What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative (...) is by far more popular, but I argue in favor of the latter, for (i) it does not suffer from a number of serious objections, and (ii) it makes it possible to restore global validity as a defined notion. (shrink)

The so-called "argument from vagueness", the clearest formulation of which is to be found in Ted Sider’s book Four-dimensionalism, is arguably the most powerful and innovative argument recently offered in support of the view that objects are four-dimensional perdurants. The argument is defective--I submit--and in a number of ways that is worth looking into. But each "defect" corresponds to a model of change that is independently problematic and that can hardly be built into the common-sense picture of (...) the world. So once all the gaps of the argument are filled in, the three-dimensionalist is left with the burden of a response that cannot rely on a passive plea for common sense. The argument is not a threat to common sense as such; it is a threat to the three-dimensionalist faithfulness to common sense. (shrink)

The so-called ‘argument from vagueness’ is among the most powerful and innovative arguments offered in support of the view that objects are four-dimensional perdurants. The argument is defective – I submit – and in a number of ways that are worth looking into. But each ‘defect’, each gap in the argument, corresponds to a model of change that is independently problematic and that can hardly be built into the common-sense picture of the world. So once all the (...) gaps of the argument are filled in, the three-dimensionalist is left with the burden of a response that cannot rely on a passive plea for common sense. The argument is not a threat to common sense as such; it is a threat to the three-dimensionalist faithfulness to common sense. (shrink)

David Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that ‘in so-and-so world’ is a restricting modifier which passes through the truth-functional connectives The outcome is a sort of subvaluational semantics which makes a contradiction ‘A & ~A’ (...) false even when both ‘A’ and ‘~A’ are true, just as supervaluational semantics makes a tautology ‘A v ~A’ true even when neither ‘A’ nor ‘~A’ are. Connections with discussive logics and complications of the account are discussed, and some general morals are drawn. (shrink)

Peter Simons has argued that the expression ‘the universe’ is not a genuine singular term: it can name neither a single, completely encompassing individual, nor a collection of individuals. (It is, rather, a semantically plural term standing equally for every existing object.) I offer reasons for resisting Simons’s arguments on both scores.

This is a revised and extended version of the formal theory of holes outlined in the Appendix to the book "Holes and Other Superficialities". The first part summarizes the basic framework (ontology, mereology, topology, morphology). The second part emphasizes its relevance to spatial reasoning and to the semantics of spatial prepositions in natural language. In particular, I discuss the semantics of ‘in’ and provide an account of such fallacious arguments as “There is a hole in the sheet. The sheet is (...) in the drawer. Ergo *there is a hole in the drawer”. (shrink)

There are two ways of understanding the notion of a contradiction: as a conjunction of a statement and its negation, or as a pair of statements one of which is the negation of the other. Correspondingly, there are two ways of understanding the Law of Non-Contradiction (LNC), i.e., the law that says that no contradictions can be true. In this paper I offer some arguments to the effect that on the first (collective) reading LNC is non-negotiable, but on the second (...) (distributive) reading it is perfectly plausible to suppose that LNC may, in some rather special and perhaps undesirable circumstances, fail to hold. (shrink)

R. Sorensen’s argument to the effect that ’vague’ is a vague predicate has been used by D. Hyde to infer that vague predicates suffer from higher-order vagueness. M. Tye has objected (convincingly) that this is too strong: all that follows from Sorensen’s result is that there are some border border cases, but not necessarily border border cases of every vague predicate. I argue that this is still too strong: Sorensen’s proof presupposes the existence of border border cases, hence cannot (...) be used to establish that fact on pain of circularity. (shrink)

An overview of the way I picture the amorphous world we live in, built around my comments and responses to nine festschrift essays by A. Borghini (on the Fedro metaphor and the art of butchery), F. Calemi (on the predication principle and metalinguistic nominalism), C. Calosi (on the argument from mereological universalism to extensonality), E. Casetta (on the role of “monsters” in the realism/antirealism debate), V. Giardino (on inductive reasoning, spatial representation, and problem solving), P. Graziani (on mereological notation), (...) P. Pedrini (on the distinction between natural and artificial boundaries), D. Santoro (on causation by omission), and G. Torrengo (on absolute vs. relational space and the problem of incongruent counterparts). (shrink)

The Doctrine of Potential Parts says that proper undetached parts are merely potential entities, entities that do not exist but would exist if they were detached from the rest. They are just aspects of the whole to which they belong, ways in which the whole could be broken down, and talk of such parts is really just talk about the modal properties of the whole. Here I offer a reconstruction of this doctrine and present an argument to illustrate its (...) hidden kinship with another, parallel but independent doctrine Doctrine of Potential Wholes. According to this second doctrine, disconnected wholes (i.e., wholes that are not in one piece) are in turn potential entities, entities that do not exist but would exist if their parts were suitably conjoined. (shrink)

This thesis is a study of the role of the phenomenon of death in Heidegger’s philosophy. The central argument is twofold. First, death is the fulcrum of Heidegger’s philosophy. As such, second, death is a crucial key to Heidegger’s thought in its entirety. Thus I claim is that a response to the question of being can be given, if one takes death into account. This thesis, therefore, investigates the four main blocks of Heidegger’s philosophy and the role of death (...) in them. I identify the four main blocks of Heidegger’s philosophy as follows. First, Heidegger’s early transcendental analysis of Dasein’s existence. Second, the thinking of being as event. Third, Heidegger’s critique of technology. Fourth, Heidegger’s engagement with language. The thesis is divided into four topical parts according to these blocks. In the first part I argue that death serves as Dasein’s utmost limit and as such death is constitutive of Dasein’s existential possibilities. The analysis of Dasein’s horizons of understanding is what leads Heidegger to turn to being itself. In the second part I identify the place of death in the thinking of the event and in Heidegger’s theory of history as the history of being. I argue that death becomes an interest of being as such and is testimony to its epochs. Third, I argue that death continues to play a significant role in Heidegger’s philosophy of technology. This is because the essence of technology is a mode of being itself in the sense that being allows for a certain understanding of the current technological age. Thus, technology is an interest of being itself, too, and the essence of technology is sheer availability. Heidegger begins to call death the refuge of being at this time, which indicates that death is as the utterly unavailable, the resting place of being. As such, I argue in parts III and IV, death coenables the fourfold, which is Heidegger’s response to the technological world. In the fourfold things are not manipulated but form the bedrock of a shared communal world. In part IV I develop Heidegger’s claim that there is an essential relation between death and language. In the information age language is reduced to a transmitter of information. Thanks to its relation with death as the utterly unavailable language retains other dimensions that elude the demands of technology. (shrink)

A plausible thought about vagueness is that it involves semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. Where there is incomplete specification of extension there is indeterminacy, an indeterminacy between various ways in which the specification of the predicate might be completed or sharpened. In this paper we show that this idea is bound to founder by presenting an argument to the effect that there are (...) vague predicates which cannot be sharpened in such a way as to meet certain basic constraints (of penumbral connection and public accessibility) that must be imposed on the very notion of a sharpening. (shrink)

There are two natural ways of thinking about negation: (i) as a form of complementation and (ii) as an operation of reversal, or inversion (to deny that p is to say that things are “the other way around”). A variety of techniques exist to model conception (i), from Euler and Venn diagrams to Boolean algebras. Conception (ii), by contrast, has not been given comparable attention. In this note we outline a twofold geometric proposal, where the inversion metaphor is understoood as (...) involving a rotation o a reflection, respectively. These two options are equivalent in classical two-valued logic but they differ significantly in many-valued logics. Here we show that they correspond to two basic sorts of negation operators—Post’s and Kleene’s—and we provide a simple group-theoretic argument demonstrating their generative power. (shrink)

An outline of the material covered in courses on Formal and Informal Logic. The outline includes chapters on mathematical approaches to logic as well as on fallacies, deduction and induction, probability, and other major topics. Logic is traditionally taught by means of problem solving exercises, so the subject is well suited to a Schaum's Outline approach.

The Clarke-Collins correspondence was widely read and frequently printed during the 18th century. Its central topic is the question whether matter can think, or be conscious. Samuel Clarke defends the immateriality of the subject of the mental against Anthony Collins’ materialism. This paper examines important assumptions about the nature of body that play a role in their debate. Clarke argued that consciousness requires an “individual being”, an entity with some sort of significant unity as its subject. They agree that body (...) does not have this type of unity, because it consists of actually distinct parts. (shrink)

Book 1, Part 4, Section 5 of Hume’s Treatise is taken up with a response to an argument for the immateriality of the soul that Hume considered “remarkable,” and that Kant was later to describes as the “Achilles” (the strongest) of all the arguments for this conclusion. This paper surveys versions of the argument offered by Cudworth, Bayle, and Clarke before going on to argue that Hume’s own treatment of the argument departs from the standard in (...) a number of important ways. The departures restate the argument in Humean terms, replacing premises concerning inherence, substance, and action, which Hume considered to be false or unintelligible, with ones mentioning conjunction at a location in space, which he considered to be at least intelligible. These changes challenge the view that Treatise 1.4.5 was intended as a satire or a lampoon. A satire or lampoon exposes a flat statement of its target view to ridicule. It does not modify that view— certainly not by way of introducing improvements to make it more intelligible. Hume meant to endorse what he said in Treatise 1.4.5. In particular, he meant to endorse the tenets that that there are mental states that are spatially extended, and that it is as difficult to explain how an immaterial soul could contain extended mental images as to explain how a material soul could contain unextended thoughts. (shrink)

INTRODUCTION TO THE ARGUMENT AND ITS HISTORY PRIOR TO THE AND CENTURIES In the history of ideas, there is an argument that has been used repeatedly, ...

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)

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)

This study examines the death of Achilles in ancient myth, focusing on the hero's imperfect invulnerability. It is concluded that this concept is of late origin, perhaps of the Hellenistic period. Early evidence about Achilles' infancy does not suggest that he was made invulnerable, and early evidence concerning his death apparently indicates that Achilles was wounded more than once. The story of Achilles' heel as we know it is therefore late, though it is demonstrable that certain (...) themes and motifs of earlier traditions about Achilles were preserved in later traditions. What caused the concept of Achilles' imperfect invulnerability to emerge, it is proposed, was the late story in which the hero is ambushed in the temple of Thymbraean Apollo. Certainly Achilles was wounded in the lower leg in early Greek myth. An explanation is needed if this does not reflect the story of his imperfect invulnerability, and the arguments of several scholars are surveyed. The theory that the "swift-footed" hero was first immobilized by a lower wound before being slain is ultimately favored, though it is suggested that invulnerable armor and poison may have played a role. A comparative approach to myth and ritual is employed, with attention given to evidence from various areas and ages in an effort to illuminate stories about the infancy and death of Achilles. The study also assesses two alleged reflections in the Iliad of Achilles' death, the death of Patroclus in Book 16 and the wounding of Diomedes in Book 11. The evidence in ancient art and literature about the death of Achilles is often obscure, but this exploration of continuity and innovation in myth about Achilles should assist our understanding of it. (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)

It is often assumed that neo-Aristotelian virtue ethics postulates an obligation to be a good human being and that it derives further obligations from this idea. The paper argues that this assumption is false, at least for Philippa Foot’s view. Our argument blocks a widespread objection to Foot’s view, and it shows how virtue ethics in general can neutralize such worries.

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)

William Paley in his famous statement in 1800 of the Argument from Design, imagined that he found a watch lying on a heath and set to wondering how it came to be there. “The inference is inevitable, that the watch must have had a maker: that there must have existed, at some time, and at some place or other, an artificer or artificers who formed it for the purpose which.

Euclid’s definition of a point as “that which has no part” has been a major source of controversy in relation to the epistemological and ontological presuppositions of classical geometry, from the medieval and modern disputes on indivisibilism to the full development of point-free geometries in the 20th century. Such theories stem from the general idea that all talk of points as putative lower-dimensional entities must and can be recovered in terms of suitable higher-order constructs involving only extended regions (or bodies). (...) Here I focus on what is arguably the first thorough proposal of this sort, Whitehead’s theory of “extensive abstraction”, offering a critical reconstruction of the theory through its successive installments: from the purely mereological version of ‘La théorie relationniste de l’espace’ (1916) to the refined versions presented in An Enquiry Concerning the Principles of Natural Knowledge (1919) and in The Concept of Nature (1920) to the last, mereotopological version of Process and Reality (1929). (shrink)

In his article ‘A Nonce-word in the Iliad’ Maurice Pope argues against the usual modern interpretation of παναώριος, a Homeric παξ λεγόμενον applied by Achilles to himself at Il. 24.540, sc. ‘of all-untimely fate’, ‘doomed to die young’, and the like. The same is also the interpretation of the scholium παντελς ωρον ποθανούμενον, whilst Herodian and Eustathius, respectively with κατ πάντα ωρον and πάντ ωρον, do no more than paraphrase the force of παν- in the compound. Pope tries to (...) establish instead the suitability of the meaning ‘out of season’, i.e. in what Achilles does or fails to do in general. His case rests on the ground of what is appropriate to or required by the context, since, as he himself shows, the word in itself can, on the analogy of closely related forms, notably the adjective ωρος, bear the meaning usually attributed to it, provided the context contains sufficient indication of a reference to death. Accordingly, the validity of his argument depends on his assessment of this context. Pope recognises that throughout the last part of the Iliad, at least starting from the conversation between Achilles and his mother at 18.70ff., Achilles is fully aware of the nearness and unavoidability of his own death, and that ‘from this point on Homer exploits the atmosphere of impending doom’. But after citing several passages in which the approach of Achilles' death is mentioned, Pope continues as follows. (shrink)

In his article ‘A Nonce-word in the Iliad’ Maurice Pope argues against the usual modern interpretation of παναώριος, a Homeric παξ λεγόμενον applied by Achilles to himself at Il. 24.540, sc. ‘of all-untimely fate’, ‘doomed to die young’, and the like. The same is also the interpretation of the scholium παντελς ωρον ποθανούμενον, whilst Herodian and Eustathius, respectively with κατ πάντα ωρον and πάντ ωρον, do no more than paraphrase the force of παν- in the compound. Pope tries to (...) establish instead the suitability of the meaning ‘out of season’, i.e. in what Achilles does or fails to do in general. His case rests on the ground of what is appropriate to or required by the context, since, as he himself shows, the word in itself can, on the analogy of closely related forms, notably the adjective ωρος, bear the meaning usually attributed to it, provided the context contains sufficient indication of a reference to death. Accordingly, the validity of his argument depends on his assessment of this context. Pope recognises that throughout the last part of the Iliad, at least starting from the conversation between Achilles and his mother at 18.70ff., Achilles is fully aware of the nearness and unavoidability of his own death, and that ‘from this point on Homer exploits the atmosphere of impending doom’. But after citing several passages in which the approach of Achilles' death is mentioned, Pope continues as follows. (shrink)

In _Necropolitics_ Achille Mbembe—a leader in the new wave of Francophone critical theory—theorizes the genealogy of the contemporary world—a world plagued by ever-increasing inequality, militarization, enmity, and terror, as well as by a resurgence of racist, fascist, and nationalist forces determined to exclude and kill. He outlines how democracy has begun to embrace its dark side, or what he calls its “nocturnal body,” which is based on the desires, fears, affects, relations, and violence that drove colonialism. This shift has hollowed (...) out democracy, thereby eroding the very values, rights, and freedoms liberal democracy routinely celebrates. As a result, war has become the sacrament of our times, in a conception of sovereignty that operates by annihilating all those considered to be enemies of the state. Despite his dire diagnosis, Mbembe draws on post-Foucault debates on biopolitics, war, and race, as well as Fanon's notion of care as a shared vulnerability, to explore how new conceptions of the human that transcend humanism might come to pass. These new conceptions would allow us to encounter the Other not as a thing to exclude, but as a person with whom to build a more just world. (shrink)

There is no doughnut without a hole, the saying goes. And that’s true. If you think you can come up with an exception, it simply wouldn’t be a doughnut. Holeless doughnuts are like extensionless color, or durationless sound—nonsense. Does it follow, then, that when we buy a doughnut we really purchase two sorts of thing—the edible stuff plus the little chunk of void in the middle? Surely we cannot just take the doughnut and leave the hole at the grocery store, (...) as we cannot just eat the doughnut and save the hole for later. But then, again, surely when we eat a doughnut we do not also eat the hole. Or do we? (shrink)

La filosofia non è una scienza empirica e si regge in buona misura sull’argomenta- zione (→), cioè sulla capacità di giustificare certe affermazioni, o tesi, sulla base di altre ritenute vere. Sin dall’antichità la teoria dell’argomentazione ha pertanto occupato una posizione di rilievo nella ricerca filosofica, e già a partire da Aristotele ha contribuito a definire quel settore disciplinare che oggi chiamiamo logica (dalla parola greca logos, che significa tra l’altro ‘discorso’, ‘ragionamento’). Aristotele stesso codificò la materia in maniera sistematica, (...) secondo schemi e principi che rimasero insuperati per oltre due millenni (→ sillogistica). A partire dal XIX secolo la teoria logica subì però mutamenti profondi, grazie soprattutto all’opera del matematico inglese George Boole e del filosofo tedesco Gottlob Frege, e nel XX secolo si è assistito a sviluppi straordinari che hanno portato all’applicazione della logica non solo in filosofia ma anche in altri ambiti di ricerca (dalla linguistica al diritto sino all’informatica). (shrink)

The five participants in this dialogue critically discuss Zeno of Elea's paradox of Achilles and the tortoise. They consider a number of solutions to and restatements of the paradox, together with their philosophical implications. Among the issues investigated include the appearance-reality distinction, Aristotle's distinction between actual and potential infinity, the concept of a continuum, Cantor's continuum hypothesis and theory of transfinite ordinals, and, as a solution to Zeno's puzzle, the distinction between infinite and indeterminate or inexhaustible divisibility.

In _Critique of Black Reason_ eminent critic Achille Mbembe offers a capacious genealogy of the category of Blackness—from the Atlantic slave trade to the present—to critically reevaluate history, racism, and the future of humanity. Mbembe teases out the intellectual consequences of the reality that Europe is no longer the world's center of gravity while mapping the relations among colonialism, slavery, and contemporary financial and extractive capital. Tracing the conjunction of Blackness with the biological fiction of race, he theorizes Black reason (...) as the collection of discourses and practices that equated Blackness with the nonhuman in order to uphold forms of oppression. Mbembe powerfully argues that this equation of Blackness with the nonhuman will serve as the template for all new forms of exclusion. With _Critique of Black Reason_, Mbembe offers nothing less than a map of the world as it has been constituted through colonialism and racial thinking while providing the first glimpses of a more just future. (shrink)