Here's an example that contradicts one of the laws of logic (and remember, most of the laws of logic were developed before Einstein):
The law of non contradition states that any proposition is false that states that something is both 'A' and 'not A' at the same time and in the same respect.
Take a one meter yardstick. Now consider two people viewing it. One is stationary relative to the yardstick, the other travelling vertically at near the speed of light. To observer # 1, the yardstick appears one meter long. To observer #2, the yardstick appears two meters long. In fact, appears is the wrong word to use-- they yardstick IS two different lengths at one and the same time. The physics of it is sound. The principle of non-contradiction has been shown fallacious because it does not take perspective into account. The yardstick is both one and two meters long at the same time and in the same respect (length).
Why am i citing this example? To show that when logic and concepts are simply assumed to be true, without any empirical evidence, you get caught going down intellectual pathways that are long, complicated and usually both sterile and fallacious. In Wittgenstein's words, its 'just metaphysics'. There is no sound reason to believe in the 'validity' or whatever you call it of such proofs, just as there is, similarly, no sound reason to believe in God.
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