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I want to study Mathematical Logic. One concept that confuses me, is that implication is equivalent to 'P or -Q'. So, I want to start from the book where this idea first started; but I'm not looking only for this idea, but also other basic ideas of Mathematical Logic.

I guess Boole's Boolean Algebra helped build Mathematical Logic. Can you give a brief explanation of how it and other ideas did (Like the previously mentioned implication definition), where they first started (in which books), and what other classic books talk about them?

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What might you have found out so far? –  Joseph Weissman Feb 25 '13 at 19:12
    
(If you really want to study mathematical logic, I suggest going to Math.SE) About your confusion: "A implicates B" = "not (A and not B)" = "not A or not (not B)" = "not P or Q". –  zaarcis Feb 26 '13 at 0:01
    
I can't help with book, but one way to look at your question is to simply consider the truth tables of both propositions and you can see that they are the same. Does that help in any way? –  Timotej Feb 26 '13 at 1:43
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I've just had a look at the Wikipedia Entry:

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

There you will find a useful overview of key ideas, protagonists and books.

Hope that helps as a starting point.

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implication is equivalent to 'P or -Q'

That is not quite precise: Material implication Q -> P is equivalent to -Q or P.

Material implication is only a very specific conception of implication, though not one that is often used in day to day language.

There are other, richer, forms of implications, such as modal implication, indicative conditional, consequential implication which tries to better capture the implication that are more commonly used in day to day language, but they cannot be represented fully using just a truth table.

Another thing you need to be aware about in Classical/Mathematical logic is the OR. In real life, people more often uses OR when they actually mean XOR. For example, the question "tea or coffee?", most people would not expect the answer "both", but in Classical/Mathematical logic, both would be a perfectly fine correct response.

I believe those two are the biggest gotcha on classical/mathematical logic.

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