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On Founding the Theory of Algorithms
, 1998
"... machines and implementations The first definition of an abstract machine was given by Turing, in the classic [20]. Without repeating here the wellknown definition (e.g., see [6]), 13 we recall that each Turing machine M is equipped with a "semiinfinite tape" which it uses both to comp ..."
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Cited by 12 (4 self)
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machines and implementations The first definition of an abstract machine was given by Turing, in the classic [20]. Without repeating here the wellknown definition (e.g., see [6]), 13 we recall that each Turing machine M is equipped with a "semiinfinite tape" which it uses both to compute and also to communicate with its environment: To determine the value f(n) (if any) of the partial function 14 f : N * N computed by M , we put n on the tape in some standard way, e.g., by placing n + 1 consecutive 1s at its beginning; we start the machine in some specified, initial, internal state q 0 and looking at the leftmost end of the tape; and we wait until the machine stops (if it does), at which time the value f(n) can be read off the tape, by counting the successive 1s at the left end. Turing argued that the numbertheoretic functions which can (in principle) be computed by any deterministic, physical device are exactly those which can be computed by a Turing machine, and the correspon...
All the existences that there are
, 2012
"... In this paper, I will defend the claim that there are three existence properties: the secondorder property of being instantiated, a substantive firstorder property (or better a group of such properties) and a formal, hence universal, firstorder property. I will first try to show what these proper ..."
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In this paper, I will defend the claim that there are three existence properties: the secondorder property of being instantiated, a substantive firstorder property (or better a group of such properties) and a formal, hence universal, firstorder property. I will first try to show what these properties are and why we need all of them for ontological purposes. Moreover, I will try to show why a Meinonglike option that positively endorses both the former and the latter firstorder property is the correct view in ontology. Finally, I will add some methodological remarks as to why this debate has to be articulated from the point of view of reality, i.e., by speaking of properties, rather than from the point of view of language, i.e., by speaking of predicates (for such properties).
On Founding the Theory of Algorithms
, 1998
"... machines and implementations The first definition of an abstract machine was given by Turing, in the classic [20]. Without repeating here the wellknown definition (e.g., see [6]), we recall that each Turing machine M is equipped with a "semiinfinite tape" which it uses both to comput ..."
Abstract
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machines and implementations The first definition of an abstract machine was given by Turing, in the classic [20]. Without repeating here the wellknown definition (e.g., see [6]), we recall that each Turing machine M is equipped with a "semiinfinite tape" which it uses both to compute and also to communicate with its environment: To determine the value f(n) (if any) of the partial function f : N * N computed by M , we put n on the tape in some standard way, e.g., by placing n + 1 consecutive 1s at its beginning; we start the machine in some specified, initial, internal state q 0 and looking at the leftmost end of the tape; and we wait until the machine stops (if it does), at which time the value f(n) can be read off the tape, by counting the successive 1s at the left end. Turing argued that the numbertheoretic functions which can (in principle) be computed by any deterministic, physical device are exactly those which can be computed by a Turing machine, and the corresponding version of this claim for partial functions has come to be known as the ChurchTuring Thesis, because an equivalent claim was made by Church at about the same time. Turing's brilliant analysis of "mechanical computation" in [20] and a huge body of work in the last sixty years has established the truth of the ChurchTuring Thesis beyond reasonable doubt; it is of immense importance in the derivation of foundationally significant undecidability results from technical theorems about Turing machines, and it has been called "the first natural law of pure mathematics." Turing machines capture the notion of mechanical computability of numbertheoretic functions, by the ChurchTuring Thesis, but they do not model faith It has also been suggested that we do not need algorithms, only the equival...
Moschovakis' Notion Of Meaning As Applied To Linguistics
, 2002
"... this paper we deal only with the case where fluents do not to contain predicates from the event calculus, so that we need not use the program for the truth predicate ..."
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this paper we deal only with the case where fluents do not to contain predicates from the event calculus, so that we need not use the program for the truth predicate