Results 1  10
of
16
Epistemology as information theory: from Leibniz to Omega, Collapse 1
 European Computing and Philosophy Conference, Västeraas
, 2006
"... In 1686 in his Discours de métaphysique, Leibniz points out that if an arbitrarily complex theory is permitted then the notion of “theory” becomes vacuous because there is always a theory. This idea is developed in the modern theory of algorithmic information, which deals with the size of computer p ..."
Abstract

Cited by 19 (3 self)
 Add to MetaCart
In 1686 in his Discours de métaphysique, Leibniz points out that if an arbitrarily complex theory is permitted then the notion of “theory” becomes vacuous because there is always a theory. This idea is developed in the modern theory of algorithmic information, which deals with the size of computer programs and provides a new view of Gödel’s work on incompleteness and Turing’s work on uncomputability. Of particular interest is the halting probability Ω, whose bits are irreducible, i.e., maximally unknowable mathematical facts. More generally, these ideas constitute a kind of “digital philosophy ” related to recent attempts of Edward Fredkin, Stephen Wolfram and others to view the world as a giant computer. There are also connections with recent “digital physics ” speculations that the universe might actually be discrete, not continuous. This système du monde is presented as a coherent whole in my book Meta Math!, which will be published this fall.
Gödel on computability
"... Around 1950, both Gödel and Turing wrote papers for broader audiences. 1 Gödel drew in his 1951 dramatic philosophical conclusions from the general formulation of his second incompleteness theorem. These conclusions concerned the nature of mathematics and the human mind. The general formulation of t ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Around 1950, both Gödel and Turing wrote papers for broader audiences. 1 Gödel drew in his 1951 dramatic philosophical conclusions from the general formulation of his second incompleteness theorem. These conclusions concerned the nature of mathematics and the human mind. The general formulation of the second theorem was explicitly based on Turing’s 1936 reduction of finite procedures to machine computations. Turing gave in his 1954 an understated analysis of finite procedures in terms of Post production systems. This analysis, prima facie quite different from that given in 1936, served as the basis for an exposition of various unsolvable problems. Turing had addressed issues of mentality and intelligence in contemporaneous essays, the best known of which is of course Computing machinery and intelligence. Gödel’s and Turing’s considerations from this period intersect through their attempt, on the one hand, to analyze finite, mechanical procedures and, on the other hand, to approach mental phenomena in a scientific way. Neuroscience or brain science was an important component of the latter for both: Gödel’s remarks in the Gibbs Lecture as well as in his later conversations with Wang and Turing’s Intelligent Machinery can serve as clear evidence for that. 2 Both men were convinced that some mental processes are not mechanical, in the sense that Turing machines cannot mimic them. For Gödel, such processes were to be found in mathematical experience and he was led to the conclusion that mind is separate from matter. Turing simply noted that for a machine or a brain it is not enough to be converted into a universal (Turing) machine in order to become intelligent: “discipline”, the characteristic
Alan Turing and the Mathematical Objection
 Minds and Machines 13(1
, 2003
"... Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet accord ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical objection ” to his view that machines can think. Logicomathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human mathematicians presumably do. Key words: artificial intelligence, ChurchTuring thesis, computability, effective procedure, incompleteness, machine, mathematical objection, ordinal logics, Turing, undecidability The ‘skin of an onion ’ analogy is also helpful. In considering the functions of the mind or the brain we find certain operations which we can express in purely mechanical terms. This we say does not correspond to the real mind: it is a sort of skin which we must strip off if we are to find the real mind. But then in what remains, we find a further skin to be stripped off, and so on. Proceeding in this way, do we ever come to the ‘real ’ mind, or do we eventually come to the skin which has nothing in it? In the latter case, the whole mind is mechanical (Turing, 1950, p. 454–455). 1.
Is the Turing test good enough? The fallacy of resourceunbounded intelligence.
"... This goal of this paper is to defend the plausibility of the argument that passing the Turing test is a sufficient condition for the presence of intelligence. To this effect, we put forth new objections to two famous counterarguments: Searle’s ”Chinese Room ” and Block’s ”Aunt Bertha. ” We take Sea ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This goal of this paper is to defend the plausibility of the argument that passing the Turing test is a sufficient condition for the presence of intelligence. To this effect, we put forth new objections to two famous counterarguments: Searle’s ”Chinese Room ” and Block’s ”Aunt Bertha. ” We take Searle’s argument to consist of two points: 1) intelligence is not merely an ability to manipulate formal symbols; it is also the ability of relating those symbols to a multisensory realworld experience; and 2) intelligence presupposes an internal capacity for generalization. On the first point, while we concede that multisensory realworld experience is not captured by the test, we show that intuitions about the relevance of this experience to intelligence are not clearcut. Therefore, it is not obvious that the Turing test should be dismissed on this basis alone. On the second point, we strongly disagree with the notion that the test cannot distinguish a machine with internal capacity for generalization from a machine which has no such capacity. This view is best captured by Ned Block, who argues that a sufficiently large lookup table is capable of passing any Turing test of finite length. We claim that, contrary to Block’s assumption, it is impossible to construct such a table, and show that it is possible to ensure that a machine relying solely on such table will fail an appropriately constructed Turing test. 1
On Dynamical Genetic Programming: Simple Boolean Networks in Learning Classifier Systems
, 2008
"... Abstract. Many representations have been presented to enable the effective evolution of computer programs. Turing was perhaps the first to present a general scheme by which to achieve this end. Significantly, Turing proposed a form of discrete dynamical system and yet dynamical representations remai ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. Many representations have been presented to enable the effective evolution of computer programs. Turing was perhaps the first to present a general scheme by which to achieve this end. Significantly, Turing proposed a form of discrete dynamical system and yet dynamical representations remain almost unexplored within conventional genetic programming. This paper presents results from an initial investigation into using simple dynamical genetic programming representations within a Learning Classifier System. It is shown possible to evolve ensembles of dynamical Boolean function networks to solve versions of the wellknown multiplexer problem. Both synchronous and asynchronous systems are considered.
Unorganised Machines in Learning Classifier Systems
, 2008
"... Many representations have been presented to enable the effective evolution of computer programs. Turing was perhaps the first to present a general scheme by which to achieve this end. Significantly, Turing proposed a form of discrete dynamical system and yet dynamical representations remain almost ..."
Abstract
 Add to MetaCart
Many representations have been presented to enable the effective evolution of computer programs. Turing was perhaps the first to present a general scheme by which to achieve this end. Significantly, Turing proposed a form of discrete dynamical system and yet dynamical representations remain almost unexplored within genetic programming. This paper presents results from an initial investigation into using Turing’s representation ideas within a Learning Classifier System. It is shown possible to evolve ensembles of dynamical Boolean function networks to solve versions of the wellknown multiplexer problem with a modification to Turing’s original scheme.
Reduction of Logic to Arithmetic
"... Abstract: It is possible to make decisions mathematically of first order predicate calculus. A new mathematical formula is found for the solution of decision problem. We can reduce a logical algorithm into simple algorithm without logical trees. I For n number of inputs, is there any mathematical fo ..."
Abstract
 Add to MetaCart
Abstract: It is possible to make decisions mathematically of first order predicate calculus. A new mathematical formula is found for the solution of decision problem. We can reduce a logical algorithm into simple algorithm without logical trees. I For n number of inputs, is there any mathematical formula that answers yes or no?[1][2][3] Now it is possible, a mathematical formula[4] is found that can be used to reduce the logical algorithm into simple algorithm without logical trees. This converts logical operation to arithmetic operation. It is a solution for decision problem of first order predicate calculus or first order logic. Therefore in a computer