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2004a), Have Your Cake and Eat It Too: The Old Principal Principle Reconciled with the New
 Philosophy and Phenomenological Research
"... Abstract. David Lewis (1980) proposed the Principal Principle (PP) and a “reformulation ” which later on he called ‘OP ’ (Old Principle). Reacting to his belief that these principles run into trouble, Lewis (1994) concluded that they should be replaced with the New Principle (NP). This conclusion le ..."
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Abstract. David Lewis (1980) proposed the Principal Principle (PP) and a “reformulation ” which later on he called ‘OP ’ (Old Principle). Reacting to his belief that these principles run into trouble, Lewis (1994) concluded that they should be replaced with the New Principle (NP). This conclusion left Lewis uneasy, because he thought that an inverse form of NP is “quite messy”, whereas an inverse form of OP, namely the simple and intuitive PP, is “the key to our concept of chance”. I argue that, even if OP should be discarded, PP need not be. Moreover, far from being messy, an inverse form of NP is a simple and intuitive Conditional Principle (CP). Finally, both PP and CP are special cases of a General Principle (GP); it follows that so are PP and NP, which are thus compatible rather than competing.
Combining Optimizations, Combining Theories
"... We consider the problem of how best to combine optimizations in imperative compilers. It is known that combined optimizations (or "superanalyses") can be strictly better than iterating separate improvement passes. We propose an explanation of why this is so by drawing connections between program an ..."
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We consider the problem of how best to combine optimizations in imperative compilers. It is known that combined optimizations (or "superanalyses") can be strictly better than iterating separate improvement passes. We propose an explanation of why this is so by drawing connections between program analysis and the algebraic and coalgebraic views of programs and processes. We argue that "optimistic" analyses decide coinductivelydefined relations and are based on bisimilarity.
Matter, Mind and Mechanics New models for dynamogenesis and rationality Synopsis of The Mechanical Foundations of Psychology and Economics
, 2000
"... The mathematical concepts of modern axiomatic rational mechanics apply more broadly than generally recognized, in that formal mechanical concepts apply directly and with slight adaptations to certain psychological and economic systems as well the familiar physical applications. These nonphysical app ..."
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The mathematical concepts of modern axiomatic rational mechanics apply more broadly than generally recognized, in that formal mechanical concepts apply directly and with slight adaptations to certain psychological and economic systems as well the familiar physical applications. These nonphysical applications provide new means for characterizing realistic notions of economic rationality and limits on reasoning abilities, translate psychology and economics into studies of new types of mechanical materials, and open traditional informal philosophical conceptions of materialism and dualism to new avenues of mathematical and experimental investigation. This semiformal article, which summarizes a detailed booklength formal treatment [13], briefly sketches modern mechanics, the adaptation of mechanical axioms to cover hybrid and discrete systems, an illustrative formalization of a representative rational psychological system from artificial intelligence, and the new perspective on psychology and economics,
EVERY COUNTABLE MODEL OF SET THEORY EMBEDS INTO ITS OWN CONSTRUCTIBLE UNIVERSE
"... Abstract. The main theorem of this article is that every countable model of set theory 〈M, ∈ M 〉, including every wellfounded model, is isomorphic to a submodel of its own constructible universe 〈L M, ∈ M 〉. In other words, there is an embedding j: M → L M that is elementary for quantifierfree a ..."
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Abstract. The main theorem of this article is that every countable model of set theory 〈M, ∈ M 〉, including every wellfounded model, is isomorphic to a submodel of its own constructible universe 〈L M, ∈ M 〉. In other words, there is an embedding j: M → L M that is elementary for quantifierfree assertions. It follows from the proof that the countable models of set theory are linearly preordered by embeddability: for any two countable models of set theory 〈M, ∈ M 〉 and 〈N, ∈ N 〉, either M is isomorphic to a submodel of N or conversely. Indeed, they are prewellordered by embeddability in ordertype exactly ω1+1. Specifically, the countable wellfounded models are ordered under embeddability exactly in accordance with the heights of their ordinals; every shorter model embeds into every taller model; every model of set theory M is universal for all countable wellfounded binary relations of rank at most Ord M; and every illfounded model of set theory is universal for all countable acyclic binary relations. Finally, strengthening a classical theorem of Ressayre, the same proof method shows that if M is any nonstandard model of PA, then every countable model of set theory—in particular, every model of ZFC plus large cardinals—is isomorphic to a submodel of the hereditarily finite sets 〈HF M, ∈ M 〉 of M. Indeed, 〈HF M, ∈ M 〉 is universal for all countable acyclic binary relations. 1.