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  1. John Brunero (2005). Instrumental Rationality and Carroll's Tortoise. Ethical Theory and Moral Practice 8 (5):557 - 569.
    Some philosophers have tried to establish a connection between the normativity of instrumental rationality and the paradox presented by Lewis Carroll in his 1895 paper “What the Tortoise Said to Achilles.” I here examine and argue against accounts of this connection presented by Peter Railton and James Dreier before presenting my own account and discussing its implications for instrumentalism (the view that all there is to practical rationality is instrumental rationality). In my view, the potential for a Carroll-style regress just (...)
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  2. Tyler Burge (1984). Epistemic Paradox. Journal of Philosophy 81 (1):5-29.
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  3. Tyler Burge (1978). Buridan and Epistemic Paradox. Philosophical Studies 34 (1):21 - 35.
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  4. Massimiliano Carrara & Davide Fassio, Reductionism and Perfectibility of Science.
    Nicholas Rescher, in The Limits of Science (1984), argued that: «perfected science is a mirage; complete knowledge a chimera» . He reached the above conclusion from a logical argument known as Fitch’s Paradox of Knowability. The argument, starting from the assumption that every truth is knowable, proves that every truth is also actually known and, given that some true propositions are not actually known, it concludes, by modus tollens, that there are unknowable truths. Prima facie, this argument seems to seriously (...)
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  5. Leo K. C. Cheung (2013). On Two Versions of 'the Surprise Examination Paradox'. Philosophia 41 (1):159-170.
    In this paper, I consider a popular version of the clever student’s reasoning in the surprise examination case, and demonstrate that a valid argument can be constructed. The valid argument is a reductio ad absurdum with the proposition that the student knows on the morning of the first day that the teacher’s announcement is fulfilled as its reductio. But it would not give rise to any paradox. In the process, I criticize Saul Kripke’s solution and Timothy Williamson’s attack on a (...)
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  6. David Phiroze Christensen (2004). Putting Logic in its Place: Formal Constraints on Rational Belief. Oxford University Press.
    What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon.
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  7. Mark Colyvan (2006). Naturalism and the Paradox of Revisability. Pacific Philosophical Quarterly 87 (1):1–11.
    This paper examines the paradox of revisability. This paradox was proposed by Jerrold Katz as a problem for Quinean naturalised epistemology. Katz employs diagonalisation to demonstrate what he takes to be an inconsistency in the constitutive principles of Quine's epistemology. Specifically, the problem seems to rest with the principle of universal revisability which states that no statement is immune to revision. In this paper it is argued that although there is something odd about employing universal revisability to revise itself, there (...)
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  8. By Igor Douven (2008). The Lottery Paradox and Our Epistemic Goal. Pacific Philosophical Quarterly 89 (2):204–225.
    Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently there is no (...)
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  9. Dorothy Edgington (2010). Possible Knowledge of Unknown Truth. Synthese 173 (1):41 - 52.
    Fitch’s argument purports to show that for any unknown truth, p , there is an unknowable truth, namely, that p is true and unknown; for a contradiction follows from the assumption that it is possible to know that p is true and unknown. In earlier work I argued that there is a sense in which it is possible to know that p is true and unknown, from a counterfactual perspective; that is, there can be possible, non-actual knowledge, of the actual (...)
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  10. Simon J. Evnine (2001). Learning From One's Mistakes: Epistemic Modesty and the Nature of Belief. Pacific Philosophical Quarterly 82 (2):157–177.
    I argue that it is not ideally rational to believe that some of one's current beliefs are false, despite the impressive inductive evidence concerning others and our former selves. One's own current beliefs represent a commitment which would be undermined by taking some of them to be false. The nature of this commitment is examined in the light of Nagel's distinction between subjective and objective points of view. Finally, I suggest how we might acknowledge our fallibility consistently with this special (...)
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  11. Simon J. Evnine (1999). Believing Conjunctions. Synthese 118 (2):201-227.
    I argue that it is rational for a person to believe the conjunction of her beliefs. This involves responding to the Lottery and Preface Paradoxes. In addition, I suggest that in normal circumstances, what it is to believe a conjunction just is to believe its conjuncts.
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  12. Henry J. Folse (1978). Quantum Theory and Atomism: A Possible Ontological Resolution of the Quantum Paradox. Southern Journal of Philosophy 16 (1):629-640.
  13. Patrick Greenough (2011). Truthmaker Gaps and the No-No Paradox. Philosophy and Phenomenological Research 82 (3):547 - 563.
    Consider the following sentences: The neighbouring sentence is not true. The neighbouring sentence is not true. Call these the no-no sentences. Symmetry considerations dictate that the no-no sentences must both possess the same truth-value. Suppose they are both true. Given Tarski’s truth-schema—if a sentence S says that p then S is true iff p—and given what they say, they are both not true. Contradiction! Conclude: they are not both true. Suppose they are both false. Given Tarski’s falsity-schema—if a sentence S (...)
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  14. Dale Jacquette (2008). Logic of the Preface Paradox. Principia 12 (2):203-216.
    http://dx.doi.org/10.5007/1808-1711.2008v12n2p203 The preface paradox is the apparent pragmatic inconsistency that occurs when the author of a book declares in its preface that despite believing that it is highly probable that everything the book maintains is true it is also highly probable that the book contains at least some errors. The preface paradox has often been presented as an example of a logically inconsistent belief that it is nevertheless rational to accept, supporting the suggestion that rationality has nothing immediately to do (...)
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  15. Thomas Kroedel (2013). The Permissibility Solution to the Lottery Paradox – Reply to Littlejohn. Logos and Episteme 4 (1):103-111.
    According to the permissibility solution to the lottery paradox, the paradox can be solved if we conceive of epistemic justification as a species of permissibility. Clayton Littlejohn has objected that the permissibility solution draws on a sufficient condition for permissible belief that has implausible consequences and that the solution conflicts with our lack of knowledge that a given lottery ticket will lose. The paper defends the permissibility solution against Littlejohn's objections.
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  16. Thomas Kroedel (2012). The Lottery Paradox, Epistemic Justification and Permissibility. Analysis 72 (1):57-60.
    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, (...)
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  17. Frederick Kroon (1993). Rationality and Epistemic Paradox. Synthese 94 (3):377 - 408.
    This paper provides a new solution to the epistemic paradox of belief-instability, a problem of rational choice which has recently received considerable attention (versions of the problem have been discussed by — among others — Tyler Burge, Earl Conee, and Roy Sorensen). The problem involves an ideally rational agent who has good reason to believe the truth of something of the form:[Ap] p if and only if it is not the case that I accept or believe p.
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  18. Jonathan Kvanvig, The Epistemic Paradoxes.
    The four primary epistemic paradoxes are the lottery, preface, knowability, and surprise examination paradoxes. The lottery paradox begins by imagining a fair lottery with a thousand tickets in it. Each ticket is so unlikely to win that we are justified in believing that it will lose.
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  19. Jonathan Kvanvig (1999). Tennant on Knowability. Australasian Journal of Philosophy 77 (4):422-428.
    The knowability paradox threatens metaphysical or semantical antirealism, the view that truth is epistemic, by revealing an awful consequence of the claim [i] that all truths are knowable. Various attempts have been made to find a way out of the paradox.
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  20. Jonathan L. Kvanvig (2006). ``Epistemic Closure Principles&Quot. Philosophy Compass 1:256-267.
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  21. Jonathan L. Kvanvig (2006). The Knowability Paradox. Oxford: Oxford University Press.
    This book thus provides a thorough investigation of the literature on the paradox, and also proposes a solution to the deeper of the two problems raised by ...
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  22. Jonathan L. Kvanvig (1998). Routledge Encyclopedia of Philosophy. Boston: Routledge.
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  23. Jonathan L. Kvanvig (1998). ``The Epistemic Paradoxes&Quot. In Routledge Encyclopedia of Philosophy. Boston: Routledge.
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  24. Jonathan L. Kvanvig (1996). ``The Knowability Paradox and the Prospects for Anti-Realism&Quot. Noûs 29:481-500.
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  25. Eong D. Lee (1998). Kroon on Rationality and Epistemic Paradox. Southwest Philosophy Review 14 (2):169-174.
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  26. Stephen Maitzen (1998). The Knower Paradox and Epistemic Closure. Synthese 114 (2):337-354.
    The Knower Paradox has had a brief but eventful history, and principles of epistemic closure (which say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows) have been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard arguments for and against skepticism seems to turn on the fate of closure. As far as I can tell, however, no one (...)
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  27. Grant Reaber (2012). Rational Feedback. Philosophical Quarterly 62 (249):797-819.
    Suppose you think that whether you believe some proposition A at some future time t might have a causal influence on whether A is true. For instance, maybe you think a woman can read your mind, and either (1) you think she will snap her fingers shortly after t if and only if you believe at t that she will, or (2) you think she will snap her fingers shortly after t if and only if you don't believe at t (...)
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  28. Robert C. Robinson (2007). S5 Solution to the Red Hat Puzzle. Disputatio 2 (22):1 - 7.
    Abstract: I argue that the solution to the Red Hat Problem, a puzzle derived from interactive epistemic logic, requires S5. Interactive epis- temic logic is set out in formal terms, and an attempt to solve the red hat puzzle is made in K, K, and K, each of which fails, showing that a stronger system, K is required.
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  29. Paul Saka (2013). Mind and Paradox. Journal of Experimental and Theoretical Artificial Intelligence 25 (3):377-87.
    Paradoxes are mind-dependent in a number of ways. First, by definition, paradoxes offer surprises or apparent contradictions. Since surprise and appearance rely on subjective psychological reactions, paradoxes rely on psychological events. Second, propositional versions of the liar paradox must eventually appeal to sentences if they are to achieve traction, yet sentential versions of the liar paradox rely on language and hence on mentality. Third, belief paradoxes such as B, "No one believes B", transparently hinge on the existence of mental states. (...)
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  30. Martin Smith (2010). A Generalised Lottery Paradox for Infinite Probability Spaces. British Journal for the Philosophy of Science 61 (4):821-831.
    Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson ([2006]) present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions—among them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform . In (...)
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  31. Martin Smith (2010). What Else Justification Could Be. Noûs 44 (1):10 - 31.
    According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought – if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely (...)
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Epistemic Paradoxes, Misc
  1. Samuel Alexander (2013). An Axiomatic Version of Fitch's Paradox. Synthese 190 (12):2015-2020.
    A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the (...)
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  2. Patrick Bondy (2013). How to Understand and Solve the Lottery Paradox. Logos and Episteme 4 (3).
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  3. Kenneth Boyce & Allan Hazlett (2014). Multi‐Peer Disagreement and the Preface Paradox. Ratio 27 (3):n/a-n/a.
    The problem of multi-peer disagreement concerns the reasonable response to a situation in which you believe P1 … Pn and disagree with a group of ‘epistemic peers’ of yours, who believe ∼P1 … ∼Pn, respectively. However, the problem of multi-peer disagreement is a variant on the preface paradox; because of this the problem poses no challenge to the so-called ‘steadfast view’ in the epistemology of disagreement, on which it is sometimes reasonable to believe P in the face of peer disagreement (...)
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  4. John Corcoran (2006). C. I. Lewis: History and Philosophy of Logic. Transactions of the Charles S. Peirce Society 42 (1):1-9.
    C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed with (...)
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  5. Igor Douven (2002). A New Solution to the Paradoxes of Rational Acceptability. British Journal for the Philosophy of Science 53 (3):391-410.
    The Lottery Paradox and the Preface Paradox both involve the thesis that high probability is sufficient for rational acceptability. The standard solution to these paradoxes denies that rational acceptability is deductively closed. This solution has a number of untoward consequences. The present paper suggests that a better solution to the paradoxes is to replace the thesis that high probability suffices for rational acceptability with a somewhat stricter thesis. This avoids the untoward consequences of the standard solution. The new solution will (...)
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  6. Simone Duca & Hannes Leitgeb (2012). How Serious Is the Paradox of Serious Possibility? Mind 121 (481):1-36.
    The so-called Paradox of Serious Possibility is usually regarded as showing that the standard axioms of belief revision do not apply to belief sets that are introspectively closed. In this article we argue to the contrary: we suggest a way of dissolving the Paradox of Serious Possibility so that introspective statements are taken to express propositions in the standard sense, which may thus be proper members of belief sets, and accordingly the normal axioms of belief revision apply to them. Instead (...)
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  7. Joseph S. Fulda (1991). The Paradox of the Surprise Test. The Mathematical Gazette 75 (474):419-421.
    Presents a /simple/ epistemic solution to the paradox of the surprise test, suitable for undergraduates. Given the Gazette's audience, recalcitrant versions, such as Sorenson's, would have been inappropriate to even mention. It is also classified under "logical paradoxes," because it can be argued that given the existence of logical, rather than epistemic, solutions, so also the paradox is logical, rather than epistemic. -/- The author was not sent proofs, because the /Gazette/ was then run on a "shoestring budget"; the 2009 (...)
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  8. Wesley H. Holliday (forthcoming). Epistemic Logic and Epistemology. In Sven Ove Hansson Vincent F. Hendricks (ed.), Handbook of Formal Philosophy. Springer.
    This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references (...)
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  9. Mark Jago (2013). The Problem of Rational Knowledge. Erkenntnis:1-18.
    Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll (...)
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  10. Brian Kim (forthcoming). This Paper Surely Contains Some Errors. Philosophical Studies.
    The preface paradox can be motivated by appealing to a plausible inference from an author’s reasonable assertion that her book is bound to contain errors to the author’s rational belief that her book contains errors. By evaluating and undermining the validity of this inference, I offer a resolution of the paradox. Discussions of the preface paradox have surprisingly failed to note that expressions of fallibility made in prefaces typically employ terms such as surely, undoubtedly, and bound to be. After considering (...)
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  11. Saul A. Kripke (2011). Two Paradoxes of Knowledge. In , Philosophical Troubles. Collected Papers Vol I. Oxford University Press.
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  12. Thomas Kroedel (2013). Why Epistemic Permissions Don't Agglomerate – Another Reply to Littlejohn. Logos and Episteme 4 (4):451–455.
    Clayton Littlejohn claims that the permissibility solution to the lottery paradox requires an implausible principle in order to explain why epistemic permissions don't agglomerate. This paper argues that an uncontentious principle suffices to explain this. It also discusses another objection of Littlejohn's, according to which we’re not permitted to believe lottery propositions because we know that we’re not in a position to know them.
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  13. Clayton Littlejohn (2013). Don't Know, Don't Believe: Reply to Kroedel. Logos and Episteme 4 (2):231-38.
    In recent work, Thomas Kroedel has proposed a novel solution to the lottery paradox. As he sees it, we are permitted/justified in believing some lottery propositions, but we are not permitted/justified in believing them all. I criticize this proposal on two fronts. First, I think that if we had the right to add some lottery beliefs to our belief set, we would not have any decisive reason to stop adding more. Suggestions to the contrary run into the wrong kind of (...)
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  14. Laureano Luna (forthcoming). Minds Vs. Machines. On Saka's Basic Blindspot Theorem. Journal of Experimental and Theoretical Artificial Intelligence.
    Under the name of ‘Basic Blindspot Theorem’, Paul Saka has proposed in the special issue on mind and paradox of this journal a Gödelian argument to the effect that no cognitive system can be complete and correct. We show that while the argument is successful as regards mechanical and formal systems, it may fail with respect to minds, so contributing to draw a boundary between the former and the latter. The existence of such a boundary may lend support to Saka’s (...)
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  15. Thomas Mulligan (2015). Disagreement, Peerhood, and Three Paradoxes of Conciliationism. Synthese 192 (1):67-78.
    Conciliatory theories of disagreement require that one lower one’s confidence in a belief in the face of disagreement from an epistemic peer. One question about which people might disagree is who should qualify as an epistemic peer and who should not. But when putative epistemic peers disagree about epistemic peerhood itself, then Conciliationism makes contradictory demands and paradoxes arise.
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  16. Joe Salerno, How to Embed Epistemic Modals Without Violating Modus Tollens.
    Epistemic modals in consequent place of indicative conditionals give rise to apparent counterexamples to Modus Ponens and Modus Tollens. Familiar assumptions of fa- miliar truth conditional theories of modality facilitate a prima facie explanation—viz., that the target cases harbor epistemic modal equivocations. However, these explana- tions go too far. For they foster other predictions of equivocation in places where in fact there are no equivocations. It is argued here that the key to the solution is to drop the assumption that (...)
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  17. Martin Smith (2014). The Arbitrariness of Belief. In Dylan Dodd & Elia Zardini (eds.), Contemporary Perspectives on Scepticism and Perceptual Justification. Oxford University Press.
    In Knowledge and Lotteries, John Hawthorne offers a diagnosis of our unwillingness to believe, of a given lottery ticket, that it will lose a fair lottery – no matter how many tickets are involved. According to Hawthorne, it is natural to employ parity reasoning when thinking about lottery outcomes: Put roughly, to believe that a given ticket will lose, no matter how likely that is, is to make an arbitrary choice between alternatives that are perfectly balanced given one’s evidence. It’s (...)
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  18. P. Roger Turner (2012). Jesus' Return as Lottery Puzzle: A Reply to Donald Smith. Religious Studies 48 (3):305-313.
    In his recent article, ‘Lottery puzzles and Jesus’ return’, Donald Smith says that Christians should accept a very robust scepticism about the future because a Christian ought to think that the probability of Jesus’ return happening at any future moment is inscrutable to her. But I think that Smith’s argument lacks the power rationally to persuade Christians who are antecedently uncommitted as to whether or not we can or do have any substantive knowledge about the future. Moreover, I think that (...)
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  19. Jonathan Weisberg (2012). The Bootstrapping Problem. Philosophy Compass 7 (9):597-610.
    Bootstrapping is a suspicious form of reasoning that verifies a source's reliability by checking it against itself. Theories that endorse such reasoning face the bootstrapping problem. This article considers which theories face the problem, and surveys potential solutions. The initial focus is on theories like reliabilism and dogmatism, which allow one to gain knowledge from a source without knowing that it is reliable. But the discussion quickly turns to a more general version of the problem that does not depend on (...)
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