Substance vs. Accidents Example

[Betterave]

How?

The Church teaches that God creates ex nihilo, from nothing, not from his own substance. I think I understand the general idea you have, but I’m pretty sure it’s just not correct in terms of the Church’s terminology.

 

[JDaniel]

Hmmm… well how about this example: You have an icicle. This is the substance “an icicle”. You apply heat, and it melts. Now you have a puddle. The old substance “the icicle” is gone, and now you have a new substance “a puddle”. Now you pour the puddle into a cube form and freeze it, and we have yet another substance, an “ice cube”.

Actually, no. You have water existing under one of its accidents, ice. Then, water existing under the accidental property of liquid. Then, water existing under the accidental property of ice again.

God bless,
jd

 

[Betterave]

It is defined in the link given from post 15, and discussed in post 17.

I didn’t ask for the definition of ‘quiddity’; I asked what a quidity is, what is its ontological status? You think you don’t need to address that?

It probably is. I was just trying to define the equivalence relation using terms from philosophy, since my use of mathematical terminology doesn’t seem to working. You complained in post 29 when I tried to define the equivalence relation directly in terms of “being the same kind of thing”.

No, I think not! Your mathematical terminology is purely formal mathematical theory. Your invocation of the term quiddity in giving a particular instantiation of an equivalence relation is supposed to give concrete content to the formal theory. The two are not merely alternate ways of expressing the same thing.

Again, if you know of some “ancient/non-modern” description of the quotient set construction, I would love to hear about it.

I think you’ve totally missed the meaning of my argument so far: the notion of the quotient set construction appears to be conceptually isomorphic with the notion of the set of all Platonic ideas; therefore the latter IS an ancient description of the quotient set construction. As such it is subject to all of the same conceptual difficulties.

You tell me. You’re the one who introduced the distinction between mathematical objects and real objects. It would seem to me that if a mathematical object is defined to be an object that can be studied using mathematics, then all real objects would also be mathematical objects, rather than being distinguished from them as you suggest in post 49. I’ve never claimed to know what you were asking here.

If you mean to say that I invented the notion that mathematical objects and real objects are distinct kinds, you are mistaken. Do you really deny that this is the case? I wonder what RD would have to say about that?

I’m using standard mathematical language. I don’t know if “give” has some special philosophical meaning.

The point is that a formal elaboration of set theory does not *give *you any real sets. In particular, in this case, it does not give us the complete set of natural kinds (obviously! - it does not give us even one single member out of the complete set… does it??).

The contribution of the modern mathematical construction of the quotient set is that it doesn’t postulate the ontological existence of canonical representatives.

If its concrete application relies upon the notion of quiddities and quiddities are canonical representatives then it most certainly does postulate the ontological existence of canonical representatives!

I don’t really see what Aristotle thought about real dogs being perfect or not has to do with this defect of the concept of Platonic ideals. Also, having two different perfect dogs doesn’t really make sense to me, since being different from perfection would seem to imply imperfection. Anyway, this more general use of the adjective “perfect” prevents it from being used to select a canonical representative, so this getting away from the main point.

You miss the point again: no dog is different from perfection if all dogs are perfectly doggy. And that is precisely the claim, if you recall.

 

[Neil_Anthony]

Actually, no. You have water existing under one of its accidents, ice. Then, water existing under the accidental property of liquid. Then, water existing under the accidental property of ice again.

God bless,
jd

So by that logic, “an icicle” is never a substance, the substance is water. So by that logic “bread” is never a substance, its actually flour, water, yeast, etc.?

 

[JDaniel]

So by that logic, “an icicle” is never a substance, the substance is water. So by that logic “bread” is never a substance, its actually flour, water, yeast, etc.?

No . . . while it is true that an icicle is not a substance and that Water is a substance, it is also true that the hydrogen and the oxygen of the water are substances. So, like water, a substance substantially changed by chemical reaction, into a molecule, such as water, is substance too. Bread is to water as flour, water and yeast are to hydrogen and oxygen.

A substance is that in which accidents can inhere.

God bless,
jd

 

[tonyrey]

The Church teaches that God creates ex nihilo, from nothing, not from his own substance. I think I understand the general idea you have, but I’m pretty sure it’s just not correct in terms of the Church’s terminology.

The Church teaches that God creates us and sustains us in existence…

 

[yppop]

Friends,

The problem in discussing “substance” is its definition; there are more than ten. For example, when one says that atoms are the substance of matter, they are using the word substance in the sense of “chemical substance”. Substance in the philosophical sense and the sense in which it used when discussing transubstantiation is “that which underlies matter and from which matter’s form and properties derive”. The implication in this definition is that substance is formless. In the theological sense, in regards to transubstantiation, the substance involved is certainly not and atom or any other particle of matter.

The question of “substance” is an important one for all Roman Catholics, since we are uniquely committed to believe that at the consecration of the bread and wine, the substance of the bread and wine is transformed (replaced) by the substance of Jesus’ body and blood. Furthermore, the transformation of substances takes place without a transformation of the form and properties (accidentals) of the bread and wine. Also we know from the doctrine of the Trinity that God exists as three persons sharing the same substance. So, we can deduce that there are at least two substances existing in reality: material and spiritual. We can presume that the spiritual substance is unique to the Trinity and therefore infinite in both extent and divisibility.

So what do we say about the material substance of the bread and wine other than it is theologically different than the spiritual substance? First of all, modern science does not deal in the concept of “substance”, material or spiritual, because the philosophical principle to which science adheres is Logical Positivism. Logical Positivism emphasizes the meaning and use of language, but also defines the tenets on which modern science is based. Logical Positivism:

1. rejects the idea that reality has some purpose;
2. rejects any attempt to explain natural phenomena by attributing to it an essence or a secret cause of things;
3. rejects as meaningless any explanation not verifiable through the senses;
4. advocates the study of constant relationship among things without delving into the underlying causes.
   Science is going to play its game on its home-field, so to deal with the nature of material substance we have to go at it philosophically.

Bread and wine are made of molecules and molecules are made of atoms. Atoms according to most scientific descriptions consist of a nucleus surrounded by a cloud of point-like electrons, organized in orbits. The diameter of the uranium atom is 23,000 times the diameter of its own nucleus. At the other end of the size spectrum, the diameter of the hydrogen atom is 145,000 times the diameter of its nucleus. Since electrons have no volume, the volume of matter resides in the nucleus, so the atom consists mostly of space. However, since the nucleus is constructed from protons and neutrons and they are compose of quarks and since quarks are point-like particles, the atom can be viewed as being completely spatial. Apparently matter dissolves into space when we subject it increasing granulation. Since the substance of all atoms is the same, and since all quarks and electrons are basically the same then all matter derives from the same substance. Thus, reality is reduced to two substances and both are of a spatial nature. Space can be either continuous or discrete. Of the two, continuous space is formless and infinite in extent and divisibility, properties that best fit the spiritual substance. Discrete space then is the substance of matter.

Yppop

 

[Just_Lurking]

I think you’ve totally missed the meaning of my argument so far: the notion of the quotient set construction appears to be conceptually isomorphic with the notion of the set of all Platonic ideas; therefore the latter IS an ancient description of the quotient set construction. As such it is subject to all of the same conceptual difficulties.

This seems to be the fundamental sticking point. The quotient set construction does not require, nor does it use, a canonical representative, such as the Platonic ideal dog.

The ancient/non-modern version uses, and indeed requires, such a canonical representative, for which the Platonic ideal is postulated and used.

This fundamental difference proves that the two versions are not conceptually isomorphic.

Mathematically, this can also be seen using constructive logic (which cannot use any non-trivial version of the Axiom of Choice) on domains that do not have canonical representatives. In such situations, the constructive quotient set does not exist.

If you mean to say that I invented the notion that mathematical objects and real objects are distinct kinds, you are mistaken.

I’m saying that you are the one who introduced the distinction between mathematical objects and real objects to this discussion. I still have no idea what your point is.

If its concrete application relies upon the notion of quiddities and quiddities are canonical representatives then it most certainly does postulate the ontological existence of canonical representatives!

It does not rely upon quiddities. I mentioned quiddities to give an alternative definition of what the equivalence relation is, since you seemed to have trouble with my first definition. Forget I ever talked about quiddity.

You miss the point again: no dog is different from perfection if all dogs are perfectly doggy. And that is precisely the claim, if you recall.

You’ve managed to redefine the word “perfect” so that it cannot be used as a canonical representative. Even so, it has no effect on the following claims:

1. Plato used a canonical representative (i.e., the Platonic ideal) to understand universals.
2. Modern mathematics has other, completely different ways of understanding universals that do not require canonical representatives. The difference between the old and new methods can be proven as a theorem of constructive mathematics.
3. These modern mathematical methods were not known in ancient Greece.

 

[MindOverMatter2]

Since modern physics pretty much disregards the notion of “substance” and focuses only on physical properties (accidents). In fact many people would deny that substance is real.

Consider a metal bowl. Its accidents include its diameter, its mass, its color, shape etc. Its substance is “bowl”. Now, imaging a craftsperson who uses a hammer to flatten the bowl into a plate. Now the metal has a different shape (one of the accidents), and a different substance. It’s new substance is “plate”.

When the craftsperson was hammering on the bowl to make it into a plate, what was the process by which the “bowl” substance went away, and the “plate” substance came into being? Did the bowl-ness slowly fade away as the height of the rim was reduced? Was there possibly an overlap time where two substances existed, bowl and plate, when it could have been used as either a shallow bowl or a deep plate? Is “bowlness” really something real, or is it just a description of what the metal object is most likely to be used as?

Your example of a substance is not a true example of a substance. The concept “bowl” is an invention of the human imagination, used to name and distinguish an object that we use for a partciluar purpose. We have found a useful shape and called it something. Your example is a useful strawman which somebody like R Daneel can use.

 

[R_Daneel]

Your example of a substance is not a true example of a substance. The concept “bowl” is an invention of the human imagination, used to name and distinguish an object that we use for a partciluar purpose. We have found a useful shape and called it something. Your example is a useful strawman which somebody like R Daneel can use.

Your disparaging remarks might (just “might”) carry a tad more weight, if you would elaborate on just what “substance” IS. By the way, the “substance” is an invention of ancient human imagination. The ancient people made up this concept (not unlike the Biblical idea of “kind” in relation to animals) which has been rendered obsolete and useless during the millenia elapsed since then.

 

[Betterave]

The Church teaches that God creates us and sustains us in existence…

True, and this sustenance (i.e., act of the divine will) would be unnecessary if our substance were identical to God’s.

 

[Betterave]

It does not rely upon quiddities. I mentioned quiddities to give an alternative definition of what the equivalence relation is, since you seemed to have trouble with my first definition. Forget I ever talked about quiddity.

Okay, I’ll stick to asking you one question this time. Give it to me again: how does modern mathematics make it possible to form equivalence classes without invoking some kind of canonical representative (such as a quiddity)?

 

[MindOverMatter2]

By the way, the “substance” is an invention of ancient human imagination.

Not according to my understanding of “substance”. So I guess this is just another example of how much you love making strawmen.

 

[JohnDamian]

Your disparaging remarks might (just “might”) carry a tad more weight, if you would elaborate on just what “substance” IS. By the way, the “substance” is an invention of ancient human imagination. The ancient people made up this concept (not unlike the Biblical idea of “kind” in relation to animals) which has been rendered obsolete and useless during the millenia elapsed since then.

Substance is quanta indeterminate; specified by quiddity.

 

[tonyrey]

True, and this sustenance (i.e., act of the divine will) would be unnecessary if our substance were identical to God’s.

It is not identical but it is derived from God - Who is not insubstantial…

 

[JDaniel]

It is not identical but it is derived from God - Who is not insubstantial…

Is He transubstantial?

God bless,
jd

 

[tonyrey]

Is He transubstantial?
God bless,
jd

Absolutely - in at least one respect!

 

[Just_Lurking]

Okay, I’ll stick to asking you one question this time. Give it to me again: how does modern mathematics make it possible to form equivalence classes without invoking some kind of canonical representative (such as a quiddity)?

From before:
In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a: [a] = { x in X | x ~ a }.

The set of all equivalence classes in X given an equivalence relation ~ is usually denoted as X / ~ and called the quotient set of X by ~.
Thus, the quotient set of X by ~ is { [x] | x in X }.

This mathematical construction works even if ~ doesn’t possess canonical representatives.

 

[Just_Lurking]

This mathematical construction works even if ~ doesn’t possess canonical representatives.

Mathematically, canonical representatives are given by a function f: X → X such that f(a) = f(b) if and only if a ~ b.

The definition of the quotient set works even in situations where ~ does not have canonical representatives.

For the ancients/non-moderns, f(Lassie) = f(Rin Tin Tin) = Platonic ideal dog.

 

[Betterave]

From before:
In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a: [a] = { x in X | x ~ a }.

The set of all equivalence classes in X given an equivalence relation ~ is usually denoted as X / ~ and called the quotient set of X by ~.
Thus, the quotient set of X by ~ is { [x] | x in X }.

Correct me if I’m wrong, but this is nothing but an axiomatic defining of the formal elements of equivalence-class theory (or whatever you want to call it). Where does it say anything about how to actually form an equivalence class? It seems that I’m asking you how to make bread and you reply, “that’s easy - go to the supermarket” or “easy - here’s a loaf of bread.”

This mathematical construction works even if ~ doesn’t possess canonical representatives.

So you claim, but how does this answer my question: how does modern mathematics make it possible to form (not just to describe - to form) equivalence classes without invoking some kind of canonical representative (such as a quiddity)?