Some theories of time entail that the present can change before or after it has hap- pened. Examp... more Some theories of time entail that the present can change before or after it has hap- pened. Examples include views on which time-travelers can change the past, the glowing block theory, Peter Geach’s mutable future view, and the moving spotlight theory. This paper argues that such ante factum or posthumous change requires a heterodox “split time” view on which earlier-than is not the converse of later-than.
Émile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. P... more Émile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. Peter Forrest instead blames the assumption that physical space has a similar structure as the real numbers. This paper argues that Banach and Tarski's result is not paradoxical and that it merely illustrates a surprising feature of the continuum: dividing a spatial region into disjoint pieces need not preserve volume.
To define new property terms, we combine already familiar predicates by means of certain logical ... more To define new property terms, we combine already familiar predicates by means of certain logical operations. Given suitable constraints, these operations may presumably include truth-functional sentence connectives and quantification over objects. What is less clear is whether we can also use modal operators for this purpose. The aim of this paper is to clarify what is involved in this question, and to argue in favor of modal property definitions. Keywords Property definitions • Modal properties • Dispositions • Causal bases • Aboutness Suppose we simplify matters by assuming that necessarily coextensive properties are identical. This means endorsing all instances of the following schema, where 'P' and 'Q' are terms for properties and ' ' the necessity operator: P = Q iff ∀x (Qx ↔ Px) (1) There are some applications, notably in accounts of belief and other intentional states, where we might need a more fine-grained notion of property (Achinstein 1974; Sober 1982; Bealer 1982; Swoyer 1996). For our purposes, these complications can be ignored. If we accept the account of property identity (1) then any property definition can be regarded as an instance of a property comprehension schema: ∃X ∀x (X x ↔ Φ(x)) (2)
Michael Dummett claims that the classical model of time as a continuum of instants has to be reje... more Michael Dummett claims that the classical model of time as a continuum of instants has to be rejected. In his view, “it allows as possibilities what reason rules out, and leaves it to the contingent laws of physics to rule out what a good model of physical reality would not even be able to describe.” This paper argues otherwise.
We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an ... more We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an application of the general construction we give a quantum determinant for the q-Lorentz group.
We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing t... more We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing the q-exterior derivative, q-Hodge star operator, q-coderivative, q-Laplace-Beltrami operator and the q-Lie-derivative. With these tools at hand, we then give a detailed exposition of the q-d'Alembert and q-Maxwell equation. For both equations we present a q-momentum-indexed family of plane wave solutions. We also discuss the gauge freedom of the q-Maxwell field and give a q-spinor analysis of the q-field strength tensor.
A perennial question in the philosophy of time concerns the relation between the objective “physi... more A perennial question in the philosophy of time concerns the relation between the objective “physical time” that features in empirical theories of motion and the subjective “human time” in which our own experiences unfold. This article is about one facet of this broader question: whether the phenomenon of consciousness allows us to make a principled distinction between the present and other times. A number of authors have argued that, without conscious observers, there would be no distinctions of past, present, and future. This paper defends the opposing thesis that there is no interesting connection between consciousness and presentness.
We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an ... more We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an application of the general construction we give a quantum determinant for the q-Lorentz group.
Even though fatalism has been an intermittent topic of philosophy since Greek antiquity, this pap... more Even though fatalism has been an intermittent topic of philosophy since Greek antiquity, this paper argues that fate ought to be of little concern to metaphysicians. Fatalism is neither an interesting metaphysical thesis in its own right, nor can it be identified with theses that are, such as realism about the future or determinism.
This paper defends three theses: (i) that presentism is either trivial or untenable; (ii) that th... more This paper defends three theses: (i) that presentism is either trivial or untenable; (ii) that the debate between tensed and tenseless theories of time is not about the status of presentism; and (iii) that there is no temporal analogue of the modal thesis of actualism. Presentism, we are told by its advocates, is the following thesis about the relation between time and existence: P: Nothing exists that is not present. In the recent literature, Bigelow (1996) and Markosian (2003) defend presentism as the commonsensical view of time. Sider (1999) is impressed by the ontological benefits of presentism, but ultimately rejects it in his (2001, Ch. 2). However, a majority of authors is opposed to the view: Putnam (1967), Sklar (1981), Savitt (2000), and Saunders (2002) all argue that presentism is incompatible with the theory of relativity, and thus false a posteriori. There is little common ground amongst these competing views, but the one thing that all sides of the debate seem to take for granted is that the status of presentism raises an important metaphysical question. It is this shared assumption that I want to challenge. In this paper, I argue that presentism is either trivially true or obviously false.
(Mind, 2005) argue that David Lewis's counterpart theory is unable to account for modal claims th... more (Mind, 2005) argue that David Lewis's counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.
According to Hans Kamp and Frank Vlach, the two-dimensional tense operators "now" and "then" are ... more According to Hans Kamp and Frank Vlach, the two-dimensional tense operators "now" and "then" are ineliminable in quantified tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It is shown that "now" and "then" are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might not be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic. Keywords quantified tense logic • "now" and "then" • actuality operator 1 Introduction Early presentations of tense logic often had only two primitives: a past tense operator P ("it was the case that") and a future tense operator F ("it will be the case that"). In spite of their simple structure, these systems of tense logic turned out to be remarkably powerful. They allow us to regiment not only a large part of temporal discourse, but also quite sophisticated claims about the structure of time itself. For example, we can express in terms of P and F alone whether the time-series branches, whether it has endpoints, and whether it is dense, complete, or well-ordered [9,4]. However, doubts began to arise in the early 1970s whether the expressive capacity of a P/F tense logic is indeed sufficient. One worry concerns the operator N ("it is now the case that"). A. N. Prior [23, p. 9] had convinced many that there is no need for such an operator because its work is already done by the convention that the untensed sentences of our formal language make claims about what is presently the case. As it turned out, this dismissal of
We present a new version of q-Minkowski space, which has both a coaddition law and an SLq(2,~)-sp... more We present a new version of q-Minkowski space, which has both a coaddition law and an SLq(2,~)-spinor decomposition. The additive structure forms a braided group rather than a quantum one. In the process, we obtain a q-Lorentz group which coacts covariantly on this q-Minkowski space.
A causal loop is a sequence of events e 1 ,. .. , e n , each element of which is one of the cause... more A causal loop is a sequence of events e 1 ,. .. , e n , each element of which is one of the causes of the next event, and whose last event e n is one of the causes of the first event e 1. The events that make up a loop need not be complete causes of one another, nor do they need to be complete effects of one another. In a causal loop, the arrows of causation go around in a circle, but there might be additional arrows that lead into the circle, or arrows that lead out of it. If there are no such branches then the loop is said to be causally isolated. Causal loops naturally arise in two different contexts. One is the time travel stories popularized by David Lewis (1976), in which there is backwards causation against the direction of time. The other cases involve models of the general theory of relativity-first discussed by Kurt Gö del (1949)that possess closed timelike curves in which time itself loops along a particular worldline. In such models, there is no backwards causation and travelling back in time requires no particular effort; one just has to follow an appropriately chosen worldline. Both types of loop permit what looks like creation ex nihilo. In the Lewis case, suppose that you would like to travel in time, but do not have enough money to buy a time machine. Here is how you could get one. At some future time t 2 , your future self uses a time machine to travel back to the present time t 1 , where he hands the machine to your present self. You hold on to the time machine until t 2 , when you will have become that future self. At that point, you use the time machine to go back to t 1. The time machine exists neither before t 1 nor after t 2 ; it just goes around in a circle. In the case of general relativity, there are solutions to Einstein's field equations due to Richard Gott and Li-Xin Li (1998) that do not start out with the usual big bang, but with a spacetime 'doughnut' from which the rest of the universe and its contents branch off. (The initial part of this spacetime looks a little bit like the handle of an amphora. While there are closed paths that circle around the handle, there are also paths that continue to the rest of the amphora.
Tense logic is often said to possess insufficient expressive resources to serve as a theory of th... more Tense logic is often said to possess insufficient expressive resources to serve as a theory of the nature of time. This paper counters this objection by showing how to obtain quantification over times in a tense logic in which all temporal distinctions are ultimately spelled out in terms of the two simple tense operators "it was the case that" and "it will be the case that." This account of times is similar to what is known as "linguistic ersatzism" about possible worlds, but there are noteworthy differences between these two cases. In particular, while linguistic ersatzism would support actualism, the view of times defended here does not support presentism.
Some theories of time entail that the present can change before or after it has hap- pened. Examp... more Some theories of time entail that the present can change before or after it has hap- pened. Examples include views on which time-travelers can change the past, the glowing block theory, Peter Geach’s mutable future view, and the moving spotlight theory. This paper argues that such ante factum or posthumous change requires a heterodox “split time” view on which earlier-than is not the converse of later-than.
Émile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. P... more Émile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. Peter Forrest instead blames the assumption that physical space has a similar structure as the real numbers. This paper argues that Banach and Tarski's result is not paradoxical and that it merely illustrates a surprising feature of the continuum: dividing a spatial region into disjoint pieces need not preserve volume.
To define new property terms, we combine already familiar predicates by means of certain logical ... more To define new property terms, we combine already familiar predicates by means of certain logical operations. Given suitable constraints, these operations may presumably include truth-functional sentence connectives and quantification over objects. What is less clear is whether we can also use modal operators for this purpose. The aim of this paper is to clarify what is involved in this question, and to argue in favor of modal property definitions. Keywords Property definitions • Modal properties • Dispositions • Causal bases • Aboutness Suppose we simplify matters by assuming that necessarily coextensive properties are identical. This means endorsing all instances of the following schema, where 'P' and 'Q' are terms for properties and ' ' the necessity operator: P = Q iff ∀x (Qx ↔ Px) (1) There are some applications, notably in accounts of belief and other intentional states, where we might need a more fine-grained notion of property (Achinstein 1974; Sober 1982; Bealer 1982; Swoyer 1996). For our purposes, these complications can be ignored. If we accept the account of property identity (1) then any property definition can be regarded as an instance of a property comprehension schema: ∃X ∀x (X x ↔ Φ(x)) (2)
Michael Dummett claims that the classical model of time as a continuum of instants has to be reje... more Michael Dummett claims that the classical model of time as a continuum of instants has to be rejected. In his view, “it allows as possibilities what reason rules out, and leaves it to the contingent laws of physics to rule out what a good model of physical reality would not even be able to describe.” This paper argues otherwise.
We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an ... more We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an application of the general construction we give a quantum determinant for the q-Lorentz group.
We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing t... more We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing the q-exterior derivative, q-Hodge star operator, q-coderivative, q-Laplace-Beltrami operator and the q-Lie-derivative. With these tools at hand, we then give a detailed exposition of the q-d'Alembert and q-Maxwell equation. For both equations we present a q-momentum-indexed family of plane wave solutions. We also discuss the gauge freedom of the q-Maxwell field and give a q-spinor analysis of the q-field strength tensor.
A perennial question in the philosophy of time concerns the relation between the objective “physi... more A perennial question in the philosophy of time concerns the relation between the objective “physical time” that features in empirical theories of motion and the subjective “human time” in which our own experiences unfold. This article is about one facet of this broader question: whether the phenomenon of consciousness allows us to make a principled distinction between the present and other times. A number of authors have argued that, without conscious observers, there would be no distinctions of past, present, and future. This paper defends the opposing thesis that there is no interesting connection between consciousness and presentness.
We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an ... more We show how to construct central and grouplike quantum determinants for FRT algebras A(R). As an application of the general construction we give a quantum determinant for the q-Lorentz group.
Even though fatalism has been an intermittent topic of philosophy since Greek antiquity, this pap... more Even though fatalism has been an intermittent topic of philosophy since Greek antiquity, this paper argues that fate ought to be of little concern to metaphysicians. Fatalism is neither an interesting metaphysical thesis in its own right, nor can it be identified with theses that are, such as realism about the future or determinism.
This paper defends three theses: (i) that presentism is either trivial or untenable; (ii) that th... more This paper defends three theses: (i) that presentism is either trivial or untenable; (ii) that the debate between tensed and tenseless theories of time is not about the status of presentism; and (iii) that there is no temporal analogue of the modal thesis of actualism. Presentism, we are told by its advocates, is the following thesis about the relation between time and existence: P: Nothing exists that is not present. In the recent literature, Bigelow (1996) and Markosian (2003) defend presentism as the commonsensical view of time. Sider (1999) is impressed by the ontological benefits of presentism, but ultimately rejects it in his (2001, Ch. 2). However, a majority of authors is opposed to the view: Putnam (1967), Sklar (1981), Savitt (2000), and Saunders (2002) all argue that presentism is incompatible with the theory of relativity, and thus false a posteriori. There is little common ground amongst these competing views, but the one thing that all sides of the debate seem to take for granted is that the status of presentism raises an important metaphysical question. It is this shared assumption that I want to challenge. In this paper, I argue that presentism is either trivially true or obviously false.
(Mind, 2005) argue that David Lewis's counterpart theory is unable to account for modal claims th... more (Mind, 2005) argue that David Lewis's counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.
According to Hans Kamp and Frank Vlach, the two-dimensional tense operators "now" and "then" are ... more According to Hans Kamp and Frank Vlach, the two-dimensional tense operators "now" and "then" are ineliminable in quantified tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It is shown that "now" and "then" are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might not be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic. Keywords quantified tense logic • "now" and "then" • actuality operator 1 Introduction Early presentations of tense logic often had only two primitives: a past tense operator P ("it was the case that") and a future tense operator F ("it will be the case that"). In spite of their simple structure, these systems of tense logic turned out to be remarkably powerful. They allow us to regiment not only a large part of temporal discourse, but also quite sophisticated claims about the structure of time itself. For example, we can express in terms of P and F alone whether the time-series branches, whether it has endpoints, and whether it is dense, complete, or well-ordered [9,4]. However, doubts began to arise in the early 1970s whether the expressive capacity of a P/F tense logic is indeed sufficient. One worry concerns the operator N ("it is now the case that"). A. N. Prior [23, p. 9] had convinced many that there is no need for such an operator because its work is already done by the convention that the untensed sentences of our formal language make claims about what is presently the case. As it turned out, this dismissal of
We present a new version of q-Minkowski space, which has both a coaddition law and an SLq(2,~)-sp... more We present a new version of q-Minkowski space, which has both a coaddition law and an SLq(2,~)-spinor decomposition. The additive structure forms a braided group rather than a quantum one. In the process, we obtain a q-Lorentz group which coacts covariantly on this q-Minkowski space.
A causal loop is a sequence of events e 1 ,. .. , e n , each element of which is one of the cause... more A causal loop is a sequence of events e 1 ,. .. , e n , each element of which is one of the causes of the next event, and whose last event e n is one of the causes of the first event e 1. The events that make up a loop need not be complete causes of one another, nor do they need to be complete effects of one another. In a causal loop, the arrows of causation go around in a circle, but there might be additional arrows that lead into the circle, or arrows that lead out of it. If there are no such branches then the loop is said to be causally isolated. Causal loops naturally arise in two different contexts. One is the time travel stories popularized by David Lewis (1976), in which there is backwards causation against the direction of time. The other cases involve models of the general theory of relativity-first discussed by Kurt Gö del (1949)that possess closed timelike curves in which time itself loops along a particular worldline. In such models, there is no backwards causation and travelling back in time requires no particular effort; one just has to follow an appropriately chosen worldline. Both types of loop permit what looks like creation ex nihilo. In the Lewis case, suppose that you would like to travel in time, but do not have enough money to buy a time machine. Here is how you could get one. At some future time t 2 , your future self uses a time machine to travel back to the present time t 1 , where he hands the machine to your present self. You hold on to the time machine until t 2 , when you will have become that future self. At that point, you use the time machine to go back to t 1. The time machine exists neither before t 1 nor after t 2 ; it just goes around in a circle. In the case of general relativity, there are solutions to Einstein's field equations due to Richard Gott and Li-Xin Li (1998) that do not start out with the usual big bang, but with a spacetime 'doughnut' from which the rest of the universe and its contents branch off. (The initial part of this spacetime looks a little bit like the handle of an amphora. While there are closed paths that circle around the handle, there are also paths that continue to the rest of the amphora.
Tense logic is often said to possess insufficient expressive resources to serve as a theory of th... more Tense logic is often said to possess insufficient expressive resources to serve as a theory of the nature of time. This paper counters this objection by showing how to obtain quantification over times in a tense logic in which all temporal distinctions are ultimately spelled out in terms of the two simple tense operators "it was the case that" and "it will be the case that." This account of times is similar to what is known as "linguistic ersatzism" about possible worlds, but there are noteworthy differences between these two cases. In particular, while linguistic ersatzism would support actualism, the view of times defended here does not support presentism.
We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing t... more We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing the q-exterior derivative, q-Hodge star operator, q-coderivative, q-Laplace-Beltrami operator and the q-Lie-derivative. With these tools at hand, we then give a detailed exposition of the q-d’Alembert and q-Maxwell equation. For both equations we present a q-momentum-indexed family of plane wave solutions. We also discuss the gauge freedom of the q-Maxwell field and give a q-spinor analysis of the q-field strength tensor. 1
This is a book about the psychology of temporal cognition, written by a philosopher. As the autho... more This is a book about the psychology of temporal cognition, written by a philosopher. As the author rightly notes in the introduction, "Philosophers have made many tentative empirical claims about time cognition, but very few have taken into account all the current scientific evidence" (p. 5). Carlos Montemayor aims to fill this lacuna in the philosophical literature.
This ambitious book aims to revive two controversial theses: that verb tenses function like sente... more This ambitious book aims to revive two controversial theses: that verb tenses function like sentential operators, and that the contents of some assertions and beliefs are temporal propositions. Unlike eternal propositions, whose truth-value remains constant over time, temporal propositions have different truth-values at different times. The subtitle promises an account of the metaphysics of propositions, but most metaphysical questions about propositions, such as their role in accounts of facts, or the nature of propositions themselves, play a minor role in the discussion. This is a book in the philosophy of language, addressed to experts in the field, and it should be appreciated as such.
Yuval Dolev, Time and Realism: Metaphysical and Antimetaphysical Perspectives. Cambridge, Mass.: ... more Yuval Dolev, Time and Realism: Metaphysical and Antimetaphysical Perspectives. Cambridge, Mass.: The MIT Press, 2007. ix + 237 pp.
Fourth IAPT Meeting. June 12-14, 2017. University of Milan, Palazzo Feltrinelli, Gargnano del... more Fourth IAPT Meeting. June 12-14, 2017. University of Milan, Palazzo Feltrinelli, Gargnano del Garda, italy
Invited Speakers: Patrick Blackburn (Roskilde), Jennifer Hornsby (Birkbeck), Jenann Ismael (Arizona), Tim Maudlin (NYU), Sven Rosenkrantz (Barcelona). Round Table on Temporal Illusions: Valterri Arstila (Turku), Adrian Bardon (Wake Forest), Sean Power (Dublin)
Organization: The Centre for Philosophy of Time: A. Bardon (Wake Forest), D. Bordini (Milan), V. Buonomo (MIlan), C. Calosi (Neuchâtel), F. Correia (Neuchâtel), S. Iaquinto (Milan), D. Ingram (Milan), U. Meyer (Colgate), K. Miller (Sydney), B. Neeser (Neuchâtel), G. Torrengo (Milan), C. Wüthrich (Geneva), and N. Young (Milan).
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Papers by Ulrich Meyer
Invited Speakers: Patrick Blackburn (Roskilde), Jennifer Hornsby (Birkbeck), Jenann Ismael (Arizona), Tim Maudlin (NYU), Sven Rosenkrantz (Barcelona).
Round Table on Temporal Illusions: Valterri Arstila (Turku), Adrian Bardon (Wake Forest), Sean Power (Dublin)
Organization: The Centre for Philosophy of Time: A. Bardon (Wake Forest), D. Bordini (Milan), V. Buonomo (MIlan), C. Calosi (Neuchâtel), F. Correia (Neuchâtel), S. Iaquinto (Milan), D. Ingram (Milan), U. Meyer (Colgate), K. Miller (Sydney), B. Neeser (Neuchâtel), G. Torrengo (Milan), C. Wüthrich (Geneva), and N. Young (Milan).