Board Thread:General Discussion/@comment-32182236-20190716014521/@comment-32182236-20190717211715

...And I just realized I didn't actually explain deductive reasoning like the title states. Just premises and conclusions.

Here's "Part 2.5" if you will.

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So, how exactly can we form conclusions from premises? By using the rules of inference.

If one statement (A) being true means another (B) must be true as well, then we say that statement A implies statement B.

If A implies B, and B implies C... A implies C.

If A implies that B is both true and false... Then A is false. Meaning that its negation (Not-A, also known as ¬A) must be true.

A negation is simply the non-truth of a statement. If premise P says "Bill is a cow", its negation is "Bill is not a cow." Likewise, if a statement says "Energy cannot be created", its negation is "Energy can be created.

Likewise, if A implies C, and B implies C... And we know that A or B is true.. Then so is C.

If A implies C, and B implies D, and A or B is true... Then C or D is true.

If A implies B, and B is false.. We can conclude that A is false as well. This is because either A is false, or B is true. (Or both.) That's what it means for A to imply B.

And, while trivial, we still need to make use of this one.. ¬¬A (not-not-A) is the same as A.

This is what we call deductive reasoning. It helps us use facts, and find more facts from it.

But it only takes us so far... And there are wrong ways to do it. These wrong ways are what we call fallacies. Which ee discuss in Part 3.