(June 9, 2010 at 2:43 pm)fr0d0 Wrote:

(June 8, 2010 at 8:39 pm)The_Flying_Skeptic Wrote: remember that this branch of posts all stemmed from my response that all universes are logical to you saying that a universe doesn't need to be logical if there are no life forms in it.

Yes I remember. That conclusion must've been a philosophical leap of faith on your part

which conclusion? my conclusion or yours?

---

(June 9, 2010 at 2:30 pm)Purple Rabbit Wrote: To say that all universes are logical means that any universe, even the ones you don't enter, must follow some internal logic. How do you manage to arrive at such a conclusion?

what's 'internal logic' ? give me an example of universe with internal logic vs. one without internal logic so I can better understand your point.

(June 8, 2010 at 1:02 am)Saerules Wrote: So there is no necessary relation between arithmetic and physical reality. There is no rule that says things in other universes should be countable at all.

For the universe to exist, it should be consisted of something quantitative, let's call it X.
If X=0, then the universe does not exist.
If the universe exist, then you can measure the quantitative magnitude of any element which is a member of X simply by using numbers.

For the universe to exist: (N is an element)
X≠0
N∈X ⇒ N≠0

(June 9, 2010 at 2:30 pm)Purple Rabbit Wrote:

(June 8, 2010 at 2:25 am)The_Flying_Skeptic Wrote: it's easy to create new counting systems but they are just different ways to describe the same thing. like how a binary counting system may be translated to our base 10 counting system in our universe (see you don't even need to go to other universes to make new counting systems). you must be sleepy... 2 + 2 = 4 in a base 10 counting system in any universe. my example of you counting four fingers had nothing to do with your fingers but just you acknowledging 4 objects, no matter the counting system you choose.

It's easy to create arithmetic that is really different from common arithemetic. Modular arithmetic is an example. It 'wraps around' like clock counting. Base 10 however differs from base 2 only in phyrepresentation.

that's what i was explaining to saerules. her 'refutation' wasn't really a refutation unless I was arguing that there could be only one counting system which I'm not.

Quote:So there is no necessary relation between arithmetic and physical reality. There is no rule that says things in other universes should be countable at all.

---

why not? what reason is there that things in other universes wouldn't be countable?

(June 8, 2010 at 1:02 am)Saerules Wrote: To say that all universes are logical means that any universe, even the ones you don't enter, must follow some internal logic. How do you manage to arrive at such a conclusion?

Read my previous post and you'll get the answer.
This mathematical process is purely logical:
X≠0 ⇒ N∈X ⇒ N≠0
If the universe has its property X=0, then it cannot exist.

(June 9, 2010 at 3:41 pm)The_Flying_Skeptic Wrote:

Quote:So there is no necessary relation between arithmetic and physical reality. There is no rule that says things in other universes should be countable at all.

why not? what reason is there that things in other universes wouldn't be countable?

The reason is that logic and reality are two seperate things. I know that this is not easy to understand and that it even might evoke some feelings of immediate rejection, but hear me out. I will try to explain.

Fiirstly, logic is a rule based framework based on a set of relatively few basic assumptions (called axioma) and basic oprations with specific characteristics. It must be consistent for one thing. But nowhere in a logical framework you will come across a conclusion that it necessarily applies to our universe. That it applies to our reality. So how is it possible that our reality follows some logic at all? In fact nobody knows. Several geniuses have tried to explain but did not succeed. Einstein marked it as the real wonder of our universe. So when you look at it from this perspective, it is not so obvious why things in our universe should be countable at all.

Secondly you should realize that we can construct new logical frameworks that are not compatible with the one we have by starting from other axioma or basic operations. Modular arithmetic is such an example (in modular arithmetic with modulo 3 you will see that 2 + 2 = 1). It is not applicable, in one sense anyway, to our universe: material objects in our universe seem countable as natural numbers and not as finite modular sets. But at the same time we can construct logic that isn't applicable to our universe at all. So in fact we have to choose the logic that matches the universe and in doing that implicitly depart from the assumption that our reality indeed follows some logic. But in the end it is nothing but an assumption. Certain parts of mathematics we have come up with have no counterpart in our universe as far as we now know. Logic does not necessitate reality. Logic is not necessarily a description of reality, our reality or any other reality that might coexist with ours.

Another notion that can arise from this is that our reality might harbour not just one logic but possibly more. Is that really possible? 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. On the other hand you could interpret this as unfinished business. We haven't achieved the situation yet in which the description of nature can be captured in one unified logical framework.

What this shows is that you cannot conclude from logic that it has a counterpart in reality and vice versa that you can't conclude that any possible reality necessarily is a reality that obeys one unified logical framework, let alone the logical framework we might arrive at for our universe.

---

(June 9, 2010 at 3:51 pm)Ramsin.Kh Wrote:

(June 8, 2010 at 1:02 am)Saerules Wrote: To say that all universes are logical means that any universe, even the ones you don't enter, must follow some internal logic. How do you manage to arrive at such a conclusion?

Read my previous post and you'll get the answer.
This mathematical process is purely logical:
X≠0 ⇒ N∈X ⇒ N≠0
If the universe has its property X=0, then it cannot exist.

Read my post above to TFS and you'll see your conclusion is build on quick sand. You start from some obscure logic and apply it to all universes. That's circular. To apply logic to universes is to assume thee universes obey your logic.

(June 9, 2010 at 5:02 pm)Purple Rabbit Wrote: Secondly you should realize that we can construct new logical frameworks that are not compatible with the one we have by starting from other axioma or basic operations. Modular arithmetic is such an example (in modular arithmetic with modulo 3 you will see that 2 + 2 = 1). It is not applicable, in one sense anyway, to our universe: material objects in our universe seem countable as natural numbers and not as finite modular sets. But at the same time we can construct logic that isn't applicable to our universe at all.

All math theorems have been proved by previous theorems and original axioms.
(2+2=1 mod 3) does not exist in math, a correct modular statement is ( 2 + 2 ≡ 1 mod 3).
(≡) is the sign of congruence, not equality. Modular arithmetic is in fact applicable in our universe, the most common thing which involves modular math is the clock.

(June 9, 2010 at 5:02 pm)Purple Rabbit Wrote: Certain parts of mathematics we have come up with have no counterpart in our universe as far as we now know. Logic does not necessitate reality. Logic is not necessarily a description of reality, our reality or any other reality that might coexist with ours.

All math theorems are proved by original axioms (ex. of axiom: 1+1=2).
Logic is very necessary for describing the universe, since all classical and modern physics involves logical math.

(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.

(June 9, 2010 at 5:02 pm)Purple Rabbit Wrote: What this shows is that you cannot conclude from logic that it has a counterpart in reality and vice versa that you can't conclude that any possible reality necessarily is a reality that obeys one unified logical framework, let alone the logical framework we might arrive at for our universe.

Logic is not a rule or something to be obeyed. Logic is not something that have properties, because you say quantum logic, different logics...
Logic is simply the study of reasoning. In all universes, you can reason and use your intellect and therefore think and deduce logically.

(June 9, 2010 at 5:02 pm)Purple Rabbit Wrote:

(June 9, 2010 at 3:41 pm)The_Flying_Skeptic Wrote:

Quote:So there is no necessary relation between arithmetic and physical reality. There is no rule that says things in other universes should be countable at all.

why not? what reason is there that things in other universes wouldn't be countable?

The reason is that logic and reality are two seperate things. I know that this is not easy to understand and that it even might evoke some feelings of immediate rejection, but hear me out. I will try to explain.

That reality and logic are two separate things is what I've been saying the whole time. just because a universe is made up of just beach balls doesn't mean that it isn't 'logical' but it's only 'logically possible' under the axiom or premise that (basically) 'anything is possible'. (response to: "A universe consisting entirely of giant pink beachballs is logically possible. said Caecilian")

Quote:Fiirstly, logic is a rule based framework based on a set of relatively few basic assumptions (called axioma) and basic oprations with specific characteristics. It must be consistent for one thing. But nowhere in a logical framework you will come across a conclusion that it necessarily applies to our universe.

yeah, i totally agree. i have not been saying that 'anything' necessarily applies to all universes besides logic. you should be able to form conclusions based on axioms in any universe. in any universe, you should be able to apply logics thus there is no such thing as an 'illogical universe'. give me an example of a hypothetical 'illogical universe'. i guess I have to bold my request since you denied it in your response. maybe you don't understand what i mean by an illogical universe: a universe or a space where logical arguments may not be created. Ramsin shows his understanding of the meaning of an illogical universe when he says "In all universes, you can reason and use your intellect and therefore think and deduce logically."

Quote:That it applies to our reality. So how is it possible that our reality follows some logic at all? In fact nobody knows. Several geniuses have tried to explain but did not succeed. Einstein marked it as the real wonder of our universe. So when you look at it from this perspective, it is not so obvious why things in our universe should be countable at all.

as you said, reality and logics are separate. and i never said there is a reason (synonymous to the belief held by theists that there is a 'reason' for our existence. [nevermind this possibly confusing reference.]) why things are countable in our universe, i said that things are countable in every universe.

Quote:Secondly you should realize that we can construct new logical frameworks that are not compatible with the one we have by starting from other axioma or basic operations. Modular arithmetic is such an example (in modular arithmetic with modulo 3 you will see that 2 + 2 = 1). It is not applicable, in one sense anyway, to our universe: material objects in our universe seem countable as natural numbers and not as finite modular sets.

modular arithmetics doesn't mean there are illogical universes or that objects in hypothetical universes wouldn't be countable.

---

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

(June 9, 2010 at 5:02 pm)Purple Rabbit Wrote: Secondly you should realize that we can construct new logical frameworks that are not compatible with the one we have by starting from other axioma or basic operations. Modular arithmetic is such an example (in modular arithmetic with modulo 3 you will see that 2 + 2 = 1). It is not applicable, in one sense anyway, to our universe: material objects in our universe seem countable as natural numbers and not as finite modular sets. But at the same time we can construct logic that isn't applicable to our universe at all.

All math theorems have been proved by previous theorems and original axioms.
(2+2=1 mod 3) does not exist in math, a correct modular statement is ( 2 + 2 ≡ 1 mod 3).
(≡) is the sign of congruence, not equality. Modular arithmetic is in fact applicable in our universe, the most common thing which involves modular math is the clock.

modular math is applicable in all universes for that matter. Purple Rabbit mentioned modular math's example in the clock, by the way. I suppose your re-mentioning isn't a big deal.

(June 9, 2010 at 5:57 pm)Ramsin.Kh Wrote: All math theorems have been proved by previous theorems and original axioms.

Axioms are by default unproven statements.
Anyway, 'proven' means proven in the language of a logical framework. This has no implicit bearing on universes.

(June 9, 2010 at 5:57 pm)Ramsin.Kh Wrote: (2+2=1 mod 3) does not exist in math, a correct modular statement is ( 2 + 2 ≡ 1 mod 3).
(≡) is the sign of congruence, not equality.

That's a matter of convention only.

(June 9, 2010 at 5:57 pm)Ramsin.Kh Wrote: Modular arithmetic is in fact applicable in our universe, the most common thing which involves modular math is the clock.

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

(June 9, 2010 at 5:57 pm)Ramsin.Kh Wrote: All math theorems are proved by original axioms (ex. of axiom: 1+1=2).

1+1=2 is not an axiom of arithmetic. In fact, to prove 1+1=2 from axiom is a rather lengthy proof.

There is no such thing as "original" axioms. Axioms are unproven assumptions of mathematics. They don't necssarily relate to our reality. Famous example: euclidean geometry was based on five axiomas. Some were later shown not to hold in our universe. As a result Einstein and Minkovski replaced it with a new geometry.

(June 9, 2010 at 5:57 pm)Ramsin.Kh Wrote: Logic is very necessary for describing the universe, since all classical and modern physics involves logical math.

Yes. So what, I'm very familiar with physics. We do inded need it because we try to describe the world in terms of patterns and mathematics fits very good for that.

(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.

Please don't parrot some lame argument about the magical connotation of QM when it's not appropiate. I've studied quantum physics. 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. That is quantum logic. Just google it. It exists and has practical scientific use in constructing quantum computers. I assume you know that quantum physics currently hasn't been unified with general relativity? If not google it. The underlying math is different. And that is a real enigma. If you can unify these realms, you can make the headlines tomorrow. This is the holy grail of physics.

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

(June 9, 2010 at 5:02 pm)Purple Rabbit Wrote: What this shows is that you cannot conclude from logic that it has a counterpart in reality and vice versa that you can't conclude that any possible reality necessarily is a reality that obeys one unified logical framework, let alone the logical framework we might arrive at for our universe.

Logic is not a rule or something to be obeyed. Logic is not something that have properties, because you say quantum logic, different logics...
Logic is simply the study of reasoning. In all universes, you can reason and use your intellect and therefore think and deduce logically.

I see no argument there. You're just asuming a whole lot on logic in other universes.
I suggest you read up on Euclidean Geometry and it's replacement by general relativity. Should be very enlightening.

(June 9, 2010 at 6:06 pm)The_Flying_Skeptic Wrote: modular math is applicable in all universes for that matter.

If modular math is applicable in all universes, then all topics of math should be so since all their branches have grown from the same axiom/root.

(June 9, 2010 at 6:06 pm)The_Flying_Skeptic Wrote: Purple Rabbit mentioned modular math's example in the clock, by the way. I suppose your re-mentioning isn't a big deal.

I wasn't aware of that while I was writing the post. I'm sure that modular math is used in computer sciences (programming) and music...

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?