Infinite equaling a finite

[thinkandmull]

Aquinas and others rightly say that matter is infinitely divisible. But doesn’t that mean that an infinite sum equals a finite thing?

 

[Rhubarb]

Infinite sums can converge to a limit, so conceptually a finite thing can be divided infinite times. Coincidentally this is a solution to Zeno’s Achilles and Tortoise paradox.

 

[Skeptic92]

Aquinas and others rightly say that matter is infinitely divisible. But doesn’t that mean that an infinite sum equals a finite thing?

You are misinterpreting the sense in which Aquinas (and other Scholastics) use the term matter, as it isn’t equivalent to material substance. A material substance is a composite unity of Act & Potency; which most explicitly in a material substance is its union of Form and Matter. These in turn form a composite union of an Essential Act which is in potency to its Act of Existence; as demonstrated in regards to spiritual substance in On Being and Essence, and systematised by Cajetan on his commentary on said work.

Matter considered of itself is a principle of potency, and matter considered on its own completely devoid of Form is what is termed Prime Matter. Matter in this sense is infinitely divisible because it is nothing in act, whilst it is everything in potency. Therefore; it is without quantity, quality, spatial placement, etc. As these accidents imply accidental form, whilst Prime Matter is completely devoid of Form.

Matter is one of those terms in Scholastic Philosophy you have to be careful about. As it has another meaning compared to the naturalist meaning of the term.

 

[thinkandmull]

well sure we can’t ever reach the end of an infinite division of matter, but its sum is reached, and it is finite. This seems like an impossible difficulty

 

[Oreoracle]

The notion of infinite divisibility is a bit misleading. For example, take a bar of gold. You could imagine breaking up the gold indefinitely, or at least until you reach the subatomic level. But then the matter you’re working with is no longer gold because, by definition, an atom of gold is the smallest piece of matter with gold’s properties.

Conversely, it’s a mistake to think that matter is just the sum of its parts, since matter has emergent properties. For example, water molecules are composed of hydrogen and oxygen, but water has properties exhibited by neither hydrogen nor oxygen.

 

[fhansen]

You are misinterpreting the sense in which Aquinas (and other Scholastics) use the term matter, as it isn’t equivalent to material substance. A material substance is a composite unity of Act & Potency; which most explicitly in a material substance is its union of Form and Matter. These in turn form a composite union of an Essential Act which is in potency to its Act of Existence; as demonstrated in regards to spiritual substance in On Being and Essence, and systematised by Cajetan on his commentary on said work.

Matter considered of itself is a principle of potency, and matter considered on its own completely devoid of Form is what is termed Prime Matter. Matter in this sense is infinitely divisible because it is nothing in act, whilst it is everything in potency. Therefore; it is without quantity, quality, spatial placement, etc. As these accidents imply accidental form, whilst Prime Matter is completely devoid of Form.

Matter is one of those terms in Scholastic Philosophy you have to be careful about. As it has another meaning compared to the naturalist meaning of the term.

So then is Prime Matter nothing IOW, other than a useful intellectual concept?

 

[Skeptic92]

So then is Prime Matter nothing IOW, other than a useful intellectual concept?

No; it is the matter which underlies substantial change. A notion of Prime Matter has found its way into modern Quantum Mechanics to attempt to account for virtual particles. This, however, is not quite right as the Quantum State appears to be secondary matter matter designated with a form, but not designated with accidental form of quality, quantity, etc. Heisenberg famously stipulated though that Quantum States should be interpreted a long the lines of Aristotelian Potencies, from which necessarily follows the concept of Prime Matter.

And, no. Prime Matter isn’t nothing, as potency is not nothing but it is something in a qualified sense of the term. As are all principles of potency; to equivocate between nothing and potency appears to fall into the error of Static Monism.

 

[fhansen]

No; it is the matter which underlies substantial change. A notion of Prime Matter has found its way into modern Quantum Mechanics to attempt to account for virtual particles. This, however, is not quite right as the Quantum State appears to be secondary matter matter designated with a form, but not designated with accidental form of quality, quantity, etc. Heisenberg famously stipulated though that Quantum States should be interpreted a long the lines of Aristotelian Potencies, from which necessarily follows the concept of Prime Matter.

And, no. Prime Matter isn’t nothing, as potency is not nothing but it is something in a qualified sense of the term. As are all principles of potency; to equivocate between nothing and potency appears to fall into the error of Static Monism.

But would that mean that Prime Matter should be able to exist without, or apart from, potency?

 

[Skeptic92]

But would that mean that Prime Matter should be able to exist without, or apart from, potency?

Prime Matter is pure potency; as it is matter devoid of all form. You would be correct in that matter cannot exist a part from any act (form), whatsoever, but this doesn’t mean that Prime Matter is not still an ontological principle of reality.

 

[thinkandmull]

I guess the answer is that it is not a definite infinity. It infinitely approaches 0 without reaching it. GREAT mystery

 

[fhansen]

Prime Matter is pure potency; as it is matter devoid of all form. You would be correct in that matter cannot exist a part from any act (form), whatsoever, but this doesn’t mean that Prime Matter is not still an ontological principle of reality.

OK, thank you. The topic’s a bit beyond me-just trying to understand it a little better.

 

[yppop]

Aquinas and others rightly say that matter is infinitely divisible. But doesn’t that mean that an infinite sum equals a finite thing?

Matter is not infinitely divisible unless it is compose of continuous space. Infinite divisibility is characteristic only of continuous space in which each point can be represented by a real number. An infinite number of points produces a finite 1 inch line. So in one sense a finite 1 inch line (or any other length however small) is infinitely divisible. But that doesn’t mean that an infinite sum equals a finite thing because you can’t count real numbers, they are not countable and hence can’t be summed. You’ve used “infinite” in different contexts.
Yppop

 

[inocente]

Aquinas and others rightly say that matter is infinitely divisible. But doesn’t that mean that an infinite sum equals a finite thing?

Think of it this way. First divide the matter in two halves.

Now divide each half into two halves. Keep repeating this, dividing again and again.

However many times you do it, you obviously still have the same amount of matter, just in tinier and tinier pieces.

Even if you keep dividing an infinite number of times.

(Although as has been said, you couldn’t keep dividing real matter forever).