note the mention of 'universals' as being the proper object of scientific knowledge; something which obviously scientists since the late medieval period would presumably rake issue with.

Quoting Wayfarer

However, says Hotschild, what this doesn't see is that there is not a 1:1 relationship between 'forms' and their manifestations:

"among all the kinds of forms which can be signified by terms, according to Aquinas, there is no one uniform way in which they exist. The existence of the form “sight,” by which the eye sees, may be some positive presence in the nature of things..."

You're re-quoting what I had just criticized as verbiage and muddled thinking.

Doesn't that bolded statement seem strange to you?

It should. It's unnatural language. It asserts the existence of a mysterious entity that has causal powers. And it doesn't explain anything. How does the eye see? By a "sight" form?!

I think we can do better. How about:

The eye is a round organ that is used for seeing.

That's an intelligible sentence describing the eye's functional shape (form) and what the eye is for (final cause).

The point is that the author doesn't need to write paragraphs elaborating on Aquinas' strategies for mitigating the problems that Occam identified. He just needs to apply Occam's Razor and start over, preferably by trying to understand the natural distinctions Aristotle was making, rather than trying to recover whatever the Scholastics were doing. Aristotle was not positing Platonic existents, he was investigating the form and function of observable things.

Quoting Wayfarer

Philosophy since Galileo has tended to through Aristotle out with the bathwater of geocentrism. I think the reason Aristotle is making a comeback, is because the notion of formal and final cause is indispensable to any mature philosophy.

I agree.

Reply to Andrew M I don’t think you’re seeing Joshua Horschild’s point, but I won’t continue to press it.

Quoting Andrew M

Aristotle was not positing Platonic existents, he was investigating the form and function of observable things.

I think here you’re squeezing Aristotle into the Procrustean bed of contemporary naturalism.

Quoting Two

For example, is a geometer's knowledge of his science already complete from the get go or is this completeness achieved with time?

As described in Aristotle's Metaphysics, the geometer's procedure of constructing and understanding geometrical figures is the actualization of potential. This is a temporal process.