Dov M. Gabbay and Larisa Maksimova
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This book focuses on interpolation and definability. This notion is not only central in pure logic, but has significant meaning and applicability in all areas where logic itself is applied, ...
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This book focuses on interpolation and definability. This notion is not only central in pure logic, but has significant meaning and applicability in all areas where logic itself is applied, especially in computer science, artificial intelligence, logic programming, philosophy of science, and natural language. The book provides basic knowledge on interpolation and definability in logic, and contains a systematic account of material which has been presented in many papers. A variety of methods and results are presented beginning with the famous Beth's and Craig's theorems in classical predicate logic (1953-57), and to the most valuable achievements in non-classical topics on logic, mainly intuitionistic and modal logic. Together with semantical and proof-theoretic methods, close interrelations between logic and universal algebra are established and exploited.Less
This book focuses on interpolation and definability. This notion is not only central in pure logic, but has significant meaning and applicability in all areas where logic itself is applied, especially in computer science, artificial intelligence, logic programming, philosophy of science, and natural language. The book provides basic knowledge on interpolation and definability in logic, and contains a systematic account of material which has been presented in many papers. A variety of methods and results are presented beginning with the famous Beth's and Craig's theorems in classical predicate logic (1953-57), and to the most valuable achievements in non-classical topics on logic, mainly intuitionistic and modal logic. Together with semantical and proof-theoretic methods, close interrelations between logic and universal algebra are established and exploited.
Nino B. Cocchiarella and Max A. Freund
- Published in print:
- 2008
- Published Online:
- October 2011
- ISBN:
- 9780195366587
- eISBN:
- 9780199851898
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195366587.001.0001
- Subject:
- Philosophy, Philosophy of Language
In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision, and philosophical insight. All of the S1-S5 modal logics of ...
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In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision, and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general.Less
In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision, and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general.
Quentin Smith (ed.)
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199264933
- eISBN:
- 9780191718472
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199264933.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology
This book offers a view of the current state of play in epistemology in the form of twelve chapters by some of the philosophers who have most influenced the course of debates in recent years. Topics ...
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This book offers a view of the current state of play in epistemology in the form of twelve chapters by some of the philosophers who have most influenced the course of debates in recent years. Topics include epistemic justification, solipsism, scepticism, and modal, moral, naturalistic, and probabilistic epistemology. Such approaches as reliabilism, evidentialism, infinitism, and virtue epistemology are here developed further by the philosophers who pioneered them.Less
This book offers a view of the current state of play in epistemology in the form of twelve chapters by some of the philosophers who have most influenced the course of debates in recent years. Topics include epistemic justification, solipsism, scepticism, and modal, moral, naturalistic, and probabilistic epistemology. Such approaches as reliabilism, evidentialism, infinitism, and virtue epistemology are here developed further by the philosophers who pioneered them.
Quentin Smith
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199264933
- eISBN:
- 9780191718472
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199264933.003.0001
- Subject:
- Philosophy, Metaphysics/Epistemology
This introductory chapter presents an overview of the different topics discussed in the subsequent chapters. These include process reliabilism, evidentialism, viral epistemology, anti-luminosity ...
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This introductory chapter presents an overview of the different topics discussed in the subsequent chapters. These include process reliabilism, evidentialism, viral epistemology, anti-luminosity argument, and modal epistemology.Less
This introductory chapter presents an overview of the different topics discussed in the subsequent chapters. These include process reliabilism, evidentialism, viral epistemology, anti-luminosity argument, and modal epistemology.
Charles S. Chihara
- Published in print:
- 2001
- Published Online:
- October 2011
- ISBN:
- 9780199246557
- eISBN:
- 9780191697609
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199246557.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology
This book gives a critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world — the universe in which we live — is just one. The ...
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This book gives a critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world — the universe in which we live — is just one. The striking success of possible-worlds semantics in modal logic has made this ontological doctrine attractive. Modal realists maintain that philosophers must accept the existence of possible worlds if they wish to have the benefit of using possible-worlds semantics to assess modal arguments and explain modal principles. The book challenges this claim, and argues instead for modality without worlds; it offers a new account of the role of interpretations or structures of the formal languages of logic.Less
This book gives a critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world — the universe in which we live — is just one. The striking success of possible-worlds semantics in modal logic has made this ontological doctrine attractive. Modal realists maintain that philosophers must accept the existence of possible worlds if they wish to have the benefit of using possible-worlds semantics to assess modal arguments and explain modal principles. The book challenges this claim, and argues instead for modality without worlds; it offers a new account of the role of interpretations or structures of the formal languages of logic.
Bob Hale and Aviv Hoffmann (eds)
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199565818
- eISBN:
- 9780191722004
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199565818.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics
The philosophy of modality investigates necessity and possibility, and related notions — are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be ...
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The philosophy of modality investigates necessity and possibility, and related notions — are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This book presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the chapters address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal logic and its relations to necessary existence and to counterfactual reasoning. The general introduction locates the individual contributions in the wider context of the contemporary discussion of the metaphysics and epistemology of modality.Less
The philosophy of modality investigates necessity and possibility, and related notions — are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This book presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the chapters address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal logic and its relations to necessary existence and to counterfactual reasoning. The general introduction locates the individual contributions in the wider context of the contemporary discussion of the metaphysics and epistemology of modality.
Arthur Prior
- Published in print:
- 1967
- Published Online:
- October 2011
- ISBN:
- 9780198243113
- eISBN:
- 9780191680632
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198243113.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics
This book is a sequel to Time and Modality. Many problems raised in that book have been resolved, and new ones have been raised in their turn. The author has recorded some of these developments, and ...
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This book is a sequel to Time and Modality. Many problems raised in that book have been resolved, and new ones have been raised in their turn. The author has recorded some of these developments, and carried on with some further ones. The book is self-contained, presupposing nothing but a few facts, mostly about the better-known systems of modal logic, which can easily be found in the literature. Topics discussed include the precursors of tense-logic, the Diodorean modal system, topology of time, non-standard tense-logics, the logic of successive world-states, metric tense-logic, time, determinism, and existence.Less
This book is a sequel to Time and Modality. Many problems raised in that book have been resolved, and new ones have been raised in their turn. The author has recorded some of these developments, and carried on with some further ones. The book is self-contained, presupposing nothing but a few facts, mostly about the better-known systems of modal logic, which can easily be found in the literature. Topics discussed include the precursors of tense-logic, the Diodorean modal system, topology of time, non-standard tense-logics, the logic of successive world-states, metric tense-logic, time, determinism, and existence.
Jacob Rosen and Marko Malink
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199644384
- eISBN:
- 9780191743344
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199644384.003.0006
- Subject:
- Philosophy, Ancient Philosophy
In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can ...
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In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can be inferred that B is possible. Aristotle is the first philosopher known to state this rule, and it stands among his most significant contributions to philosophical thought about modality. He applies the possibility rule in arguments that are central to his physical and metaphysical views, in works such as the Physics, De caelo, De generationeetcorruptione, and the Metaphysics. These arguments have proved difficult to understand, largely because the exact nature of the possibility rule and its role in each argument is often unclear. The chapter offers a comprehensive treatment of the arguments throughout Aristotle's works, resulting in a better understanding both of the possibility rule and of the individual arguments in which it appears.Less
In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can be inferred that B is possible. Aristotle is the first philosopher known to state this rule, and it stands among his most significant contributions to philosophical thought about modality. He applies the possibility rule in arguments that are central to his physical and metaphysical views, in works such as the Physics, De caelo, De generationeetcorruptione, and the Metaphysics. These arguments have proved difficult to understand, largely because the exact nature of the possibility rule and its role in each argument is often unclear. The chapter offers a comprehensive treatment of the arguments throughout Aristotle's works, resulting in a better understanding both of the possibility rule and of the individual arguments in which it appears.
David Lewis
- Published in print:
- 1983
- Published Online:
- November 2003
- ISBN:
- 9780195032048
- eISBN:
- 9780199833382
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195032047.001.0001
- Subject:
- Philosophy, General
This book contains 15 papers by the influential American philosopher, David Lewis. All previously published (between 1966 and 80), these papers are divided into three groups: ontology, the philosophy ...
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This book contains 15 papers by the influential American philosopher, David Lewis. All previously published (between 1966 and 80), these papers are divided into three groups: ontology, the philosophy of mind, and the philosophy of language. Lewis supplements eight of the fifteen papers with postscripts in which he amends claims, answers objections, and introduces later reflections. Topics discussed include possible worlds, counterpart theory, modality, personal identity, radical interpretation, language, propositional attitudes, the mind, and intensional semantics. Among the positions Lewis defends are modal realism, materialism, socially contextualized formal semantics, and functionalism of the mind. The volume begins with an introduction in which Lewis discusses his philosophical method.Less
This book contains 15 papers by the influential American philosopher, David Lewis. All previously published (between 1966 and 80), these papers are divided into three groups: ontology, the philosophy of mind, and the philosophy of language. Lewis supplements eight of the fifteen papers with postscripts in which he amends claims, answers objections, and introduces later reflections. Topics discussed include possible worlds, counterpart theory, modality, personal identity, radical interpretation, language, propositional attitudes, the mind, and intensional semantics. Among the positions Lewis defends are modal realism, materialism, socially contextualized formal semantics, and functionalism of the mind. The volume begins with an introduction in which Lewis discusses his philosophical method.
Sarah Waterlow
- Published in print:
- 1982
- Published Online:
- October 2011
- ISBN:
- 9780198246565
- eISBN:
- 9780191681011
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198246565.003.0008
- Subject:
- Philosophy, Ancient Philosophy, Metaphysics/Epistemology
This chapter argues that the charge that Aristotle merges modal with extensional concepts is baseless. His doctrines A' and B' link possibility and necessity with realization at some and at all ...
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This chapter argues that the charge that Aristotle merges modal with extensional concepts is baseless. His doctrines A' and B' link possibility and necessity with realization at some and at all times. Correctly interpreted, these propositions support the opposite view: that for him, these connections are syntheses of irreducibly different concepts. There is his temporalized approach to modality, where possibility is seen as relative to an actual state of affairs in the history of the universe. Time has a bearing here, since the possibility itself belongs at the time, as would the realization should it occur. The discussion argues that this is his only conception of possibility. A' and B' in the versions considered here depend on the non-formal assumptions cogent only in the archaic context of Aristotle's organic metaphysics of substance.Less
This chapter argues that the charge that Aristotle merges modal with extensional concepts is baseless. His doctrines A' and B' link possibility and necessity with realization at some and at all times. Correctly interpreted, these propositions support the opposite view: that for him, these connections are syntheses of irreducibly different concepts. There is his temporalized approach to modality, where possibility is seen as relative to an actual state of affairs in the history of the universe. Time has a bearing here, since the possibility itself belongs at the time, as would the realization should it occur. The discussion argues that this is his only conception of possibility. A' and B' in the versions considered here depend on the non-formal assumptions cogent only in the archaic context of Aristotle's organic metaphysics of substance.
Trenton Merricks
- Published in print:
- 2007
- Published Online:
- May 2007
- ISBN:
- 9780199205233
- eISBN:
- 9780191709302
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205233.003.0005
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter argues that neither the modal realism of David Lewis nor abstract possible worlds reductionism can satisfy Truthmaker or TSB when it comes to truths of de re modality. On the contrary, ...
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This chapter argues that neither the modal realism of David Lewis nor abstract possible worlds reductionism can satisfy Truthmaker or TSB when it comes to truths of de re modality. On the contrary, both Truthmaker and TSB lead straight to irreducible modal properties. Thus, Truthmaker and TSB have significant implications for the nature of modality and the inventory of irreducible properties.Less
This chapter argues that neither the modal realism of David Lewis nor abstract possible worlds reductionism can satisfy Truthmaker or TSB when it comes to truths of de re modality. On the contrary, both Truthmaker and TSB lead straight to irreducible modal properties. Thus, Truthmaker and TSB have significant implications for the nature of modality and the inventory of irreducible properties.
Geoffrey Hellman
- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780198240341
- eISBN:
- 9780191597664
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198240341.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to ...
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Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities. Modal logic is combined with notions of part/whole (mereology) enabling a systematic interpretation of ordinary mathematical statements as asserting what would be the case in any (suitable) structure there (logically) might be, e.g. for number theory, functional analysis, algebra, pure geometry, etc. Structures are understood as comprising objects, whatever their nature, standing in suitable relations as given by axioms or defining conditions in mathematics proper. The characterization of structures is aided by the addition of plural quantifiers, e.g. ‘Any objects of sort F’ corresponding to arbitrary collections of Fs, achieving the expressive power of second‐order logic, hence a full logic of relations. (See the author's ‘Structuralism without Structures’, Philosophia Mathematica 4 (1996): 100–123.) Claims of absolute existence of structures are replaced by claims of (logical) possibility of enough structurally interrelated objects (modal‐existence postulates). The vast bulk of ordinary mathematics, and scientific applications, can thus be recovered on the basis of the possibility of a countable infinity of atoms. As applied to set theory itself, these ideas lead to a ‘many worlds’—– as opposed to the standard ‘fixed universe’—view, inspired by Zermelo (1930), respecting the unrestricted, indefinite extendability of models of the Zermelo–Fraenkel axioms. Natural motivation for (‘small’) large cardinal axioms is thus provided. In sum, the vast bulk of abstract mathematics is respected as objective, while literal reference to abstracta and related problems with Platonism are eliminated.Less
Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities. Modal logic is combined with notions of part/whole (mereology) enabling a systematic interpretation of ordinary mathematical statements as asserting what would be the case in any (suitable) structure there (logically) might be, e.g. for number theory, functional analysis, algebra, pure geometry, etc. Structures are understood as comprising objects, whatever their nature, standing in suitable relations as given by axioms or defining conditions in mathematics proper. The characterization of structures is aided by the addition of plural quantifiers, e.g. ‘Any objects of sort F’ corresponding to arbitrary collections of Fs, achieving the expressive power of second‐order logic, hence a full logic of relations. (See the author's ‘Structuralism without Structures’, Philosophia Mathematica 4 (1996): 100–123.) Claims of absolute existence of structures are replaced by claims of (logical) possibility of enough structurally interrelated objects (modal‐existence postulates). The vast bulk of ordinary mathematics, and scientific applications, can thus be recovered on the basis of the possibility of a countable infinity of atoms. As applied to set theory itself, these ideas lead to a ‘many worlds’—– as opposed to the standard ‘fixed universe’—view, inspired by Zermelo (1930), respecting the unrestricted, indefinite extendability of models of the Zermelo–Fraenkel axioms. Natural motivation for (‘small’) large cardinal axioms is thus provided. In sum, the vast bulk of abstract mathematics is respected as objective, while literal reference to abstracta and related problems with Platonism are eliminated.
John P. Burgess and Gideon Rosen
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250128
- eISBN:
- 9780191597138
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250126.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Numbers and other mathematical objects are exceptional in having no locations in space and time and no causes or effects in the physical world. This makes it difficult to account for the possibility ...
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Numbers and other mathematical objects are exceptional in having no locations in space and time and no causes or effects in the physical world. This makes it difficult to account for the possibility of mathematical knowledge, leading many philosophers to embrace nominalism, the doctrine that there are no abstract entities. It has also led some of them to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects, eliminating so‐called ontological commitment to numbers, sets, and the like. These projects differ considerably in the apparatus they employ, and the spirit in which they are put forward. Some employ synthetic geometry, others modal logic. Some are put forward as revolutionary replacements for existing mathematics and science, others hermeneutic hypotheses about what they have meant all along. We attempt to cut through technicalities that have obscured previous discussions of these projects, and to present concise accounts with minimal prerequisites of a dozen strategies for nominalistic interpretation of mathematics. We also examine critically the aims and claims of such interpretations, suggesting that what they really achieve is something quite different from what the authors of such projects usually assume.Less
Numbers and other mathematical objects are exceptional in having no locations in space and time and no causes or effects in the physical world. This makes it difficult to account for the possibility of mathematical knowledge, leading many philosophers to embrace nominalism, the doctrine that there are no abstract entities. It has also led some of them to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects, eliminating so‐called ontological commitment to numbers, sets, and the like. These projects differ considerably in the apparatus they employ, and the spirit in which they are put forward. Some employ synthetic geometry, others modal logic. Some are put forward as revolutionary replacements for existing mathematics and science, others hermeneutic hypotheses about what they have meant all along. We attempt to cut through technicalities that have obscured previous discussions of these projects, and to present concise accounts with minimal prerequisites of a dozen strategies for nominalistic interpretation of mathematics. We also examine critically the aims and claims of such interpretations, suggesting that what they really achieve is something quite different from what the authors of such projects usually assume.
Craig Bourne
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199212804
- eISBN:
- 9780191707094
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199212804.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology
I begin by laying down three conditions which any theory of time should meet: it should accord with our view that certain statements about the past are true; that the truthmakers for those statements ...
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I begin by laying down three conditions which any theory of time should meet: it should accord with our view that certain statements about the past are true; that the truthmakers for those statements should be clear; and should accommodate the truth‐value links between various times. I show how two different kinds of presentism cannot meet these requirements, including that put forward by Prior. I develop a version of presentism, analogous to ersatz modal realism in the possible worlds debate, which does satisfy the requirements.Less
I begin by laying down three conditions which any theory of time should meet: it should accord with our view that certain statements about the past are true; that the truthmakers for those statements should be clear; and should accommodate the truth‐value links between various times. I show how two different kinds of presentism cannot meet these requirements, including that put forward by Prior. I develop a version of presentism, analogous to ersatz modal realism in the possible worlds debate, which does satisfy the requirements.
Craig Bourne
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199212804
- eISBN:
- 9780191707094
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199212804.003.0009
- Subject:
- Philosophy, Metaphysics/Epistemology
I discuss Gödel's philosophical position on the nature of time. I describe Gödel's model, which contains closed time‐like curves allowing us to take a journey into our future and arrive in our past, ...
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I discuss Gödel's philosophical position on the nature of time. I describe Gödel's model, which contains closed time‐like curves allowing us to take a journey into our future and arrive in our past, and show how it is incompatible with presentism. I do not discuss the well‐known implications of this for time travel, but focus on Gödel's subtler ‘modal’ argument. I discuss various ways of rejecting this argument and show that the conclusion that presentists must draw is that tense is not an essential feature of it: whether time is presentist or tenseless is an entirely contingent matter. I conclude by considering the extent to which metaphysics can tell us about the nature of time as it actually is.Less
I discuss Gödel's philosophical position on the nature of time. I describe Gödel's model, which contains closed time‐like curves allowing us to take a journey into our future and arrive in our past, and show how it is incompatible with presentism. I do not discuss the well‐known implications of this for time travel, but focus on Gödel's subtler ‘modal’ argument. I discuss various ways of rejecting this argument and show that the conclusion that presentists must draw is that tense is not an essential feature of it: whether time is presentist or tenseless is an entirely contingent matter. I conclude by considering the extent to which metaphysics can tell us about the nature of time as it actually is.
Alvin Plantinga
Matthew Davidson (ed.)
- Published in print:
- 2003
- Published Online:
- November 2003
- ISBN:
- 9780195103762
- eISBN:
- 9780199833573
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195103769.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology
This book is a collection of my essays, dating from 1969, concerning the metaphysics of modality. The first two chapters are a defense of the idea of modality de re against criticisms from William ...
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This book is a collection of my essays, dating from 1969, concerning the metaphysics of modality. The first two chapters are a defense of the idea of modality de re against criticisms from William Kneale and W. V. Quine, and an elaboration on the notions of possible worlds and essences. In the third chapter, I conclude that the Theory of Worldbound Individuals is false, even when fortified with Counterpart Theory. Chapter 4 contains an argument for the conclusion that there neither are, nor could have been, possible but nonexistent objects. In the next chapter, I develop this theme in greater detail and argue for the compatibility of actualism – i.e., the view that there neither are, nor could have been, any nonexistent objects – and possible worlds. Both Chs. 6 and 7 contain an account of the relationship between proper names and essences, my view being that proper names express essences and that sometimes different proper names for the same object express different essences of that object. The end of Ch. 7 and all of Ch. 8 are an examination of existentialism (the theory that propositions and states of affairs ontologically depend on their subjects) and arguments against it. In Ch. 9, I defend my theory of modality against objections raised by John Pollock. In Ch. 10, I sketch out what the commitments of modal realism are, and argue that David Lewis's modal theory is not a modal realist theory. Finally, in the concluding chapter I argue that propositions cannot be concrete objects.Less
This book is a collection of my essays, dating from 1969, concerning the metaphysics of modality. The first two chapters are a defense of the idea of modality de re against criticisms from William Kneale and W. V. Quine, and an elaboration on the notions of possible worlds and essences. In the third chapter, I conclude that the Theory of Worldbound Individuals is false, even when fortified with Counterpart Theory. Chapter 4 contains an argument for the conclusion that there neither are, nor could have been, possible but nonexistent objects. In the next chapter, I develop this theme in greater detail and argue for the compatibility of actualism – i.e., the view that there neither are, nor could have been, any nonexistent objects – and possible worlds. Both Chs. 6 and 7 contain an account of the relationship between proper names and essences, my view being that proper names express essences and that sometimes different proper names for the same object express different essences of that object. The end of Ch. 7 and all of Ch. 8 are an examination of existentialism (the theory that propositions and states of affairs ontologically depend on their subjects) and arguments against it. In Ch. 9, I defend my theory of modality against objections raised by John Pollock. In Ch. 10, I sketch out what the commitments of modal realism are, and argue that David Lewis's modal theory is not a modal realist theory. Finally, in the concluding chapter I argue that propositions cannot be concrete objects.
Alvin Plantinga
- Published in print:
- 1978
- Published Online:
- November 2003
- ISBN:
- 9780198244141
- eISBN:
- 9780191598241
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198244142.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology
This book is a study of the concept of necessity. In the first three chapters, I clarify and defend the distinction between modality de re and modality de dicto. Also, I show how to explain de re ...
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This book is a study of the concept of necessity. In the first three chapters, I clarify and defend the distinction between modality de re and modality de dicto. Also, I show how to explain de re modality in terms of de dicto modality. In Ch. 4, I explicate the concept of a possible world and define what it is for an object x to have a property P essentially. I then use the concept of an essential property to give an account of essences and their relationship to proper names. In Ch. 6, I argue that the Theory of Worldbound Individuals—even when fortified with Counterpart Theory—is false. Chapters 7 and 8 address the subject of possible but non‐existent objects; I argue here for the conclusion that there is no good reason to think that there are any such objects. In Ch. 9, I apply my theory of modality to the Problem of Evil in an effort to show that the Free Will Defense defeats this particular objection to theism. In Ch. 10, I present a sound modal version of the ontological argument for the existence of God. Finally, in the appendix, I address Quinean objections to quantified modal logic.Less
This book is a study of the concept of necessity. In the first three chapters, I clarify and defend the distinction between modality de re and modality de dicto. Also, I show how to explain de re modality in terms of de dicto modality. In Ch. 4, I explicate the concept of a possible world and define what it is for an object x to have a property P essentially. I then use the concept of an essential property to give an account of essences and their relationship to proper names. In Ch. 6, I argue that the Theory of Worldbound Individuals—even when fortified with Counterpart Theory—is false. Chapters 7 and 8 address the subject of possible but non‐existent objects; I argue here for the conclusion that there is no good reason to think that there are any such objects. In Ch. 9, I apply my theory of modality to the Problem of Evil in an effort to show that the Free Will Defense defeats this particular objection to theism. In Ch. 10, I present a sound modal version of the ontological argument for the existence of God. Finally, in the appendix, I address Quinean objections to quantified modal logic.
Daniel Stoljar
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780195306583
- eISBN:
- 9780199786619
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195306589.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter discusses the idea that it is mistaken to suppose that there is a genuinely philosophical problem of experience at all. According to one version of the challenge, the problem should be ...
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This chapter discusses the idea that it is mistaken to suppose that there is a genuinely philosophical problem of experience at all. According to one version of the challenge, the problem should be rejected on methodological grounds: it is mistaken to reason from conceivability to possibility at all. It is argued that this reasoning is ubiquitous in philosophy, and thus to the extent that there is a problem here it is everyone’s rather than the author’s. According to another version of the challenge, the problem should be rejected on conceptual grounds: the thesis of physicalism certainly made sense at a particular moment in the history of science, but that moment is long gone and contemporary interpretations of it do not permit the questions typical of philosophy of mind to be legitimately raised. Physicalism and related concepts play an illustrative or inessential role, rather than an essential role, in the logical problem, and once this is appreciated, the basis for skepticism evaporates.Less
This chapter discusses the idea that it is mistaken to suppose that there is a genuinely philosophical problem of experience at all. According to one version of the challenge, the problem should be rejected on methodological grounds: it is mistaken to reason from conceivability to possibility at all. It is argued that this reasoning is ubiquitous in philosophy, and thus to the extent that there is a problem here it is everyone’s rather than the author’s. According to another version of the challenge, the problem should be rejected on conceptual grounds: the thesis of physicalism certainly made sense at a particular moment in the history of science, but that moment is long gone and contemporary interpretations of it do not permit the questions typical of philosophy of mind to be legitimately raised. Physicalism and related concepts play an illustrative or inessential role, rather than an essential role, in the logical problem, and once this is appreciated, the basis for skepticism evaporates.
Daniel Stoljar
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780195306583
- eISBN:
- 9780199786619
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195306589.003.0004
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter takes up the conditional thesis that if the ignorance hypothesis is true, the logical problem is solved. The defense of this thesis begins from the idea that there are a number of ...
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This chapter takes up the conditional thesis that if the ignorance hypothesis is true, the logical problem is solved. The defense of this thesis begins from the idea that there are a number of distinctive ways that a modal argument can go wrong — a number of standard mistakes. The philosophical challenge presented by the modal arguments that are constitutive of the logical problem is that it is hard to see in these cases that we are making any of these standard mistakes. On the other hand, if the ignorance hypothesis is true, it becomes immediately plausible to suppose that we are making one of (or a combination of) these mistakes. This suggests in turn that E1 is true: if the ignorance hypothesis is true, the logical problem is solved.Less
This chapter takes up the conditional thesis that if the ignorance hypothesis is true, the logical problem is solved. The defense of this thesis begins from the idea that there are a number of distinctive ways that a modal argument can go wrong — a number of standard mistakes. The philosophical challenge presented by the modal arguments that are constitutive of the logical problem is that it is hard to see in these cases that we are making any of these standard mistakes. On the other hand, if the ignorance hypothesis is true, it becomes immediately plausible to suppose that we are making one of (or a combination of) these mistakes. This suggests in turn that E1 is true: if the ignorance hypothesis is true, the logical problem is solved.
Paola Monachesi
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780199274758
- eISBN:
- 9780191705908
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199274758.001.0001
- Subject:
- Linguistics, Syntax and Morphology
This book explores the interface between syntax and the other components of the grammar, particularly phonology, morphology, and argument structure. It contains case studies, on subjects such as ...
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This book explores the interface between syntax and the other components of the grammar, particularly phonology, morphology, and argument structure. It contains case studies, on subjects such as clitics and complex predicates (auxiliary and modal verbs) in Romance and grounding theoretical analysis in constant exemplification. It shows that a careful analysis of their properties can lead to a better understanding of the interaction of the various components of the grammar. The syntactic properties of clitics are considered in relation to their phonological and morphological characteristic. The properties of auxiliary verbs are analysed from the perspective of the interface between argument structure and syntactic structure. Modal verbs are examined at the interface between syntax and phonology. The analyses of clitics and auxiliaries shed new light on the link between Romanian and Balkan/Slavic.Less
This book explores the interface between syntax and the other components of the grammar, particularly phonology, morphology, and argument structure. It contains case studies, on subjects such as clitics and complex predicates (auxiliary and modal verbs) in Romance and grounding theoretical analysis in constant exemplification. It shows that a careful analysis of their properties can lead to a better understanding of the interaction of the various components of the grammar. The syntactic properties of clitics are considered in relation to their phonological and morphological characteristic. The properties of auxiliary verbs are analysed from the perspective of the interface between argument structure and syntactic structure. Modal verbs are examined at the interface between syntax and phonology. The analyses of clitics and auxiliaries shed new light on the link between Romanian and Balkan/Slavic.
