Mysticism And Logic, And Other Essays

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Now, in the beginnings, everything is self-evident ; and it is very hard to see whether one self-evident proposition follows from another or not. Obviousness is always the enemy to correctness. Hence we invent some new and difficult symbolism, in which nothing seems obvious.
Then we set up certain rules for operating on the symbols, and the whole thing becomes mechanical. In this way we find out what must be taken as premiss and what can be demonstrated or defined. For instance, the whole of |
...Arithmetic and Algebra has been shown to require three indefinable notions and five indemonstrable propositions.
But without a s5mibolism it would have been very hard to find this out. It is so obvious that two and two are four, that we can hardly make ourselves sufficiently sceptical to doubt whether it can be proved. And the same holds in other cases where self-evident things are to be proved.
But the proof of self-evident propositions may seem, to the uninitiated, a somewhat frivolous occupation.


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