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I've run into an interesting metaphysical problem. Obviously we cannot deny the axioms of metaphysics without contradiction. The axioms represent the minimum solid ground on which we can base knowledge. The question is: do the axioms need to have infinite extent, or could they be finite truths? For instance, is existence infinite in extent or a finite quantity? Are we always free or is our time line of free will like swiss cheese, full of holes? What about identity, does the principle of non-contradiction always hold, or is there a boundary to existence where the principle starts to break down?

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Obviously we cannot deny the axioms of metaphysics without contradiction.

Which axioms?

For instance, is existence infinite in extent or a finite quantity?

Are you asking if you can have infinite material in the universe or something else?

What about identity, does the principle of non-contradiction always hold, or is there a boundary to existence where the principle starts to break down?

As in religion, mysticism etc?

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Which axioms?

The metaphysical axioms of Objectivism.

Are you asking if you can have infinite material in the universe or something else?

That too, infinity of any kind.

As in religion, mysticism etc?

No, at special aspects of the physical universe (time,space, scale). One possible candidate would be scale at the quantum level. One way of interpreting QM noise is that one approaches the end of existence and the principle of non-contradiction therefore starts to break down.

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What about identity, does the principle of non-contradiction always hold, or is there a boundary to existence where the principle starts to break down?

It never breaks down. Non-contradiction always holds. Contradictions cannot exist in reality, not in part, nor in whole, not here, not anywhere in the universe. A contradiction is when something is not of its own nature. But since everything must have anature to exist, it must therefore be of its own nature and therefore not have contradictions. This holds for everything and everywhere.

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I've run into an interesting metaphysical problem. Obviously we cannot deny the axioms of metaphysics without contradiction. The axioms represent the minimum solid ground on which we can base knowledge. The question is: do the axioms need to have infinite extent, or could they be finite truths? For instance, is existence infinite in extent or a finite quantity? Are we always free or is our time line of free will like swiss cheese, full of holes? What about identity, does the principle of non-contradiction always hold, or is there a boundary to existence where the principle starts to break down?

The ONLY the only ground FULLSTOP we can base knowledge upon,m as knowledge is based on realisation of reality, which requires acceptance of the axioms of existence, identiy and conscioussness. No other "ground' can exist upon at tbhe most fundamental levels, upon which to base knowledge.

An axiom is a statement identifiying the base of knowledge, and is neccessary before any measurements are possible.

Trying to assign a "boundary" to the axioms is ridicolous. You seem to be trying to treat the axioms like some weird spacial construct with shapes and boundaries. They are elementary statements dealing with facts which must be accepted if one wishes to learn anything else, talking of "extents" or if they are "finite' or "infinite' is nonsensical. Elementary statements identifying the basis of knowledge do not have sizes, they do not have "extents", or any other measurements. They are the case and that is that, no measurement is possible or sensible. You cannot "quantities" of absoulety true statements such as this.

Existence designtes that which exists, that is it, it makes no indication of the size of that which it deals with. It merely says there are things that exist. It makes no mention of quantities or measurements

Identity basically says a thing is itself, contradictions cannot exist. Measurements cannot apply here...the statement is an absoulute, things ARE what they are, without contradiction there is no more to it. There can be no exception, something cannot be itself and yet another at the same time, or exist according to its nature and contradict its nature, this fact must be accepted as self-elementary, there is no room for sensible doubt.

Conscioussness IS..no measurement of IS is possible, something exists or not, but this is not a measurement, but a statement.

Free will exists to some extent, it is fundamentally the minds freedom to think or not to think. Nothing can take this away as long as you are alive nd your brain properly functions. Even a slave in a cell has soem free will, he has the ability to decide to think or not, to make the best choices given his situation or to not do so, whatever the consequences of his choices may be.

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No, at special aspects of the physical universe (time,space, scale). One possible candidate would be scale at the quantum level. One way of interpreting QM noise is that one approaches the end of existence and the principle of non-contradiction therefore starts to break down.

What the hell are you babbling on about? I am NOT sorry to burst your silly bubble, but even on the quantum scale, the Law of Identity remains valid. There is no scale of matter smaller than which something ceases to exist :this is what you are saying when "matter on a small enough scale might not be bound by Identity". EVERYTHING that exists is bound by it, to exist is to have Identity, if it has no Identity it does not exist.

Something cannot approach the end of existence, that makes no sense. If something exists, it exists, there is no "nearly on the edge of non-existence" or any such thing.

The laws of non-contradictoin hold for all matter, in all places, in all cases, nothing that exists can be an exception, no matter how weird it might seem. If you think QM implies non-contradiciton can break down, check your premises. Contradictions cannot exist in reality, if you think they do, one of your assumptions/preimises is wrong.

Edited by Prometheus98876
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Trying to assign a "boundary" to the axioms is ridicolous.

No it is not. It is essentially the task of identifying the boundaries of existence. It is finding the corners of reality where you must say "nothing exists beyond this point. This is the end of existence."

You seem to be trying to treat the axioms like some weird spacial construct with shapes and boundaries.

No, but the axioms do describe the fabric of existence.

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Something cannot approach the end of existence, that makes no sense. If something exists, it exists, there is no "nearly on the edge of non-existence" or any such thing.

This may or may not be true. But there are obvious candidates for such limits. Is space infinite? Is time infinite? Is scale infinite? If not, obviously there is a boundary to existence.

The laws of non-contradictoin hold for all matter, in all places, in all cases, nothing that exists can be an exception, no matter how weird it might seem.

I agree with this statement, but it doesn't really address the question at hand. Obviously the law of non-contradiction holds in all places, because all places are part of reality. But what happens when we reach the end of space? Is there such a place? What happens there? We know there is nothing *beyond* this limit, so it must represent some kind of limitation on reality. Exactly how does that limit work?

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It is essentially the task of identifying the boundaries of existence. It is finding the corners of reality where you must say "nothing exists beyond this point. This is the end of existence."
The mistake you're making is that you're reifying space. You're saying that there is something -- something exists -- corresponding to "there", but also that there there's no "thing", no existence, there. The very concept of "beyond" that you're relying on assumes an infinite existent, space-time, in which entities are embedded. Don't look at the universe that way: look at space-time as a relationship between entities instead. There is no need to talk about "beyond existence" in that case. If "space" is an independent entity and not a measurement relationship between entities, then it is finite. If "space" is a measurement relationship between entities, each such relationship is a specific, finite value.

The only interesting question, from what I can see, is whether space and time are infinitessimal, i.e. if you have two very tiny particles being a very tiny distance apart, can then be half that distance apart? Ad infinitessimus. That's a scientific question that has no answer at present, though I see no problem in assuming that there is a smallest quantum of space-time.

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No. Outside of existence there is no "is" or "there."

I didn't ask if there was a place outside of existence (obviously there isn't), I asked if there is an *end* of existence, a point beyond which there is nothing. If you think this makes little sense, then think concretely. Is space infinite? If not then it must be finite, which means that there must be some end to space.

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I asked if there is an *end* of existence, a point beyond which there is nothing.
I take it you didn't understand my explanation why the question assumes a contradiction.
Is space infinite?
What do you mean, "is space infinite"? What could that possibly mean? Are you asking if space is a set of entities with infinite cardinality? It isn't.
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The mistake you're making is that you're reifying space.

I'm well aware of this kind of error, and it's always good to be reminded of it, even though I don't think I'm making it now.

The very concept of "beyond" that you're relying on assumes an infinite existent, space-time, in which entities are embedded.

Actually it doesn't. I specifically say that "nothing lies beyond this point," and unless you objectify nothingness as a kind of existent there is no reification, merely a statement about the limitations of space at a particular point. This is not a trick question. It is a very real problem. Is space inifinite? If not, there must be an end point. What is the behavior of reality at this end point?

Don't look at the universe that way: look at space-time as a relationship between entities instead.

Yes, finite absolutism.

There is no need to talk about "beyond existence" in that case.

Agreed, but that is not what I am talking about either. I am talking about the behavior of existence when pushed to a particular boundary. What this means is that if you inquire existence persistently in one of its properties (e.g. time, space, scale) you should sooner or later bump into its end -- if existence is limited.

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Is space inifinite? If not, there must be an end point.
What is the meaning of "end point"?
What is the behavior of reality at this end point?
I dunno, but my default assumption is "the same as anywhere else". If you have some evidence for a meaningful "edge" and that somehow it matters whether there are things "to the east, south and north" but not "to the west", we can revisit the assumption.
I am talking about the behavior of existence when pushed to a particular boundary.
I don't understand what you mean by "boundary". I don't assume that there is a "theoretically most distant particle" which is intrinsically limited so that it metaphysically could not be moved beyond where it is. Why would one assume such a thing? If that's not what you mean, I have no idea what you mean. Unless, again, you're taking seriously the idea that if things don't exist "beyond" a certain relationship (i.e. for the two furthest-separated particles in existence there is a maximum separation distance), then there is some kind of hard boundary. I don't assume such a limit, and I don't know of a reason to assume such a limit on relationships.
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I don't understand what you mean by "boundary". I don't assume that there is a "theoretically most distant particle" which is intrinsically limited so that it metaphysically could not be moved beyond where it is

I think this point is important. You must realize that "space" is a relational concept and as such only describes relationships among entities and is not itself an entity, therefore it need not be bound by such limitations as finitude.

So since space is not material, it can not possess and edge, only entities possess edges.

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Do you consider the surface of a sphere to be infinite? If not, then where are its "end points"? Your logic is flawed.

This is a very good example of how identifying the behavior of a finite existence is non-trivial. If space indeed is spheric then finity would express itself in terms of repetition when moving in one direction. Mathematically 3D space COULD actually be spherical. In fact, there exists only three such spheres without singularities (poles), namely S1, S3 and S7. S1 is the 2-dimensional sphere built from a 1-dimensional space (a line), essentially a circle. S3 is a 4-dimensional sphere built from a 3D "surface" and S7 is an 8-dimensional sphere built from a 7D "surface." It would be an odd but beautiful coincidence if our own universe turned out to be one of these three possible spheres.

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I think this point is important. You must realize that "space" is a relational concept and as such only describes relationships among entities and is not itself an entity, therefore it need not be bound by such limitations as finitude.

So since space is not material, it can not possess and edge, only entities possess edges.

I think this is interesting and it could very well be correct, but why couldn't space be an existent? Given how Einstein's theory of relativity works, space (and time) seems to be something more than just relations. When the Earth makes one full rotation around the sun, it hasn't in fact rotated 360 degrees due to "frame dragging." Space is actually dragged along in the gravitational field. To me that sounds a lot like space is a kind of "liquid" which is stirred by the objects in it.

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That may be how many interpret relativity theory ... but no. Even under the mathematical framework of relativity theory, space and time (taken inseparably together) are relationships among entities.

Tell me again why relations between existents cannot themselves be existents?

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This passage might clear things up further:

...entities are the only primary existents (Attributes cannot exist by themselves, they are merely the characteristics of entities; motions are motions of entities; relationships are relationships of entties).
- Introduction to Objectivist Epistemology page 18.

And this:

1. An entity means a self-sufficent form of existence - as agaisntg a quality, an action, a relationship, etc, which are simply aspects of an entity; that we sepeerate out by specialized focus. An entity is a thing.
- Leonard Peikoff, 'The Philosophy of Objectivism"
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