New Paradox for the "Principles of Physics".

Mac
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21 years 7 months ago #5335 by Mac

Replied by Mac on topic Reply from Dan McCoin

Tom,

You say the alphabet is not infinite therefore no analogy applies.

You say Existance is infinite but yet you say Infinity is purely mathematical an can never be physical. Aren't you saying existance is therefore "Non-physical"?

123...

quote:
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Conversely, if we knew the number of elements in the integer set, we can deduce the size of the largest positive (or negative) integer. So, if the set of all integers is infinite, the largest positive integer is (infinity/2) - 1, exactly. So, what is infinity/2 - 1? From what I remember, it is infinity. Thus, if you knew the number of elements in the integer set is infinite, we can conclude that the finite integers become infinite in size.
******************

Has an old man forgotten his algebra but doesn't your satement say this?:

Infinity = (Infinity/2 - 1) and doesn't that resolve to Infinity = -2?

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1234567890
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21 years 7 months ago #5594 by 1234567890

Replied by 1234567890 on topic Reply from

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
Tom,

You say the alphabet is not infinite therefore no analogy applies.

You say Existance is infinite but yet you say Infinity is purely mathematical an can never be physical. Aren't you saying existance is therefore "Non-physical"?

123...

quote:
********************
Conversely, if we knew the number of elements in the integer set, we can deduce the size of the largest positive (or negative) integer. So, if the set of all integers is infinite, the largest positive integer is (infinity/2) - 1, exactly. So, what is infinity/2 - 1? From what I remember, it is infinity. Thus, if you knew the number of elements in the integer set is infinite, we can conclude that the finite integers become infinite in size.
******************

Has an old man forgotten his algebra but doesn't your satement say this?:

Infinity = (Infinity/2 - 1) and doesn't that resolve to Infinity = -2?

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Yes if infinity were some unknown variable here. I actually meant it as ? = (infinity/2) - 1. And after the operation of the expression on the right, we get the answer to ?, or ? = infinity.

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tvanflandern
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21 years 7 months ago #5336 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[123...]: I disagree with the idea of censorship really.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

No argument there. I despise censorship.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Especially when the process is a subjective one and not by a democratic vote- your idea of offensive may be different than mine.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Well, that's a good point. But could we rely on the voters to apply the standards of the Board objectively, as opposed to considering whose side the party was on? Remember, I have issued cautions before to two people who were supporting my own position in a debate. So I think I've been fairly objective in applying the written rules.

To help ensure uniform standards, we have Moderators. Ordinarily, I leave these matters to them. But inasmuch as I issued the two previous warnings in this case, and the party involved said he was "gone" anyway, there didn't seem to be much to consult about. Moderators have been given the authority to act on their own for the reason that we can't all cover all the messages all the time, and tnings can get out of hand in the time it takes to consult.

If you have reason to think we have not been faithful to our own posted standards, you have a right to complain. We listen to our Board participants. But most things in life have subjective elements. I hope we earn the confidence of our participants by applying our standards in a visibly fair way to all, regardless of their stance on the issues.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote><BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[tvf]: Every integer is finite.
Every integer is in the set of all integers.
The set of all integers is infinite.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Every integer in the integer set is produced by adding 1 to 0 and then taking the sum and adding 1 to it, ad infinitum, for the positive integers and subtracting 1 from 0 and subtracting 1 from the difference, ad infinitum, do we agree with this process?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Yes, but the process is utterly unimportant to the analogy. We could adopt only even integers, or only prime integers. Or the integers could be associated with names instead of numbers: [A, B, ..., Z, AA, AB, ..., AZ, BA, BB, ..., BZ, ..., ..., AAA, AAB, ...]. There would be just as many, the same set of rules would apply, but each integer would have no special relationship to the one before or after itself in the sequence.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>"The set of all integers" is an enumeration of the number of elements inside the set, do we agree? Thus, since the process of generating successive positive integers is the same enumeration process, if we knew the largest positive integer and multiplied it by 2 then add 1 for the number 0, we get the number of elements in the set of all integers.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

The essence of the meaning of "infinite" is "unbounded". The set of all integers is unbounded. So there is no possible way to enumerate it. There is no such thing as "the largest positive integer".

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Conversely, if we knew the number of elements in the integer set, we can deduce the size of the largest positive (or negative) integer. So, if the set of all integers is infinite, the largest positive integer is (infinity/2) - 1, exactly. So, what is infinity/2 - 1? From what I remember, it is infinity. Thus, if you knew the number of elements in the integer set is infinite, we can conclude that the finite integers become infinite in size.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

The integers are unbounded. Although every single integer, without exception, is finite, the size of the set of all integers is infinite. But we've already been over that. Your change of wording to "the finite integers become infinite in size" is highly ambiguous. All integers remain finite. It's the set of all integers that is infinite in size. None of the integers, no matter how large, is anywhere near being infinite, because "infinite" means "unbounded".

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Show me where the logic is wrong. If you can not then you can't use the concept of infinity in your analog.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

My original analogy is correct. Your changes of wording change the meaning in ways that are incorrect.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>: How about this:
1. Substance is an irreducible form, much like the electron is presently recognized as an irreducible particle (this is why I chose the alphabet analog earlier).<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

But substance is not itself a form, but is the essence common to all forms. And substance is infinitely divisible -- the opposite of irreducible.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>2. The assemblage of irreducible forms is itself a form.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

This would be true if substance were irreducible.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>From these definitions, some premises:
1. Substance exists.
2. Existence is eternal.
3. All forms which are reducible are finite in duration.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

There is no need for this last qualification. All forms are finite in duration, and all are infinitely divisible.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>it's easy to see that the irreducible forms themselves did not ever come into or out of existence<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

There are no irreducible forms in MM. All forms are temporary, even if they last trillions of years. -|Tom|-

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tvanflandern
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21 years 7 months ago #5595 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[Mac]: You say Existance is infinite but yet you say Infinity is purely mathematical an can never be physical. Aren't you saying existance is therefore "Non-physical"?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

"Existence" is a concept, not a material, tangible thing. So yes, in that sense, it is not something "physical".

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Infinity = (Infinity/2 - 1) and doesn't that resolve to Infinity = -2?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Infinity has a whole different set of rules in mathematics that you might be interested in studying. I mentioned a few of the rules for arithmetic in my post of 18 March at 17:53:51 ET. -|Tom|-

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1234567890
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21 years 7 months ago #5653 by 1234567890

Replied by 1234567890 on topic Reply from

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
But substance is not itself a form, but is the essence common to all forms.
<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

I can't pinpoint your definition of substance nor your distinction
between form and substance. If substance is the essence of forms, and this essence is eternal, how can forms be finite in duration? You are attributing two logically opposite properties to the word "form". You are saying forms are both eternal and finite in duration.

If there is no irreducible form then your assertion that every form is finite in duration and also that every form is composed of substance that is eternal is a contradiction.

If all forms are substance, and substance cannot come into or out of existence, how does a form come into and out of existence?

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tvanflandern
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21 years 7 months ago #5716 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[123...]: If substance is the essence of forms, and this essence is eternal, how can forms be finite in duration?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Suppose substance was just atoms and atoms were eternal. Nonetheless, everything made of atoms -- molecules, compounds, water drops, bricks, asteroids, planets, stars, galaxies, ... -- has a finite lifetime and eventually explodes, decays, or gets absorbed. So that is a parallel example of finite forms being made of eternal substance.

Does that answer your question? -|Tom|-

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