Teleological
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« Reply #150 on: August 08, 2010, 13:41:37 PM » 

Hey Tele, how about you show some understanding that idealised geometric models and the proofs involving them are only useful to the extent that they actually mirror reality. If your model of reality is wrong, your proofs are meaningless.
Well, there are several problems with those statements for you from your philosophical naturalistic point of view. 1) You have no way of knowing what reality is in the first place. There is no self, enduring agent that observes reality. How you think your above statement makes sense is a mystery anyway. (If you think this is an ad hominem directed at you or your silly naturalism, don't worry, I am with you in thinking you have no self or enduring firstperson agent to direct any ad hominems at ) 2) You fail to recognize or distinguish the difference between an analytical judgment and an empirical judgment. An analytical judgment is independent of experiencing the fact through our senses. For example, when two quantities are added to give a third (say 1 + 21 = 22), you consciously realize this is true. There is no need to sense 22 stones or coins or whatever to realize the fact is true. The same goes for geometrical and other proofs. I think you problem as a naturalist is that you can not take consciousness seriously in the first place as well and therefore find it difficult to take abstract geometrical proofs seriously. 3) You fail to distinguish between universals and particulars. Universals are idealized abstractions of reality generated by our brains. When you think about a dog, you have some abstract universal idea of what a dog is. It has two eyes, four legs, canine teeth etc. However this abstract idealization of a dog does not exist in reality, only specific, actual dogs such this particular Fido or that particular Brutus or that particular Bongo over there or whatever. The same goes for triangles. They have three sides and on Euclidean planes their interior angles ALWAYS add up to half of a full rotation (again, this is an analytical judgment not an empirical one). In reality, these universal idealizations of triangles do not exist, only this particular triangle or that particular triangle. Realty does not exist as universal idealizations, but what you also seem to fail to understand is that from particulars we are able to intellectually grasp abstract universal idealizations and make analytical judgments. All this of course (as mentioned above) is one massive problem for the naturalist since the philosophical naturalist can not take consciousness seriously and mathematics becomes a bit of a burden since it too is meaningless tripe (for the naturalist).


« Last Edit: August 08, 2010, 19:26:36 PM by Teleological »

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Hermes


« Reply #151 on: August 10, 2010, 14:56:07 PM » 

Universals are idealized abstractions of reality generated by our brains. When you think about a dog, you have some abstract universal idea of what a dog is. It has two eyes, four legs, canine teeth etc. However this abstract idealization of a dog does not exist in reality, only specific, actual dogs such this particular Fido or that particular Brutus or that particular Bongo over there or whatever. The same goes for triangles. They have three sides and on Euclidean planes their interior angles ALWAYS add up to half of a full rotation (again, this is an analytical judgment not an empirical one). In reality, these universal idealizations of triangles do not exist, only this particular triangle or that particular triangle. Realty does not exist as universal idealizations, but what you also seem to fail to understand is that from particulars we are able to intellectually grasp abstract universal idealizations and make analytical judgments.
Pearls of wisdom, shiver my bones! And to think that you are casting it to us swine.... A universal truth holds under all circumstances. A mathematical theorem proves such universality. It has nothing to do with the "abstract idealization of a dog". If there is a theorem that proves all dogs to have four legs, I'd like to hear it. "Intellectually grasp abstract universal idealizations" nogal.



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Teleological
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« Reply #152 on: August 10, 2010, 16:22:10 PM » 

A universal truth holds under all circumstances. A mathematical theorem proves such universality. It has nothing to do with the "abstract idealization of a dog". If there is a theorem that proves all dogs to have four legs, I'd like to hear it.
Monkey sees a three sides figure. Monkey draws three sided figure. Monkey figures out all three sides figures on an Euclidean plane have interior angles that always add up to half a rotation. Monkey calls it a triangle on an Euclidean plane. Monkey also sees examples of triangles that are not perfect, in fact the monkey has not observed a perfect triangle, he just intellectually grasps the idea of triangles. Monkey sees a four legged creature with two eyes and looks like a wolf. Monkey figures out this particular fourlegged creature can be domesticated. Monkey calls it a dog. Monkey also sees dogs with three or two legs due to birth defects or other accidents, in fact, monkey has not seen a perfect dog, he just intellectually grasps the idea of what a dog is. If P, then Q P, Therefore Q If threesided figure on Euclidean plane, then interior angles always add up to half a rotation. Given threesided figure on Euclidean plane. Therefore interior angles add up to half a rotation. Or If domesticated form of the gray wolf, then it is a dog. You see a domesticated form of the gray wolf, Therefore it is a dog



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Hermes


« Reply #153 on: August 10, 2010, 17:17:28 PM » 

Round about the crackpot go: In the poison'd entrails throw. Fillet or a fenny snake, In the crackpot boil and bake; Eye of newt and toe of frog, Wool of bat and tongue of dog.
Double, double toil and trouble; Fire burn and crackpot bubble.



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Teleological
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« Reply #154 on: August 10, 2010, 18:20:56 PM » 

Round about the crackpot go: In the poison'd entrails throw. Fillet or a fenny snake, In the crackpot boil and bake; Eye of newt and toe of frog, Wool of bat and tongue of dog.
Double, double toil and trouble; Fire burn and crackpot bubble.
Ouch, those poor skeptical crackpots .



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Hermes


« Reply #155 on: August 11, 2010, 13:26:07 PM » 

Ouch, those poor skeptical crackpots . Monkey gives a weak reply.


« Last Edit: August 11, 2010, 13:41:55 PM by Hermes »

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Teleological
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« Reply #156 on: August 11, 2010, 13:46:27 PM » 

Ouch, those poor skeptical crackpots . Monkey gives a weak reply. Monkey see monkey do.



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Hermes


« Reply #157 on: August 11, 2010, 15:18:05 PM » 

Teleological, the triangle sum theorem can be proven to hold in all cases. You do not "intellectually grasp" the difference between an axiom and a theorem. The only way to assess whether dogs or gods exist is to rely on empirical evidence.


« Last Edit: August 11, 2010, 15:44:24 PM by Hermes »

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Teleological
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« Reply #158 on: August 11, 2010, 15:34:02 PM » 

Teleological, the triangle sum theorem can be proven to hold in all cases. You do not "intellectually grasp" the difference between an axiom and a theorem. What on earth are you talking about? Do elaborate. I smell straw...



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Hermes


« Reply #159 on: August 11, 2010, 15:47:08 PM » 

What on earth are you talking about? Do elaborate. I smell straw...
I fail to understand what you fail to understand.



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Teleological
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« Reply #160 on: August 11, 2010, 16:03:14 PM » 

What on earth are you talking about? Do elaborate. I smell straw...
I fail to understand what you fail to understand. Are you perhaps confused about modus ponens logic, axioms and theorems?



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Hermes


« Reply #161 on: August 11, 2010, 16:42:08 PM » 

Are you perhaps confused about modus ponens logic, axioms and theorems?
No, it appears that you are confused between an axiom and a theorem. An axiom is a selfevident truth, whereas a theorem requires a chain of reasoning. (Oxford Dictionary)



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Teleological
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« Reply #162 on: August 11, 2010, 17:08:30 PM » 

Are you perhaps confused about modus ponens logic, axioms and theorems?
No, it appears that you are confused between an axiom and a theorem. An axiom is a selfevident truth, whereas a theorem requires a chain of reasoning. (Oxford Dictionary) It appears you are chewing straw... again gasp. Yes, axioms are selfevident truths. Theorems are true statements derived from axioms (you got that right). If you were sharp, you would realise that modus ponens, axioms and theorems can be used to make this: If threesided figure on Euclidean plane (axiom), then interior angles always add up to half a rotation (theorem). Given threesided figure on Euclidean plane. Therefore interior angles add up to half a rotation. Or to put it differently: If axiom P, then theorem Q is true Axiom P is given, Therefore theorem Q is true. Need a toothpick?



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Hermes


« Reply #163 on: August 12, 2010, 16:06:11 PM » 

It appears you are chewing straw... again gasp.
Yes, axioms are selfevident truths. Theorems are true statements derived from axioms (you got that right).
If you were sharp, you would realise that modus ponens, axioms and theorems can be used to make this:
If threesided figure on Euclidean plane (axiom), then interior angles always add up to half a rotation (theorem). Given threesided figure on Euclidean plane. Therefore interior angles add up to half a rotation.
Or to put it differently: If axiom P, then theorem Q is true Axiom P is given, Therefore theorem Q is true.
Need a toothpick?
At last you got the difference between an axiom and a theorem right! I'm glad to have been of assistance. Now all you need to realize is that you cannot prove the validity of a theorem with a modus ponens. It is quite irrelevant to the argument.



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Teleological
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« Reply #164 on: August 12, 2010, 16:27:18 PM » 

At last you got the difference between an axiom and a theorem right! I'm glad to have been of assistance. Ok then, if you say so lol. Now all you need to realize is that you cannot prove the validity of a theorem with a modus ponens. It is quite irrelevant to the argument.
I tried to prove the validity of a theorem with modus ponens? ROFL, more straw from you.



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