From Roger Schafir
Max Tegmark’s hypothesis that mathematics is the ultimate physical reality seems to be a variant on the idea that anything which is logically possible must “exist”, in some sense of the word (15 September, p 38).
His argument appears to start from the notion that there is a dualism of logical and mathematical truth on the one hand and physical truth on the other; this dualism usually regards logical and mathematical truth as the more basic. He then seeks to abolish this dualism in the most difficult way: taking the logical/mathematical world as the real one, but without casting any light on what the nature of this entity is.
Some of us think the opposite far more likely: that logical/mathematical truth is subordinate to the physical facts of the universe.
Moreover, his hypothesis seems to require that logical/mathematical truth is a fixed thing, so that there can exist other universes in which any logically valid fact is physically true. Yet a mathematical proof depends on how symbols can be arranged along a line in our actual space, so mathematical facts might be different in a universe with different laws. This adds another difficulty to the notion that there must exist a universe in which any fact that we can mathematically derive is true.
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