This paper shows that a collection of modal relevant logics are conservatively extended by the ad... more This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.
This proof would not be well received. But it is valid, in fact sound, on the classical logicians... more This proof would not be well received. But it is valid, in fact sound, on the classical logicians' definition. The premise cannot be true in any possible circumstance in which the conclusion is false. For the conclusion is necessarily true. And the premise is true. Thus the argument ...
英文摘要Notoriously, in Theory of Knowledge Russell postulates logical forms as objects. Several auth... more 英文摘要Notoriously, in Theory of Knowledge Russell postulates logical forms as objects. Several authors have examined Russell's reification of forms from the point of view of their role in the multiple relation theory of judgment. But logical forms are also supposed to play ...
The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Mey... more The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Meyer semantics, can be given without using the Routley star operator to treat negation. In the resulting semantics, negation is treated implicationally. It is shown that, by ...
Σ h (length (In))< ε. Kaufman proved that for any h as above, any closed M0-set has a ... more Σ h (length (In))< ε. Kaufman proved that for any h as above, any closed M0-set has a closed subset which is an M0-set of Hausdorff h-measure 0. He asked whether the same result holds for M-sets. In the first paper under review, the authors provide a negative answer. ...
This paper shows that a collection of modal relevant logics are conservatively extended by the ad... more This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.
This proof would not be well received. But it is valid, in fact sound, on the classical logicians... more This proof would not be well received. But it is valid, in fact sound, on the classical logicians' definition. The premise cannot be true in any possible circumstance in which the conclusion is false. For the conclusion is necessarily true. And the premise is true. Thus the argument ...
英文摘要Notoriously, in Theory of Knowledge Russell postulates logical forms as objects. Several auth... more 英文摘要Notoriously, in Theory of Knowledge Russell postulates logical forms as objects. Several authors have examined Russell's reification of forms from the point of view of their role in the multiple relation theory of judgment. But logical forms are also supposed to play ...
The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Mey... more The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Meyer semantics, can be given without using the Routley star operator to treat negation. In the resulting semantics, negation is treated implicationally. It is shown that, by ...
Σ h (length (In))< ε. Kaufman proved that for any h as above, any closed M0-set has a ... more Σ h (length (In))< ε. Kaufman proved that for any h as above, any closed M0-set has a closed subset which is an M0-set of Hausdorff h-measure 0. He asked whether the same result holds for M-sets. In the first paper under review, the authors provide a negative answer. ...
This paper sets out a probabilist theory of logic revision and discusses some of its consequences... more This paper sets out a probabilist theory of logic revision and discusses some of its consequences and the philosophical challenges that if faces. The probability theory is semantic. It is built upon a model for a very weak logic (the logic of bounded lattices) but that has sub-models for a wide variety of other logical systems – modal logics, relevant logics, linear logics, other substructural logics, fuzzy logic, and so on. The probability theory used is itself non-classical, although in those regions of the model in which classical logic holds probabilities act classically. Suggestions are made as to the treatments of debate and negotiation about logical rules and about the problems of logical omniscience and the apriority of logic.
This paper is dedicated to Peter Schotch. During the year I spent at Dalhousie in the early 1990s... more This paper is dedicated to Peter Schotch. During the year I spent at Dalhousie in the early 1990s, Peter was going through an S1 phase. During that year, and afterwards, I spent many hours discussing possible semantics for S1 with Peter. This was also my first introduction to the philosophy of logic of C.I. Lewis. I found Peter's thoughts on this topic, as on all topics in logic and philosophy, full of interesting ideas, only some of which I really understood at the time. More recently, Peter and I have engaged in a discussion about Lewis's notion of entailment. This paper presents my side of that conversation.
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