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Brass Tacks
Dear John:
After eight successive readings of C. K. Bradley's truly fascinating articles on symbolic logic and paradoxes I am obsessed by the notion that the mere existence of paradoxes is a paradox in itself. To inflict you and your readers with a dreadful sentence: it appears to me illogical for logical minds to try to deal logically with the basically illogical.
Offhand I can think of nothing abstract or concrete that can be said to exist entirely as a thing-in-itself and therefore can be contemplated, so to speak, in vacuo. This applies especially to any so-called paradox which can exist as such only within its particular frame of reference. Within a framework too tight and rigid there must be distortion. My notion of illogicality derives from the philosophical convention that efforts to straighten out the distortion must be made without altering the framework.
To cite Russell's Paradox, quoted by Bradley. The framework here consists of an arbitrary ruling: "All adjectives are self-descriptive or non-self-descriptive" with the addendum that this exhausts all possible classes. The paradox: "Into which class falls the adjective 'non-self-descriptive'?" It's said to be a prize baffler. But is it? What's wrong? The paradox? Or its framework?
Brass Tacks
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