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Informationtheoretic Limitations of Formal Systems
 JOURNAL OF THE ACM
, 1974
"... An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these ..."
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An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the axioms.
Spacetime the one substance
, 2009
"... Abstract What is the relation between material objects and spacetime regions? Supposing that spacetime regions are one sort of substance, there remains the question of whether or not material objects are a second sort of substance. This is the question of dualistic versus monistic substantivalism. I ..."
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Abstract What is the relation between material objects and spacetime regions? Supposing that spacetime regions are one sort of substance, there remains the question of whether or not material objects are a second sort of substance. This is the question of dualistic versus monistic substantivalism. I will defend the monistic view. In particular, I will maintain that material objects should be identified with spacetime regions. There is the spacetime manifold, and the fundamental properties are pinned directly to it. Keywords Spacetime Substantivalism Supersubstantivalism Monism ‘‘Space and Time, so far from being the least selfsubsistent of things, are in truth in their indissoluble union the ultimate reality in its simplest and barest terms;…’’ (Alexander 1950, p. 233) 1 Substantivalisms, dualistic and monistic What is the relation between material objects and spacetime regions? I will be presupposing that spacetime regions are one sort of substance, and posing the question of whether to think of material objects as a second sort of substance. But first I should clarify the presupposition and the question. What I am presupposing is that spacetime regions are one sort of substance, where a substance is a fundamental entity. A fundamental entity is basic, ultimate, and irreducible. It is not dependent on, grounded in, or derivative from anything