Existence exists?

[Michael Stuart Kelly]

GS,

Sure.

Try to teach calculus to a person who has not learned how to count without teaching him how to count.

Can't be done.

Michael

[BaalChatzaf]

This is correct, but only for a narrow and specific branch of math.

I have a physics background, but I have some exposure to pure math and know the difference between pure and applied mathematics.

String theory and brane theory require the most abstract forms of mathematics including category theory, the theory of manifolds, the theory of connections. It is not just differential equations any more.

How much manifold theory do you know?

Ba'al Chatzaf

[Dragonfly]

One shouldn't confuse the content of mathematics with the human activity of doing mathematics. You could argue that every human activity is utlimately based on using sensory input, but that is rather trivial and beside the point. Neither is the way we arrive at mathematical theories relevant, whether we use intuition, images, blood, toil, tears and sweat, etc. The mathematical theories and theorems in themselves are not dependent on human activity (even if that's obviously the only way we can gain mathematical knowledge and we can express those theorems). The proverbial intelligent Martian spider will find the same value for pi as us earthlings, and it will also find the same irreducible representations of SU(3). Those mathematical results are independent of the existence of human beings or Martian spiders.

Edited April 8, 2009 by Dragonfly

[bmacwilliam]

This is correct, but only for a narrow and specific branch of math.

I have a physics background, but I have some exposure to pure math and know the difference between pure and applied mathematics.

String theory and brane theory require the most abstract forms of mathematics including category theory, the theory of manifolds, the theory of connections. It is not just differential equations any more.

How much manifold theory do you know?

Ba'al Chatzaf

None, but I'm reasonably proficient at fluid dynamics. Are you? Wait... It doesn't matter. Why? Because you claimed

"I can tell you its starts with intuition based on everyday sensory input. That is not where it ends up, but without that start the abstract end cannot be attained."

What you and Michael are missing and confusing is that we NEED senses to learn anything, but math can begin, end, and exist entirely in the abstract. It doesn't matter that some math concepts are intuitive and based on experience, some are clearly not. The fact that learning math (and every human activity) requires the senses is beside the point as Dragonfly pointed out. The question is whether math is connected to anything we could call reality? The answer, clearly, is sometimes yes and sometimes no.

The claim that:

"Mathematics is a tool for doing physics. "

Is a truly absurd claim without the clarification that there is much math that has no connection to physics at all.

Edited April 8, 2009 by Bob_Mac

[Michael Stuart Kelly]

The proverbial intelligent Martian spider will find the same value for pi as us earthlings, and it will also find the same irreducible representations of SU(3). Those mathematical results are independent of the existence of human beings or Martian spiders.

Dragonfly,

The proverbial intelligent Martian spider will also have something to count to start with if it uses conceptual thinking. So it will build higher math from simple math just the same as humans do.

Also, you are making one hell of a presumption that the spider will use the same intelligence system that humans do. It might have a totally different form of processing knowledge. I have never met one so I personally cannot say.

If you can cut humans off from math for intelligence, why do you leave them in with Martian spiders for intelligence?

Michael

[Michael Stuart Kelly]

What you and Michael are missing and confusing is that we NEED senses to learn anything, but math can begin, end, and exist entirely in the abstract.

Bob,

There is no abstract without a living conceptual brain to do the abstracting. "Abstract" is not an existent like a light wave is. It is an activity of the brain.

Michael

[Michael Stuart Kelly]

Here is a good example of what happens when higher math is applied to reality without taking into account that it is based on reality (since many of the scientists also believe math is cut off from human experience): much of the man made global warming stuff.

The logarithms and mathematical projections and computer scaling and modeling are wonders to behold. It's a shame reality is not so cooperative with the math.

Reality will win in the end. It always does.

Michael

[tjohnson]

Sure.

Try to teach calculus to a person who has not learned how to count without teaching him how to count.

Can't be done.

Why not? I bet I could.

[Alfonso Jones]

Maybe there is supernatural being who questions whether or not 'existence exists', does he exist?

This is a stolen concept. I did not say "maybe" and I did not say "supernatural being."

Let's take this to the personal level: You (GS) have to exist in order to question whether existence exits.

If you (GS) don't exist, you can't say anything, much less question something specific. That is where existence an axiomatic concept instead of an assumption.

I do agree that your "maybe" and your "supernatural being" are assumptions. I do not agree that your existence is an assumption, at least not so long as you post here. smile.gif

... there is only "to the best of our knowledge right now"

In relation to what? What determines best and worst? What standard do you use to make this measurement?

Thought I'd better start a new thread. After considering this some more it seems to me that the statement "existence exists" means existence is undefinable. So we must accept this term and move on but I cannot do this. Let me ask you this, do atoms exist? Do quarks exist? Do tachyons exist? All of a sudden 'exists' is not so cut and dried is it? No, this term 'exist' or 'existence' is way too vague to be axiomatic. In fact, what does this phrase even mean? It's almost as if you are defining 'existence' with the word 'exists' which amounts to saying nothing.

I suggest reading in Peikoff's OPAR (Objectivism: The Philosophy of Ayn Rand), pages 4 - 12. You're posting on an Objectivist bulletin board, and it would make sense to find out the basic definitional information on the subject...

You may have questions about the content there. Or not. Or disagreements, or agreements. But at least they will be better informed. And not on a level with "Ayn Rand says we should be selfish? Oh! Then I will go rob some banks, because I want money!"

Regards,

Bill P

[tjohnson]

There is no abstract without a living conceptual brain to do the abstracting. "Abstract" is not an existent like a light wave is. It is an activity of the brain.

Michael

What do mean a light wave is an existent? There is some phenomena we call a light wave sometimes and other times we call it a photon.

[tjohnson]

I suggest reading in Peikoff's OPAR (Objectivism: The Philosophy of Ayn Rand), pages 4 - 12. You're posting on an Objectivist bulletin board, and it would make sense to find out the basic definitional information on the subject...

You may have questions about the content there. Or not. Or disagreements, or agreements. But at least they will be better informed. And not on a level with "Ayn Rand says we should be selfish? Oh! Then I will go rob some banks, because I want money!"

Regards,

Bill P

I sometimes get the feeling that objectivism was created to justify some political/economic belief systems.

[Dragonfly]

The proverbial intelligent Martian spider will also have something to count to start with if it uses conceptual thinking. So it will build higher math from simple math just the same as humans do.

You're missing the point. No matter how the Martian spider arrives at mathematical thinking, it can only arrive at exactly the same results, it will never find that pi = 10 or that 12 is a prime number (that

it'll use some kind of notation that might be incomprehensible to us is of course as irrelevant as the fact that for many of us Chinese texts are incomprehensible). And that implies that mathematical theorems do exist independently of intelligent beings. Not in the physical world, but in some abstract Platonic realm. Of course you'll need those intelligent beings to discover and express those theorems, but the content is fixed, immutable, and therefore does not depend on humans or spiders. Even if God existed, he couldn't make pi = 10, he would have to bow for the existence of mathematical truths that he couldn't do anything about.

Also, you are making one hell of a presumption that the spider will use the same intelligence system that humans do. It might have a totally different form of processing knowledge. I have never met one so I personally cannot say.

You mean that it might use a logic in which A is not A, and in which contradictions can exist?

[bmacwilliam]

What you and Michael are missing and confusing is that we NEED senses to learn anything, but math can begin, end, and exist entirely in the abstract.

Bob,

There is no abstract without a living conceptual brain to do the abstracting. "Abstract" is not an existent like a light wave is. It is an activity of the brain.

Michael

Not the point. The point I objected to was that math was no more than a tool for physics. This is not true.

[bmacwilliam]

I sometimes get the feeling that objectivism was created to justify some political/economic belief systems.

I am quite convinced that this is indeed the case. I came to this conclusion quite early on during my reading of her stuff. To me, it is the simplest explanation behind some of the glaring problems I see in Objectivism. She had to hold on to some rather foolish arguments in order to hold her political views together. I really do think Objectivism is nothing more than an attempt to justify the polar opposite of the political 'hell' she escaped. It was so bad, that only the exact opposite has to be the 'right' way. So she worked backwards from her political views - jamming all sorts of square pegs into round holes.

Edited April 8, 2009 by Bob_Mac

[BaalChatzaf]

What you and Michael are missing and confusing is that we NEED senses to learn anything, but math can begin, end, and exist entirely in the abstract.

Bob,

There is no abstract without a living conceptual brain to do the abstracting. "Abstract" is not an existent like a light wave is. It is an activity of the brain.

Michael

Not the point. The point I objected to was that math was no more than a tool for physics. This is not true.

Not all mathematics was formulated as a tool for the physicists (it turns out the calculus and differential equations were so formulated). However many purely abstract disciplines have been drafted into the service of physics. For example category theory, theory of manifolds (which is really a branch of geometry), topology (ditto) and the theory of abstract vector spaces (Hilbert and Banch spaces) which was drafted by Dirac and von Neuman into the service of quantum physics. If one waits long enough, the most abstruse branches of mathematics are likely to be put to use in physics. Would you believe that the theory of non-distributive lattices has been drafted as a possible logic for quantum physics? Hooda thunkit?

Ba'al Chatzaf

[Michael Stuart Kelly]

What do mean a light wave is an existent?

GS,

The referent of the concept. You called it "phenomena" below.

There is some phenomena we call a light wave sometimes and other times we call it a photon.

You are confusing concepts with words.

You're missing the point.

Dragonfly,

Actually I am not missing the point. You explained the point below, with which I thoroughly disagree (and shows clearly that I was right on point):

And that implies that mathematical theorems do exist independently of intelligent beings. Not in the physical world, but in some abstract Platonic realm.

Mathematical theorems exist in "some abstract Platonic realm"?

There is not much else to say. We disagree about this. Christians also say heaven and hell exist. I guess it depends on your faith...

You mean that it might use a logic in which A is not A, and in which contradictions can exist?

Maybe something more intimately tied to quantum physics or whatever. As I said, I have not met any Martian spiders and I am not in possession of detailed knowledge of everything in existence.

The problems I find with your thinking are two:

1 - An arbitrary assertion that an abstract mathematics realm exists independent of perceived reality, and

2 - All of existence is delimited by the human form of understanding mathematics.

This second especially appears to be terribly presumptuous in light of everything we do not yet know, including Martian spiders.

Michael

[Dragonfly]

Mathematical theorems exist in "some abstract Platonic realm"?

There is not much else to say. We disagree about this. Christians also say heaven and hell exist. I guess it depends on your faith...

So you think that "A is A" is just another faith? When I call this a Platonic realm I'm just saying in other words that mathematical theorems are independent of who or what discovered them. Do you really think that pi could be 10? That 12 could be a prime? That A could be not-A?

You mean that it might use a logic in which A is not A, and in which contradictions can exist?

Maybe something more intimately tied to quantum physics or whatever. As I said, I have not met any Martian spiders and I am not in possession of detailed knowledge of everything in existence.

That is an evasion. Of course that Martian spider is a hypothetical creature for illustrative purposes, just like Rand's indestructible robot. The question is: do you really think that some intelligent beings could develop a logic in which A is not A? Because that would be the implication of arriving at different mathematical results. Quantum mechanics has nothing to do with it, we're talking about pure logic (you shouldn't be misled by terms like fuzzy logic or quantum logic, they are all based on the same fundamental rules of logic).

The problems I find with your thinking are two:

1 - An arbitrary assertion that an abstract mathematics realm exists independent of perceived reality,

If you think that logic is a valid method of reasoning, this is the inescapable result. A realm "independent of perceived reality" is just another way of saying that mathematical results are invariant. But perhaps you think logic is not universal? That for some entities A could be not equal to A? You really sound like a postmodern relativist...

2 - All of existence is delimited by the human form of understanding mathematics.

Or in other words, by the human form of understanding logic. Are there other forms, in which A is not-A?

[Michael Stuart Kelly]

Dragonfly,

The difference between our approaches is that I believe human beings evolved conceptual reasoning (including math) as part of existence. You have stated several times that you consider abstractions to be a separate realm, a separate existence from the physical one.

So you keep asking if I am saying "A is not A." Nope.

I am saying that reality is bigger than us and it is where we come from. So "A is A" is a statement that depends on a human brain to understand it and the law of identity is how knowledge has worked so far. If there are parts of this single existence as yet unknown where the law of identity becomes obscured or delimited by the size of human sense organs or the integrating capacity of the human brain, then new reasoning methods will have to evolve to deal with them. Just like conceptual thinking (including math) evolved from a more primitive manner of awareness.

This is speculation, of course, not fact. I presume this by looking at the evolutionary pattern of what has developed so far. I see evidence of a growing capacity of intelligence over the history of life and no reason to believe the growth pattern has halted for some unstated reason.

Your manner of thinking (from what I gather in your posts) eliminates this possibility for all time in all places in the universe.

I see no reason for this.

I posit one existence only where abstractions reflect physical reality. From what I understand, you posit two existences, one physical and one abstract, with the physical existence being subordinate consistency-wise to the abstract existence when the two get entangled.

Michael

[Ian]

When we discovered the planet Neptune it was clear that it exist before anyone had any idea it was there.

This is where we disagree. It is not clear to me that something exists when nobody has any knowledge of it. We can only assume it existed before. I guess my position is that existence and knowledge are inseparable. You can't have one without the other.

I've a small question:

"Existence and knowledge are inseparable?" But isn't the map (knowledge or belief, something you've constructed in your head) a different thing than the territory (that reality which your map is presumably intended to describe/locate)? How does the absence of an item on your map prevent the existence of anything in the territory?

[Brant Gaede]

Sure.

Try to teach calculus to a person who has not learned how to count without teaching him how to count.

Can't be done.

Why not? I bet I could.

This sounds like an invalid example. I doubt this brain that cannot count can be found in an appropriate subject (non-brain damaged and non-infant/child).

--Brant

[tjohnson]

I've a small question:

"Existence and knowledge are inseparable?" But isn't the map (knowledge or belief, something you've constructed in your head) a different thing than the territory (that reality which your map is presumably intended to describe/locate)? How does the absence of an item on your map prevent the existence of anything in the territory?

It doesn't prevent the existence of anything. But the existence is only assumed until it is verfied by our knowledge. Possibly you are restricting 'knowledge' to mean only verbal knowledge but I mean it to include non-verbal knowledge as well, ie. sensory knowledge.

[Brant Gaede]

When we discovered the planet Neptune it was clear that it exist before anyone had any idea it was there.

This is where we disagree. It is not clear to me that something exists when nobody has any knowledge of it. We can only assume it existed before. I guess my position is that existence and knowledge are inseparable. You can't have one without the other.

I've a small question:

"Existence and knowledge are inseparable?" But isn't the map (knowledge or belief, something you've constructed in your head) a different thing than the territory (that reality which your map is presumably intended to describe/locate)? How does the absence of an item on your map prevent the existence of anything in the territory?

It doesn't, of course. What is missing is particular knowledge of the item. Knowledge is inseparable from existence, but existence is separate from knowledge. GS regards this last statement as an assumption. What this assumption accomplishes by those who actually accept it is anything or nothing can go, so why go? We'll just talk about assumptions, they being more real than anything else assumed. The scientist doesn't need this gibberish. He only needs to understand the scientific method and the tentativeness of knowledge, but not the tentativeness of existence itself. Otherwise he's on the premise of his own tentativeness, ultimately, and that reality is really unknowable and, perhaps, always shifting as alleged aspects of it are tossed around between different knowers each having his own special understanding.

--Brant

Edited April 8, 2009 by Brant Gaede

[tjohnson]

Sure.

Try to teach calculus to a person who has not learned how to count without teaching him how to count.

Can't be done.

Why not? I bet I could.

This sounds like an invalid example. I doubt this brain that cannot count can be found in an appropriate subject (non-brain damaged and non-infant/child).

--Brant

The derivative of y=x^2 is y=2x. Learn that and you are doing calculus. Where's the counting? Of course, it may not mean much to the person but that is besides the point. It doesn't mean much to the average student who learns it either.

[BaalChatzaf]

The counting is implicit in the algebra that leads to the result.

Ba'al Chatzaf

[bmacwilliam]

You have stated several times that you consider abstractions to be a separate realm, a separate existence from the physical one.

Well, that seems to make the most sense to me too. The history of science shows us that there are always deeper truths and new conceptual discoveries and models awaiting to be discovered. If we don't know about them, do they exist? I'd say yes, just like the rock we haven't seen yet.

Why does the rock exist when we don't know about it, but the undiscovered Grand Unification Theory does not? We don't say it doesn't exist. We just say we haven't found it yet, just like the rock. It seems to me that these mathematical/conceptual/abstract truths exist in a non-physical, but nonetheless legitimate and invariant way.

To me, if this abstract realm does not exist independent of us, then neither does the rock.