Substance vs. Accidents Example

[Betterave]

So… in this example does the substance of the banana disappear when it is eaten?

The being of accidents (properties, in modern lingo) is to be in a substance. The substance has natural properties that belong to it. When a banana is eaten, it’s properties begin to break down, and as they do the banana itself (i.e., substance) ceases to exist.

And if you used the banana to make two banana splits, what happens to the substance-]s/-]? Does the substance of the banana disappaer, [no] and two new banana split substances appear? [yes] Can substances appear and disappear like that? [no and yes] Or do you still have the substance banana, but it now has the accident of being “cut into two” and “chewed up”? [yes]

You’re probably just confusing things when you say ‘banana split substances.’ A ‘banana split substance’ just is the banana split, and the ‘substance of the banana’ just is the banana. With that in mind I have suggested answers to your questions above.

 

[rvilbig]

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?

Universals can sometimes overlap in a substance (a union of matter and form). This is because the substantial world is only a shadow of the world of forms. So in the case of the bowl-plate-transformation, there is a time in the process in which it actualizes both the form of both a bowl and a plate. It’s the same thing in evolution, a ring species is one in which neighboring subsets can interbreed while the endpoints cannot; in this sense, the set is simultaneously a single species and two distinct species, and the two forms (the species) exist in one substance (the population). This is because universals are at war with each other due to the fall, as John Henry Newman wrote:

" ‘All men have their price, Fabricus is a man; [therefore] he has his price;’ but he had not his price; how is this? Because he is more than a universal; because he falls under other universals; because universals are ever at war with each other; because what is called a universal is only a general; because what is only general does not lead to a necessary conclusion. “Men have a conscience; Fabricus is a man; he has a conscience.” Until we have actual experience of Fabricus, we can only say, that, since he is a man, perhaps he will take a bribe, and perhaps he will not. “Latet dolus in generalibus;” [trans: Fraud lurks in generalities] they are arbitrary and fallacious, if we take them for more than broad views and aspects of things, serving as our notes and indications for judging of the particular, but not absolutely touching and determining facts." (Grammar of Assent, page 279)

So in the bowl-plate-transformation and ring-species-evolution the universals are vying for a substance and neither has yet emerged victorious. Only at the end of time will all forms be re-united in harmony:

“The wolf shall dwell with the lamb, and the leopard shall lie down with the kid, and the calf and the lion and the fatling together, and a little child shall lead them.” (Is 11:6)

Those are my thoughts anyways. Perhaps someone else has better insight into this,

-Ryan Vilbig
ryan.vilbig@gmail.com

 

[Just_Lurking]

Huh…? Here was my challenge:
*If you have any evidence of anyone being able to form equivalence classes in the absence of canonical representatives, I would be glad to read it. *

Now I’m pretty sure the article you referred me to does not address this question. If it does please show me where.

The first and third sentences:

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 ~.

I’m criticizing your claim that the philosophical issue here is in any way furthered by your reference to modern mathematical theory. The mention of who held the concept is a response to the naive claim that the ancients would have seen the light, everything would have been clear, if only they had had modern mathematical theories available to them.

Here is my argument in more detail:

1. Using the modern mathematical concept of equivalence classes, we can define the concept of “dog-ness” as [Lassie], or equivalently as [Rin Tin Tin].
2. The ancient Greeks did not have this level of mathematical sophistication available, and could only define “dog-ness” in terms of a posited “ideal dog”. See here for the Allegory of the Cave, and here for Plato’s Theory of Forms. The first sentence of the latter article: Plato’s theory of Forms or theory of Ideas[1][2][3] asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality.

 

[Just_Lurking]

If you try reading the Parmenides you’ll realize that not even Plato was a Platonist (at least in the naive sense you’re imagining).

All Parmenides shows is that Plato was aware that there were problems with his theory regarding the ontological existence of universals. This has nothing to do with my claim, which is that the modern mathematical construction of universals as equivalence classes was not known to ancient Greek thought.

 

[tonyrey]

So… in this example does the substance of the banana disappear when it is eaten?

 

[Neil_Anthony]

Neil_Anthony;6868714:

Obviously the banana disappears but it doesn’t disappear into thin air!

If a banana splits obviously there are now two entities but the substance of which they are made is identical. The substance consists of the organic chemical compounds - which in turn consist of atomic particles. And then? Atomic particles don’t consist of nothing!

The substance is the chemical compounds? Now you’re using the word substance like modern people use it, to refer to a compound or element, or some other uniform substance. I don’t think this is the classical meaning anymore.

 

[tonyrey]

The substance is the chemical compounds? Now you’re using the word substance like modern people use it, to refer to a compound or element, or some other uniform substance. I don’t think this is the classical meaning anymore.

In that case I have fulfilled your request!

Although the concept of God as the ultimate Substance is not exactly modern…

 

[Neil_Anthony]

The being of accidents (properties, in modern lingo) is to be in a substance. The substance has natural properties that belong to it. When a banana is eaten, it’s properties begin to break down, and as they do the banana itself (i.e., substance) ceases to exist.

You’re probably just confusing things when you say ‘banana split substances.’ A ‘banana split substance’ just is the banana split, and the ‘substance of the banana’ just is the banana. With that in mind I have suggested answers to your questions above.

quote:
And if you used the banana to make two banana splits, what happens to the substances? Does the substance of the banana disappaer, [no] and two new banana split substances appear? [yes] Can substances appear and disappear like that? [no and yes] Or do you still have the substance banana, but it now has the accident of being “cut into two” and “chewed up”? [yes]

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”.

Now, melt that ice cube down, and drip it in freezing temperatures to get an icicle again. Now we have an icicle, but its a completely new icicle. All of the properties of the new icicle are identical to the old one, and its the same molecules, but it is a new substance: a new icicle. This is transubstantiation!

 

[Betterave]

If you have any evidence of anyone being able to form equivalence classes in the absence of canonical representatives, I would be glad to read it.

The first and third sentences:

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 ~.

First sentence: “given an equivalence relation ~ on X…”
No equivalence relation means no equivalence classes, correct? So how are you able to form an equivalence relation without canonical representatives? No explanation here so far as I can see…
Also: “In mathematics”: I’m not sure how this is even supposed to be relevant to classes of real as opposed to mathematical objects. Can you explain?

Third sentence: I have no idea how this is supposed to be relevant.

Here is my argument in more detail:

1. Using the modern mathematical concept of equivalence classes, we can define the concept of “dog-ness” as [Lassie], or equivalently as [Rin Tin Tin].

I don’t know how this is supposed to work (care to explain?), but supposing it did, wouldn’t Lassie or RTT become the canonical representative?

 

[Betterave]

…the ultimate Substance of everything is God!

This statement clearly contradicts the Church’s position.

 

[Betterave]

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”.

Now, melt that ice cube down, and drip it in freezing temperatures to get an icicle again. Now we have an icicle, but its a completely new icicle. All of the properties of the new icicle are identical to the old one, and its the same molecules, but it is a new substance: a new icicle. This is transubstantiation!

I don’t particularly like it. What’s wrong with good old bread and wine? You *can *use any example you like to illustrate that things (substances) come to be and pass away. But the important point with transubstantiation is missing: that the substance of bread and wine is miraculously instantaneously annihilated, while its properties are miraculously preserved without the support of any substance.

 

[Just_Lurking]

First sentence: “given an equivalence relation ~ on X…”
No equivalence relation means no equivalence classes, correct? So how are you able to form an equivalence relation without canonical representatives? No explanation here so far as I can see…

I’ve already defined the equivalence relation: A is equivalent to B if and only if they have the same quiddity.

Also: “In mathematics”: I’m not sure this is even relevant to classes of real as opposed to mathematical objects. Can you explain?

I don’t see why the type of object would matter. Nothing about the equivalence class construction makes any assumption about the type of object involved.

Third sentence: I have no idea how this is supposed to be relevant.

The quotient set gives the set of Platonic ideals. It is constructed mathematically, rather than postulated to exist ontologically.

I don’t know how this is supposed to work (care to explain?), but supposing it did, wouldn’t Lassie or RTT become the canonical representative?

Unless you think Lassie or Rin Tin Tin is the perfect dog, they are merely representatives, not canonical representatives. The mathematics to see this does go beyond middle school, however. It is easy to define the function from real-world objects to the corresponding Platonic ideals. However, a function from real-world objects to arbitrary representatives (such as Lassie or Rin Tin Tin) cannot be proven to exist without assuming the Axiom of Choice.

Thus, since the ancient Greeks were not aware of the Axiom of Choice, they had no choice but to postulate canonical representatives, which were then philosophically endowed with the properties of ontological existence as well as perfection.

 

[JDaniel]

The substance is the chemical compounds? Now you’re using the word substance like modern people use it, to refer to a compound or element, or some other uniform substance. I don’t think this is the classical meaning anymore.

Neil:

Substance is the matter of which a thing consists. It has nothing to do with “bowl-ness” except that “bowl-ness” happens to be an accidental form or shape of the matter at this time. If the bowl is made of copper, then the substance of the object is each and every copper atom whether it is presented as a bowl or a plate or an oven hood. Shape, color, shiny-ness, etc. are all accidental to substance, that is to say accidents of matter (or substance). Nothing more and nothing less. This is the meaning as understood by St. Thomas.

God bless,
jd

 

[rvilbig]

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”.

Now, melt that ice cube down, and drip it in freezing temperatures to get an icicle again. Now we have an icicle, but its a completely new icicle. All of the properties of the new icicle are identical to the old one, and its the same molecules, but it is a new substance: a new icicle. This is transubstantiation!

This differs from your original question, which was whether a bowl hammered into a plate possessed two forms. And the answer, in my humble opinion, is yes. Consider Plato’s allegory of the cave: two forms could overlap to generate one shadow, and thus two forms are simultaneously in one substance. In the bowl-plate-transformation, the intermediary may be said to simultaneously possess the form of a bowl and plate.

This however, is very different from Transubstantiation. Because the substance of the bread has been completely changed into the substance of flesh. It is not an intermediary between bread and flesh, and it did not transubstantiate into flesh and then return to being the substance of bread. It is the accidents that are the same. So if the Host were viewed under an electron microscope, the electrons would deflect as if they had hit carbohydrates. Likewise, when the Host is digested, the digestive enzymes break down the molecules as if they were carbohydrates, and the taste receptors transduce signals as if they were carbohydrates. So the accidents remain the same.

Hope this helps,

-Ryan Vilbig
ryan.vilbig@gmail.com

 

[Betterave]

I’ve already defined the equivalence relation: A is equivalent to B if and only if they have the same quiddity.

And what is a quiddity? Why is it not a ‘canonical representative’? And how is this an innovative view relative to ‘the ancients’ (and I would prefer to refer more generally to the ‘non-moderns’)??

I don’t see why the type of object would matter. Nothing about the equivalence class construction makes any assumption about the type of object involved.

So mathematical constructions don’t presuppose mathematical objects? That’s news to me!

The quotient set gives the set of Platonic ideals. It is constructed mathematically, rather than postulated to exist ontologically.

It does not ‘give’ it; if there were such a thing, it would be equivalent to it. But is there such a thing? If there is, what is contributed by modern mathematics, other than a direct translation of old terms into new ones?

Unless you think Lassie or Rin Tin Tin is the perfect dog, they are merely representatives, not canonical representatives. The mathematics to see this does go beyond middle school, however. It is easy to define the function from real-world objects to the corresponding Platonic ideals. However, a function from real-world objects to arbitrary representatives (such as Lassie or Rin Tin Tin) cannot be proven to exist without assuming the Axiom of Choice.

Thus, since the ancient Greeks were not aware of the Axiom of Choice, they had no choice but to postulate canonical representatives, which were then philosophically endowed with the properties of ontological existence as well as perfection.

I think Aristotle would say that all dogs are perfect dogs. Being a dog is all or nothing. Rex may be a ‘bad’ dog, but as regards his substance, if he is a dog, then he is a perfect dog. So I’m not sure where that leaves your comments on canonical representatives and the Axiom of Choice… Can you explain?

 

[Just_Lurking]

And what is a quiddity?

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

Why is it not a ‘canonical representative’?

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”.

And how is this an innovative view relative to ‘the ancients’ (and I would prefer to refer more generally to the ‘non-moderns’)??

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

So mathematical constructions don’t presuppose mathematical objects? That’s news to me!

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.

It does not ‘give’ it; if there were such a thing, it would be equivalent to it. But is there such a thing?

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

If there is, what is contributed by modern mathematics, other than a direct translation of old terms into new ones?

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

I think Aristotle would say that all dogs are perfect dogs. Being a dog is all or nothing. Rex may be a ‘bad’ dog, but as regards his substance, if he is a dog, then he is a perfect dog. So I’m not sure where that leaves your comments on canonical representatives and the Axiom of Choice… Can you explain?

I’m criticizing the concept of the Platonic ideal, that is, the “non-material abstract (but substantial) forms (or ideas)” that supposedly “possess the highest and most fundamental kind of reality”, as I quoted in post 43. Without the quotient set construction, ancient/non-modern/whatever philosophers had to rely on using representatives to understand equivalence classes. Without the Axiom of Choice to provide arbitrary representatives, they had to rely on 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.

 

[R_Daneel]

Uh, yeah, that’s actually the kind of radically naive assumption I was trying to warn you against. (I would say the same to RD too, of course, whom I’ve had to school on nonsensical pseudo-mathematical claims in the past.)

Got to love the arrogant self-assurance of the ignorant layman who dares to school the professionals in their own fields.

 

[tonyrey]

This statement clearly contradicts the Church’s position.

How?

 

[inocente]

I think Fr. Hardon is objecting to certain specific attempts to re-phrase what transubstantiation means, because they actually change the original meaning. I’m trying to express the original meaning in modern terms, so that I can understand what it really means. So far I don’t really get it.

While they were eating, Jesus took bread, gave thanks and broke it, and gave it to his disciples, saying, “Take and eat; this is my body.”
Then he took the cup, gave thanks and offered it to them, saying, “Drink from it, all of you. This is my blood of the covenant, which is poured out for many for the forgiveness of sins.
I tell you, I will not drink of this fruit of the vine from now on until that day when I drink it anew with you in my Father’s kingdom.”

Mat 26:26-29 NIV
The promise of the last verse quoted may just indicate that Jesus was talking about something holy rather than expecting a methodical deconstruction.

 

[Betterave]

Got to love the arrogant self-assurance of the ignorant layman who dares to school the professionals in their own fields.

Cute, RD, but what I said is true and if you choose to deny it with this lame appeal to your own authority…