I ran across para-consistent logic.

http://en.wikipedia.org/wiki/Paraconsistent_logic

It is interesting to me, I hadn't thought about it before, however I definitely believe that it is possible to reason with inconsistent information or in the absence of certain information, and not just in a "fuzzy" way, and the "Principle of Explosion" or being able to derive anything from a contradiction does seem like a systemic weakness in classical reasoning, especially when I encounter a large "philosophical" work. I always ask: Where is that little subtle contradiction that they used to derive all of "it"?

my favorite logical paradox:
let's start off with the assumption that identical things are identical.
now imagine i make an exact copy of the entire universe.
will i do the same thing in both universes a week from friday?
if yes, then we don't really have free will. that is, our actions are predetermined by that state of the elements in us and around us.
if no, then the identity principle doesn't hold.
so which would you perfer, identity but no free will, or free will but no identity?

so which would you perfer, identity but no free will, or free will but no identity?

my favorite logical paradox:
let's start off with the assumption that identical things are identical.
now imagine i make an exact copy of the entire universe.
will i do the same thing in both universes a week from friday?
if yes, then we don't really have free will. that is, our actions are predetermined by that state of the elements in us and around us.
if no, then the identity principle doesn't hold.
so which would you perfer, identity but no free will, or free will but no identity?

By the way, most philosophical works (large or not) do not rely on the principle of explosion to derive their conclusions.

Personally I prefer a one-valued logic, e.g. a logic with only the truth-value "true" that basically behaves like an only syntactical logic. It's simple and I'm always right^^.

@Monadology

Thx, that was a hell of a read!!!

I'm still skeptic about those non-classical logics, because they all rely on classical logic in their meta-language (where a logic is ruled and made sense of). Another point: Priest introduces this logic that has the truth values: true, false, truefalse, none, ineffable. What about a sixth truth value of "ineffability of all the previous truth values" and so on and you got an infinite value logic^^.

Also, modern higher math uses variables to prove things about infinite sets. E.g. they prove that there are infinite natural numbers, because every number n has a successor n+1, so that there can't be a last one. BUT: That assumes that "n" stands for all possbile natural numbers, infinitely many as we just saw. How can one assume that?

Also, modern higher math uses variables to prove things about infinite sets. E.g. they prove that there are infinite natural numbers, because every number n has a successor n+1, so that there can't be a last one. BUT: That assumes that "n" stands for all possbile natural numbers, infinitely many as we just saw. How can one assume that? How can a single letter stand for 1. a single number but 2. at the same time for all?

You do not have to assume that.

Suppose that there is a largest natural number. Call it L. Then there is a natural number, L + 1. Call it M. Then M > L, which means that L is not the largest natural number, and our supposition is false.

@Monadology

Thx, that was a hell of a read!!!

I'm still skeptic about those non-classical logics, because they all rely on classical logic in their meta-language (where a logic is ruled and made sense of). Another point: Priest introduces this logic that has the truth values: true, false, truefalse, none, ineffable. What about a sixth truth value of "ineffability of all the previous truth values" and so on and you got an infinite value logic^^.

That would just prove that L is not the largest number, but what about M? You would need to repeat your proof for M since L did stand just for a concrete number (the supposed biggest one). Only if L stands for any number in N then the proof works. But that requires that variables can stand for any number in N and that sounds like weirdo metaphysics. Because first how can a variable stand for infinite numbers? Because by definition infinity is never over, so that a variable could never stand for all numbers in an infinite set. Secondly, how can one imagine this? Obviously a variable contains only space for one number, a variable is not a set. So how can a space for one number contain all infinite numbers somehow? Even if we imagine a Turing machine with infinite power and infinitely fast that can put all numbers in a row into a variable like x then still it wouldn't contain all, because there are infinitely many natural numbers. You cannot say that the infinitely fast turing maschine would beat the infinite many numbers, can't u?

That would just prove that L is not the largest number, but what about M?

You would need to repeat your proof for M since L did stand just for a concrete number (the supposed biggest one). Only if L stands for any number in N then the proof works. But that requires that variables can stand for any number in N and that sounds like weirdo metaphysics.

Because first how can a variable stand for infinite numbers? Because by definition infinity is never over, so that a variable could never stand for all numbers in an infinite set.

Obviously a variable contains only space for one number, a variable is not a set.