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This is starting to get too philosophical. I've come to realise that there is no way with which I can answer this problem satisfactoraly.
I can't get away from circular reasonig, but I have concluded that it may perhaps be impossible to define the infrastructure of mathematics in a non self-referencing manner. I'm not allowed to use logic to explain what it is for something to be logic. Can you at least see how that very act is necesary and yet at the same time is self-referencing?? Any valid argument must substantiate its claim with a logical backing. How can I argue what logic is by using my own logical intuition....?? Circular reasoning is almost inevitable in this argument and therefore I cannot push on any further in forging ever more clever arguments to back up my point.....I don't even know what my point is at this point. My previous school of thought must simply be invalid. |
