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Showing posts with label law of non-contradiction. Show all posts
Showing posts with label law of non-contradiction. Show all posts

## Thursday, May 23, 2013

### Discovering the Philosopher in You Part 4: Logic: What Is Valid Reasoning?

I'm sorry for such a long time between entries!  If you're following my series, or my blog in general, the last entry was on the nature of truth.  This lecture/entry is on logic and reasoning.  There's a few courses available on this topic available at Coursera.org.  As we've been discussion truth is objective in relation to reality, or as Prof McGinn says, "Beliefs are true or false; reasoning is valid or invalid."  So here we are discussion logic in relation to validity NOT truth/falsehood. The best classical example comes from Aristotle, All men are mortal; Socrates is a man; therefore, Socrates is mortal.  The thing I like (and hate at the same time) about logic is the way it can be expressed somewhat mathematically.  The problem comes in knowing what the symbols mean.  I learned about this use of symbols in a class on logic but I haven't really gotten the hang of how to use all the symbols.  This simple lecture from Prof McGinn doesn't really go into all that but I feel it's worth mentioning here.  That classical example would be written something like:

∀ P ⇒ Q     All Ps are Q               All men are mortal
A ⇒ P        A is a P                      Aristotle is a man
∴ A ⇒ Q      Therefore, A is Q    Therefore Aristotle is mortal

If everything of a group has a certain property, then every particular part of that group also has that property.  Also, if one particular thing has a property, then something has that property.  I know it sounds silly and basic, but that's the way it's supposed to be.  Logic, for the most part, is straightforward and basic.

While Prof McGinn doesn't go over that symbolic logic, he does cover the three main classical laws of logic.  As I understand it, they were codified by Aristotle and the lectures refer to them as, "three traditional laws of logic: the law of identity, the law of excluded middle, and the law of noncontradiction."  I don't necessarily agree with this idea as common sensical as it seems, but Prof McGinn says that these laws of logic are inescapable and the even the concept of a universe where these rules don't hold true is inconceivable (you keep using that word, I don't think it means what you think it means).  The book, Gödel, Escher, Bach: An Eternal Golden Braid seems to say that "kōans (公案)" are examples of mankind's ability to step outside this idea that logic is inescapable.  I don't completely agree with everything that book says but it seems that is the case.  One of problems I have is these sayings are just that, sayings.  They may indicate that mankind can think illogically, but that doesn't mean one can escape the rules of logic.

Take the law of identity, everything is identical to itself.  It seems to me that it's possible to conceive of a place where that isn't the case.  But, just because one can conceive it doesn't mean one can actually go to such a place or make something that doesn't follow that law.  Or the law of excluded middle, which says that everything has a given property or it lacks it.  Or the law of non-contradiction, which says that nothing can have a given property and not have the same property at the same time.  So, we can conceive of things that don't follow these laws, but we can't actually make things or find things that don't follow said laws.

 Now that's a snake