Graham Priest has focused attention on an intriguing but neglected paradox posed by José Benardete in 1964. Benardete viewed the paradox as a threat to the intelligibility of the spatial and temporal continua and offered several different versions of it. Priest has selected one of those versions and formalized it. Although Priest has succeeded nicely in sharpening the paradox, the version he chose to formalize has distracting and potentially problematic features that are absent from some of (...) class='Hi'>Benardete's other versions. I offer a formalization of a simpler version of the paradox, the one that presents most plainly Benardete's challenge to the spatial continuum. Proposed resolutions of Benardete's paradox should address this version of the paradox as well as the one formalized by Priest. (shrink)

The paper analyses Benardete's paradox of the gods from a more general perspective (the convergence approach) than several of the most important proposals made to date, but in close relation (and sharp contrast) with them. The new theory, based on the notion of limit, is systematically applicable in different possible scenarios involving a denumerable infinity of objects. In particular, it reveals in what way ω-consistency can be compromised in an otherwise consistent description of such "infinitary" situations.

I consider a puzzling case presented by Jose Benardete, and by appeal to this case develop a paradox involving counterfactual conditionals. I then show that this paradox may be leveraged to argue for certain non-obvious claims concerning the logic of counterfactuals.

This volume is a tribute to the thought of Seth Benardete by contributors who had the rare good fortune of studying with him or those who discovered the treasure of his writings. Benardete was fully immersed in the world of the ancients, starting with Homer, but their works opened up for him a way to the fundamental questions-about justice and love, nature and law, human and divine. Finding "the problem of the human good grounded in the city, and the problem (...) of being in god," he was led to the conclusion that "Political philosophy is the eccentric core of philosophy." While Benardete wrote this statement reflecting on the theological-political issue in the work of his teacher, Leo Strauss, the paradoxical notion of an "eccentric core," in giving this volume its title, is meant to capture a characteristic of his own way of thinking. The essays in this collection-on the Bible and Homer, the pre-Socratics, Plato, Aristotle, and the Roman writers-indicate the range of Benardete's studies and teaching. The centrality of Plato is evident at the same time in those pieces as well as in the reviews of Benardete's books included here, along with three of his own previously unpublished essays. Book jacket. (shrink)

The majority of disucssions of Benardete’s Paradox conclude that the traveller approaching the infinite series of gods will be mysteriously halted despite none of the gods erecting any barriers. Using a revision-theoretic analysis of Benardete’s puzzle, four distinct possible outcomes that might occur given Benardete’s set-up are distinguished. This analysis provides additional insight into the puzzle at hand, via identifying heretofore unnoticed possible outcomes, but it also serves as an example of how the revision theoretic framework can be used (...) to construct exhaustive taxonomies of potential outcomes in apparently contradictory situations. (shrink)

In this section-by-section commentary, Benardete argues that Plato's _Republic_ is a holistic analysis of the beautiful, the good, and the just. This book provides a fresh interpretation of the _Republic_ and a new understanding of philosophy as practiced by Plato and Socrates. "Cryptic allusions, startling paradoxes, new questions... all work to give brilliant new insights into the Platonic text."—Arlene W. Saxonhouse, _Political Theory_.

Whatever one may think of Schmidt’s intuition, it is still nothing but intuition, and the variety of syntactic structures which εἶναι admits of is neither articulated nor unified. Kahn, on the other hand, by the use of Transformational Grammar, is able to a large extent to generate in a regular way from a posited notion of "kernel sentence" all the Greek sentences in which εἶναι occurs. Kahn’s original plan was "to correlate every intuitive difference of meaning in the use of (...) εἰμί with a formal description of the corresponding sentence-type", but he admits that he cannot always do so. Whether this is a failure inherent in Transformational Grammar itself, or in the version Kahn uses, can for the moment be left aside. First, an example of the success and another of the failure of the technique, as Kahn practices it, are in order. Kahn formulates the rule for the recognition of periphrasis somewhat as follows: εἶναι is used periphrastically with the participle if and only if it is impossible to obtain two kernel sentences, one of which has a finite form of εἶναι and the other a finite form of the participle, but if two kernel sentences can be so obtained, the usage is not periphrastic. This rule is both simple and elegant; it will no doubt become in time a standard part of Greek grammar. The enchantment, however, which mathematical clarity can cast is best illustrated in the case of another construction. ἔστιν ὅστις... is not uncommon. It looks like the existential operator of modern logic, and the fact that it occurs far more often with οὐκ than without seems to be, linguistically, irrelevant. Now, Kahn asserts that, though he looked hard for examples, he could only find one in which the second clause has the copula, and he offers a proof as to why this should be the case. He is mistaken. Euripides has οὐκ ἔστι θνητῶν ὅστις ἕστ’ ἐλεύθερος, and Sophocles καὶ οὐδὲν τούτων ὅ τι μὴ Ζεύς, and there are several examples in just one passage of Plato’s Charmides. The Sophoclean example is important since it illustrates a double "zeroing" of εἶναι, and whereas for traditional grammar such nominal sentences are treated as primary, with the insertion of ἐστί as a secondary development, in Kahn’s use of Transformational Grammar no distinction between the presence or the absence of the verb can be allowed. For deep structure, the verb is always present, and it might be no more than an apparent paradox that a verb, whose primitive meaning is said to designate presence, can in its absence make its presence equally felt. Can a verb which is almost always eliminable be the word for reality and truth? Or is it because "being" is the only word that cannot be just a word that it can so easily be suppressed in speech? (shrink)

Godel's and Tarski's theorems were inspired by paradoxes: the Richard paradox, the Liar. Godel, in the 1951 Gibbs lecture argued from his metatheoretical results for a metaphysical claim: the impossibility of reducing, both, mathematics to the knowable by the human mind and the human mind to a finite machine (e.g. the brain). So Godel reasoned indirectly from paradoxes for metaphysical theses. I present four metaphysical theses concerning mechanism, reductive physicalism and time for the only purpose of suggesting how it (...) could be argued for them directly from paradoxical sentences. (shrink)

Benardete presents a version of Zeno's dichotomy in which an infinite sequence of gods each intends to raise a barrier iff a traveller reaches the position where they intend to raise their barrier. In this paper, I demonstrate the abstract form of the Benardete Dichotomy. I show that the diagnosis based on that form can do philosophical work not done by earlier papers rejecting Priest's version of the Benardete Dichotomy, and that the diagnosis extends to a paradox not normally (...) classified as a dichotomy. I show how the form is exploited to generate paradox. Introduction The form of the Benardete dichotomy 2.1 The unsatisfiable pair diagnosis Applying the unsatisfiable pair diagnosis 3.1 Perez Laraudogoitia 3.2 Hawthorne 3.3 Angel 3.4 Yablo and Sorensen Exploiting the form. (shrink)

I shall begin by discussing Benardete’s string paradox. Then, a new puzzle involving supertasks and causality is proposed and discussed. Finally, the new string paradox facilitates the discovery of a surprising example of irreversible mechanical process.

We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning.

Plato, Allan Bloom wrote, is "the most erotic of philosophers," and his Symposium is one of the greatest works on the nature of love ever written. This new edition brings together the English translation of the renowned Plato scholar and translator, Seth Benardete, with two illuminating commentaries on it: Benardete's "On Plato's _Symposium_" and Allan Bloom's provocative essay, "The Ladder of Love." In the _Symposium,_ Plato recounts a drinking party following an evening meal, where the guests include the poet (...) Aristophanes, the drunken Alcibiades, and, of course, the wise Socrates. The revelers give their views on the timeless topics of love and desire, all the while addressing many of the major themes of Platonic philosophy: the relationship of philosophy and poetry, the good, and the beautiful. (shrink)

Koons (2014) claims that Benardete’s Grim Reaper Scenario affords grounds for denying that there can be bounded non-well-founded sequences of time intervals. Pruss (2018) claims that Benardete’s Grim Reaper Scenario affords grounds for affirming causal finitism. I shall argue that what you take to be a minimal response to the Benardete scenario is not something that you can arrive at independently from making a determination about whether causal finitism is true and whether there can be bounded non-well-founded sequences of time (...) intervals. In particular, whether you think that the specification of the dispositions of the reapers in Benardete’s scenario is complete depends upon whether or not you think that causal finitism is true. (shrink)

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of (...) universal or conditional claims in everyday life. (shrink)

The aim of this paper is to distinguish between, and examine, three issues surrounding Humphreys's paradox and interpretation of conditional propensities. The first issue involves the controversy over the interpretation of inverse conditional propensities — conditional propensities in which the conditioned event occurs before the conditioning event. The second issue is the consistency of the dispositional nature of the propensity interpretation and the inversion theorems of the probability calculus, where an inversion theorem is any theorem of probability that makes (...) explicit (or implicit) appeal to a conditional probability and its corresponding inverse conditional probability. The third issue concerns the relationship between the notion of stochastic independence which is supported by the propensity interpretation, and various notions of causal independence. In examining each of these issues, it is argued that the dispositional character of the propensity interpretation provides a consistent and useful interpretation of the probability calculus. (shrink)

G. E. Moore observed that to assert, 'I went to the pictures last Tuesday but I don't believe that I did' would be 'absurd'. Over half a century later, such sayings continue to perplex philosophers. In the definitive treatment of the famous paradox, Green and Williams explain its history and relevance and present new essays by leading thinkers in the area.

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and (...) logic-based approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

Simpson's Paradox is introduced and analysed via the mishaps of a researcher who at first falls afoul of the traps Simpson-reversals can set, and then he learns to exploit those traps to advantage. (Note: An error in the treatment of the Sure Thing Principle is corrected in "Simpson's Paradox: A Logically Benign, Empirically Treacherous Hydra").

_Theaetetus_, the _Sophist_, and the _Statesman_ are a trilogy of Platonic dialogues that show Socrates formulating his conception of philosophy as he prepares the defense for his trial. Originally published together as _The Being of the Beautiful_, these translations can be read separately or as a trilogy. Each includes an introduction, extensive notes, and comprehensive commentary that examines the trilogy's motifs and relationships. "Seth Benardete is one of the very few contemporary classicists who combine the highest philological competence with a (...) subtlety and taste that approximate that of the ancients. At the same time, he as set himself the entirely modern hermeneutical task of uncovering what the ancients preferred to keep veiled, of making explicit what they indicated, and hence...of showing the naked ugliness of artificial beauty."—Stanley Rose, _Graduate Faculty Philosophy Journal_ Seth Benardete was professor of classics at New York University. He was the author or translator of many books, most recently _The Argument of the Action, Plato's "Laws," and Plato's "Symposium,"_ all published by the University of Chicago Press. (shrink)

Galileo's paradox of infinity involves comparing the set of natural numbers, N, and the set of squares, {n2 : n ∈ N}. Galileo sets up a one-to-one correspondence between these sets; on this basis, the number of the elements of N is considered to be equal to the number of the elements of {n2 : n ∈ N}. It also characterizes the set of squares as smaller than the set of natural numbers, since ``there are many more numbers than (...) squares". As a result, it concludes that infinities cannot be compared in terms of greater--lesser and the law of trichotomy does not apply to them. Cantor's cardinal numbers provide a measure for sets. Cantor gives a definition of the relation greater–lesser between cardinal numbers and establishes the law of trichotomy for these numbers. Yet, when Cantor's theory is applied to subsets of N, it gives that any set can be either finite or of the power ℵ0. Thus, although the set of squares is the subset of N, they are of the same cardinality. Benci, Di Nasso introduces specific numbers to measure sets called numerosities. With numerosities, the following claim is true: numerosity of A < numerosity of B, whenever A ⊈ B. In this paper, we present a simplified version of the theory of numerosities that applies to subsets of N. This theory complies with Galileo's presupposition that when A ⊈ B, then the number of elements in A is smaller than the number of elements in B. Specifically, we show that as the numerosity of N is the number α, the numerosity of the set of squares is the integer part of the number √α, that is ⌊√α⌋, and the inequality ⌊√α⌋ < α holds. (shrink)

THE OPENING OF THE THEAETETUS is curious. The report we have of another opening of nearly the same length indicates that it was always a curiosity. If both openings are Plato’s, and the rest of the dialogue they preface were not different, then Plato changed his mind about how to start off the trilogy to which the Theaetetus belongs. If the second version is spurious, someone thought he could surpass Plato and make a more sensible introduction. If ours is spurious, (...) however, then we cannot hope to interpret it. If we assume its genuineness and that it represents Plato’s only or final recension—the other one is said to be spurious and rather frigid—then the Theaetetus opens with our listening in on a recital of the conversation Socrates had with Theaetetus and Theodorus shortly before his death, while we supposedly are hearing it in Megara many years after the conversation occurred. (shrink)

Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in (...) 1998 and a modified version of the problem that Benardete introduced in 1964. Finally, we present a solution to the three isomorphic problems. (shrink)

_The Being of the Beautiful_ collects Plato’s three dialogues, the _Theaetetus_, _Sophist_, and _Statesmen_, in which Socrates formulates his conception of philosophy while preparing for trial. Renowned classicist Seth Benardete’s careful translations clearly illuminate the dramatic and philosophical unity of these dialogues and highlight Plato’s subtle interplay of language and structure. Extensive notes and commentaries, furthermore, underscore the trilogy’s motifs and relationships. “The translations are masterpieces of literalness.... They are honest, accurate, and give the reader a wonderful sense of the (...) Greek.”—Drew A. Hyland, _Review of Metaphysics_. (shrink)

My aim in this paper is to suggest a new outlook concerning the nature of Zeno’s paradoxes. The attention is directed towards the three famous paradoxes known as “Dichotomy,” “Achilles and the Tortoise,” and “The Arrow.” An analysis of the paradigmatic proposals for a solution shows that an adequate solution has not yet been reached. An answer is provided instead to the question “How Zeno’s paradoxes emerge in their quality of aporiae?,” that is to say in their quality of impasses, (...) of problem situations without an exit, what is the original meaning of the Greek word “aporia.” It is my claim that this is the correct rational approach for solving these conceptual puzzles. In other words, I am not proposing formal solutions by criticizing and/or altering their premises assuming the continuous or discrete nature of space and time, but I try to draw the philosophical attention to the way we possess the phenomenon of motion as a result of the perception of space-time in human experience. (shrink)

G. E. Moore famously observed that to assert ‘I went to the pictures last Tuesday but I do not believe that I did’ would be ‘absurd’. Moore calls it a ‘paradox’ that this absurdity persists despite the fact that what I say about myself might be true. Krista Lawlor and John Perry have proposed an explanation of the absurdity that confines itself to semantic notions while eschewing pragmatic ones. We argue that this explanation faces four objections. We give a (...) better explanation of the absurdity both in assertion and in belief that avoids our four objections. (shrink)

The first major piece of unpublished work by Leo Strauss to appear in more than thirty years, this volume offers the public the unprecedented experience of encountering this renowned scholar as his students did. Given as a course in autumn 1959 under the title "Plato's Political Philosophy," these provocative lectures—until now, never published, but instead passed down from one generation of students to the next—show Strauss at his subtle and insightful best.

The Laws was Plato's last work, his longest, and one of his most difficult. In contrast to the Republic, which presents an abstract ideal not intended for any actual community, the Laws seems to provide practical guidelines for the establishment and maintenance of political order in the real world. With this book, the distinguished classicist Seth Benardete offers an insightful analysis and commentary on this rich and complex dialogue. Each of the chapters corresponds to one of the twelve books of (...) the Laws, illuminating the major themes and arguments, which have to do with theology, the soul, justice, and education. The Greek word for law, "nomos," also means musical tune. Bernardete shows how music--in the broadest sense, including drama, epic poetry, and even puppetry--mediates between reason and the city in Plato's philosophy of law. Most broadly, however, Benardete here uncovers the concealed ontological dimension of the Laws, explaining why it is concealed and how it comes to light. In establishing the coherence and underlying organization of Plato's last dialogue, Benardete makes a significant contribution to Platonic studies. (shrink)

In 1964 José Benardete invented the “New Zeno Paradox” about an infinity of gods trying to prevent a traveller from reaching his destination. In this paper it is argued, contra Priest and Yablo, that the paradox must be resolved by rejecting the possibility of actual infinity. Further, it is shown that this paradox has the same logical form as Yablo’s Paradox. It is suggested that constructivism can serve as the basis of a common solution to New (...) Zeno and the paradoxes of truth, and a constructivist interpretation of Kripke’s theory of truth is given. (shrink)

Aristotle begins not with the question of being but with its correlative, the question of knowledge and wisdom. This question is the substitute for the lack of anything self-evidently prior to that which metaphysics itself establishes. The theme of the first chapter is delight and admiration—the delight we ourselves take in any effortless acquisition of knowledge, and the admiration we grant to anyone who is manifestly superior to ourselves in knowledge. That which unites that kind of delight with this kind (...) of admiration is the absence in both of calculation. Without any regard to our own advantage, we no less want by nature to know than are we willing to admire discoverers and inventors. Our admiration for discoverers and inventors is the intersubjective analogue to our own natural curiosity. The selflessness Aristotle detects in curiosity and admiration culminates in the freedom that belongs preeminently to the highest kind of wisdom. The freedom from need which is manifest even in the senses is the natural origin of the freeman’s being his own cause. (shrink)

_Theaetetus_, the _Sophist_, and the _Statesman_ are a trilogy of Platonic dialogues that show Socrates formulating his conception of philosophy as he prepares the defense for his trial. Originally published together as _The Being of the Beautiful_, these translations can be read separately or as a trilogy. Each includes an introduction, extensive notes, and comprehensive commentary that examines the trilogy's motifs and relationships. "Seth Benardete is one of the very few contemporary classicists who combine the highest philological competence with a (...) subtlety and taste that approximate that of the ancients. At the same time, he as set himself the entirely modern hermeneutical task of uncovering what the ancients preferred to keep veiled, of making explicit what they indicated, and hence...of showing the naked ugliness of artificial beauty."—Stanley Rose, _Graduate Faculty Philosophy Journal_ Seth Benardete was professor of classics at New York University. He was the author or translator of many books, most recently _The Argument of the Action, Plato's "Laws," and Plato's "Symposium,"_ all published by the University of Chicago Press. (shrink)

Prawitz observed that Russell’s paradox in naive set theory yields a derivation of absurdity whose reduction sequence loops. Building on this observation, and based on numerous examples, Tennant claimed that this looping feature, or more generally, the fact that derivations of absurdity do not normalize, is characteristic of the paradoxes. Striking results by Ekman show that looping reduction sequences are already obtained in minimal propositional logic, when certain reduction steps, which are prima facie plausible, are considered in addition to (...) the standard ones. This shows that the notion of reduction is in need of clarification. Referring to the notion of identity of proofs in general proof theory, we argue that reduction steps should not merely remove redundancies, but must respect the identity of proofs. Consequentially, we propose to modify Tennant’s paradoxicality test by basing it on this refined notion of reduction. (shrink)

There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with (...) action. (shrink)

_Theaetetus_, the _Sophist_, and the _Statesman_ are a trilogy of Platonic dialogues that show Socrates formulating his conception of philosophy as he prepares the defense for his trial. Originally published together as _The Being of the Beautiful_, these translations can be read separately or as a trilogy. Each includes an introduction, extensive notes, and comprehensive commentary that examines the trilogy's motifs and relationships. "Seth Benardete is one of the very few contemporary classicists who combine the highest philological competence with a (...) subtlety and taste that approximate that of the ancients. At the same time, he as set himself the entirely modern hermeneutical task of uncovering what the ancients preferred to keep veiled, of making explicit what they indicated, and hence...of showing the naked ugliness of artificial beauty."—Stanley Rose, _Graduate Faculty Philosophy Journal_ Seth Benardete was professor of classics at New York University. He was the author or translator of many books, most recently _The Argument of the Action, Plato's "Laws," and Plato's "Symposium,"_ all published by the University of Chicago Press. (shrink)

In _The Tragedy and Comedy of Life,_ Seth Benardete focuses on the idea of the good in what is widely regarded as one of Plato's most challenging and complex dialogues, the _Philebus._ Traditionally the _Philebus_ is interpreted as affirming the doctrine that the good resides in thought and mind rather than in pleasure or the body. Benardete challenges this view, arguing that Socrates vindicates the life of the mind over the life of pleasure not by separating the two and advocating (...) a strict asceticism, but by mixing pleasure and pain with mind in such a way that the philosophic life emerges as the only possible human life. Benardete combines a probing and challenging commentary that subtly mirrors and illuminates the complexities of this dialogue with the finest English translation of the _Philebus_ yet available. The result is a work that will be of great value to classicists, philosophers, and political theorists alike. (shrink)

After introducing Fitch’s paradox of knowability and the knower paradox, the paper critically discusses the dialetheist unified solution to both problems that Beall and Priest have proposed. It is first argued that the dialetheist approach to the knower paradox can withstand the main objections against it, these being that the approach entails an understanding of negation that is intolerably weak and that it commits dialetheists to jointly accept and reject the same thing. The lesson of the knower (...) paradox, according to dialetheism, is that human knowledge is inconsistent. The paper also argues that this inconsistency has not been shown by dialetheists to be wide enough in its scope to justify their approach to Fitch’s problem. The connection between the two problems is superficial and therefore the proposed unified solution fails. (shrink)