What is it to base a belief on reasons? Existing attempts to give an account of the basing relation encounter a dilemma: either one appeals to some kind of neutral process that does not adequately reflect the way basing is a content‐sensitive first‐personal activity, or one appeals to linking or bridge principles that over‐intellectualize and threaten regress. We explain why this dilemma arises, and diagnose the commitments that are key obstacles to providing a satisfactory account. We explain why they should (...) be rejected anyway, and then offer a new, knowledge‐first virtue epistemological theory of the basing relation that shows how we can substantially theorize about mental processes without these commitments. The resulting view plausibly captures the way in which basing is an inherently mental and content‐sensitive process. (shrink)

This dialogue between Achilles and the Tortoise – in the spirit of those of Carroll and Hofstadter – argues against the idea, identified with the “traditional” interpretation of Aristotle’s “sea battle argument”, that future contingents are an exception to the Principle of Bivalence. It presents examples of correct everyday predictions, without which one would not be able to decide and to act; however, doing this is incompatible with the belief that the content of these predictions lacks a truth-value. The cost (...) of using a non-classical logic to cope with that may be too high for Stagirite’s defenders, and they would still need to explain why our ordinary predictions seem to have a binary truth-value. In the end, the paper suggests that the problem of future contingents – and of free will – is not a logical problem at all, but rather a limit on what an agent can believe before taking a decision. (shrink)

The four antinomies of Zeno of Elea, especially Achilles and the tortoise continue to be provoking issues which are even now not always satisfactory solved. Aristotle himself used this antinomy to develop his understanding of movement: it is a fluent continuum that has to be treated as a whole. The parts, if any, are only potentially present in the whole. And that is exactly what quantum mechanics is claiming: movement is quantized in contrast to classical mechanics. The objective of this (...) study is to show the merits of the Aristotelian approach. It is a good candidate for serving as the philosophical background for understanding fundamental aspects of quantum mechanics. Especially mentioned are the influence of the final state in quantum mechanics that in philosophy could be correlated with the final cause. Like in the work of Aristotle also in this study examples from science are presented to illustrate the philosophical approach. But, in contrast to ancient Greek, the examples now relate to issues which are only fully accessible to the scientifically trained reader. As the main conclusion the dialogue between scientists and philosophers is strongly recommended which will result in progress in both disciplines. (shrink)

Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography.

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...) other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems). (shrink)

The value of extending the human lifespan remains a key philosophical debate in bioethics. In building a case against the extension of the species-typical human life, Nicolas Agar considers the prospect of transforming human beings near the end of their lives into Galapagos tortoises, which would then live on decades longer. A central question at stake in this transformation is the persistence of human consciousness as a condition of the value of the transformation. Agar entertains the idea that consciousness (...) could persist in some measure, but he thinks little is to be gained from the transformation because the experiences available to tortoises pale in comparison to those available to human beings. Moreover, he thinks persisting human consciousness and values would degrade over time, being remade by tortoise needs and environment. The value available in the transformation would not, then, make the additional years of life desirable. Agar’s account does not, however, dispose of the tortoise transformation as a defensible preference. Some people might still want this kind of transformation for symbolic reasons, but it would probably be better that no continuing human consciousness persist, since that consciousness would be inexpressible as such. Even so, it is not irrational to prefer various kinds of lifespan extension even if they involve significant modifications to human consciousness and values. (shrink)

This paper offers an expressivist account of logical form, arguing that in order to fully understand it one must examine what valid arguments make us do (or: what Achilles does and the Tortoise doesn’t, in Carroll’s famed fable). It introduces Charles Peirce’s distinction between symbols, indices and icons as three different kinds of signification whereby the sign picks out its object by learned convention, by unmediated indication, and by resemblance respectively. It is then argued that logical form is represented by (...) the third, iconic, kind of sign. It is noted that icons uniquely enjoy partial identity between sign and object, and argued that this holds the key to Carroll’s puzzle. Finally, from this examination of sign-types metaphysical morals are drawn: that the traditional foes metaphysical realism and conventionalism constitute a false dichotomy, and that reality contains intriguingly inference-binding structures. (shrink)

I propose that an irreducible property of physical space — consistency — is the origin of logic. I propose that an inconsistent space is inconceivable and that this inconceivability can be recognized as the force behind logical propositions. The implications of this argument are briefly explored and then applied to address two paradoxes: Zeno of Elea’s paradox regarding the race between Achilles and the Tortoise, and Lewis Carroll’s paradox regarding the Tortoise’s conversation with Achilles after the race. I conclude that (...) Achilles would have won on both accounts, in the race and the argument, by invoking the consistency of space as the foundation of both movement across space and logical argument. (shrink)

There was a time in my school years when I have learned about Achilles and Tortoise “paradox” originated from Zeno. It was then clear that the ancient Greeks were arguing about this problem but contemporary science has clarified the issue. Yet to my surprise the problem is still debated over and over, despite the fact there exist mathematical proofs. I feel like reminding myself why this is not a paradox beyond reasonable doubt. This is a draft to a section of (...) a future publication. (shrink)

NOTE: this is a substantial revision of a previously uploaded draft. Intuitions are often thought of as inputs to theoretical reasoning. For example, you might form a belief by taking an intuition at face value, or you might take your intuitions as starting points in the method of reflective equilibrium. The aim of this paper is to argue that in addition to these roles intuitions also play action-guiding roles. The argument proceeds by reflection on the transmission of justification through inference. (...) According to inferential internalists, in order to gain justification for believing the conclusion of an argument by inferring it from the premises in that argument one must “see” that the premises support the conclusion. I motivate this view and endorse the idea that one’s “seeing” such a support relation consists of one’s having an intuition. In a number of recent papers, Paul Boghossian has pressed a regress argument against inferential internalism inspired by Lewis Carroll’s dialogue “What the Tortoise Said to Achilles.” I develop a response to Bogossian’s argument according to which intuitions work like mental imperatives and inferences are mental actions performed by obeying them. After developing this response to Boghossian’s argument, I take up the question of what it is in virtue of which intuitions play a guidance role, when they do so. (shrink)

This paper considers the question of what knowing a logical rule consists in. I defend the view that knowing a logical rule is having propositional knowledge. Many philosophers reject this view and argue for the alternative view that knowing a logical rule is, at least at the fundamental level, having a disposition to infer according to it. To motivate this dispositionalist view, its defenders often appeal to Carroll’s regress argument in ‘What the Tortoise Said to Achilles’. I show that this (...) dispositionalist view, and the regress that supposedly motivates it, operate with the wrong picture of what is involved in knowing a logical rule. In particular I show that it gives us the wrong picture of the relation between knowing a logical rule and actions of inferring according to it, as well as of the way in which knowing a logical rule might be a priori. (shrink)

I discuss a neglected solution to the skeptical problem introduced by Lewis Carroll’s “What the Tortoise Said to Achilles” (1895) in terms of a self-citational inferential license. I then consider some responses to this solution. The most significant response on behalf of the skeptic utilizes the familiar distinction between two ways of accepting a rule: as action-guiding and as a mere truth. I argue that this is ultimately unsatisfactory and conclude by opting for an alternative conception of rules as representations (...) of behavior deployed for various purposes, some theoretical and others practical. This alternative conception does not allow the skeptical problem to get off the ground. (shrink)

There is more responsibility on heaven and earth than dreamt of in most philosophy. This dissertation explores three debates in three sub-fields of philosophy, highlighting in each responsibilities agents find themselves with whether they like it or not. In the chapter "Trust Logic, Not Tortoises", I propose an answer to Wright’s Justification Question – to what extent are we justified in our knowledge of logic? – arguing early knowledge of logic is a species of know-how underwritten by dispositions to (...) infer that are themselves often refined into more sophisticated dispositions to infer as we develop. Given how foundational such know-how is to our understanding of the world, we find ourselves responsible for cultivating more sophisticated reasoning, whatever its provenance. In the chapter Ties that Undermine, I argue attributions to an agent of moral responsibility are largely influenced by the perceived rareness of that agent's ability to provide aid or prevent harm, degree of aid provided or harm prevented, and cost to that agent in providing aid or preventing harm. Voluntary adoption of such moral responsibility is not necessary for an agent to be morally responsible. I generalize this result to the epistemic domain in the chapter Speak No Evil: Understanding Hermeneutical (In)justice, arguing attributions to an agent of epistemic responsibility are also influenced by the perceived rareness of that agent's ability to generate true beliefs in themselves and others, extent of benefit provided and harm prevented by having such true beliefs, and cost to that agent in generating such true beliefs. Here, we see voluntary adoption of such epistemic responsibility is not necessary for an agent to be epistemically responsible. By exploring the relevance of such responsibility to three distinct debates in three distinct sub-fields of philosophy, this dissertation highlights how pervasive responsibility is to the lives of agents, and the work of philosophers. (shrink)

Several interesting themes emerge from G. E. Moore’s previously unpub­lished review of _The Principles of Mathematics_. These include a worry concerning whether mathematical notions are identical to purely logical ones, even if coextensive logical ones exist. Another involves a conception of infinity based on endless series neglected in the Principles but arguably involved in Zeno’s paradox of Achilles and the Tortoise. Moore also questions the scope of Russell’s notion of material implication, and other aspects of Russell’s claim that mathematics reduces (...) to logic. (shrink)

‘...if you learn to think like Peter Cave – with freshness, humour, objectivity and penetration – you will have been amply rewarded.’ :::: Prof. Felipe Fernandez-Armesto, University of Notre Dame __________________ Chapter Titles:>>> ___ 1 Lao Tzu: The Way to Tao >>> 2 Sappho: Lover >>> 3 Zeno of Elea: Tortoise Backer, Parmenidean Helper >>> 4 Gadfly: aka ‘Socrates’ >>> 5 Plato: Charioteer, Magnificent Footnote Inspirer – ‘Nobody Does It Better’ >>> 6 Aristotle: Earth-Bound, Walking >>> 7 Epicurus: Gardener, Curing (...) the Soul, Ably Assisted by Lucretius >>> 8 Avicenna: Flying Man, Unifier >>> 9 Descartes: With Princess, With Queen >>> 10 Spinoza: God-Intoxicated Atheist >>> 11 Leibniz: Monad Man >>> 12 Bishop Berkeley, ‘That Paradoxical Irishman’: Immaterialist, Tar-Water Advocate >>> 13 David Hume: The Great Infidel or Le Bon David >>> 14 Kant: Duty Calls, Categorically >>> 15 Schopenhauer: Pessimism With Flute >>> 16 John Stuart Mill: Utility Man, With Harriet, Soul-Mate >>> 17 Søren Kierkegaard: Who? >>> 18 Karl Marx: Hegelian, Freedom-Fighter >>> 19 Lewis Carroll: Curiouser and Curiouser >>> 20 Nietzsche: God-Slaying Jester, Trans-Valuer >>>> 21 Bertrand Russell: Radical, Aristocrat >>> 22 G. E. Moore: Common-Sense Defender, Bloomsbury’s Sage >>> 23 Heidegger: Hyphenater >>> 24 Jean-Paul Sartre: Existentialist, Novelist, French >>> 25 Simone Weil: Refuser and Would-Be Rescuer >>> 26 Simone de Beauvoir: Situated, Protester, Feminist >>> 27 Ludwig Wittgenstein: Therapist >>> 28 Hannah Arendt: Controversialist, Journalist? >>> 29 Iris Murdoch: Attender >>> 30 Samuel Beckett: Not I >>>. (shrink)

Lewis Carroll’s 1895 paper “Achilles and the Tortoise” showed that we need a distinction between rules of inference and premises. We cannot, on pain of regress, treat all rules simply as further premises in an argument. But Carroll’s paper doesn’t say very much about what rules there must be. Indeed, it is consistent with what Carroll says there to think that the only rule is -elimination. You might think that modern Bayesians, who seem to think that the only rule of (...) inference they need is conditionalisation, have taken just this lesson from Carroll. But obviously nothing in Carroll’s argument rules out there being other rules as well. (shrink)

- Applying the law of conservation of time to solve the Achilles and the tortoise paradox. - Applying the smallest unit of time T_min in the universe to solve the Dichotomy paradox. - Applying the disappearing property of matter when moving to solve the Arrow paradox.

Abstract: Folktale is universal. It is found in all parts of the world. One of the outstanding characteristics of folktale is the possession of trickster. Trickster has different name in the tales of different ethnic groups of the world. In Hausa, he is “ereke”, in Yoruba he is “ijapa”, in Ashanti (Ghana) he is “ananse”, in Trinidad, he is fox, in other parts of Europe, he is either rabbit, monkey or hare etc. A trickster is often something of a rogue. (...) He manages to extricate himself from intrigue and sometimes saves himself from dangerous situation by a display of mental ability. The trickster of the folktales of the Igbo people of Nigeria is tortoise ‘Mbe’. Tortoise is not an outstanding animal. In the case of gathering of animals, he would least be noticed. There are large, ferocious, and beautiful animals that would make the presence of tortoise unnoticed. But when it comes to folktales, tortoise is the smallest among the characters. He so much defeats other characters by his deceptions. His greatest weapon is lies. Most of Igbo folktales are moral tales. They teach moral, yet trickster plays prominent role in the tales of Igbo people. In other words trickster is used in the education of the young. The writer investigated to find reasons for such development through reading books and journals relating to the topic. She studied six Igbo folktales and also through oral interviews of some prominent Igbo people of ages ranging from 20-70 yrs of age. The writer found out amongst other things that Igbo world view on life is responsible to the use of tricksters in their education of the young. (shrink)

Simon Blackburn has not shied away from the use of vivid imagery in developing, over a long and prolific career, a large-scale philosophical vision. Here one might think, for instance, of ‘Practical Tortoise Raising’ or ‘Ramsey's Ladder’ or ‘Frege's Abyss’. Blackburn develops a ‘quasi-realist’ account of many of our philosophical and everyday commitments, both theoretical (e.g., modality and causation) and practical (e.g., moral judgement and normative reasons). Quasi-realism aims to provide a naturalistic treatment of its targeted phenomena while earning the (...) right to deploy all of the ‘trappings’ of realism—i.e., while eschewing any idea that our normal thought and talk about such phenomena are pervasively in error. The quasi-realist project is that of explaining how (as Huw Price puts it here) ‘the folk come to “talk the realist talk” without committing ourselves—us theorists, as it were—to “walking the metaphysical walk”’ (p. 136). Quasi-realism, too, can speak of truth, facts, properties, belief, knowledge, and so on. The imagery in this collection also abounds, though, in capturing a different view of quasi-realism: No fewer than three of the contributors picture Blackburn as wanting to have his cake and eat it too (Louise Antony asking, in addition, ‘Who doesn't? It's cake’ [p. 19]). (shrink)