Formal Logic and Scientific Method

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20 years 8 months ago #8476 by

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<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by jrich
 <blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by 1234567890
Can you see more pixels than the number of holes in the shadow mask of your monitor? How does the idea of these holes representing the smallest size possible on your monitor lead to contradiction then?
Can you divide these holes into smaller parts without changing the composite parts of your monitor, i.e., without changing the "universe" of the monitor?.The universe that comprises of the images on a specific monitor then is completely self consistent with the idea of a minimum distance and is incompatible with the idea of infinite divisibility. Any image appearing on your monitor can only be divided into integal parts of the smallest sized holes.<hr height="1" noshade id="quote"></blockquote id="quote">
Obviously, a finitely divisible monitor screen cannot be infinitely divided without voiding the warranty[

] But what is your point? I'm not arguing that a universe that is assumed from the start to be only finitely divisible can somehow be made to be infinitely divisible. Why do you keep putting up this straw horse? I am arguing that a finitely divisible universe must necessarily have properties which are incongruous with the properties of our universe. The question at hand isn't whether logically consistent finite universes may be devised, the question is whether a finite universe with the properties of our universe is logically consistent. Do you not see the distinction? Do you have no understanding of logical proofs?

JR
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I've given examples about the finite properties of man made objects (such as the size of pixels on the monitor), and the discrete properties of natural phenomena, such as the angular momentum and spin angular momentum of the electron in the atom, and the discrete energy levels of photon emission and absorption as observed in spectroscopy. And I also finished convincing you with my logical arguments that a finitely divided universe can be logically constructed.

You on the other hand provided two imaginary spheres
that you defined as the minimum volume spheres which you then contradict yourself by constructing lengths smaller than the defined minimum length and you end up using that as proof that our universe is infinitely divisible.

Who's not understanding logical proofs here? Why don't you provide at least the minimal evidence that the smallest particles we know of are spherical?

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Larry Burford
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20 years 8 months ago #8478 by Larry Burford

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jrich,

I'm not positive, but I think he said 'no'.

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jrich
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20 years 8 months ago #8479 by jrich

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<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by 1234567890
I've given examples about the finite properties of man made objects (such as the size of pixels on the monitor), and the discrete properties of natural phenomena, such as the angular momentum and spin angular momentum of the electron in the atom, and the discrete energy levels of photon emission and absorption as observed in spectroscopy.
<hr height="1" noshade id="quote"></blockquote id="quote">
So your argument is that since physical objects have some finite properties, that they must be finitely divisible?
<blockquote id="quote">quote:<hr height="1" noshade id="quote">And I also finished convincing you with my logical arguments that a finitely divided universe can be logically constructed.<hr height="1" noshade id="quote"></blockquote id="quote">
You deserve no credit for this. Constructing a logically consistent finite universe is trivial. Constructing one that behaves like our universe is the hard part.
<blockquote id="quote">quote:<hr height="1" noshade id="quote">You on the other hand provided two imaginary spheres
that you defined as the minimum volume spheres which you then contradict yourself by constructing lengths smaller than the defined minimum length and you end up using that as proof that our universe is infinitely divisible.

Who's not understanding logical proofs here? Why don't you provide at least the minimal evidence that the smallest particles we know of are spherical?<hr height="1" noshade id="quote"></blockquote id="quote">
Your characterization of my argument is mistaken. I assumed a finitely divisible universe and infered that there must then exist particles of smallest dimension (SDPs for short) and a smallest non-zero distance of space. I originally assumed the smallest dimension of the SDPs was the same as the smallest distance, but this is not required and may be discarded. I also inferred that since contact is possible at the macro level it must also be possible for SDPs to touch each other. I took a sphere to be the geometry of the SDPs and showed that this led to a contradiction that there is a miminum distance.

Now the contradiction could be resolved several ways:<ul><li>another valid SDP geometry could be used</li><li>SDPs may not touch</li><li>all of the above</li></ul>
You didn't raise any objection to the assertion that SPDs may touch, and considering that the classic argument against infinite divisibility is that it appears to make contact impossible, you probably have good reason not to. You did object to the spherical geometry, but couldn't provide an alternative. I have some ideas, but I'm not inclined to do any more of your thinking for you.

JR

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jrich
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20 years 8 months ago #8481 by jrich

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<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by Larry Burford
 jrich,

I'm not positive, but I think he said 'no'.
<hr height="1" noshade id="quote"></blockquote id="quote">
We'll know for sure soon enough.

JR

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20 years 8 months ago #8487 by

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[jrich]
So your argument is that since physical objects have some finite properties, that they must be finitely divisible?

<hr height="1" noshade id="quote"></blockquote id="quote">

[123]

Well, would it make more sense to say that since physical objects have some finite properties, they must be infinitely divisible?
What physical example have you given that physical objects can be divided infinitely? You have cited not one physical phenomenon that has infinitesimal qualities all throughout this discussion and yet you seem absolutely bewildered at my suggestion, which was based on multiple physical examples, that finite divisibility is consistent with being one of the properties of our universe.

I think you have the scientific method backwards. You started with some assumptions given by Euclidean geometry (the example with the spheres) to arrive at the physical principle that neither space nor matter is finitely divisible when you should have started like I did with some physical observations to arrive at a possible geometry of our universe.

If your line of mathematical induction was any accurate representation of properties of our universe, you should have no problem finding more than the mere 100 or so elements on our periodic table , since there should exist particles and energy levels, according to infinite divisibility, at every possible scale.
In fact, this is one of the conclusions of the Meta Model. So where are these infinite different types of elements? If they exist, they are apparentely inert to known matter. So, how is this any different than believing in Santa Claus, the Easter Bunny, the Green Goblin, cats walking with a back pack, the Lochness monster, the tooth fairy, Bart Simpson, Pokemon, the Great Pumpkin, purple dinosaurs, MM, et al?

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20 years 8 months ago #8489 by

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<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by jrich
Your characterization of my argument is mistaken. I assumed a finitely divisible universe and infered that there must then exist particles of smallest dimension (SDPs for short) and a smallest non-zero distance of space. I originally assumed the smallest dimension of the SDPs was the same as the smallest distance, but this is not required and may be discarded. I also inferred that since contact is possible at the macro level it must also be possible for SDPs to touch each other. I took a sphere to be the geometry of the SDPs and showed that this led to a contradiction that there is a miminum distance.

Now the contradiction could be resolved several ways:
another valid SDP geometry could be used
SDPs may not touch
all of the above

You didn't raise any objection to the assertion that SPDs may touch, and considering that the classic argument against infinite divisibility is that it appears to make contact impossible, you probably have good reason not to. You did object to the spherical geometry, but couldn't provide an alternative. I have some ideas, but I'm not inclined to do any more of your thinking for you.

JR

JR
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From your arguments, I get the impression that you've tried and succeeded in climbing down a rabbit hole. Yes, the rabbit hole proves that there are spaces smaller than a human being, but where is the logic in concluding that since the rabbit hole exists, human beings the size of rabbits must exist? Or the existence of rat holes proving that humans the size of rats exist; or the existence of antholes proving that humans the size of ants exist, ad infinitum,
ad absurdum?

Or referring back to your example, how does the fact that two smallest sized spheres touching with space smaller than the diameter of the spheres above and below the point of contact lead to a logical contradiction with the fact that these spheres are of the smallest sizes attainable by matter? If you can infer from the space between the spheres that smaller spheres must exist, i.e. that matter is infinitely divisible, you really ought to go in competition with Ms. Cleo's psychic hotline.

By your logic, there cannot be any space left that is not filled with matter since such a discovery would immediately contradict the result obtained by the principle of infinite divisibility that there be no distances smaller than the smallest matter. This is trivially disproven by my typing of this post.

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