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

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:

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.

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.

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. — DS1517

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...

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.) — DS1517

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"

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).

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. — Andrew M

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?

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). — Wayfarer

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.

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

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.

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

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'.

"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. — Andrew M

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

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.
— Joshua Hothschild

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

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.

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?

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.

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..." — Wayfarer

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.

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. — Wayfarer

I agree.

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

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

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

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

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.