1. Might the world be a mathematical structure? My question is not: might the world have a mathematical structure, but might it be identical with one? There are two general ways of interpreting this question. If it is whether, given that mathematical structures are abstract objects, the world is an abstract object, the answer has to be negative. Think of the world as wholly concrete (space, time and the spatio-temporal denizens of the world) or as a mix of the concrete and the abstract (if we include universals, laws, propositions and the like), but whichever of these is the case, the world is not purely abstract, as a formal structure is.

One might claim, however, that the world is a structure1 in the sense...

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