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twoshots
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12 May 2008, 4:53 pm

ToadOfSteel wrote:
Here's a paradox for you: What is the simplest reason for Occam's Razor to exist?

PS: come to think of it, the fact that so many paradoxes (sp?) exist is proof that the universe is fundamentally inconsistent.

Occam's razor, like logic, is a human construct. Paradoxes are symptomatic of poorly thought out constructs, just as inconsistency is a product of human language.



lau
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12 May 2008, 5:11 pm

ToadOfSteel wrote:
...
Too bad you can't make a cat fly by strapping buttered toast to its back...

Wow! Someone else who knows the origin of the strange sound reported to emanate from UFOs.


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ToadOfSteel
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12 May 2008, 7:31 pm

No, that's a theremin...



D1nk0
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12 May 2008, 8:43 pm

twoshots wrote:
ToadOfSteel wrote:
Here's a paradox for you: What is the simplest reason for Occam's Razor to exist?

PS: come to think of it, the fact that so many paradoxes (sp?) exist is proof that the universe is fundamentally inconsistent.

Occam's razor, like logic, is a human construct. Paradoxes are symptomatic of poorly thought out constructs, just as inconsistency is a product of human language.


I seriously call this into question-that logic is just a human construct rather than the basis of reality.



abstrusemortal
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12 May 2008, 10:00 pm

Gromit wrote:
abstrusemortal wrote:
Light has a wave-particle duality as does everything. Even a baseball. Both cannot exist as one in a visual image.

Light has two different faces. A particle face; and a wave face. Young's double slit experiment confirms the wave part. Photoelectric effect; Compton's effect confirm the particle side, etc...

I think the photoelectric effect shows both, because the energy of the electrons depends on the frequency of light.



no, the photoelectric effect is proof of the particle side. The wave theory predicts that the intensity is proportional to the energy of light while the particle side predicts the frequency part:

E = hf


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Izaak
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12 May 2008, 10:41 pm

LoveableNerd wrote:
Izaak wrote:
That problem isn't physics. It's Philosophy. More specifically Metaphysics. Aristotle was the first to outline this aspect, and it is called the Law of Identity.

http://www.importanceofphilosophy.com/M ... ntity.html

As such it is an Axiom. A self-evident truth at the foot of all knowledge. It is proved evidenced each time you do a more complex proof in mathematics. But there is no way to prove the axiom itself. You must assume it (or not) as it stands with the evidence coming from the fact that (as your knowledge of an entity improves) you discover it has no contradictions. That the Law of Identity holds at ALL times. And that apparent contradictions are only an indication of our misunderstanding or lack of knowledge about an entity.


As the above posters alluded to, the Law of Identity breaks down at the quantum level. According to the Law of Identity, a car can be red or blue, or both red and blue but not at the same time and place. However, a photon is both a wave and a particle at the same time.


I don't think the Law of Identity breaks down. A photon is still a photon no matter how we might perceive it. Whatever we think about it, the Law of Identity states that: A photon is what it is, and it isn't anything else.

Then again, I am no physicist. A photon may very well be a photon AND something else at the same time.



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13 May 2008, 2:33 am

Izaak wrote:
LoveableNerd wrote:
Izaak wrote:
That problem isn't physics. It's Philosophy. More specifically Metaphysics. Aristotle was the first to outline this aspect, and it is called the Law of Identity.

http://www.importanceofphilosophy.com/M ... ntity.html

As such it is an Axiom. A self-evident truth at the foot of all knowledge. It is proved evidenced each time you do a more complex proof in mathematics. But there is no way to prove the axiom itself. You must assume it (or not) as it stands with the evidence coming from the fact that (as your knowledge of an entity improves) you discover it has no contradictions. That the Law of Identity holds at ALL times. And that apparent contradictions are only an indication of our misunderstanding or lack of knowledge about an entity.


As the above posters alluded to, the Law of Identity breaks down at the quantum level. According to the Law of Identity, a car can be red or blue, or both red and blue but not at the same time and place. However, a photon is both a wave and a particle at the same time.


I don't think the Law of Identity breaks down. A photon is still a photon no matter how we might perceive it. Whatever we think about it, the Law of Identity states that: A photon is what it is, and it isn't anything else.

Then again, I am no physicist. A photon may very well be a photon AND something else at the same time.



the only entity that knows what a photon is, is a photon (and God of course).

All of these models are "logical constructions" (Betrand Russel). They have validity so as long as they work well with nature.


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13 May 2008, 2:43 am

Wave particle duality does exist; reciprocal functions.

I think the discrepency lies, in practical terms, with how this duality is interpreted. For ex: The bunning Hypothesis: "Succesive adjustments of photoperiod phase will quickly results in a math between circadian cycle & the impoased extneral cycle." Then, I wrote, ....ryegrass is acutely adept at adaptation.

This applies to physics - photosynthetically (Krebs Cycle, and Citric Acid Cycle), photons are perceived as particles. However, photons have wave properties as given by mathemathical properties/chem. So, the duality is real. This is in fact the Heisenberg Uncertainty Principle.

Instrumentation uses photons with assumption of wave theory (theorectical), whereas in practicality (like photosynthetic Photophil phase), the circadian rythym recognizes photon as particulate.


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Escuerd
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13 May 2008, 8:53 am

Willard wrote:
Gromit wrote:
In mathematics, a theorem can be disproven by showing it would lead to a contradiction. A theorem can be proven by showing that there would be a contradiction if it were false.

I am fairly confident that the physical universe must be free of contradictions, that if ever there is a grand unified theory of physics, it can't have contradictory rules that say both that something must happen and can't happen. But I couldn't prove that the universe must be logically consistent in this way. Is there a proof?


Light is made up of particles.

Light is made up of waves.

Light is not made of waves of particles.

All of these statements are true. Schroedinger's Cat showed us that the universe is not necessarily without internal contradictions.


Don't confuse models of reality with reality itself.

Waves and particles are both outdated models for light's behavior each of which works in a restricted domain. We currently have a better model than either of those that encompasses both aspects, but doesn't correspond exactly to anything in our intuitive experience.

The quantum mechanical model could be included or not under "particle" and/or under "wave" depending on how restrictive the definitions of these terms are. But it can't both be "made of particles" and "not made of particles" without exploiting some ambiguity on what qualifies as a particle.



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13 May 2008, 8:59 am

LoveableNerd wrote:
As the above posters alluded to, the Law of Identity breaks down at the quantum level. According to the Law of Identity, a car can be red or blue, or both red and blue but not at the same time and place. However, a photon is both a wave and a particle at the same time.


First you have to establish that "red" and "blue" or "wave" and "particle" are both well-defined, and mutually exclusive. Otherwise no logical contradiction has been demonstrated. The vagueness of natural language leaves room for things that are intuitively contradictory, but logically compatible.



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13 May 2008, 9:23 am

Gromit wrote:
In mathematics, a theorem can be disproven by showing it would lead to a contradiction. A theorem can be proven by showing that there would be a contradiction if it were false.

I am fairly confident that the physical universe must be free of contradictions, that if ever there is a grand unified theory of physics, it can't have contradictory rules that say both that something must happen and can't happen. But I couldn't prove that the universe must be logically consistent in this way. Is there a proof?


Is there a proof that the universe is non-contradictory? Sure, I'll give you a proof by contradiction. ;)

More seriously, I don't see any way one could prove it. It's sort of fundamental to the concept of "truth."
I can think of little as fundamental as this concept.

If the truth is out there, then the universe is non-contradictory. If the truth is not out there, well, then I guess we can't trust if-then statements anyway, so why bother? :)



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13 May 2008, 5:09 pm

Light (and everything else) is neither particle nor wave, but something totally different that has elements of both a particle and a wave, it is excitations of a quantum field. Quantum fields are similar to the fields of classical mechanics except that energy is quantinized, and this quantization is what leads to all the kinds of quantum weirdness. This is because quantization causes the energy to be expressed in discrete bits, and thus you have particles with associated "probability waves" instead of classical waves.


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wolphin
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14 May 2008, 5:20 am

D1nk0 wrote:
twoshots wrote:
ToadOfSteel wrote:
Here's a paradox for you: What is the simplest reason for Occam's Razor to exist?

PS: come to think of it, the fact that so many paradoxes (sp?) exist is proof that the universe is fundamentally inconsistent.

Occam's razor, like logic, is a human construct. Paradoxes are symptomatic of poorly thought out constructs, just as inconsistency is a product of human language.


I seriously call this into question-that logic is just a human construct rather than the basis of reality.


Formal logic settles this fairly nicely, even. Model theory talks about "reality" and proof theory talks about "human constructs". Tarski and Godel demonstrated most of the connections between the two (and where they fail to connect)



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15 May 2008, 2:31 am

i've never understood deductive reasoning, i can only see inductive reasoning

life is not like a programing language where you start off knowing an absolute set of rules, science demonstrates this perfectly, we are figuring it out as we go along and logic is what we have been using to do it

but i don't think you can logically rule out the possibility that logic itself is flawed


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15 May 2008, 3:48 am

mouapp wrote:
i've never understood deductive reasoning, i can only see inductive reasoning

life is not like a programing language where you start off knowing an absolute set of rules, science demonstrates this perfectly, we are figuring it out as we go along and logic is what we have been using to do it


True, but one often needs to work backwards a little from one's hypothesis. One needs to see its implications to test it, and these implications may be subtle.

mouapp wrote:
but i don't think you can logically rule out the possibility that logic itself is flawed


You may not think so...but can you logically out the possibility that you can logically rule it out? ;)

That was a joke, but I suppose that there is Gödel's proof that for an important class of formal systems of logic, one can't prove that one's axioms are consistent. But that's a far cry from a proof that reality actually is inconsistent (modern math avoids being bound to reality anyway, lest it be contaminated). I guess that means that even with a set of true axioms that completely constrained reality, one couldn't logically determine that those truths weren't in fact contradictory. I need to sharpen up my background in formal logic, methinks.

Ultimately, I think asking "Does logic apply to reality?" amounts to asking "Is there truth?". Logic basically amounts to careful way of thinking about what statements mean.

I'm no Zen master, but maybe a useful koan would be "What is meaning without logic?". I've pondered on it from a distinctly non-Zen perspective for a while and come up with no answers that I think are good.



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15 May 2008, 9:05 am

Escuerd wrote:
mouapp wrote:
i've never understood deductive reasoning, i can only see inductive reasoning

life is not like a programing language where you start off knowing an absolute set of rules, science demonstrates this perfectly, we are figuring it out as we go along and logic is what we have been using to do it


True, but one often needs to work backwards a little from one's hypothesis. One needs to see its implications to test it, and these implications may be subtle.

mouapp wrote:
but i don't think you can logically rule out the possibility that logic itself is flawed


You may not think so...but can you logically out the possibility that you can logically rule it out? ;)

That was a joke, but I suppose that there is Gödel's proof that for an important class of formal systems of logic, one can't prove that one's axioms are consistent. But that's a far cry from a proof that reality actually is inconsistent (modern math avoids being bound to reality anyway, lest it be contaminated). I guess that means that even with a set of true axioms that completely constrained reality, one couldn't logically determine that those truths weren't in fact contradictory. I need to sharpen up my background in formal logic, methinks.

Ultimately, I think asking "Does logic apply to reality?" amounts to asking "Is there truth?". Logic basically amounts to careful way of thinking about what statements mean.

I'm no Zen master, but maybe a useful koan would be "What is meaning without logic?". I've pondered on it from a distinctly non-Zen perspective for a while and come up with no answers that I think are good.


Firstly: Gödel was talking about arithmetic.

Secondly: Logic can ONLY apply to reality. It is the rules governing the correct employment of one's cognitive faculty in ALL aspects. If something is logical it is necessarily true. This doesn't mean that one is infallible, just that if one discovers that one is wrong logic will provide the methods to correct the mistake and arrive at truth. Truth can be discovered in an illogical manner, but one would have no way of knowing or proving one's position against further challenge. Or indeed lack the tools to correct their position if it was discovered that they were mistaken.

Third: Axioms don't "constrain" reality. Axioms explain those parts of reality that are inescapable. It is complex knowledge gained at the perceptual level. It can not be proved. Example one can not PROVE existence exists. But regardless it is there and it exists. It must be accepted, and the declaration of it is: Existence exists. A circular definition is usually an axiom. Existence exists, A is A (law of identity), Consciousness is consciousness. As for consciousness one can not PROVE that we are conscious. It is implicit knowledge. Of course, implicit knowledge that is not grasped and integrated explicitly can easily be lost. Observe any person that denies free will (hasn't grasped the axiom of consciousness), or the religious person who claims an unknowable realm in which a god resides (failed to grasp Existence exists) or the mystic that will pray for some external event with no reference to causality (Failed to grasp the law of identity). So again, axioms don't "constrain" reality, they just state explicitly certain implicit elements of existence.

Lastly: Zen is NOT logic.