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Papers by Tony Roy
The Australasian Journal of Logic, Mar 20, 2006
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How to Prove It, 2019
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The Journal of Philosophy, 1996
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Textbook for symbolic logic, beginning at a level appropriate for beginning students, continuing ... more Textbook for symbolic logic, beginning at a level appropriate for beginning students, continuing through Godel\u27s completeness and incompleteness theorems. Excerpted from the longer text including chapter 1 and the first parts of chapters 2 - 7. From the preface: There is, I think, a gap between what many students learn in their first course in formal logic, and what they are expected to know for their second. While courses in mathematical logic with metalogical components often cast only the barest glance at mathematical induction or even the very idea of reasoning from definitions, a first course may also leave these untreated, and fail explicitly to lay down the definitions upon which the second course is based. The aim of this text is to integrate material from these courses and, in particular, to make serious mathematical logic accessible to students I teach. The first parts introduce classical symbolic logic as appropriate for beginning students; the last parts build to Göde...
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Journal of Philosophical Logic, 2009
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Nous, 2000
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Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relev... more Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relevant logic has seemed unmo-tivated to some. I set a version of relevant semantics in a context to make sense of its different elements. Suppose a view which makes room for structured properties-or related entities which combine in arbitrary ways to form structured ones. Then it may seem natural to say entailment supervenes upon the structures, so that P entails Q just when part of the condition for being p is being q. If P stands in this relation to Q, a result is that there is no possible world where P but not Q, so that P classically entails Q. But the conditions are not equivalent. For all possible worlds, but not all properties, are maximal and consistent. I suggest that relevant semantics is naturally seen as modeling entailment grounded in property structure and makes sense insofar as it reflects this fundamental and intuitive notion.
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version 7.0
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The Bloomsbury Companion to Metaphysics
This is a piece written with Tony Roy. In it we think about new sorts of problems and methods tha... more This is a piece written with Tony Roy. In it we think about new sorts of problems and methods that will arise in metaphysics. Published in The Bloomsbury Companion to Metaphysics (2015).
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Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relev... more Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relevant logic has seemed unmotivated to some. I set a version of relevant semantics in a context to make sense of its different elements. Suppose a view which makes room for structured properties — or related entities which combine in arbitrary ways to form structured ones. Then it may seem natural to say entailment supervenes upon the structures, so that P entails Q just when part of the condition for being p is being q. If P stands in this relation to Q, a result is that there is no possible world where P but not Q, so that P classically entails Q. But the conditions are not equivalent. For all possible worlds, but not all properties, are maximal and consistent. I suggest that relevant semantics is naturally seen as modeling entailment grounded in property structure and makes sense insofar as it reflects this fundamental and intuitive notion.
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The first says that there is a dot in upper box, and the second that there is a dot in lower box.... more The first says that there is a dot in upper box, and the second that there is a dot in lower box. The first is true and the second is false. What is the difference? Intuitively, the statements say something about the way things are, and what they say is true if and only if things are, in fact, that way. The first is true because things are the way it represents them to be, and the second is false because things are not the way it represents them to be. What the first says corresponds to reality, but what the second says does not; so the first is true and the second is not. Similarly, “The earth is round” is true because things are the way the statement represents them to be, and “The earth is flat” is false because things aren’t the way it represents them to be.1 And, more generally, it is natural to think that an arbitrary statement is true if and only if reality is as the statement represents it to be─if and only if what it says corresponds to reality─and false if and only if it d...
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I4 An interpretation for the basic logic DW is 〈W,N,N,R,R, h〉 where W is a set of worlds; N,N ⊆ W... more I4 An interpretation for the basic logic DW is 〈W,N,N,R,R, h〉 where W is a set of worlds; N,N ⊆ W are normal worlds for truth and non-falsity respectively; R,R ⊆ W 3 are access relations for truth and non-falsity respectively; and h is a function which assigns 1 or 0 to each /p/ at each w ∈ W . When hw(/p/) = 1 we say /p/ holds at w and otherwise fails. As a constraint on interpretations we require also,
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Bloomsbury Companion to Metaphysics, 2015
This is a piece written with Tony Roy. In it we think about new sorts of problems and methods tha... more This is a piece written with Tony Roy. In it we think about new sorts of problems and methods that will arise in metaphysics. Published in The Bloomsbury Companion to Metaphysics (2015).
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The Australasian Journal of Logic
This document collects natural derivation systems for logics described in Priest, An Introduction... more This document collects natural derivation systems for logics described in Priest, An Introduction to Non-Classical Logic [4]. It provides an alternative or supplement to the semantic tableaux of his text. Except that some chapters are collapsed, there are sections for each chapter in Priest, with an additional, final section on quantified modal logic. In each case, (i) the language is briefly described and key semantic definitions stated, (ii) the derivation system is presented with a few examples given, and (iii) soundness and completeness are proved. There should be enough detail to make the parts accessible to students would work through parallel sections of Priest.
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Philosophical Studies, 1995
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The Australasian Journal of Logic, Mar 20, 2006
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How to Prove It, 2019
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The Journal of Philosophy, 1996
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Textbook for symbolic logic, beginning at a level appropriate for beginning students, continuing ... more Textbook for symbolic logic, beginning at a level appropriate for beginning students, continuing through Godel\u27s completeness and incompleteness theorems. Excerpted from the longer text including chapter 1 and the first parts of chapters 2 - 7. From the preface: There is, I think, a gap between what many students learn in their first course in formal logic, and what they are expected to know for their second. While courses in mathematical logic with metalogical components often cast only the barest glance at mathematical induction or even the very idea of reasoning from definitions, a first course may also leave these untreated, and fail explicitly to lay down the definitions upon which the second course is based. The aim of this text is to integrate material from these courses and, in particular, to make serious mathematical logic accessible to students I teach. The first parts introduce classical symbolic logic as appropriate for beginning students; the last parts build to Göde...
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Journal of Philosophical Logic, 2009
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Nous, 2000
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Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relev... more Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relevant logic has seemed unmo-tivated to some. I set a version of relevant semantics in a context to make sense of its different elements. Suppose a view which makes room for structured properties-or related entities which combine in arbitrary ways to form structured ones. Then it may seem natural to say entailment supervenes upon the structures, so that P entails Q just when part of the condition for being p is being q. If P stands in this relation to Q, a result is that there is no possible world where P but not Q, so that P classically entails Q. But the conditions are not equivalent. For all possible worlds, but not all properties, are maximal and consistent. I suggest that relevant semantics is naturally seen as modeling entailment grounded in property structure and makes sense insofar as it reflects this fundamental and intuitive notion.
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version 7.0
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The Bloomsbury Companion to Metaphysics
This is a piece written with Tony Roy. In it we think about new sorts of problems and methods tha... more This is a piece written with Tony Roy. In it we think about new sorts of problems and methods that will arise in metaphysics. Published in The Bloomsbury Companion to Metaphysics (2015).
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Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relev... more Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relevant logic has seemed unmotivated to some. I set a version of relevant semantics in a context to make sense of its different elements. Suppose a view which makes room for structured properties — or related entities which combine in arbitrary ways to form structured ones. Then it may seem natural to say entailment supervenes upon the structures, so that P entails Q just when part of the condition for being p is being q. If P stands in this relation to Q, a result is that there is no possible world where P but not Q, so that P classically entails Q. But the conditions are not equivalent. For all possible worlds, but not all properties, are maximal and consistent. I suggest that relevant semantics is naturally seen as modeling entailment grounded in property structure and makes sense insofar as it reflects this fundamental and intuitive notion.
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The first says that there is a dot in upper box, and the second that there is a dot in lower box.... more The first says that there is a dot in upper box, and the second that there is a dot in lower box. The first is true and the second is false. What is the difference? Intuitively, the statements say something about the way things are, and what they say is true if and only if things are, in fact, that way. The first is true because things are the way it represents them to be, and the second is false because things are not the way it represents them to be. What the first says corresponds to reality, but what the second says does not; so the first is true and the second is not. Similarly, “The earth is round” is true because things are the way the statement represents them to be, and “The earth is flat” is false because things aren’t the way it represents them to be.1 And, more generally, it is natural to think that an arbitrary statement is true if and only if reality is as the statement represents it to be─if and only if what it says corresponds to reality─and false if and only if it d...
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I4 An interpretation for the basic logic DW is 〈W,N,N,R,R, h〉 where W is a set of worlds; N,N ⊆ W... more I4 An interpretation for the basic logic DW is 〈W,N,N,R,R, h〉 where W is a set of worlds; N,N ⊆ W are normal worlds for truth and non-falsity respectively; R,R ⊆ W 3 are access relations for truth and non-falsity respectively; and h is a function which assigns 1 or 0 to each /p/ at each w ∈ W . When hw(/p/) = 1 we say /p/ holds at w and otherwise fails. As a constraint on interpretations we require also,
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Bloomsbury Companion to Metaphysics, 2015
This is a piece written with Tony Roy. In it we think about new sorts of problems and methods tha... more This is a piece written with Tony Roy. In it we think about new sorts of problems and methods that will arise in metaphysics. Published in The Bloomsbury Companion to Metaphysics (2015).
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The Australasian Journal of Logic
This document collects natural derivation systems for logics described in Priest, An Introduction... more This document collects natural derivation systems for logics described in Priest, An Introduction to Non-Classical Logic [4]. It provides an alternative or supplement to the semantic tableaux of his text. Except that some chapters are collapsed, there are sections for each chapter in Priest, with an additional, final section on quantified modal logic. In each case, (i) the language is briefly described and key semantic definitions stated, (ii) the derivation system is presented with a few examples given, and (iii) soundness and completeness are proved. There should be enough detail to make the parts accessible to students would work through parallel sections of Priest.
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Philosophical Studies, 1995
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