Wouldn’t the claim of the existence of such a bodily substance be an empirical claim? If it’s a substance, then either it can be detected by scientific means, or it can be declared a false hypothesis. — Wayfarer

Without judging the claim, a lack of data does not falsify a hypothesis. It may make it unnecessary and unparsimonious.

Wouldn’t the claim of the existence of such a bodily substance be an empirical claim? — Wayfarer

That the heavenly bodies exist is an empirical claim. That they are imperishable is also an empirical claim, by the standards of the time. Generation after generation they stay the same neither coming into being or passing away. Since they are visible they are bodies, but since they do not change they must be a body that is different from terrestrial bodies.

Are you denying that discrete objects can be counted? Or continuous quantities measured? I am not sure what you are objecting to. — Dfpolis

I see no difference between the claim that a number-potential is guaranteed to exist and the claim that a number is guaranteed to exist. Where are those potentials? Do they exist? Are they potential potentials or actual potentials? I think you are just giving the numbers a fancy name.
There is a 1 potential which must always have existed actually as I can count to 1.
There is a 2 potential which must always have existed actually as I can count to 2.
....

Do they exist for every mind? Do they exist independently of mind? Does your mind make such potentials exist for my mind?

Thereby providing justification for all those who say that Aristotle should be relegated to history with the geocentric universe and the crystalline spheres.

There is still a great deal of interest in Aristotle, and not just historical interest. Although my guess is that interest does not extend to his astronomy.

I thought it might have a metaphysical interpretation but perhaps not.

Aristotle's astronomy tried to account for how beings found within the 'sublunary sphere' had anything to do with those observed outside of it. Now that we understand that they are not different kinds of beings, the view of all beings belonging to a single cosmos is strengthened by our increase in knowledge.

I had rather thought if the phrase used ‘principle’ instead of ‘substance’ it might remain defensible.

I see no difference between the claim that a number-potential is guaranteed to exist and the claim that a number is guaranteed to exist. — Heiko

So, you think a potential statue is no different from an actual statue? A block of marble and the Pieta carved from it are the same? I cannot believe that that is your position.

Where are those potentials? — Heiko

As I already explained, they are in the sets that can be counted or in the various things we can measure.

I think you are just giving the numbers a fancy name. — Heiko

So, you think there is no difference between a group of sheep and the number that results from counting them.

Philosophy is not about fancy names. It is about understanding human experience, including human mathematical experience, consistently. As any science, philosophy has technical terms so that its practitioners can speak and write with precision. Since numbers do not exist in the same way as rocks or fish, it is reasonable to ask what is meant by the phrase "there exists" as used in mathematics. I have given an answer that is consistent with our experience with numbers. It does not agree with your preconceptions. So, we have come to an impasse. I do not see that we are making progress, but if you think we are, let me know.

There is a 1 potential which must always have existed actually as I can count to 1.
There is a 2 potential which must always have existed actually as I can count to 2.
.... — Heiko

To give you the courtesy of an answer, possibility may always exist, potentials do not. There seems to have been a point early in the evolution of the universe, when it was not yet discrete objects (and so had nothing countable) and nothing measurable (because of problems associated with Planck scale objects). At that point, there was no basis in reality for our number concepts, and so no potential numbers -- only the possibility of numbers in the future when beings capable of counting, measuring, and conceiving numbers would come to be.

‘God created the integers. All else is the work of man.’ Leopold Kronicker.

If that is so then the alphabet was created by man. Combining the two to make algebra must surely have been the work of the devil.

Biological consciousness is the instrument the physical world plays, and the melody is apparent reality.

Aristotle's astronomy tried to account for how beings found within the 'sublunary sphere' had anything to do with those observed outside of it. Now that we understand that they are not different kinds of beings, the view of all beings belonging to a single cosmos is strengthened by our increase in knowledge. — Paine

The question of our relationship to the heavens is an interesting one.

In the Republic Socrates says:

It is the "fourth study" after solid geometry. It is the study "which treats motion of what has depth" (528e)

Glaucon says "astronomy compels the soul to see what's above and leads it there away from the things here". Socrates corrects him. When studied in this way it causes the soul to look downward. (529a)

He calls the stars "decorations in the heavens embroidered on a vaulted ceiling". The image of the starry night, is the opposite of the image of Good in the sun. Astronomy when studied as Socrates proposes is not the study of visible things in the heavens, it is about "what must be grasped by argument and thought, not sight" (529d)

Aristotle calls the heavenly bodies divine. He may have regarded our relationship to them as one of distance, the difference between divine and imperfect being. Or perhaps just the opposite, our closeness to the divine through our perception of them. I suspect this is addressed in On the Heavens. @Wayfarer.

That they are not different kinds of beings might be regarded, at least by some, as nothing special. But the ability to see the night sky without light pollution is, despite what Socrates said, an awesome experience. The images of the Webb telescope may also have bearing on how one regards and feels in relation to the cosmos.

The Muslims invented it but Old Nick sure knows how to bend it to his ends.

If humanity were to vanish and the potential of rational beings extinguished, so would go the potentials of mathematics - or not? The potential of rational beings is a necessary condition for potentials of mathematics. But is it a sufficient condition?

If humanity were to vanish and the potential of rational beings extinguished, so would go the potentials of mathematics - or not? — jgill

Any rational sentient beings would presumably make some of the same discoveries. That’s the meaning of ‘true in all possible worlds.’

There is a 1 potential which must always have existed actually as I can count to 1.
There is a 2 potential which must always have existed actually as I can count to 2. — Heiko

For the Greeks "2" is always two of something counted. In order to count there must be the unit, some one, some "what" of the count.There is no count unless and until it is known what it is that is being counted - apples or bananas or pieces of fruit.

There is a potential for "1" or "2" or any number of things only as long as you or someone else is able to count and there is something to be counted and those things are visible and each one distinguishable. Counting them actualizes the potential.

The idea that we have the same chemistry as stars is astonishing. The telescopes keep pushing the border of the 'sublunary' sphere further away. The disagreement between Glaucon and Socrates underscores how the view of what is 'immaterial' is not self-explanatory but is always a part of looking for explanations that reflect better than others. If the idea of the 'immaterial' has a job, the 'eternal' has one too. I read Aristotle to be unhappy with the divide between Glaucon and Socrates. The following supports that view:

If there is something that is capable of moving things or acting on them, but that is not actively doing so, there will not [necessarily] be movement, since it is possible for what has a capacity not to activate it. There is no benefit, therefore, in positing eternal substances, as those who accept the Forms do, unless there is to be present in them some starting-point that is capable of causing change. Moreover, even this is not enough, and neither is another substance beyond the Forms. For if it will not be active, there will not be movement. Further, even if it will be active, it is not enough, if the substance of it is a capacity. For then there will not be eternal movement, since what is potentially may possibly not be. There must, therefore, be such a starting-point, the very substance of which is activity. Further, accordingly, these substances must be without matter. For they must be eternal, if indeed anything else is eternal. Therefore they must be activity. — Metaphysics, 1071b12–22, translated by C.D.C Reeve

Saying: "if indeed anything else is eternal" puts the explanations into a hierarchy.

Further, accordingly, these substances must be without matter — Metaphysics, 1071b12–22, translated by C.D.C Reeve

There’s that oxymoronic term again.

I am using Reeve's translation for convenience. Present one you like better.
Or is your beef with Aristotle?

It’s the use of the word ‘substance’ especially when said to ‘immaterial substance’ . That’s what I say is oxymoronic. But then, ‘substance’ is not the word that Aristotle would have used. (Actually wasn’t it in this context where the word ‘dunamis’ was used?)

Aristotle used ousia in numerous places regarding the 'immaterial',if you are suggesting they were always connected with matter.
I don't like Reeve for some expressions, but he is extremely consistent. He never translates dunamis as 'activity' or subtance (ousia)

No, again it’s that ‘substance’ is a misleading translation of ‘ousia’, (as per Joe Sachs’ comment earlier in the thread). It’s not that ‘ouisua’ suggest a material thing, but that ‘substance’ does. If in the quotation we’re considering, the term used for ‘ouisua’ was ‘being’ or ‘principle’ I think it would convey the meaning much more effectively.

How does that 'suggestion' square against Aristotle using the word without that limitation??
How does that change what is said in Reeve's translation given above?

If you are interested in the Greek, the passage I quoted is here. The English translation is given by selecting that on the upper right-hand side of that page. I think Reeve's is better but the difference does not matter regarding the use of ousia that you refer to.

If humanity were to vanish and the potential of rational beings extinguished, so would go the potentials of mathematics - or not? — jgill

Any rational sentient beings would presumably make some of the same discoveries. That’s the meaning of ‘true in all possible worlds.’ — Wayfarer

You answered the second question, not the first. If the potential of existence of rational beings is extinguished, would the potential of mathematics vanish as well?

If you are interested in the Greek, the passage I quoted is here. — Paine

I can't read Greek. Sophisticated readers (such as yourself) will understand the use of the word 'substance' in philosophy as being different to normal usage, but it jars every time I read it. My point (and it's a pet peeve) is that the use of the word 'substance' to translate 'ousia' tends to skew the meaning of many of these passages, indeed the entire milieu. As Joe Sachs says, 'substance' is 'a word designed by the anti-Aristotelian Augustine to mean a low and empty sort of being [which] turns up in our translations of the word whose meaning Aristotle took to be the highest and fullest sense of being....' . The ealier reference to 'divine substance' is an example. I'm not sure what other word in the modern lexicon would do the job but perhaps 'principle' might.

These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they.

What 'bodily substance' he talking about? Endocrines?

'Substance' introduces the problem of reification - turning an idea into a thing.

I ran the question 'what is reification in philosophy' by the chatbot and it said:

The problem of reification in philosophy refers to the tendency to treat abstract concepts or mental constructs as if they were concrete objects with independent existence. It involves treating something that is abstract or conceptual as if it were a physical thing that exists independently of our thoughts or language.

Whereas I think intelligible objects are at once, only graspable by nous (mind) but at the same time, they're not mental constructs :rage:

If the potential of existence of rational beings is extinguished, would the potential of mathematics vanish as well? — jgill

No. My belief is that while the truths of reason can only be grasped by the mind, they're not the product of the mind. Hence Bertrand Russell: 'Thus universals are not thoughts, though when known they are the objects of thoughts.'

There's a deep issue here, which I keep running up against in these debates. I'm not well-read in philosophy and metaphysics and, at this stage in life, I'll acknowledge I'm unlikely ever to be, but I intuitively sense some really vital issue in all of this (running up and down the beach, waving arms and appearing to shout).

those who accept the Forms — Metaphysics, 1071b12–22, translated by C.D.C Reeve

We might assume Aristotle is talking about Plato and this is not entirely wrong, but the argument in the Timaeus acknowledges the problem of the Forms and:

some starting-point that is capable of causing change. — Metaphysics, 1071b12–22, translated by C.D.C Reeve

In the discussion of astronomy in the Republic Socrates says:

Perhaps your belief is a fine one and mine innocent. (229c)

This echoes Socrates' discussion of the inadequacy of the Forms in the Phaedo, where he calls the hypothesis "innocent".

So, by those who accept the Forms I think he means those who accept them and are unaware of the problems Plato raises.

On the issue of the starting point Plato and Aristotle take opposite sides, but agree that it:

must be grasped by argument and thought, not sight. (529c-d)

Aristotle's argument is:

There must, therefore, be such a starting-point, the very substance of which is activity. — Metaphysics, 1071b12–22, translated by C.D.C Reeve

A reasonable argument, but reasonable and true are not necessarily the same.

Timaeus says:

So then, Socrates, if, in saying many things on many topics concerning gods and the birth of the all, we prove to be incapable of rendering speeches that are always and in all respects in agreement with themselves and drawn with precision, don’t be surprised. (29c)

The question is whether Aristotle accepts what is reasonable as true. Surely he is aware of the problem of giving an account of the arche.

I started a discussion of the limits of knowledge in Aristotle's Metaphysics.

I need to think about this matter of giving accounts of the arche between Aristotle and Plato.
I will reply on your thread.

What 'bodily substance' he talking about? Endocrines? — Wayfarer

For the nature of the stars is eternal, because it is a certain sort of substance, and the mover is eternal and prior to the moved, and what is prior to a substance must be a substance. It is evident, accordingly, that there must be this number of substances that are in their nature eternal and intrinsically immovable, and without magnitude (due to the cause mentioned earlier). It is evident, then, that the movers are substances, and that one of these is first and another second, in accord with the same order as the spatial movements of the stars. But when we come to the number of these spatial movements, we must investigate it on the basis of the mathematical science that is most akin to philosophy, namely, astronomy. For it is about substance that is perceptible but eternal that this produces its theoretical knowledge, whereas the others are not concerned with any substance at all—for example, the one concerned with numbers and geometry. — Metaphysics 1073a30, translated by C.D.C Reeve