15th Mar 2014, 5:47 AM

To write it in expanded formal logic, instead of the alternate form we used above of ~ [ ( P → Q ) → ( Q → P ) ], the fallacious argument would go:

P: It is raining.

Q: Someone is wet.

1. ( P → Q ) / This is our initial assumption.

2. Q / Mike sees Gib is wet.

Therefore, P!

But this last step doesn't work! Our initial assumption is that IF it rains, THEN someone is wet. Someone being wet necessarily follows that it's raining in our system (check "modus ponens" if you are interested in finding out more), but it DOES NOT mean that someone being wet causes it to be raining (“I spilled a cup of water on myself, must be raining”). That would be asserting Q → P, which is different then what we assumed and additionally doesn’t correspond with reality (making it a faulty premise).

These logical rules are somewhat arbitrary, as they are defined in respect to a very specific system. But regardless, this example might illustrate it. Suppose we know that in every known instance of raining, people get wet. But someone could be taking a shower, or getting pelted by temporally inappropriate sprinklers, getting wet without it having rained. So if someone is wet, all we know is that it MIGHT have rained, but there are an infinite number of alternative possibilities that could cause Gib to be wet.

As you can see, logic is an excellent way to make the world a more complicated place! That's why I like it. More seriously, people sometimes misunderstand what logic means. All logic does is tell you what MUST happen, based on (the important part) your initial assumptions. As long as you have different initial assumptions than another person, no amount of logic will bring you closer together. Faulty premises will get you nowhere even in a perfect logical system. Hence, the pointlessness of atheist/theist debates. Neither side can possibly convince the other, since they disagree on extremely different metaphysical assumptions in the first place. We need more people like David Hume in the world.

But logic remains a useful tool for determining the validity of arguments, and identifying fallacies. Which is rather important on its own, since many political "moves" rely on deliberately making a fallacious argument and having it slip past unnoticed. And of course, with sufficiently advanced logic, you can spend 30 minutes or so to construct the axiomatic system of addition, and then another 30 minutes to prove 2+3=5! Practical applications abound.

I'm really liking the photo textures you're incorporating.