Clearly a very foundational figure in the history of philosophy. For any particular question, it seems to be best to first consider what Aristotle had to say about it. It’s a fact that the most straightforward metaphysical arguments were be discovered first in human history and are therefore are to be found in ancient texts. Occam's Razor tells us to prefer straightforward arguments. So it is unwise to ignore the works of the ancient philosophers. Aristotle's departure from Plato on the theory of forms was very wise. Aristotle seems like a switched on, realistic sort of guy. He was the first I believe to come up with the cosmological argument for God.

I would take issue with him on one point: he held seemingly contradictory views. On the one hand he argued against the existence of the Actually Infinite and on the other he argued for eternal time (which is a form of Actual Infinity). Aristotle’s arguments for Eternal/Infinite time:

1. Time had no start because for any time, we can imagine an earlier time.
2. Time had no start because everything in the world has a prior cause.

The first argument can be countered by examining the overall structure of eternal time; it has no initial starting moment. For each individual moment, we can imagine a prior moment, but we know the system as a whole has no overall starting moment so it cannot exist as a whole (the first moment defines all the others). We can also appeal to modern physics and the Big Bang singularity - a moment for which it appears there was no preceding moment.

The 2nd argument can be by countered affirming causality: his argument leads to an infinite regress which undesirable and also impossible - there must logically be something which did itself not have a cause - the first cause - which itself must be beyond causality (timeless) - else nothing else can logically exist.

but what the people here think about Aristotle work? It's outdated, or have much more to say that all modern philosophy? — Gilliatt

Good philosophy is never outdated.

I would take issue with him on one point: he held seemingly contradictory views. — Devans99

This has been noted throughout the ages. Modern readers might see this as a defect but it was previously seen as intentional. Contemporary scholars who understand this include David Boloton's "An Approach to Aristotle's Physics: With Particular Attention to the Role of His Manner of Writing", Christopher Bruell's "Aristotle as Teacher: His Introduction to a Philosophic Science", Ronna Burger's "Aristotle's Dialogue with Socrates: On the Nicomachean Ethics".

Not familiar with those works. What is the reasoning behind holding a belief in eternity but not actual infinity?

One way in which Aristotle describes the subject matter of the Metaphysics is theology. Think of it as analogous to Plato banishing the poets from the Republic and replacing them with his own philosophical poetics, his own images of the divine. Aristotle, like Plato and Socrates, is a skeptic when it comes to the divine and questions of the beginning or arche and the whole. He knows that no one knows such things, but if he left it there he leaves it open to the theologians, those who make claims regarding the gods, origins, and the whole. It is a continuation of what Plato called the old quarrel between philosophy and poetry.

Whoever inquires into Aristotle’s sciences, peruses his books, and takes pains with them will not miss the many modes of concealment, blinding and complicating in his approach, despite his apparent intention to explain and clarify.
– Alfarabi, Harmonization

Aristotle, like Plato and Socrates, is a skeptic when it comes to the divine and questions of the beginning or arche and the whole. He knows that no one knows such things, but if he left it there he leaves it open to the theologians, those who make claims regarding the gods, origins, and the whole — Fooloso4

The greek pantheon and the stories associated with the individual greek gods are quite unbelievable - its a wonder anyone believed in it at all - Aristotle was too sensible for that. What Aristotle propounded is much closer to what deists believe I think:

"Aristotle argues, in Book 8 of the Physics and Book 12 of the Metaphysics, "that there must be an immortal, unchanging being, ultimately responsible for all wholeness and orderliness in the sensible world""

https://en.wikipedia.org/wiki/Unmoved_mover

It was not simply a question of the gods of myth but of the supernatural.

There are problems and contradictions inherent in Aristotle's discussion surrounding the claim that there must be an immortal, unchanging being, ultimately responsible for all wholeness and orderliness in the sensible world. If we do not have knowledge of the whole then any claims about what there must be are suspect. The question of the being of beings for Aristotle is the question of the causes and principles of being. The answer cannot be being or a being because the same question could be asked of the being who is the being or cause of being.

Well bearing in mind Aristotle believed in infinite time, it seems to me he would have had no option but to also believe in some sort of immortal-in-time being. Such a being, a necessary being, would be required. Causality absolutely requires a first cause.

Aristotle's conclusion is presumably that such a being must be itself uncreated, IE immortal-in-time.

My personal view is that there was a start of time and that the first cause is timeless so beyond causality - hence not needing to be created itself - it just is.

Well bearing in mind Aristotle believed in infinite time — Devans99

You miss the point. Aristotle did not know if time was infinite or not. But my view is not the mainstream view today, so I will leave it to you to decide whether Aristotle was aware of the contradictions or not, and if he was, how to reconcile them.

Aristotle seems to have believed past time was infinite:

"The ancient philosopher Aristotle argued that the world must have existed from eternity in his Physics as follows. In Book I, he argues that everything that comes into existence does so from a substratum. Therefore, if the underlying matter of the universe came into existence, it would come into existence from a substratum. But the nature of matter is precisely to be the substratum from which other things arise. Consequently, the underlying matter of the universe could have come into existence only from an already existing matter exactly like itself; to assume that the underlying matter of the universe came into existence would require assuming that an underlying matter already existed. As this assumption is self-contradictory, Aristotle argued, matter must be eternal."

https://en.wikipedia.org/wiki/Eternity_of_the_world

I think that it is possible that matter could have existed timelessly and and thus not requiring a 'substratum' to exist. Or there is the zero energy universe hypothesis - matter was created in exchange for negative gravitational energy - again not requiring a substratum. Also his argument implies that matter must exist forever in time which I would argue is not possible - the matter would have no start / no coming into being - meaning it could not exist at all.

Once again, I am saying that the standard contemporary reading of Aristotle is at odds with the approach that I have pointed to. Quoting Wikipedia ignores that distinction.

But I don't think Aristotle is your main concern here. What interests you here is the same thing that interests you in everything you post on every forum I have seen you post on - presenting and defending your own views on time, eternity, etc.

Once again, I am saying that the standard contemporary reading of Aristotle is at odds with the approach that I have pointed to. Quoting Wikipedia ignores that distinction. — Fooloso4

I'd be interested to hear what you think is wrong with Wikipedia's summary. I can't claim to be an expert on Aristotle myself.

But I don't think Aristotle is your main concern here. What interests you here is the same thing that interests you in everything you post on every forum I have seen you post on - presenting and defending your own views on time, eternity, etc. — Fooloso4

So you don't present and defend your own views yourself then? Seems to me that is an essential part of philosophy. It is the clash of differing opinions that can lead to a productive discussion and progress.

Getting back to your initial questions. There has been a resurgence of interest in Aristotle. Many turned to him because of dissatisfaction with modern ethics and political theory. Modern physical science is clearly superior but does not get at the fundamental questions that Aristotle asked about science (knowledge). De Anima is important because it provides a view of non-mythologized pre-Christian notions of the soul.

A word of advice, be wary of anachronistic translations and commentaries. He should be understood on his own terms rather than foreign terminology and framework.

I think that Aristotle is the greatest mind known to history, and that most of the errors in contemporary philosophy can be corrected by one familiar with his work.

On the time issue: Aristotle defined time as the measure of motion according to before and after. In his discussion of quantity in Metaphysics Delta, he points out that there are no actual numbers in nature, but that natural things have quantity in virtue of being countable or measurable. He would see an endless succession of natural change as measurable, but not measured. Thus, the associated time, as a measure, is a potential, not an actual, infinity.

With regard to an infinite regress of causes, we must distinguish, as Aristotle does, essential or concurrent causality from accidental or time-ordered causality. Aristotle and Aquinas reject the possibility of an infinite regress of essential causes, but allow the possibility of an infinite regress of accidental causes.

Yes, translations of Aristotle usually have some degree of interpretive spin. The Loeb Classical Library Edition is useful because it has the Greek and English on facing pages. Used copies are cheap, and with the aid of Lindell and Scott's dictionary, looking at the Greek often clarifies disputed issues. Once you've mastered the alphabet, Aristotle's Greek is not that hard.

Should not Aristotle have distinguished between:

- Past eternity. The past is complete, it has actually happened. Past eternity implies a greater than any finite number of days has elapsed - an actual infinity - which is impossible.

- Future eternity. For most models of time, the future is not complete - so it is a potential infinity.

Accepting eternalism, the two are clearly quite different?

My understanding of Aquinas is that he rejects a time ordered infinite regress. From the prime mover argument:

"If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand"

The 2nd of the 5 ways contains a similar argument against a time ordered infinite regress:

"Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate cause, whether the intermediate cause be several, or only one. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false. Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God."

I think Aristotle's message on a time ordered infinite regress in not clear. From Wikipedia:

"Aristotle argued against the idea of a first cause, often confused with the idea of a "prime mover" or "unmoved mover" (πρῶτον κινοῦν ἀκίνητον or primus motor) in his Physics and Metaphysics. Aristotle argued in favor of the idea of several unmoved movers, one powering each celestial sphere, which he believed lived beyond the sphere of the fixed stars, and explained why motion in the universe (which he believed was eternal) had continued for an infinite period of time. Aristotle argued the atomist's assertion of a non-eternal universe would require a first uncaused cause – in his terminology, an efficient first cause – an idea he considered a nonsensical flaw in the reasoning of the atomists."

https://en.wikipedia.org/wiki/Cosmological_argument

So it seems he argues for a time ordered infinite regress on the basis that a first uncaused cause is impossible?

I'm in agreement with Aquinas here - a time ordered infinite regress is clearly impossible. The objection of what caused the first cause goes away if time has a start - then the first cause is timeless and thus itself beyond causality - it in itself does not need a cause.

The past is complete, it has actually happened. Past eternity implies a greater than any finite number of days has elapsed - an actual infinity - which is impossible. — Devans99

I think that in virtue of his discussion of quantity in the Metaphysics, Aristotle would say that infinity is a property of numbers, and unmeasured change, however extended, is not a number, but a measurable -- and therefore not an actual, but a potential infinity. That is how he resolves Zeno's half-the-distance paradox. He argues that while the distance to the goal is infinitely divisible, it is not actually infinitely divided. His stance seems to be that to have an actual infinity requires someone to actually count or measure and infinite quantity. We might say that applying "infinite" to something that is not an actual count or measure is a category error.

My understanding of Aquinas is that he rejects a time ordered infinite regress. From the prime mover argument — Devans99

That is the error Kant makes in criticizing the cosmological argument. The argument is based on essential, not accidental, causality. Aristotle defines change/movement as the actualization of a potency insofar as it is still in potency. For a potency to be actualized requires an agent to be concurrently active -- here and now, not in the past.

Aristotle's paradigm case of essential causality is a builder building a house. As long as the builder is building, the house is being built. When the builder is not building, the house is not being built. That is why all cases in the regress must act concurrently with the observed change. If they did not the potency defining the change could not be actualized.

On the other hand, as Hume noted (and as was known to the Scholastics), accidental or time-sequenced causality has no intrinsic necessity. Thus, "proofs" based on accidental causality lack necessity.

Aquinas says explicitly that there is no philosophical reason to reject Aristotle's view that the cosmos is indefinitely old. Creation in time is, for Aquinas, an article of faith, not a conclusion of reason.

I think Aristotle's message on a time ordered infinite regress in not clear. From Wikipedia: — Devans99

The Wikipedia is wrong. Aristotle believed that each circular motion mathematical astronomers were then finding was caused by a distinct "intelligence," later Christianized into angels. He is quite clear that the intelligences do this because constant circular motion is the closest they can come to the nature of the unmoved mover. Further, he calls the causality linking the intelligences to the unmoved mover "desire," thus seeing it as a species of intentionality.

Being able to identify key terms is certainly helpful, but there is more to language than words. Understanding the grammar is essential to understanding how the word is being used in any particular case. In addition, philosophers often use some words in idiosyncratic ways. But, of course, this is a problem even when reading works in one's native language. I put my time into learning Greek many years ago, but even before I forgot much of what I learned I was always dependent upon translation and commentary.

None of this should dissuade someone from reading Aristotle or anyone else. It is simply the condition under which we read.

I think we agree. When I study a text I also read a number of translations and commentaries. I wasn't suggesting that there is no need for grammar. I'm saying that using a dictionary can help us see the associations and alternate meanings of terms that are translated by a single English term, often with entirely different associations.

I think that in virtue of his discussion of quantity in the Metaphysics, Aristotle would say that infinity is a property of numbers, and unmeasured change, however extended, is not a number, but a measurable -- and therefore not an actual, but a potential infinity. — Dfpolis

Time is not IMO 'unmeasured change'... time has a start so it must be physical. But assuming for arguments sake that time is 'unmeasured change', then it still measurable and has a quantity associated with it. Infinity is a property of quantity in general (as well as number). If past time is postulated to be eternal then the associated quantity of past time must be actually infinite... hence Aristotle is holding a contradictory view.

That is how he resolves Zeno's half-the-distance paradox. He argues that while the distance to the goal is infinitely divisible, it is not actually infinitely divided — Dfpolis

The very act of attaining the goal would seem to me to infinitely divide the distance to the goal - it is not possible, after all, to teleport over portions of the distance so to avoid infinitely dividing it. I am not convinced that Aristotle resolved Zeno's paradoxes. The solution is probably discrete spacetime.

His stance seems to be that to have an actual infinity requires someone to actually count or measure and infinite quantity. We might say that applying "infinite" to something that is not an actual count or measure is a category error. — Dfpolis

His stance seems strange. Does a falling tree make a sound if no-one is present? Does time or space have duration or distance if no-one measures it? Surely yes to both questions. I think actual infinity, if it existed, which it does not, would exist independently of any count or measure, so it is inconsistent to hold a believe in past eternity but to deny actual infinity.

That is the error Kant makes in criticizing the cosmological argument. The argument is based on essential, not accidental, causality. — Dfpolis

The cosmological argument is fundamentally a time-based argument so we are talking about a time based infinite regress - which is impossible - which is what Aquinas says in the 5 ways.

On the other hand, as Hume noted (and as was known to the Scholastics), accidental or time-sequenced causality has no intrinsic necessity. Thus, "proofs" based on accidental causality lack necessity. — Dfpolis

The fact that X exists means that it is intrinsically necessary that a prior cause of X existed. Thus we can trace backwards all along the causal chain establishing that each node is necessary to establish the state of affairs as today.

Aquinas says explicitly that there is no philosophical reason to reject Aristotle's view that the cosmos is indefinitely old. Creation in time is, for Aquinas, an article of faith, not a conclusion of reason. — Dfpolis

I do not see how Aquinas can reject a time ordered infinite regress and maintain a belief in an eternal cosmos - the second implies a time ordered infinite regress. The cosmos cannot be infinitely old, matter cannot exist 'forever' - that would imply matter with no temporal start, which in turn implies the matter does not exist.

The Wikipedia is wrong. Aristotle believed that each circular motion mathematical astronomers were then finding was caused by a distinct "intelligence," later Christianized into angels. He is quite clear that the intelligences do this because constant circular motion is the closest they can come to the nature of the unmoved mover. Further, he calls the causality linking the intelligences to the unmoved mover "desire," thus seeing it as a species of intentionality. — Dfpolis

That makes sense, thanks.

I think we agree. — Dfpolis

As do I. I was just pointing to further challenges that face us when reading in translation.

Even advanced knowledge of a language may not be sufficient for understanding the work of a philosopher. There is no translation that is not interpretation. The best translations are those written by scholars who have a grasp of the language, the issues, and the philosopher.

There are some who hold to what Gadamer called a fusion of horizons and others who like Strauss strive to understand a text from the perspective of a reader at the time of writing. I think this is best understood as an attitude or stance one takes in approaching the text rather than what one thinks is accomplished.

Time is not IMO 'unmeasured change'... time has a start so it must be physical. — Devans99

We are discussing Aristotle's consistency, so we have to use his definitions. Aristotle defined time as the measure of motion according to before and after. So, for him, time is a measure. "Unmeasured change" is how I would think Aristotle would describe the unlimited prior history of the cosmos -- as to have any kind of time would require a measurement.

The very act of attaining the goal would seem to me to infinitely divide the distance to the goal — Devans99

That is not Aristotle's view. I also think it is factually incorrect. We do not do division into parts (which is an intellectual operation) when we run a race, and if we did, it would take forever to do the actual dividing which is why Aristotle is denying actual numerical infinities. The same applies to time. You can only measure from a beginning to an end, and if change has no beginning, you can't actually measure all of it.

His stance seems strange. Does a falling tree make a sound if no-one is present? — Devans99

This is a question that Aristotle has elaborated position on. He distinguishes the sensible from the sensed and the intelligible from the understood. So, he would say that the result of the tree falling is audible, but not heard. If you define "sound" as audibility, then it makes a sound, but Aristotle would requires the completion of actual hearing for an actual sound. So he'd say it was an audible event, but not a sound.

Does time or space have duration or distance if no-one measures it? Surely yes to both questions. — Devans99

Aristotle says that quantity as a property is either discrete or continuous, but neither is an actual number unless counted or measured. This is because numbers are quantity as understood (as it exists in the mind). So, unless there is an enumerating mind, there are no numbers. There is, however, actual extension = parts outside of parts.poten

it is inconsistent to hold a believe in past eternity but to deny actual infinity. — Devans99

It is not inconsistent to hold that something can be potentially infinite, but always actually finite. That is how counting is. There is no intrinsic limit to a count, but actual counts are always finite.

The cosmological argument is fundamentally a time-based argument so we are talking about a time based infinite regress - which is impossible - which is what Aquinas says in the 5 ways. — Devans99

There are cosmological arguments based on accidental causality, such as the Kalam argument popularized by Craig, and arguments based on essential causality, such as those of Aristotle and Aquinas. The Kalam argument is persuasive, but logically unsound because, as Hume argued, accidental causality has no intrinsic necessity.

The fact that X exists means that it is intrinsically necessary that a prior cause of X existed. — Devans99

Ontologically prior (first in order of actualization), yes. Temporally prior, no. There is can be no logically necessary connection between events at separate times and places. This is because there is always the possiblity of intervention. There is no possibility of intervention with essential causality because the agent actualizing the patient is (identically) the patient being actualized by the agent. (The builder building the house is identically the house being built by the builder.)

I do not see how Aquinas can reject a time ordered infinite regress and maintain a belief in an eternal cosmos - the second implies a time ordered infinite regress. — Devans99

Aquinas is open to infinite regresses in time and rejects the Kalam argument. That is why creation in time is a faith claim for St. Thomas.

that would imply matter with no temporal start, which in turn implies the matter does not exist. — Devans99

Asserting that something has no beginning does not entail that it does not exist.

That makes sense, thanks. — Devans99

You are welcome.

There are some who hold to what Gadamer called a fusion of horizons and others who like Strauss strive to understand a text from the perspective of a reader at the time of writing. I think this is best understood as an attitude or stance one takes in approaching the text rather than what one thinks is accomplished. — Fooloso4

My approach is to try to stand next to the author and see what he or she saw.

My approach is to try to stand next to the author and see what he or she saw. — Dfpolis

But our distance intervenes. I suspect that no matter how close we get, or rather, no matter how close we think we get, there will still be a great deal that stands between us in terms of our views, concerns, and understanding of ourselves and the world. I think that no matter how close we may get Aristotle remains foreign.

Aristotle defined time as the measure of motion according to before and after. So, for him, time is a measure. "Unmeasured change" is how I would think Aristotle would describe the unlimited prior history of the cosmos -- as to have any kind of time would require a measurement. — Dfpolis

So is Aristotle saying when we measure it time exists (measured change); when we don't, it does not (unmeasured change), so a past eternity is possible without accepting actual infinity in reality? Putting QM aside for the moment, measuring does not change what is measured. So if something cannot be actually infinite because we can measure it, the same something cannot be actually infinite when we cannot measure it. IMO he should have concluded the past cannot be eternal.

That is not Aristotle's view. I also think it is factually incorrect. We do not do division into parts (which is an intellectual operation) when we run a race, and if we did, it would take forever to do the actual dividing which is why Aristotle is denying actual numerical infinities. The same applies to time. You can only measure from a beginning to an end, and if change has no beginning, you can't actually measure all of it. — Dfpolis

But our bodies do the division of space into parts for us in a race. So Aristotle is saying because we are not conscious of the division of space, it is not happening?

I think actual infinity cannot be regarded as a purely intellectual construct; it represents a fundamental characteristic of the continuum. If the continuum exists (which I doubt), then actual infinity is a fundamental part of reality and every movement we make is a division of space into actually infinitely small components. The fact we do not compute the divisions mentally does not mean they are not happening in reality. The fact the divisions took place in the past I suppose could be argued that actual infinity is not realised in the present, but it is realised in the past which is as bad to my mind - the past happened and was real.

It is like he is saying actual infinity is an artefact of the measuring process, along with number in general I suppose. He seems to be classing actual infinity as a human construct only. But maths mirrors reality and true continuity of spacetime surely requires something physically equivalent to actual infinity?

It is not inconsistent to hold that something can be potentially infinite, but always actually finite. That is how counting is. There is no intrinsic limit to a count, but actual counts are always finite. — Dfpolis

Counting extends forward into a potentially infinite future so I agree that it is always actually finite. But it is an infinite past that I contend requires actual infinity. We can, as a thought experiment, imagine an ever-lasting time traveller travelling backwards in time whilst counting. From our perspective, the past is completed, so the time traveller must have counted every number if the past is infinite. But there is no largest number so we can only conclude the traveller counted to actual infinity somehow. So past eternity seems to require actual infinity.

There are cosmological arguments based on accidental causality, such as the Kalam argument popularized by Craig, and arguments based on essential causality, such as those of Aristotle and Aquinas. The Kalam argument is persuasive, but logically unsound because, as Hume argued, accidental causality has no intrinsic necessity. — Dfpolis

I see all the cosmological arguments as either explicitly or implicitly time-based. Causality and time are inextricably linked; movement and time are likewise linked. From the second way:

"The second way is from the nature of the efficient cause. In the world of sense we find there is an order of efficient causes. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible"

Aquinas is talking about efficient causes being time ordered IMO. The 3rd way is temporal in its phraseology, the first way is all about motion hence time.

Ontologically prior (first in order of actualization), yes. Temporally prior, no. There is can be no logically necessary connection between events at separate times and places. This is because there is always the possiblity of intervention. There is no possibility of intervention with essential causality because the agent actualizing the patient is (identically) the patient being actualized by the agent. (The builder building the house is identically the house being built by the builder.) — Dfpolis

Can you explain how the actualisation order could be different from the temporal order?

The possibility of intervention by God? I thought that Aristotle had God as external to the universe, existing in the heavenly spheres - a deist view of a non-interventionist God.

Asserting that something has no beginning does not entail that it does not exist. — Dfpolis

If something never started existing, it does not exist. Time is like space in this regard: if something has no beginning in space, it does not exist. Likewise if something has no temporal start, it has no temporal start + 1, start + 2, etc..., so by induction, it does not exist. A beginning is also required for instantiation of innate attributes, like the mass/charge of a particle. Without a beginning, matter would not have innate attributes and would be null and void.

The fact we do not compute the divisions mentally does not mean they are not happening in reality. The fact the divisions took place in the past I suppose could be argued that actual infinity is not realised in the present, but it is realised in the past which is as bad to my mind - the past happened and was real. — Devans99

I don't think Aristotle is saying that what is potential is not "happening." In De Anima, knowledge is described this way:

Actual knowledge is identical with its object. But potential knowledge is prior in the individual. but not prior even in time in general; for all things that come to be are derived from that which is so actually.
Chapter 7 translated by D.W. Hamlyn

This suggests there is a disconnect between what the one who "knows" needs to presume to make sense of time and the actuality of knowledge when this identity occurs. The past is just one set of potentialities. Otherwise, all that is possible will have occurred.

I think that no matter how close we may get Aristotle remains foreign. — Fooloso4

Aristotle and we share a common purpose -- to understand reality. By standing beside him and looking at what he was looking at, there is every chance that we will see what he saw -- if he saw rightly. Of course, we have different conceptual spaces than he did, but there is no reason that we cannot expand our spaces to include his concepts, just as we expand it any time we delve into a new subject.

As knowledge is a subject-object relation, we will never know in exactly the same way as Aristotle did, but then neither can we know in exactly the same way our contemporaries do. Still, in both cases, there is much we can learn by looking in the same direction form the same standpoint.

My approach is to try to stand next to the author and see what he or she saw. — Dfpolis

To which Ezra Pound would have added - did add - that as well you would have had to be him. Maybe by a rigorous standard that's the insight into the fact of the necessity of interpretation - you just cannot get theah from heah!

So is Aristotle saying when we measure it time exists (measured change); when we don't, it does not (unmeasured change), so a past eternity is possible without accepting actual infinity in reality? — Devans99

He is saying that change has the potential to yield time, and that when we measure change according to before and after, we actualize that potential. This is because he sees time as a number, and numbers as existing only in enumerating minds.

Granting for the sake of argument that measuring does not change what is measured, it still actualizes a relational potential in the measurable. The measurable has a potential relation to minds that can know its measure number, but that relation is not actual because until it is measured, there is no measure number to be known. Further, the measure number depends on how we measure. We get different numbers using centimeters or inches, in different frames of reference, and, in QM, by using different operations. Measure numbers do not pre-exist measurements, because they are determined jointly by the properties of the measurable and the details of the measurement operation.

IMO he should have concluded the past cannot be eternal. — Devans99

If a thing can't be measured because it has no starting point, that doesn't preclude it having indefinite extent.

So Aristotle is saying because we are not conscious of the division of space, it is not happening? — Devans99

There is no actual division in a continuous extent. There is only a potential mental division. In other words, we can think of it having a first part and a second part. If we do, it has mental parts, but is still a physical unity. If we do not divide it in thought, a unity has no actual parts, only potential parts.

I think actual infinity cannot be regarded as a purely intellectual construct; it represents a fundamental characteristic of the continuum. — Devans99

Potentially, yes. Actually, no. We can divide indefinitely, but at any point in time, we will only have done a finite amount of division.

The fact we do not compute the divisions mentally does not mean they are not happening in reality. — Devans99

What is the operation that makes them "happen," if it is not mental or physical? Note that moving is not dividing, even though motion can be divided mentally.

It is like he is saying actual infinity is an artefact of the measuring process, along with number in general I suppose. — Devans99

Exactly! If we are talking about numerical infinity, it can apply only to numbers. If we are talking about being unbounded, but not a number, Aristotle would agree that we can have operations, such as division or thinking back in history, that can be continued indefinitely. It is just that at any actual point, they only go so far.

But maths mirrors reality and true continuity of spacetime surely requires something physically equivalent to actual infinity? — Devans99

How would we know? We have no capacity to experience such a thing.

Also, in mathematics, infinity does not work like an actual number. You can't operate with it and get a well-defined result. What is ∞ - ∞? Or ∞/∞?

the time traveller must have counted every number if the past is infinite. — Devans99

There is no finite "every number." The traveler keeps counting finite numbers endlessly -- going forward or backward.

I see all the cosmological arguments as either explicitly or implicitly time-based. Causality and time are inextricably linked; movement and time are likewise linked. — Devans99

Only accidental causality is time based, and as Hume showed, it lacks intrinsic necessity.

Essential causality is concurrent. The builder is building only when the house is being built. The law of conservation of energy is only conserving energy when energy is being conserved.

As a side note, there seems to be a point (the Planck time) at which time can no longer be defined. Beyond it, accidental causality is meaningless. Essential causality remains meaningful.

There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible — Devans99

The priority here is ontological, not temporal. It means first in order of actualization. A builder, for example, must be actual (ontologically) prior to any actual building work -- even though the actuality of the builder is co-temporal with the actuality of building operations.

Can you explain how the actualisation order could be different from the temporal order? — Devans99

I just did.

The possibility of intervention by God? — Devans99

Not necessarily. I drop a ball and expect it to hit the ground. Then, an asteroid hits and the ball is vaporized. While this my be far fetched, the possibility of intervention shows a lack of necessity and separation allows intervention.

I thought that Aristotle had God as external to the universe, existing in the heavenly spheres - a deist view of a non-interventionist God. — Devans99

Aristotle's God is not physical, but "Self-thinking Thought," and has no location. His view was deist in that he believed the unmoved mover had no interest in human beings, "There can be no friendship between God and man."

If something never started existing, it does not exist. — Devans99

That would mean that God could not exist.

This is because he sees time as a number, and numbers as existing only in enumerating minds. — Dfpolis

Personally I have numbers existing in the mind only but corresponding/representing to real life quantities. I do not believe that whether some macroscopic real world quantity is measured or not effects its value in any way. The measure of the object is intrinsic to the object and measurement just makes that known to an observer. So if numbers cannot be actually infinite (which they cannot), nor can real world quantities (measured or unmeasured).

There is no finite "every number." The traveler keeps counting finite numbers endlessly -- going forward or backward. — Dfpolis

But with past eternity and a counting, backwards travelling, time traveller, we have a measure of eternity - any number we can think of, the traveller must have counted it. So when we ask what is the length of that past eternity, it must be greater than any finite number. Only actual infinity has that property and actual infinity does not exist IMO.

What is the operation that makes them "happen," if it is not mental or physical? Note that moving is not dividing, even though motion can be divided mentally. — Dfpolis

A particle moving along a real number line continuum must pass through every possible sub-division (sub-segment) of the line over time. So for any sub-division I care to choose, say one 10^-10 in length, it is guaranteed that there are always smaller sub-divisions that compose it that the particle also travelled through. The act of movement - positional change from one moment to the next - creates the sub-divisions. If spacetime is continuous, then there must be sub-divisions in length smaller than any finite number we care to name. For that, one can only appeal to 1/actual infinity... which does not exist IMO.

Only accidental causality is time based, and as Hume showed, it lacks intrinsic necessity. — Dfpolis

I trust my senses and experience more than Hume on this point.

As a side note, there seems to be a point (the Planck time) at which time can no longer be defined. Beyond it, accidental causality is meaningless. Essential causality remains meaningful. — Dfpolis

Two events would not be able to share a cause and effect relationship if they are separated in time by less than Planck time? Concurrent events cannot share a cause and effect relationship anyway. So I still believe that time-based causality cosmological arguments have merit.

That would mean that God could not exist. — Dfpolis

... could not exist in time, but his presence seems necessary, so he must exist outside of time. God cannot have a temporal start or end to his existence. He would just 'be' with no tense. God would be both finite and eternal - which is only possible outside of time.