During his historic Galápagos visit in 1835, Darwin spent nine days making scientific observations and collecting specimens on Santiago (James Island). In the course of this visit, Darwin ascended twice to the Santiago highlands. There, near springs located close to the island's summit, he conducted his most detailed observations of Galapagos tortoises. The precise location of these springs, which has not previously been established, is here identified using Darwin's own writings, satellite maps, and GPS technology. Photographic evidence from excursions (...) to the areas where Darwin climbed, including repeat photography over a period of four decades, offers striking evidence of the deleterious impact of feral mammals introduced after Darwin's visit. Exploring the impact that Darwin's Santiago visit had on his thinking - especially focusing on his activities in the highlands - raises intriguing questions about the depth of his understanding of the evolutionary evidence he encountered while in the Galápagos. These questions and related insights provide further evidence concerning the timing of Darwin's conversion to the theory of evolution, which, despite recent claims to the contrary, occurred only after his return to England. (shrink)

Based on a popular legend in Gansu, the far western province of China, The Tortoise in Asia recounts the exploits of Marcus, a young Roman centurion schooled in the Greek classics who, after a devastating loss in a battle with the Parthians, is taken prisoner, marched along the Silk Road, and pressed into service as a border guard on the eastern frontier. After a daring escape, Marcus has many adventures working with the Hun army as a mercenary. Throughout this harrowing (...) journey, Marcus learns about Chinese philosophies, uncovering the startling similarities between these philosophies and those of Greece. (shrink)

In this paper I am not so much concerned with movements of the mind, as movements of the will. But my question bears a similarity to that of the tortoise. I want to ask whether the will is under the control of fact and reason, combined. I shall try to show that there is always something else, something that is not under the control of fact and reason, which has to be given as a brute extra, if deliberation is ever (...) to end by determining the will. This is, of course, a Humean conclusion, and the only novelty comes in the way I wish to argue for it. I believe that many philosophers think, erroneously, that Hume relies on a naive and outdated conception of facts, or on an even more naive and outdated conception of reason, in order to put passion on their throne. My tortoise defends Hume: what we do with our premises is not itself construed as acceptance of a premise. As it stands the project is only described metaphorically. Presumably everything, including movement of the will, is under the control of facts in some sense, for even if they are only facts about our physiology or chemistry, still, they make us move. I am interested only in cognitive control, or control by the apprehension of fact and reason. (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 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)

Practical philosophy and ethics -- Practical tortise raising -- Truth, beauty, and goodness -- Dilemmas: dithering, plumping, and grief -- Group minds and expressive harm -- Trust, cooperation, and human psychology -- Must we weep for sentimentalism? -- Through thick and thin -- Perspectives, fictions, errors, play -- The steps from doing to saying -- Success semantics -- Wittgenstein's irrealism -- Circles, finks, smells, and biconditionals -- The absolute conception: Putnam vs. Williams -- Julius Caesar and George Berkeley play leapfrog (...) -- The majesty of reason -- Fiction and conviction. (shrink)

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 paper discusses a novel response to two closely related regress arguments from Bolzano’s Theory of Science and Carroll’s What the Tortoise Said to Achilles. Bolzano’s argument aims to refute the thesis that full grounds must include propositions involving notions such as entailment, grounding or lawhood which link the respective grounds to their groundee. This thesis is motivated, Bolzano’s argument is reconstructed, and a response based on self-referential linking propositions is developed and defended against objections concerning self-reference and Curry’s paradox. (...) Finally, the idea is applied to a reading of Carroll’s dialogue and a corresponding solution to the so-called infinite regress problem of inference is proposed. (shrink)

Simon Blackburn has claimed that on a theory of revealed preference it is tautological that any eligible player - one whose preferences are consistent - plays hawk, chooses a strategy of non-cooperation with the other prisoner. This claim is examined and rejected. A prisoner in the appropriate sense is defined not by preferences over actions (playing hawk or playing dove) but by preferences over the four possible outcomes which result from the players' actions jointly (both playing hawk, both playing dove, (...) the first playing hawk and the second dove, and vice versa). It is not inconsistent to suppose that a prisoner has the appropriate preferences over outcomes but nevertheless chooses to play dove. This can happen either if the prisoner believes for some reason that the full range of outcomes is not available, or if the prisoner is simply a bad strategic thinker. It is perhaps tautological that a player with the appropriate preferences over outcome and with suitable beliefs will if rational choose to play hawk. However, rationality would then involve an appeal to a further principle, the sure-thing principle: if a prisoner would choose hawk knowing that the other will choose hawk, and would also choose hawk knowing that the other will choose dove, then hawk should be chosen when it is uncertain what the other will choose. (shrink)

Even if you believe just what you rationally ought to believe, you may be open to rational criticism if you do so ‘for the wrong reasons’, as we say. Some have thought that this familiar observation supports the idea that there are diachronic norms of epistemic rationality – namely, norms of good reasoning. Partly drawing upon Carroll's story of Achilles and the Tortoise, this article criticises this line of thought on the grounds that it rests on a mistaken conception of (...) inference. (shrink)

A great deal of ink has been spilt debating the relative merits of foundationalism and coherentism in contemporary epistemology. In this dissertation, I argue that the debate itself, lively as it's been, rides atop a fundamental mistake. Careful examination of the defenses of these views indicates that both sides rest on a set of problematic presuppositions about justification and the nature of mind. More specifically, they all assume, in one form or another, that epistemic dependence must be inferential, and, as (...) a result, that direct access to the world could only be understood as resting on a class of entities which asymmetrically convey justification to other beliefs without receiving support from them. Revealing these assumptions promises to show that there is a much larger range of options for explaining our knowledge of the world than we can see when we are in the grips of an approach to epistemology and the philosophy of mind which requires us to choose between foundationalism and coherentism. (shrink)

What the Tortoise Taught Us offers a lively, concise journey through western philosophy that explores the lives of major philosophers, their ideas, and how their thinking continues to influence our lives today.

What the Tortoise Taught Us offers a lively, concise journey through western philosophy that explores the lives of major philosophers, their ideas, and how their thinking continues to influence our lives today.

Rationality requires us to have certain propositional attitudes (beliefs, intentions, etc.) given certain other attitudes that we have. Carroll’s Tortoise repeatedly shows up in this discussion. Following up on Brunero (Ethical Theory Moral Pract 8:557–569, 2005), I ask what Carroll-style considerations actually prove. This paper rejects two existing suggestions, and defends a third.

It is widely held that the paradox of Achilles and the Tortoise, introduced by Zeno of Elea around 460 B.C., was solved by mathematical advances in the nineteenth century. The techniques of Weierstrass, Dedekind and Cantor made it clear, according to this view, that Achilles’ difficulty in traversing an infinite number of intervals while trying to catch up with the tortoise does not involve a contradiction, let alone a logical absurdity. Yet ever since the nineteenth century there have been dissidents (...) claiming that the apparatus of Weierstrass et al. has not resolved the paradox, and that serious problems remain. It seems that these claims have received unexpected support from recent developments in mathematical physics. This support has however remained largely unnoticed by historians of philosophy, presumably because the relevant debates are cast in mathematical-technical terms that are only accessible to people with the relevant training. That is unfortunate, since the debates in question might well profit from input by philosophers in general and historians of philosophy in particular. Below we will first recall the Achilles paradox, and describe the way in which nineteenth century mathematics supposedly solved it. Then we discuss recent work that contests this solution, reiterating the dissident dogma that no mathematical approach whatsoever can even come close to solving the original Achilles. We shall argue that this dissatisfaction with a mathematical solution is inadequate as it stands, but that it can perhaps be reformulated in the light of new developments in mathematical physics. (shrink)

Continuing the conversation between Achilles and the tortoise begun by Carroll, this paper proves that, in a supertask context, there are free actions (in general, contingent states of affairs) that can be predicted by means of purely logical reasons.

How things were a decade ago: The largest rain forest of our planet abides in the Amazon Basin, a tenth of the entire world biomass. It is one of the last great frontiers on earth; only the bottom of the sea presents terra incognita on so rich and grand a scale. Perhaps half the planet's species dwell in Amazonia, most of them still unknown to our own technological encampment. No mere ocean of green, this community is so intricately interwoven as (...) to constitute a single vast organism, the one true Leviathan, outweighing all the whales in all the oceans of the world that have ever lived. It is the last and greatest forest on earth, and now it is disappearing before it has been discovered: At nearly an acre a second, the TransAmazon highway system and the land clearing operations it has enabled are extinguishing the forest before it can be explored. From space, Landsat pictures show the burned-over patches spreading with the highway network year by year, magenta sores in the false-color images. We, the voracious Lilliputians now, antlike, are dismantling the greatest biochemical engine on earth at a scale so vast that the carbon dioxide economy of the entire planetary atmosphere suffers. In a century of genocides, perhaps the penultimate great extinction unfolds, prologue to the threatening self-immolation of our own species. (shrink)

There is no philosophically interesting distinction to be made between inference-rules and premises. That there is such a distinction is often held to follow from the possibility of infinite regress illustrated by Carroll's story of Achilles and the tortoise. I will argue that this is wrong on three separate grounds. Consequently, Carroll's fable provides no motivation to abandon the traditional logical separation of arguments into their premises and conclusions. There is no proposition that must be taken to be a rule (...) and must not be taken as a premise. (shrink)

There is no philosophically interesting distinction to be made between inference-rules and premises. That there is such a distinction is often held to follow from the possibility of infinite regress illustrated by Carroll's story of Achilles and the tortoise. I will argue that this is wrong on three separate grounds. Consequently, Carroll's fable provides no motivation to abandon the traditional logical separation of arguments into their premises and conclusions. There is no proposition that must be taken to be a rule (...) and must not be taken as a premise. (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)

In On Certainty, Wittgenstein addressed the issue of beliefs that are not to be argued for, either because any grounds we could produce are less certain than the belief they are supposed to ground, or because our interlocutors would not accept our reasons. However, he did not address the closely related issue of justifying a conclusion to interlocutors who do not see that it follows from premises they accept. In fact, Wittgenstein had discussed the issue in the Remarks on the (...) Foundations of Mathematics; his view had been that certain inferential practices are constitutive of our notions of thinking and inferring. I argue that his treatment of unfounded beliefs in On Certainty essentially replicates, mutatis mutandis, his treatment of basic logical inference. (shrink)

Carroll's short piece “What the Tortoise said to Achilles” in many ways anticipates issues that arise in a number of contemporary controversies. One might argue, for example, that initially plausible attempts to deal with the problem of easy knowledge will land one in the unfortunate position of Achilles who followed the Tortoise down a road that leads to vicious infinite regress. Or consider the conditions required for inferential justification. For idealized inferential justification, I have defended the view that to be (...) justified in believing P on the basis of E one needs to be not only justified in believing E, but justified in believing that E makes probable P. And again, critics have argued that such a strong requirement fails to learn the lesson that Achilles should have been taught by the Tortoise. Even more generally, one might well argue that strong access internalists will need to deal with a variation of Carroll's puzzle even for their accounts of non-inferential justification. In this paper I'll examine these controversies with a mind to reaching a conclusion about just exactly how one can accept intellectually demanding conditions on justified belief without encountering vicious regress. (shrink)

In this paper, I present a discrete solution for the paradox of Achilles and the tortoise. I argue that Achilles overtakes the tortoise after a finite number of steps of Zeno’s argument if time is represented as discrete. I then answer two objections that could be made against this solution. First, I argue that the discrete solution is not an ad hoc solution. It is embedded in a discrete formulation of classical mechanics. Second, I show that the discrete solution cannot (...) be falsified experimentally. (shrink)

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)