(June 9, 2010 at 5:57 pm)Ramsin.Kh Wrote:

(June 9, 2010 at 5:02 pm)Purple Rabbit Wrote: Well, a startling find with the discovery of quantum mechanics seems to suggest that this indeed is the case. At the quantum level of our very own universe even countability breaks down due to the Heisenberg Uncertainty Principle. In this realm a different logic, quantum logic, is used to describe the phenomena.

I don't see any reason of bringing quantum physics here, it only appears magical to public.
Same math axioms and theorems are used in quantum physics, you can see that in any physics book.
There is no 'our realm' and quantum realm, every macroscopic event can be explained by quantum physics, but the classical physics is used for that because it's simpler and gives a fair approximate answer.

Quote: This is not an argument that suggests some mystical phenomenon from QM. All I say is that QM can be described with a logic that's different from the normal stuff. [/quote ]

[deleted all the useless stuff and added bold emphasis] Whatever logic that was derived, based on, or refers to quantum mechanics was derived from 'normal logic' and that is what Ramsin said in slightly different words.

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(June 9, 2010 at 7:26 pm)Caecilian Wrote:

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One way of looking at it might be this:

Any system of logic has axioms. These are statements that are assumed to be true, and cannot be deduced from within the system.

A particular set of axioms applies within our universe- for example, the axiom of equality (x = x). The axioms that apply in our universe produce a logic that applies in our universe.

However, the set of axioms that apply in our universe is a very small sub-set of the total set of possible axioms.

There is no real reason at all to think that the axioms that apply in our universe will necessarily apply in other universes. Other universes may have the same, or different axioms to ours, or indeed no axioms at all (why not?).

As I said before, we find it difficult, if not impossible, to conceive of what those other, very different, universes would be like. But so what? Since when was possibility limited by the human imagination?

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logics is abstract from any reality (any universe), thus logics is applicable in any universe. i said that a universe or a reality may exist of just beach balls but that is only 'logically possible' under the premise that 'anything is possible'; however, this universe is not illogical simply because it only contains beachballs. an illogical universe is a universe where logical arguments may not be formed and that's impossible. x = x applies in any universe. i guess you could say x=x is transuniversal.

(June 9, 2010 at 7:01 pm)Purple Rabbit Wrote: A clock is an abstraction of time by humans, not time itsel. Presenting it in a periodic cycle is a handy way to sync our practical daily use time to the rotation of the earth, but it is not applicable to time as a dimension of our universe. That is, as we currently understand it, a continuous timeline

What do you exactly mean? Knowing what time is is still arguable.
I just wanted to make an easy example.

(June 9, 2010 at 7:01 pm)Purple Rabbit Wrote: Axioms are unproven assumptions of mathematics.

Such axioms are self-evident.

(June 9, 2010 at 7:01 pm)Purple Rabbit Wrote: Some were later shown not to hold in our universe. As a result Einstein and Minkovski replaced it with a new geometry.

Give me an example. What do you mean by "not to be held in our universe"? Because the new geometry is developed from the old one.
Do you mean like, straight lines in Euclidean-geometry and geodesics in modern geometry?

(June 9, 2010 at 7:01 pm)Purple Rabbit Wrote: All I say is that QM can be described with a logic that's different from the normal stuff. That is quantum logic.

All its math is evolved from the simple logical math, its math has its roots in the self-evident axioms.

(June 9, 2010 at 7:01 pm)Purple Rabbit Wrote: I assume you know that quantum physics currently hasn't been unified with general relativity? If not google it. The underlying math is different.

What has this to do with our discussion of logic? I know they are two different theories, and the major problem is that gravity is not unified the three other fundamental forces.
They are different mathematical models but uses the same underlying logical rules of math.

@Rhamsin.Kh

All this stuff about axioms being 'self-evident'. Of course they are. But why? Surely its because thats the way our universe works. If the axioms that applied to our universe were different, then they'd be 'self-evident'.

In other words: that our particular set of axioms is 'self-evident' is a consequence of them being our particular set of axioms.

(June 9, 2010 at 7:58 pm)Caecilian Wrote: @Rhamsin.Kh

All this stuff about axioms being 'self-evident'. Of course they are. But why? Surely its because thats the way our universe works. If the axioms that applied to our universe were different, then they'd be 'self-evident'.

In other words: that our particular set of axioms is 'self-evident' is a consequence of them being our particular set of axioms.

can you think of a universe where (x=x) wouldn't be an axiom? To me saying that x=x wouldn't serve as an axiom in other universes is like saying that in other universes there are edged circles or triangles with angle sums greater than 180 degrees.

(June 9, 2010 at 7:58 pm)Caecilian Wrote: There is no real reason at all to think that the axioms that apply in our universe will necessarily apply in other universes.

(June 9, 2010 at 7:58 pm)Caecilian Wrote: Surely its because thats the way our universe works. If the axioms that applied to our universe were different, then they'd be 'self-evident'.

Excellent point. You may have totally different deduced theorems and theories in another universe.
Therefore if every universe has its own set of axioms, then every universe should be logical.
Even a universe with an empty set of axioms has an axiom, since the axiom is the proposition of having an empty set.

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If you ask an ancient man, "Why is the feather falling slower than the rock?", the man will answer because the feather is less massive. His answer is logical for him. If you directly say, without any explanation, that air resistance makes the feather's falling velocity slower, then the person will think that what you've said is illogical, because he can't easily or has no reason to conceive that earth attracts both masses with the same acceleration rate during the absence of air. Conclusion: he's ignorant.

To put it on the other way, when you're able to enter another universe with totally different axioms, then at the very first moment you're totally ignorant of the new observed universe. In that universe, events occur while you have no explanation for them since they do not match to your knowledge and therefore appear illogical to you. As time passes, you think and begin understanding the universe, and therefore deducing from universe's axioms in order to think logically.

(June 9, 2010 at 9:33 pm)The_Flying_Skeptic Wrote: [hide]

(June 9, 2010 at 7:58 pm)Caecilian Wrote: @Rhamsin.Kh

All this stuff about axioms being 'self-evident'. Of course they are. But why? Surely its because thats the way our universe works. If the axioms that applied to our universe were different, then they'd be 'self-evident'.

In other words: that our particular set of axioms is 'self-evident' is a consequence of them being our particular set of axioms.

can you think of a universe where (x=x) wouldn't be an axiom? To me saying that x=x wouldn't serve as an axiom in other universes is like saying that in other universes there are edged circles or triangles with angle sums greater than 180 degrees.[hide]

No, I can't think of a universe where (x=x) is not an axiom. But the fact that I can't conceive of it is totally irrelevant to whether or not it is possible. Which is the point that I've been trying to make.

I think that you'll find that in spherical trigonometry the sum of the angles of a triangle is always greater than 180 degrees.

@Ramsin.Kh

Yeah, in an important sense every universe is logical in terms of its own logic, bearing in mind that 'its own logic' may be a sort of empty set, or may be incomprehensible or inconceivable to us.

Its important not to conflate this with a universe being logical in our terms.

I encounter only one problem,

a) We exist in our universe, and we're thinking about the possibility of other universes with possibly different axioms.
b) If so, how can we use our axioms (ex. a=a) for many universes? Since we're saying that they have different axioms.
c) Arguing about a universe (A) is different from universe (B) but as the same as universe © demands the very basic axiom, since: A=C≠B.
d) We can't use our axioms for multitude universes, unless all of them share at least one fundamental axiom, in this case (a=a).
e) Therefore the discussion of many universes without any single axiom is totally useless.

Here comes another question, whether those universes are in a system with each others or are totally set apart from each others?
There is no evidence for something to be totally separated, since every known and predicted entity is in a system.
Even if a universe appears to be totally isolated, you can think of it and compare it to another. Its existence is possible because you're comparing it to others by using axioms. Therefore that universe should be in a system.
If those universes are in a system, then all of them should share at least one fundamental axiom.

(June 10, 2010 at 8:20 am)Ramsin.Kh Wrote:

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I encounter only one problem,

a) We exist in our universe, and we're thinking about the possibility of other universes with possibly different axioms.
b) If so, how can we use our axioms (ex. a=a) for many universes? Since we're saying that they have different axioms.
c) Arguing about a universe (A) is different from universe (B) but as the same as universe © demands the very basic axiom, since: A=C≠B.
d) We can't use our axioms for multitude universes, unless all of them share at least one fundamental axiom, in this case (a=a).
e) Therefore the discussion of many universes without any single axiom is totally useless.

Here comes another question, whether those universes are in a system with each others or are totally set apart from each others?
There is no evidence for something to be totally separated, since every known and predicted entity is in a system.
Even if a universe appears to be totally isolated, you can think of it and compare it to another. Its existence is possible because you're comparing it to others by using axioms. Therefore that universe should be in a system.
If those universes are in a system, then all of them should share at least one fundamental axiom.

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I don't think that it is particularly fruitful to talk about universes with different (or no) axioms. Apart from anything else, its extremely difficult to do so, since its difficult/ impossible to actually conceive of what such universes would be like. And given this, its hard to see what role they can play in philosophical discussions.

Ime, philosophers are concerned with 2 sorts of possible world/ universe:

- Logically possible worlds. That is: worlds that share our logic, but not necessarily our physical laws.

- Nomologically possible worlds. That is: worlds which have the same physical laws as ours, but may be different in other respects.

Clearly, the set of nomologically possible worlds is a subset of the set of logically possible worlds.

(June 10, 2010 at 5:48 am)Caecilian Wrote:

(June 9, 2010 at 9:33 pm)The_Flying_Skeptic Wrote: [hide]

(June 9, 2010 at 7:58 pm)Caecilian Wrote: @Rhamsin.Kh

All this stuff about axioms being 'self-evident'. Of course they are. But why? Surely its because thats the way our universe works. If the axioms that applied to our universe were different, then they'd be 'self-evident'.

In other words: that our particular set of axioms is 'self-evident' is a consequence of them being our particular set of axioms.

can you think of a universe where (x=x) wouldn't be an axiom? To me saying that x=x wouldn't serve as an axiom in other universes is like saying that in other universes there are edged circles or triangles with angle sums greater than 180 degrees.[hide]

No, I can't think of a universe where (x=x) is not an axiom. But the fact that I can't conceive of it is totally irrelevant to whether or not it is possible. Which is the point that I've been trying to make.

I think that you'll find that in spherical trigonometry the sum of the angles of a triangle is always greater than 180 degrees.

@Ramsin.Kh

Yeah, in an important sense every universe is logical in terms of its own logic, bearing in mind that 'its own logic' may be a sort of empty set, or may be incomprehensible or inconceivable to us.

Its important not to conflate this with a universe being logical in our terms.

spherical triangles... ugh. why did you even bring that up? it's a tangent that there is a group of shapes called spherical triangles. You can't think of a universe were x = x would not be a starting point because it's illogical. it's like saying God can do the logically impossible or the illogical like make edged circles... Sure you can say it but it's senseless. this discussion parallels arguments against a deity that doesn't need to be created, and you're the one saying 'God exists outside of our universe, he doesn't need to be created.' You're reasoning looks the same: "just because you can't imagine it or find reason in it, doesn't mean it's not true"

(June 10, 2010 at 2:39 pm)The_Flying_Skeptic Wrote: spherical triangles... ugh. why did you even bring that up? it's a tangent that there is a group of shapes called spherical triangles. You can't think of a universe were x = x would not be a starting point because it's illogical. it's like saying God can do the logically impossible or the illogical like make edged circles... Sure you can say it but it's senseless. this discussion parallels arguments against a deity that doesn't need to be created, and you're the one saying 'God exists outside of our universe, he doesn't need to be created.' You're reasoning looks the same: "just because you can't imagine it or find reason in it, doesn't mean it's not true"

We're talking about other universes here. In our own universe, the rules of our logic apply.

Something akin to 'god' might exist in another universe- no reason why not. But in our universe, 'god' is incoherent nonsense.

As for spherical triangles- you're the one who brought the subject of triangles up. I agree that its tangential to the thread.