In an article in Scientific American (March 1994, pp. 68–74) entitled “The Quantum Physics of Time Travel”, Oxford physicist David Deutsch and Oxford philosopher Michael Lockwood give a defense of the physical possibility of time travel based on the “Many Worlds” interpretation of quantum mechanics. This positive view of theirs is not my concern, however—I want to quarrel with their argument that time travel cannot be accommodated in any other way.1 The best way to spell out the traditional “grandfather (...) paradox” that appears to threaten the possibility of time travel involves the notion of ability, or personal possibility, or free will. An example of David Lewis’s: Tim travels back in time with the intent to kill his grandfather.2 Let us fix the case as one in which Tim in fact will not kill Grandfather; still, it seems that he can kill Grandfather because he is a good shot, has a gun, and is alone with Grandfather at close range. As Lewis says, Tim “has what it takes” to kill Grandfather. However, it is also compelling that Tim cannot kill Grandfather, because if Grandfather had been killed in his youth, Tim would not have existed to kill him. It is important to realize that the paradox essentially involves the notion of ability. No inconsistency results from supposing that Tim does not kill Grandfather. As for the case in which Tim does kill Grandfather, there are various possibilities. We could tell a consistent time travel story in which Tim kills Grandfather, but Grandfather is miraculously resurrected. Or one in which Tim kills Grandfather, but in which Grandfather has already had a child. Or one in which Tim kills Grandfather permanently, before Grandfather has any children, but in which Tim’s grandfather is someone other than Grandfather. As for the story in which Tim both kills Grandfather permanently in such a way that Grandfather has no children, and also is descended from Grandfather, this is an inconsistent time travel story; but of course the existence of some.... (shrink)

1000 time-travelers travel back in time, each with the intention of killing their own infant-self. If there is no branching time, then on pain of bringing about a logical contradiction, all must fail. But this seems inexplicable: what is to ensure that the time-travelers are stopped? For a time, this inexplicability objection was thought to provide evidence that there is something incoherent about the possibility of backwards time travel in a universe without branching time. There is now near-consensus, however, that (...) the objection has no bite: there is nothing inexplicable about the mass failure. Lewis, Sider and Ismael independently argue that since it is built into the description of the class of cases considered that the time-travelers must fail – and so we consider only unsuccessful attempts – there is no mystery. Smith argues that the absence of possible worlds at which auto-infanticide is committed suffices as a complete explanation for the failures. And Baron and Colyvan maintain that available causal and logical explanations jointly account for everything that needs accounting for. I argue that these are wrong. There is remaining, problematic inexplicability. For backwards time travel not to lead to logical contradiction, something would need to do logic’s bidding, after all. (shrink)

In this discussion piece, I argue that David Lewis fails to support his claim that time-travelling Tim cannot kill his Grandfather in 1921. This result, in turn, undermines Lewis’s contextualist solution to the Grandfather Paradox—i.e. conceding that Tim can and cannot kill Grandfather, but relative to different contexts in each case.

Time travel, it has been argued, leads to paradoxes, and in particular to a problem known as the grandfather paradox. Lewis has famously argued for the now standard view that the grandfather paradox is merely apparent. But underlying Lewis's solution is a faulty account of ability statements – one, according to which ability statements express possibility statements. I argue, contrary to Vihvelin and others, that an ameliorated view of ability statements allows for the same treatment of (...) the seeming paradox. Hence, Lewis's take on the grandfather paradox stands despite the failure of the particular view of ability statements it is built upon. (shrink)

Assume that, even with a time machine, Tim does not have the ability to travel to the past and kill Grandfather. Why would that be? And what are the implications for traditional debates about freedom? We argue that there are at least two satisfactory explanations for why Tim cannot kill Grandfather. First, if an agent’s behavior at time _t_ is causally dependent on fact _F_, then the agent cannot perform an action (at _t_) that would require _F_ to (...) have not obtained. Second, if an agent’s behavior at time _t_ is causally dependent on fact _F_, then the agent cannot perform an action (at _t_) that would prevent _F_ from obtaining. These two explanations have distinct upshots for more traditional debates over freedom. The first implies that causal determinism is incompatible with the ability to do otherwise and also raises questions about the traditional arguments for the incompatibility of divine foreknowledge and the ability to do otherwise; the second does neither. However, both explanations imply that the Molinist account of divine providence renders agents unable to do otherwise, at least in certain circumstances. (shrink)

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)

Most arguments against the possibility of time travel use the same old, familiar objection: If I could travel back in time, then I could kill my earlier (i.e. younger) self. Since I do exist such an action would result in a contradiction. Therefore time travel is impossible. This is a statement of the Principal Paradox of Time Travel. Some philosophers have argued that such actions as attempting to kill one’s earlier self would always fail and that there is nothing (...) especially strange about such failures. Despite these arguments, the problem generally is not viewed as being solved in favour of time travel. The above objection to time travel is also used to dismiss a particular class of cosmological models as being unphysical. This paper provides a solution to the Principal Paradox by exploring both the logical and causal implications of time travel. (shrink)

There is a tension between Dispositionalism––the view that all metaphysical modality is grounded in actual irreducible dispositional properties––and the possibility of time travel. This is due to the fact that Dispositionalism makes it much harder to solve a potentiality-based version of the grandfather paradox. We first present a potentiality-based version of the grandfather paradox, stating that the following theses are inconsistent: 1) time travel is possible, 2) powers fully ground modality, 3) self-defeating actions are impossible, 4) (...) time-travellers retain their intrinsic powers upon time-travelling, and 5) time-travellers are ordinary agents with basic intrinsic potentialities. We then consider a number of potential solutions, and find them wanting. We argue that the metaphysical impossibility of performing a self-defeating action acts as a necessary perfect mask––while time-travel lets us “slip” the potentiality under the mask, thus generating the contradiction. We conclude considering what are the options for the dispositionalist. (shrink)

The question of time travel stimulates the imagination and provides material for whimsical stories. A work on the topic of "time travel" forces us to deal with the concept of "time". The complexity and the antinomic character of this concept make it difficult to grasp "time" more precisely. We encounter time as a form of perception in its deeply subjective aspect, as a biological rhythm, as a social phenomenon in the sense of a collective determination of time, but also as (...) a physical quantity. Einstein's theory of relativity revolutionized our ideas of space and time. His Special Theory of Relativity (1905) allows "travel into the future" through the effect of time dilation he predicted, and Einstein's theory of gravity allows for closed time lines as solutions to its equations (e.g., Gödel cosmos, anti-de Sitter cosmos). However, traveling in a time loop would immediately lead to a number of paradoxes (e.g., grandfather paradox, information paradox). Although, surprisingly, the basic laws of physics (apart from extremely rare and macroscopically non-appearing quantum mechanical effects) would not be violated in a time reversal, there seems to be a fundamental prohibition of traveling into the past in nature. (shrink)

The question of time travel stimulates the imagination and provides material for whimsical stories. A work on the topic of "time travel" forces us to deal with the concept of "time". The complexity and the antinomic character of this concept make it difficult to grasp "time" more precisely. We encounter time as a form of perception in its deeply subjective aspect, as a biological rhythm, as a social phenomenon in the sense of a collective determination of time, but also as (...) a physical quantity. Einstein's theory of relativity revolutionized our ideas of space and time. His Special Theory of Relativity (1905) allows "travel into the future" through the effect of time dilation he predicted, and Einstein's theory of gravity allows for closed time lines as solutions to its equations (e.g., Gödel cosmos, anti-de Sitter cosmos). However, traveling in a time loop would immediately lead to a number of paradoxes (e.g., grandfather paradox, information paradox). Although, surprisingly, the basic laws of physics (apart from extremely rare and macroscopically non-appearing quantum mechanical effects) would not be violated in a time reversal, there seems to be a fundamental prohibition of traveling into the past in nature. (shrink)

Do time travellers retain their normal freedom and abilities when they travel back in time? Lewis, Horwich and Sider argue that they do. Time-travelling Tim can kill his young grandfather, his younger self, or whomever else he pleases—and so, it seems can reasonably deliberate about whether to do these things. He might not succeed. But he is still just as free as a non-time traveller. I’ll disagree. The freedom of time travellers is limited by a rational constraint. Tim can’t (...) reasonably deliberate on killing his grandfather, certain that he’ll fail. If Tim follows his evidence, and appropriately self-predicts, he will be certain he won’t kill his grandfather. So if Tim is both evidentially and deliberatively rational, he can’t deliberate on killing his grandfather. This result has consequences. Firstly, it shows how evidential limits in the actual world contribute to our conception of the future as open. Secondly, it undercuts arguments against the possibility of time travel. Thirdly, it affects how we evaluate counterfactuals in time travel worlds, as well as our own. I’ll use the constraint to motivate an evidential and temporally neutral method of evaluating counterfactuals that holds fixed what a relevant deliberating agent has evidence of, independently of her decision. Using this method, an agent’s local abilities may be affected by what happens globally at other times, including the future. (shrink)

Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement with certainty, and we discuss an important difference between “Deutschian” CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett (...) and Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set of linearly independent quantum states, and we prove that it is not possible for such a party to distinguish a set of linearly dependent states. The power of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still applies to circuits using them, regardless of their ability to conspire in violating the uncertainty principle. We then discuss how different notions of a quantum mixture that are indistinguishable in linear quantum mechanics lead to dramatically differing conclusions in a nonlinear quantum mechanics involving P-CTCs. Finally, we give explicit circuit constructions that can efficiently factor integers, efficiently solve any decision problem in the intersection of NP and coNP, and probabilistically solve any decision problem in NP. These circuits accomplish these tasks with just one qubit traveling back in time, and they exploit the ability of postselected closed timelike curves to create grandfather paradoxes for invalid answers. (shrink)

Time travel is metaphysically possible. Nikk Effingham contends that arguments for the impossibility of time travel are not sound. Focusing mainly on the Grandfather Paradox, Effingham explores the ramifications of taking this view, discusses issues in probability and decision theory, and considers the potential dangers of travelling in time.

The last few years have been good for time machines. Kip Thorne's renowned general relativity group at Caltech invented a new quantum gravitational approach to building a time gate, and, in an international collaboration, gave a plausible rebuttal of "grandfather paradox" arguments against time travel. Another respected group suggested time machines that exploit quantum mechanical time uncertainty. The technical requirements for these suggestions exceed our present capabilities, but each new approach seems less onerous than the last. There is (...) hope yet that time travel will eventually become possible, even cheap. (shrink)

David Lewis’s analysis of “can” in “The Paradoxes of Time Travel” has been widely accepted both as a definitive analysis of “can” and as a successful resolution of the Grandfather Paradox for time travel. I argue that the central feature of his analysis puts it on all fours with a fallacy frequently imputed to fatalists such as Richard Taylor. I go on to consider two moves that might be made to avoid the fallacy, arguing that one of them (...) leads to the unavailability of an all-things-considered “can” and the other to a new primitive modality, not analyzable in Lewis’s way. (shrink)

Recent years have seen a growing consensus in the philosophical community that the grandfather paradox and similar logical puzzles do not preclude the possibility of time travel scenarios that utilize spacetimes containing closed timelike curves. At the same time, physicists, who for half a century acknowledged that the general theory of relativity is compatible with such spacetimes, have intensely studied the question whether the operation of a time machine would be admissible in the context of the same theory (...) and of its quantum cousins. A time machine is a device which brings about closed timelike curves—and thus enables time travel—where none would have existed otherwise. The physics literature contains various no-go theorems for time machines, i.e., theorems which purport to establish that, under physically plausible assumptions, the operation of a time machine is impossible. We conclude that for the time being there exists no conclusive no-go theorem against time machines. The character of the material covered in this article makes it inevitable that its content is of a rather technical nature. We contend, however, that philosophers should nevertheless be interested in this literature for at least two reasons. First, the topic of time machines leads to a number of interesting foundations issues in classical and quantum theories of gravity; and second, philosophers can contribute to the topic by clarifying what it means for a device to count as a time machine, by relating the debate to other concerns such as Penrose's cosmic censorship conjecture and the fate of determinism in general relativity theory, and by eliminating a number of confusions regarding the status of the paradoxes of time travel. The present article addresses these ambitions in as non-technical a manner as possible, and the reader is referred to the relevant physics literature for details. (shrink)

The Multiverse Thesis is a proposed solution to the Grandfather Paradox. It is popular and well promulgated, found in fiction, philosophy and (most importantly) physics. I first offer a short explanation on behalf of its advocates as to why it qualifies as a theory of time travel (as opposed to mere 'universe hopping'). Then I argue that the thesis nevertheless has an unwelcome consequence: that extended objects cannot travel in time. Whilst this does not demonstrate that the Multiverse (...) Thesis is false, the consequence should give pause for concern. Even if it does not lead one to reject the thesis, I briefly detail some reasons to think it is interesting nonetheless. (shrink)

Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to (...) kill your grandfather. Doesn't this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics. (shrink)

David Lewis’s analysis of “can” in “The Paradoxes of Time Travel” (Lewis, American Philosophical Quarterly, 13, 145–52, 1976) has been widely accepted both as a definitive analysis of “can” and as a successful resolution of the Grandfather Paradox for time travel. I argue that the central feature of his analysis puts it on all fours with a fallacy frequently imputed to fatalists such as Richard Taylor. I go on to consider two moves that might be made to avoid (...) the fallacy, arguing that one of them leads to the unavailability of an all-things-considered “can” and the other to a new primitive modality, not analyzable in Lewis’s way. (shrink)

Suppose that you travel back in time to talk to your younger self in order to tell her that she should have done some things in her life differently. Of course, you will not be able to make this plan work, we know that from the many versions of `the grandfather paradox' that populate the philosophical literature about time travel. What will be my centre of interest in this paper is the conversation between you and... you - i.e. (...) the older you that travelled back in time and the younger you, when you first meet. As we shall see, given this situation, endurantists will have to endorse a strange consequence of their view: you will turn out to be a universal while your properties will turn out to be particulars. (shrink)

There is an extensive literature on time travel in both philosophy and physics. Part of the great interest of the topic stems from the fact that reasons have been given both for thinking that time travel is physically possible—and for thinking that it is logically impossible! This entry deals primarily with philosophical issues; issues related to the physics of time travel are covered in the separate entries on time travel and modern physics and time machines. We begin with the definitional (...) question: what is time travel? We then turn to the major objection to the possibility of backwards time travel: the Grandfather paradox. Next, issues concerning causation are discussed—and then, issues in the metaphysics of time and change. We end with a discussion of the question why, if backwards time travel will ever occur, we have not been visited by time travellers from the future. (shrink)

Demonstrates that slapstick film comedies display a canny and sometimes profound understanding of their medium. Slapstick film comedy may be grounded in idiocy and failure, but the genre is far more sophisticated than it initially appears. In this book, Burke Hilsabeck suggests that slapstick is often animated by a philosophical impulse to understand the cinema. He looks closely at movies and gags that represent the conditions and conventions of cinema production and demonstrates that film comedians display a canny and sometimes (...) profound understanding of their medium—from Buster Keaton’s encounter with the film screen in Sherlock Jr. (1924) to Harpo Marx’s lip-sync turn with a phonograph in Monkey Business (1931) to Jerry Lewis’s film-on-film performance in The Errand Boy (1961). The Slapstick Camera follows the observation of philosopher Stanley Cavell that self-reference is one way in which “film exists in a state of philosophy.” By moving historically across the studio era, the book looks at a series of comedies that play with the changing technologies and economic practices behind film production and describes how comedians offered their own understanding of the nature of film and filmmaking. Hilsabeck locates the hidden intricacies of Hollywood cinema in a place where one might least expect them—the clowns, idiots, and scoundrels of slapstick comedy. “From its analysis of the vaudevillian Victorian origins to early Hollywood expressions, and from defining classical performances by the likes of Keaton to recent postmodern recapitulations, Hilsabeck’s theoretically rigorous and wide-ranging study masterfully weaves a path through the historical, technical, and philosophical art of slapstick comedy. A must for scholars working in this field.” — Daniel Varndell, author ofHollywood Remakes, Deleuze and the Grandfather Paradox. (shrink)

Lewis argued that although paradoxes such as the famous Grandfather Paradox can be solved, only a limited set of time travel fiction is consistent. In this paper, I discuss how to extend a Lewisian approach to a class of time travel fiction not considered by Lewis: transmigration or mental time travel fiction. To this end, Lewis’s definition of personal time needs refining, and this is the primary focus of my paper. I discuss some alternative refinements of Lewis’s definition: (...) a Solely Mental definition and a Causal definition. I end by also applying these definitions to cases of reverse aging. (shrink)

This paper focuses on problems for time travel that specifically concern continuous time-travel to the past, problems to do with potential collisions with past obstacles such as former time-slices of the time traveler herself. These problems have not been discussed nearly as much as other questions about time travel, such as the Grandfather Paradox. Here I focus on discussions by Bernstein, Dowe, Grey and Le Poidevin. After examination, I conclude that only the problems of turning around in time (...) have any merit and present a new proposal of my own for turning around in time without collisions. I assume a Lewisian framework throughout. (shrink)

In this chapter I articulate the threat that time travel to the past allegedly poses to the free will of the time traveler, and I argue that on the traditional way of thinking about free will, the incompatibilist about time travel and free will wins the day. However, a residual worry about the incompatibilist view points the way toward a novel way of thinking about free will, one that I tentatively explore toward the end of the chapter.

Notoriously, the Einstein equations of general relativity have solutions in which closed timelike curves occur. On these curves time loops back onto itself, which has exotic consequences: for example, traveling back into one's own past becomes possible. However, in order to make time travel stories consistent constraints have to be satisfied, which prevents seemingly ordinary and plausible processes from occurring. This, and several other "unphysical" features, have motivated many authors to exclude solutions with CTCs from consideration, e.g. by conjecturing a (...) chronology protection law. In this contribution we shall investigate the nature of one particular class of exotic consequences of CTCs, namely those involving unexpected cases of indeterminism or determinism. Indeterminism arises even against the backdrop of the usual deterministic physical theories when CTCs do not cross spacelike hypersurfaces outside of a limited CTC-region|such hypersurfaces fail to be Cauchy surfaces. We shall compare this CTC-indeterminism with four other types of indeterminism that have been discussed in the philosophy of physics literature: quantum indeterminism, the indeterminism of the hole argument, non-uniqueness of solutions of differential equations and lack of predictability due to insuffcient data. By contrast, a certain kind of determinism appears to arise when an indeterministic theory is applied on a CTC: things cannot be different from what they already were. Again we shall make comparisons, this time with other cases of determination in physics. We shall argue that on further consideration both this indeterminism and determinism on CTCs turn out to possess analogues in other, familiar areas of physics. CTC- indeterminism is close to the epistemological indeterminism we know from statistical physics, while the "fixedness" typical of CTC-determinism is pervasive in physics. CTC- determinism and CTC-indeterminism therefore do not provide incontrovertible grounds for rejecting CTCs as conceptually inadmissible. (shrink)

Closed time-like curves (CTCs) naturally appear in a variety of chronology-violating space{times. In these space{times, the principle of self-consistency demands a harmony between local and global a airs that excludes grandfather-like paradoxes. However, selfexisting objects trapped in CTCs are not seemingly avoided by the standard interpretation of this principle, usually constrained to a dynamical framework. In this letter we discuss whether we are committed to accept an ontology with self-existing objects if CTCs actually occur in the universe. In addition, (...) the epistemological status of the principle of self-consistency is analyzed and a discussion on the information flux through CTCs is presented. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Dmitry Khanin THE POSTMODERN POSTURE Postmodernists—the sectarians ofour day—proclaim that the old kingdom of historical narrative and historical subject has perished, and is now being replaced by a new one of ahistorical discourses and ahistorical characters. According to these prophets, "history" is anyway just changes in ways of talking about history. Anyone who does not agree with the ahistoricity of the postmodern world oudook may be accused—and tried on (...) the spot—of defending the cause of the totalitarian Reason against the most liberating movement of today. This postmodernist abuse of history is paradoxical, since the very notion of history coming to its end and giving way to the ahistorical kingdom of freedom and merry debauchery is itself a very old idea, even a mythological one. The description ofhistory as marching toward its own demise relies on a whole tradition which portrays history as a drama. Aristode's conception of tragedy as a sequence of actions culminating in a dénouement has no doubt shaped this view of historical process. Christian and other religious millenarians have announced the end of history already many times. Yet another notorious instance of such eschatological daydreaming is the futurology of Karl Marx, who envisaged the kingdom of communism as occupying this same ahistorical space. A rather obsolete idea, perhaps, but it seems still to attract postmodernists, though they give it a characteristic twist, since they sincerely believe theory, discourse, écriture (i.e., theoretico-symbolical activity) are much more important than any actual historical contentprocesses and events. One of the most notable spokesmen for this approach is Arthur Danto, who insists that world history evolved in a good Hegelian manner until the theorists came to understand that history depends on their Philosophy and Literature, © 1990, 14: 239-247 240Philosophy and Literature texts much more than theorists themselves depend on historical processes and events.1 Many theoreticians working in an otherwise Marxist tradition similarly are glad to assert with FredricJameson that we must say farewell to Marx's positivistic illusion that history is driven by laws disguised as economic forces.2 In the epoch of "late capitalism," says Jameson, consumption gains the upper hand over production and becomes the mainspring of history. Of course, in light of recent doings in Europe I am tempted to ask if we owe it to postmodernists—and their ahistorical, inconsistent, and generally confounding claims about history lying in ruins—that the Berlin Wall actually is in ruins and Vaclav Havel is president of Czechoslovakia. Even more daring theorists may now declare an era of "very late capitalism." Here it will not be merely the mass media that act transformatively on society (as McLuhan claimed), but rather consumer goods themselves, like state-of-the-art washing machines or French perfumes, which create a new aura of intellectual discourse. TL· Postmodern Scene: Excremental Culture and Hyper-AesÜietics, a book by two Canadian authors, Arthur Kroker and David Cook, promotes such a sea change in the theoretical landscape and along the way presents a joyous recapitulation ofthe latest fads in postmodern thinking. The new apostolic generation ofpostmodern critics seems to enjoy the beautiful new things that can be bought for bucks, worrying at the same time that bucks may be losing some of their purchasing power. Like Hari-Krishnas dancing in the street they luckily possess a sort of happy consciousness which also recalls their puritanical great grandfathers who regarded profligacy as the greatest sin and much preferred saving to spending. In what follows I want to draw a portrait of this new postmodern posture. A few main assumptions underlie Kroker's and Cook's wake for postmodernism, which, in its peculiar genre of philosophic obituary, epitomizes and thus prepares for future oblivion views which were exceedingly popular in the preceding decade. First of all, the authors adopt Baudrillard's equation of Marx and Nietzsche: "Marx and Nietzsche shared a deep and common affinity in meditating upon historical (Christian) and materialistic (capitalist) expressions ofthewill ofpower."3 From Baudrillard's perspective Marx appears as a pathetic romantic who tried to defend the "referential illusion" by renaturalizing concrete labor even though its entirely abstract character was brilliandy revealed in Das Kapital. Baudrillard... (shrink)

What one can say about the past, present and future of set theory depends on what one expects or at least hopes set theory will accomplish. In order to gauge the early expectations, I begin with a quote from the inaugural lecture in 1903 of my mathematical grandfather, the internationally known Finnish mathematician Ernst Lindelöf. The subject of his lecture was – guess what – Cantor’s set theory. In his conclusion, Lindelöf says of Cantor’s results: For mathematics they have (...) lent new tools and opened up new fields of research, they have thrown entirely new light on the foundations of analysis and brought clarity and order where there was only disorder and contradictions. Thus they have greatly contributed to the harmony that is the essence of mathematics, a harmony a grasp of which is the reward of mathematical research. (Quoted in Olli Lehto, Tieteen aatelia, Otava, Helsinki, 2008, p. 263) We can all agree with the compliments Lindelöf pays to set theory as an impressive specimen of mathematical research, including the theory of infinite cardinals and ordinals. But as far as the foundational role of set theory is concerned, in the perspective of the subsequent century his words read as an example of supreme historical irony. Far from bringing harmony into the foundations of mathematics, problems arising from set theory led to a schism between different schools of thought. Few mathematicians think of set theory as a tool for reaching new results outside set theory.. On the contrary, an interesting rich tradition called reverse mathematics takes significant mathematical results and asks what set-theoretical assumptions are needed to prove them. Set-theoretical paradoxes have greatly increased mathematicians’ concerns about contradictions instead of assuaging them. Many foundationalists would blandly deny that we have even now, more than a hundred years later, reached “clarity and order” about the foundations of analysis. What Lindelöf took to be the results of set theory thus were in reality so many hopes that set theory was expected to fulfill.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:144 JOURNAL OF THE HISTORY OF PHILOSOPHY 28" 1 JANUARY 199o name neo-Kantianism is generally used only for the time following 188o.s And is K6hnke really beingjust toward later neo-Kantianism in reckoning the 187os as a high point after which only a period of decline could follow? HELMU'r HOLZHEY Universityof Zurich Robert J. Richards. Darwin and the Emergenceof Evolutionary TheoriesofMind and Behav- /or. Science and Its Conceptual Foundations Series. (...) Chicago: The University of Chicago Press, 1987. Pp. xvii + 7oo. $34.95. This fascinating book operates at two levels, possibly three. At the most straightforward level, it is a history of science, telling the tale of the fate of evolutionary ideas as they have been applied to mind and behavior during the past two centuries, with special emphasis on the nineteenth century. At another level, Richards is acting qua philosopher, for he thinks the story he has to tell has important implications for philosophy. In particular, he thinks the people he discusses show the way to compelling theories of evolutionary epistemology and evolutionary ethics. To this end he attaches two philosophical appendices to his book, articulating and defending his philosophical claims. Then, at perhaps a third level, Richards uses his historical narrative as a case study (and possibly an exemplar) for his philosophy, especially his epistemology, trying to justify and illustrate his position. Let me take these levels in turn, briefly. First, we have the history. Anybody who knows anything at all about the history of science will know that the subject is clogged with overproduction and overinterpretation around a few key figures. Chief among these is Charles Darwin, and if ever anyone writes anything again on his discovery of natural selection, I for one will scream. What I have long suspected-- and what Richards shows in full detail--is that, because of their tunnel vision, the historians of science thereby ignore huge fertile areas, which go untouched. And the paradox is that the narrow perspective means that important aspects of those overdiscussed figures go unanalyzed! Certainly, Richards plows virgin territories, and thereby throws new light on many important figures in biology, psychology, and philosophy--not the least of which is Darwin himself. Richards starts in the eighteenth century with the first growths of evolutionary thought, showing that from the beginning thinkers recognized that humankind had to be part of the problem, and that this meant (in particular) human thought and behavior. I was glad to see a full discussion of Charles Darwin's grandfather, Erasmus Darwin. We are now starting to realize how he merits interest in his own right, not just as a curious anticipation of his more famous grandson. Moving forward, Richards shows how Erasmus Darwin struggled constantly with the problem of the human mind, as did Frenchmen like Lamarck. These and other thinkers were all known to s See H. Holzhey, "Neukandanismus," in HistorischesWOrterbuchderPhilosopfiie,vol.6 (1984), column 747ft. BOOK REVIEWS 145 Charles Darwin, and a significant part of Richards's discussion is devoted to showing just how much of Charles Darwin's thought on mind and behavior was built out of the work of others--with his own distinctive twists. Richards emphasizes, and I am sure he is right here, that natural theology was crucial to the development of Charles Darwin's thinking. It was not, as many critics have claimed, a case of Darwin throwing off religion and then taking up evolution. Rather, he has led to his evolution through his religion. Richards is almost unique among twentieth-century thinkers in finding virtue in the work of Herbert Spencer. I am still not convinced that Spencer was other than a tedious Victorian chauvinist. But no doubt I will not be the only scholar who is happy to have a Spencer apologist against whom one can test one's critical opinions. To be commended without reservation, however, is Richards's detailed analysis of the psychobiological thinking of William James. Richards delicately balances his knowledge of James's own psychological states (including facts still suppressed) with conceptual analysis of James's scientific claims. I do not know if this counts as "externalist" or "internalist " history of science, but it certainly shows that knowledge... (shrink)

A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.

The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox (...) synthesises elements of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

Wiredu argues intriguingly that some philosophical questions only arise in certain linguistic settings. So philosophical questions are, on occasion, linguistically relative or, more vividly, Tongue Dependent. The phenomenon however does not rest on expressive differences between languages, or, better, on failures of translation. Though rejecting his example, I endorse the general possibility he constructs. I do so provided that there is a solution to the Paradox of Analysis. Indeed I point out that the possibility of Tongue Dependency is both (...) necessary and sufficient for a solution to the Paradox of Analysis. I then offer a solution to the Paradox of Analysis in a Fregean setting, by distinguishing within the cognitive value of a claim between cognitive accomplishment and cognitive significance. The results of analysis involve cognitive accomplishment, though have no cognitive significance. I recommend my account as dealing well with a problem Salmon raised for the Church-Frege account. Finally, I direct my account on vocabularies rather than claims and note that, though possible, actual cases of Tongue Dependency within natural languages are highly doubtful. The phenomenon does not have the cultural significance Wiredu claims for it. (shrink)

Zermelo once wrote that he had anticipated Russell's contradiction of the set of all sets that are not members of themselves. Is this sufficient for having anticipated Russell's Paradox — the paradox that revealed the untenability of the logical notion of a set as an extension? This paper argues that it is not sufficient and offers criteria that are necessary and sufficient for having discovered Russell's Paradox. It is shown that there is ample evidence that Russell satisfied (...) the criteria and that Zermelo did not. (shrink)

There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.

The lottery paradox can be solved if epistemic justification is assumed to be a species of permissibility. Given this assumption, the starting point of the paradox can be formulated as the claim that, for each lottery ticket, I am permitted to believe that it will lose. This claim is ambiguous between two readings, depending on the scope of ‘permitted’. On one reading, the claim is false; on another, it is true, but, owing to the general failure of permissibility (...) to agglomerate, does not generate the paradox. The solution generalizes to formulations of the paradox in terms of rational acceptability and doxastic rationality. (shrink)

The last decade has witnessed the emergence of a paradox perspective on corporate sustainability. By explicitly acknowledging tensions between different desirable, yet interdependent and conflicting sustainability objectives, a paradox perspective enables decision makers to achieve competing sustainability objectives simultaneously and creates leeway for superior business contributions to sustainable development. In stark contrast to the business case logic, a paradox perspective does not establish emphasize business considerations over concerns for environmental protection and social well-being at the societal level. (...) In order to contribute to the consolidation of this emergent field of research, we offer a definition of the paradox perspective on corporate sustainability and a framework to delineate its descriptive, instrumental, and normative aspects. This framework clarifies the paradox perspective’s contents and its implications for research and practice. We use the framework to map the contributions to this thematic symposium on paradoxes in sustainability and to propose questions for future research. (shrink)