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Originally Posted by bobleplask  I actually took philosophy of logic but I failed it. I am starting to understand why now 
in the man made system called mathematics 1 = 1 and if not then as you say, mathematics will fail. We not do really know if the same rules applies to the real world. We just take it for granted. It could be that 1 really, really, really is 2, but we just have not figured it out yet. |
Doesn't matter if 1 is actually "2" or "643" or "whoozie". The numbers are abstract representations of physical entities. They represent ideas in reality - entities - and therefore what they actually *are called* does not matter. The principle is the same.
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Originally Posted by shaun Yes, by its very nature. A cannot be non-A.
Forget senses - you're still thinking that truth is defined by perception. I am arguing that it is not; that truth is exclusive. You can use logic to prove such without using physical senses. Knowing truth is a whole other topic that is unrelated to absolute truth.
A = A is a tautology - a propositional formula that is true in any possible valuation or context.
Could be what? No, A cannot be Non-A. If you want to say it can, you must prove otherwise. I have shown that A is A, and therefore cannot be non-A.
The proof is: ~(P v ~P) |
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Within "a system" called logic based on claims, you have proven that "A = A". Also to say that "A = not A" you say I have to prove it. These are rules from Logic101.
I say that we can't know if "A = A" or if "A = not A" and we can not prove either of them.
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You might enjoy this quote from the philosopher Avicenna:
"Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned."
If I am sitting in a chair, I am therefore by necessity not not sitting in a chair.
If I am eating an apple, I am therefore by necessity not not eating an apple.
If I am typing this reply to you to get you to understand first principles, then I am therefore by necessity not not typing this reply to you to get you to understand first principles.
If you're going to deny First Principles and our knowledge of them, then I suggest seeing how the very way you live - even your post to me - relies on First Principles.
When you said that you "say we can not prove either of them", you assumed the law of non-contradiction that states that something is either proven or not proven. You also assumed that "them" is "them", and not "not-them".
We can simply "say" things are not knowable, but unless you show me
any sort of evidence why First Principles are unknowable, you're just spouting off at the wind. Let's be reasonable, here.
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These statements we more or less take for granted and it's hard to find reasons for them not to be true. But can it be doubted that A = A? Or does there exist something that tells with out doubt that A = A?
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Originally Posted by shaun These laws are a priori - they are self-evident and self-proving. If you doubt First Principles, then all knowledge and philosophy breaks down and you cannot deduce anything. The statement that A = A might not always be true without First Principles, specifically the law of identity. |
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These laws are a priori because we say they are. They can be doubted by many things, for instance Descartes deceiving god and his evil demon for all we know. On the other hand they might be true. It just can not be known.
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Straw Man fallacy - I did not say they are a priori because we say they are. I said they are
a priori on
their own self-evident nature. Whether or not we percieve that A = A is irrelevant. A is still A. The truth of the statement exists outside of your perception, but yet can still be percieved but not defined by that perception.
To simply say "they might be true" is nonsense. Either they are or they are not. And if they are not, then you have run into an impossibility, for to have something be "not", it must have an opposite "be", which implies that to "be not" is not to "be". Ergo, the law of non-contradiction.
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I doubt First Principles and do not think we can deduce anything.
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No offense, but that's a lie. You deduced that very statement, even if it was an incorrect one.
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I do see First Principles as helpful for making decisions and basic living, but I see a big room for error if we use something that might be false to find something that is true.
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You can either live in doubt of everything and eventually go mad because of living in intellectual contradiction, or accept basic foundational principles that are logically sound and coherent.
You can believe whatever you want, doubt whatever you want, but that does not change that A = A and A is not non-A. In fact, it even reinforces it.