An object being it's own cause

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Just_Lurking said:
I view mathematician David Hilbert’s program of finitism (using only finitistic principles to prove the consistency of mathematical reasoning) an interesting mathematical experiment that ended in failure when Godel proved his Incompleteness Theorem. But metaphysically speaking, I thought his end goal was to justify the mathematical use of achieved infinities to people who didn’t believe in them, which is why he focused on finitistic principles that had universal agreement.

Interestingly enough, modern proof theory uses some fairly sophisticated infinite ordinal numbers to rank the strength of various mathematical systems (see here).
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Can you provide an example of an actual infinity of non-numerical, extramental objects?
 
1holycatholic said:
Can you provide an example of an actual infinity of non-numerical, extramental objects?
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I’m not sure exactly what you are asking here, but the problems came up with Cantor’s diagonalization proof that a set S has strictly smaller cardinality than Power(S), the power set of S, when S is infinite. The proof involves an infinite construction, but that construction has to be fully completed in order to construct the counter-example set that finishes the proof.

Non-constructive mathematicians still consider the proof to be valid, no matter what the size of S is, including infinite sets of any size, Aleph_0, Aleph_1, Aleph_2, …, all the way up.
 
Matthias123 said:
If someone mentions a virtual particle in a vacuum I am going to have to hurt you. Physicists do not have the right to claim a break in causality when this is metaphysically impossible. For all we know it is coming from a parallel universe.
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there’s plenty of philosophers out there who challenge traditional metaphysics quite effectively. I’m not sure I buy into it … but it’s interesting stuff.

In today’s environment, given how much we’ve advanced since Aristotle, if someone proposed a “god hypothesis” … it would seem like a theory created because of frustration (not to mention few in the scientific community would take it seriously). Most would say just because we haven’t discovered the natural cause for the occurrence of A or B doesn’t mean there isn’t one. Moreover, just because men like Aquinas believed an infinite chain of causation is impossible … it doesn’t mean he was right (of course no one, at this point in time, can prove him wrong either).

Indeed it’s very frustrating when we think about the origins of the universe (and what preceded it … and where that came from). It seems like at some point you need a beginning (even if some of the more far fetched theories, like multi-verses, wind up having a drop of truth in them).

As for me, I examine religion through a much more pragmatic lens. Logically speaking there is no nexus between the obscure idea of a creator god and the various religions on earth. Therefore, each respective religion should be examined on its own merits (aside from unanswerable questions like how was the universe created, what was here before the universe, etc.). When you see preceding mythological systems that contained substantially similar stories (as compared to the stories in both the new and old testaments) it certainly creates a veracity problem for the Abrahamic faiths. There are obviously many other logical problems I have with religion; but my point in this response is that religion should only be examined according to its own merits. When I say merit I don’t mean how good or bad of a system it is (which is generally a subjective question). I mean how credible are its claims.
 
yankee_doodle said:
I mean how credible are its claims.
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The resolve of this is a matter of understanding the words properly. They don’t mean what you think they mean even though very many read them just as you do. They have had thousands of years to become what they never were.

Once you get that straight, the issue of the beginning of the universe gets resolved pretty quickly.
 
Just_Lurking said:
I’m not sure exactly what you are asking here, but the problems came up with Cantor’s diagonalization proof that a set S has strictly smaller cardinality than Power(S), the power set of S, when S is infinite. The proof involves an infinite construction, but that construction has to be fully completed in order to construct the counter-example set that finishes the proof.

Non-constructive mathematicians still consider the proof to be valid, no matter what the size of S is, including infinite sets of any size, Aleph_0, Aleph_1, Aleph_2, …, all the way up.
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You could have offered the following mathematical as actual infinities:
  1. *]The set of positive integers.
    *]The set of negative integers.
    *]The union of the set of positive and the set of negative integers.

    All three examples have the same number of members :hypno:

    Those exist only conceptually, but I’m not looking for a mathematical concept. I’m looking for an example of a tangible actual infinity.
 
James_S_Saint said:
Once you get that straight, the issue of the beginning of the universe gets resolved pretty quickly.
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I’m in this thread jumping late … so could you explain how you resolve the issue of the beginning of the universe?
 
James_S_Saint said:
Mathematics
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Let me rephrase my question JS … what is your particular theory of mathematics (or physics) regarding the origins of the universe? Like I said I’m coming in late here, so perhaps you already explained your theory (if so maybe you can direct me to the post).

I’m personally in favor of a randomness theory in terms of biological evolution (and I know there’s pretty good models out there), but I haven’t heard about any theoretical models to simulate the origins of the universe (we don’t even have a generally accepted unifying theory of physics yet)?
 
As I was just pointing out to Just_Lurking, discussing it on an open Catholic forum might be consequential, thus until I get an idea if such a discussion would upset the Church, I refrain from doing so.

But what is a “tangible actual infinity”?
 
James_S_Saint said:
And what is a “tangible actual infinity”? 😊
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Can you provide an example of an actual infinity of non-numerical, extramental objects?

I’m looking for an example that doesn’t exist solely as a mathematical concept, but exists tangibly, that is to say outside the mental construct.
 
But infinity IS a mental construct. :ehh:

The only way to have an “object” involved in infinity is to “mentally” divide the object up, or to have the object infinitely large.

Or perhaps if you consider the number of possible wave frequencies. But that is a number.

If you are asking for an example of an actual physical set of infinite items, I suspect your out of luck.

Well, now that I think, I know you are out of luck. It is a physical impossibility.
 
James_S_Saint said:
If you are asking for an example of an actual physical set of infinite items, I suspect your out of luck.

Well, now that I think, I know you are out of luck. It is a physical impossibility.
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That’s exactly my point. The claim is that there is an achieved actual infinity, but achieved actual infinities are not possible.
 
James_S_Saint said:
As I was just pointing out to Just_Lurking, discussing it on an open Catholic forum might be consequential, thus until I get an idea if such a discussion would upset the Church, I refrain from doing so.

But what is a “tangible actual infinity”?
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well OK, I know what an actual infinity is (and I can take from that & discern what a “tangible” actual infinity is).

I guess I find it a little peculiar that your worried about the CC (but I guess who knows right). Although we’re on a CC web site, information is freely available these days (so no matter where it exists it’s accessible by virtually everyone). Can’t be paranoid of everything, so why be paranoid of anything?

Anyway, don’t get me wrong I love talking about the physics (and metaphysics) aspect of this debate, but I frankly don’t believe you need either discipline to debunk religion. Any religion should be examined on the merits of its claims; apart from imagining whether or not some sort of creator god exists.
 
1holycatholic said:
That’s exactly my point. The claim is that there is an achieved actual infinity, but achieved actual infinities are not possible.
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I see. Well, I haven’t looked into it, but I settled at thinking they were merely naming something an “achieved infinity”.

Calculus involves the achieved summation of infinite sets. Thus any calculation of an finite actual volume would yield an “achieved infinite summation”.
 
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