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Knowledge, understanding, and computational complexity
 In
, 1997
"... Searle’s arguments that intelligence cannot arise from formal programs are refuted by arguing that his analogies and thoughtexperiments are fundamentally flawed: he imagines a world in which computation is free. It is argued instead that although cognition may in principle be realized by symbol pr ..."
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Searle’s arguments that intelligence cannot arise from formal programs are refuted by arguing that his analogies and thoughtexperiments are fundamentally flawed: he imagines a world in which computation is free. It is argued instead that although cognition may in principle be realized by symbol processing machines, such a computation is likely to have resource requirements that would prevent a symbol processing program for cognition from being designed, implemented, or executed. In the course of the argument the following observations are made: (1) A system can have knowledge, but no understanding. (2) Understanding is a method by which cognitive computations are carried out with limited resources. (3) Introspection is inadequate for analyzing the mind. (4) Simulation of the brain by a computer is unlikely not because of the massive computational power of the brain, but because of the overhead required when one model of computation is simulated by another. (5) Intentionality is a property that arises from systems of sufficient computational power that have the appropriate design. (6) Models of cognition can be developed in direct analogy with technical results from the field of computational complexity theory. Penrose [30] has stated... I am inclined to think (though, no doubt, on quite inadequate grounds) that unlike the basic question of computability itself, the issues of complexity theory are not quite the central ones in relation to mental phenomena. On the contrary, I intend to demonstrate that the principles of computational complexity theory can give insights into cognition. In 1980, Searle [36] published a critique of Artificial Intelligence that almost immediately caused a flurry of debate and commentary in academic circles. The paper distinguishes
Modélisation de la démarche du décideur politique dans la perspective de l’intelligence artificielle
, 1996
"... ..."
A Reflection on Russell's Ramified Types and Kripke's Hierarchy of Truths
 Journal of the Interest Group in Pure and Applied Logic 4(2
, 1996
"... Both in Kripke's Theory of Truth ktt [8] and Russell's Ramified Type Theory rtt [16, 9] we are confronted with some hierarchy. In rtt, we have a double hierarchy of orders and types. That is, the class of propositions is divided into different orders where a propositional function can only ..."
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Both in Kripke's Theory of Truth ktt [8] and Russell's Ramified Type Theory rtt [16, 9] we are confronted with some hierarchy. In rtt, we have a double hierarchy of orders and types. That is, the class of propositions is divided into different orders where a propositional function can only depend on objects of lower orders and types. Kripke on the other hand, has a ladder of languages where the truth of a proposition in language Ln can only be made in Lm where m ? n. Kripke finds a fixed point for his hierarchy (something Russell does not attempt to do). We investigate in this paper the similarities of both hierarchies: At level n of ktt the truth or falsehood of all ordernpropositions of rtt can be established. Moreover, there are ordernpropositions that get a truth value at an earlier stage in ktt. Furthermore, we show that rtt is more restrictive than ktt, as some type restrictions are not needed in ktt and more formulas can be expressed in the latter. Looking back at the dou...
A Re ection on Russell's Ramied Types and Kripke's Hierarchy of Truths
"... Both in Kripke's Theory of Truth ktt [8] and Russell's Ramied Type Theory rtt [16, 9] we are confronted with some hierarchy. In rtt, we have a double hierarchy of orders and types. That is, the class of propositions is divided into dierent orders where a propositional function can only dep ..."
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Both in Kripke's Theory of Truth ktt [8] and Russell's Ramied Type Theory rtt [16, 9] we are confronted with some hierarchy. In rtt, we have a double hierarchy of orders and types. That is, the class of propositions is divided into dierent orders where a propositional function can only depend on objects of lower orders and types. Kripke on the other hand, has a ladder of languages where the truth of a proposition in language L n can only be made in L m where min. Kripke nds a xed point for his hierarchy (something Russell does not attempt to do). We investigate in this paper the similarities of both hierarchies: At level n of ktt the truth or falsehood of all ordernpropositions of rtt can be established. Moreover, there are ordernpropositions that get a truth value at an earlier stage in ktt. Furthermore, we show that rtt is more restrictive than ktt, as some type restrictions are not needed in ktt and more formulas can be expressed in the latter. Looking back at the double hierarchy of Russell, Ramsey [11], and Hilbert and Ackermann [7] considered the orders to cause the restrictiveness, and therefore removed them. This removal resulted in Church's Simple Type Theory stt [1]. We show however that orders in rtt correspond to levels of truth in ktt. Hence, ktt can be regarded as the dual of stt where types have been removed and orders are maintained. As rtt is more restrictive than ktt, we can conclude that it is the combination of types and orders that was the restrictive factor in rtt.