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An introduction to substructural logics
, 2000
"... Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1 ..."
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Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1
Continuity and the Logic of Perception by
"... following observation: If we imagine a chessboard with alternate blue and red squares, then this is something in which the individual red and blue areas allow themselves to be distinguished from each other in juxtaposition, and something similar holds also if we imagine each of the squares divided ..."
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following observation: If we imagine a chessboard with alternate blue and red squares, then this is something in which the individual red and blue areas allow themselves to be distinguished from each other in juxtaposition, and something similar holds also if we imagine each of the squares divided into four smaller squares also alternating between these two colours. If, however, we were to continue with such divisions until we had exceeded the boundary of noticeability for the individual small squares which result, then it would no longer be possible to apprehend the individual red and blue areas in their respective positions. But would we then see nothing at all? Not in the least; rather we would see the whole chessboard as violet, i.e. apprehend it as something that participates simultaneously in red and blue. In this paper I will describe a simple and natural framework—a logic of perception—in which this “simultaneous participation ” or superposition of
Is Quantum Logic a Logic
 Handbook of Quantum Logic and Quantum Structures, volume Quantum Logic
, 2008
"... Is a Quantum Logic a Logic? [1] in which they strengthen a previous negative ..."
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Is a Quantum Logic a Logic? [1] in which they strengthen a previous negative
Losing Your Marbles in
, 1999
"... Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Ghirardi, Rimini, and Weber [1986]) can only solve the problem of wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues tha ..."
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Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Ghirardi, Rimini, and Weber [1986]) can only solve the problem of wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues that the GRW theory must violate the enumeration principle: that ‘if marble 1 is in the box and marble 2 is in the box and so on through marble n, then all n marbles are in the box ’ ([1997], p. 321). Ghirardi and Bassi ([1999]) have replied that it is meaningless to say that the enumeration principle is violated because the wavefunction Lewis uses to exhibit the violation cannot persist, according to the GRW theory, for more than a split second ([1999], p. 709). On the contrary, we argue that Lewis’s argument survives Ghirardi and Bassi’s criticism unscathed. We then go on to show that, while the enumeration principle can fail in the GRW theory, the theory itself guarantees that the principle can never be empirically falsified, leaving the applicability of arithmetical reasoning to both micro and macroscopic objects intact.
Costing NonClassical Solutions to the Paradoxes of SelfReference
, 1998
"... naive T scheme, to the effect that T hAi $ A where hi is some nameforming functor, taking propositions to names, and where $ is some form of biconditional. This scheme says, in effect, that T hAi is true under the same circumstances as A. To say that A is true, is saying no more and no less ..."
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naive T scheme, to the effect that T hAi $ A where hi is some nameforming functor, taking propositions to names, and where $ is some form of biconditional. This scheme says, in effect, that T hAi is true under the same circumstances as A. To say that A is true, is saying no more and no less than saying A. 1 Not only do we keep the naive T scheme, but we ensure that our language has a degree of selfreference. As a result, we can express sentences such as the liar: "This very sentence is not true." If the language in question is a natural language, then indexicals will do the trick. If the language is a formal language 1 This is rather naive, of course, for more must be said about propositions. If we take the bearers of truth to be<F49.6
Paraconsistency Everywhere
, 2002
"... logic, inconsistencies need not entail everything. However, there is more than one way a body of information can be inconsistent. In this paper I distinguish contradictions from other inconsistencies, and I show that many different logics are in an important sense, “paraconsistent ” in virtue of bei ..."
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logic, inconsistencies need not entail everything. However, there is more than one way a body of information can be inconsistent. In this paper I distinguish contradictions from other inconsistencies, and I show that many different logics are in an important sense, “paraconsistent ” in virtue of being inconsistency tolerant without thereby being contradiction tolerant. For example, even though no inconsistencies are tolerated by intuitionistic propositional logic, some inconsistencies are tolerated by intuitionistic predicate logic. In this way, intuitionistic predicate logic is, in a mild sense, paraconsistent. So too are orthologic and quantum propositional logic, and other formal systems. Given this fact, a widespread view— that traditional paraconsistent logics are especially repugnant because they countenance inconsistencies—is undercut. Many wellunderstood nonclassical logics countenance inconsistencies as well. “Paraconsistent ” means “beyond the consistent ” [3, 15]. Paraconsistent logics tolerate inconsistencies in a way that traditional logics do not. In a paraconsistent logic, the inference of explosion A, ∼A ⊢ B
Printed in the United States of America and the laws of physics * Abstract can be found on page 705.
"... peror] I attempt to put forward a point of view (which I believe to be new) concerning the nature of the physics that might underlie conscious thought processes. As part of my argument, I point out that there could well be room, within physical laws, for an action that is not algorithmic i.e., that ..."
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peror] I attempt to put forward a point of view (which I believe to be new) concerning the nature of the physics that might underlie conscious thought processes. As part of my argument, I point out that there could well be room, within physical laws, for an action that is not algorithmic i.e., that cannot be properly simulated by any computer though I argue that it is likely that such nonalgorithmic action can arise only in an area of physics where there is an important gap in our present physical understanding: the noman'sland between quantum and classical physics. (Mathematical processes of a nonalgorithmic kind certainly do exist, but the question I am raising is whether such processes have a role to play in physics.) I also argue that there is good evidence that conscious thinking is itself not an algorithmic activity, and