The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I think (...) that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worldsConsidered as two languages for describing the same subject matter, modal and purely quantificational languages show interesting differences. The operator variables of the purely quantificational languages give them more power than the modal languages, but at least some of the functions performed by the apparatus of operator variables are also performed, in a more primitive and less versatile way, by actuality operators in modal languages.A final note. Quine has written much on the inter-relations of quantifiers, identity, and the concept of existence. These, he holds, form a tightly knit conceptual system which has been evolved to a high point of perfection, but which might conceivably change yet further.29 He has also dropped hints about the possibility of a simpler, primitive or defective version of the system, in which the quantifiers are not backed up in their accustomed way by the concept of identity. He has dubbed the resulting concept a ‘pre-individuative’ concept of existence, or a concept of ‘entity without identity.’ What would a pre-individuative concept of existence be like? Quine has sometimes suggested that one might be embodied in the use of mass nouns, but the identity concept is used in connection with stuff as well as with things: “is that the same coffee that was in the cup last night?” I would submit that modality provides a better case. In view of the comparative weakness of modal languages, compared to the explicitly quantificational ones Quine takes as canonical, there is surely a sense in which the concept of existence embodied in that disguised existential quantifier, the possibility operator, is a defective one. And as we have seen, one of the differences between modal operators and explicit quantifiers is that modal operators cannot be joined with the identity predicate in the way quantifiers with operator variables can. Surely, then, there is a sense in which ordinary speech, as opposed to the metaphysical theorizing of a Leibniz or a David Lewis, conceives of possible worlds as entities without identity. (shrink)

We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of the actuality (...) operator in the actuality extension of any normal propositional modal logic and of any “classical” modal logic. As an application, we provide an alternative proof of a result of Williamson’s to the effect that the compound operator A□ behaves, in any normal logic between T and S5, like the simple necessity operator □ in S5. (shrink)

Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...) considering a Sheffer function for intuitionistic logic. (shrink)

The logic of paradox, LP, is a first-order, three-valued logic that has been advocated by Graham Priest as an appropriate way to represent the possibility of acceptable contradictory statements. Second-order LP is that logic augmented with quantification over predicates. As with classical second-order logic, there are different ways to give the semantic interpretation of sentences of the logic. The different ways give rise to different logical advantages and disadvantages, and we canvass several of these, concluding that it will be extremely (...) difficult to appeal to second-order LP for the purposes that its proponents advocate, until some deep, intricate, and hitherto unarticulated metaphysical advances are made. (shrink)

Not the least admirable of the late David Lewis’s attributes was his disdain for technical terminology and jargon. His writings are a model demonstrating that, with skill and care, it is possible to discuss even the most mathematical aspects of logic and semantics in clear English prose, and with only a minimum of symbolism. The main text of Parts of Classes [1, hereafter: PoC], a 120-page essay on the foundations of set theory, follows Aristotle in using letters as variables, and (...) has a few dashes and ellipses where it mentions schemata, but is otherwise free of logical notation. The essential advantages of what Church called “the logistic method” do not depend on its typographical accidents!) It is only natural that writers following him have taken one of his expressive words and turned it into a technical term: he allowed ‘atomless gunk’ as a possible complication in the mereological analysis of things, and ‘gunk’ is now a technical term in mereology. Gunk is stuff every part of which contains further parts, stuff which can be divided endlessly without ever arriving at an indivisible atom. (shrink)

The French philosopher Jean Buridan's work on the logical paradoxes is currently attracting more attention than it has for several centuries. In part this is due to a general resurgence of interest in the paradoxes, but the immediate occasion is the recent publication of G. E. Hughes's edition, translation, and commentary on the chapter of Buridan's Sophismata most immediately concerned with the paradoxes. It is worth noting, therefore, that Buridan's theory fails, and in a way that makes it seem unlikely (...) that it can be developed into a serious rival of more modern theories. (shrink)

Logics that have many truth values—more than just True and False—have been argued to be useful in the analysis of very many philosophical and linguistic puzzles. In this paper, which is a followup to, we will start with a particularly well-motivated four-valued logic that has been studied mainly in its propositional and first-order versions. And we will then investigate its second-order version. This four-valued logic has two natural three-valued extensions: what is called a “gap logic”, and what is called a (...) “glut logic”. We mention various results about the second-order version of these logics as well. And we then follow our earlier papers, where we had added a specific conditional connective to the three valued logics, and now add that connective to the four-valued logic under consideration. We then show that, although this addition is “conservative” in the sense that no new theorems are generated in the four-valued logic unless they employ this new conditional in their statement, nevertheless the resulting second-order versions of these logics with and without the conditional are quite different in important ways. We close with a moral for logical investigations in this realm. (shrink)

A 1971 paper by Roman Suszko, ‘Identity Connective and Modality’, claimed that a certain identity-free schema expressed the condition that there are at most two objects in the domain. Section 1 here gives that schema and enough of the background to this claim to explain Suszko’s own interest in it and related conditions—via non-Fregean logic, in which the objects in question are situations and the aim is to refrain from imposing this condition. Section 3 shows that the claim is false, (...) and suggests a diagnosis as to why it might have been made, in terms of quantifier scope distinctions as they bear on schematic formulations. In between, Section 2 discusses an issue brought up by this discussion but not involving the mistaken claim itself, and shows that Suszko was familiar with two different ways to set an upper or lower finite bound to the domain—a contrast which some contemporary readers may associate with David Lewis. (shrink)

Nelson has presented a constructive arithmetic with a negation opera- tion () dierent from the ordinary intuitionistic one . In [5] he presents a variant of Kleene's realization semantics for intuitionistic arithmetic, and proves that relative to this interpretation the arithmetic language with { has the same expressive power as the usual intuitionistic one, and fact certain theories of arithmetic incorporating his negation are equivalent to corresponding systems of intuitionistic arithmetic. A Fitch style natural deduction formulation ) of the pure (...) rst order logic that may be extracted, from Nelson's work may be obtained from that for intuitionistic rst order logic by rst dropping the intuitionistic rule of negation intro- duction and then adding rules guaranteeing the De Morgan equivalences, their quantier analogues, and the equivalence of anegated implication with the conjunction of its antecedent and the negation of its consequent. Given the De Morgan equivalences, conjunction and the existential quantier may he treated as dened operators. (shrink)

Ian Hacking's [6] is a spirited romp though a broad field of metaphysics, touching on a variety of important questions, and appealing to deep results in mathematical logic while remaining free of logical pedantry. Philosophical journals might be more fun to read if others could write in his style. It is an essay in applying the theory of logic expounded in more detail in his very interesting [7]. Unfortunately, despite my sympathy for his project, I have a number of criticisms (...) to make of his argument. Some of them are picky logical points, but the major conclusions of [6] are affected. (shrink)

Il platonista sostiene che le verità della matematica e della logica siano letteralmente vere, ossia che descrivano (in qualche modo: non voglio legare la definizione a una particolare teoria semantica) realtà che non sono create o decise da noi. Il convenzionalista sostiene invece che le proposizioni che chiamiamo verità della matematica siano in qualche misura convenzionali: esse esprimerebbero convenzioni che abbiamo adottato noi, o certe loro conseguenze. Le due posizioni sono apparenteme...

There are good reasons to want logics, including many-valued logics, to have usable conditionals, and we have explored this in certain logics. However, it turns out that we “accidentally” chose some favourable logics. In this paper, we look at some of the unfavourable logics and describe where usable conditionals can be added and where it is not possible.

This book critically reviews all principal contributions to the American animal rights debate by activists, campaigners, academics, and lawyers, while placing animal rights in context with other related and competing movements.

This celebratory Festschrift dedicated to Charles Kahn comprises some 23 articles by friends, former students and colleagues, many of whom first presented their papers at the international "Presocratics and Plato" Symposium in his honor. The conference was organized and sponsored by the HYELE Institute for Comparative Studies, Parmenides Publishing, and Starcom AG, with endorsements from the International Plato Society, and the Dean of the School of Arts and Sciences, University of Pennsylvania. While Kahn's work reaches far beyond the Presocratics and (...) Plato, it is in these subject areas that the distinction of his scholarship has come to be regarded as virtually unrivaled. The articles contributed to this volume are by some of the most renowned scholars working on these topics today, their breadth and depth bearing witness to his profound impact and influence on the discipline of Ancient Greek Philosophy._ Charles Kahn taught Classics and Philosophy at Columbia University from 1957 to 1965, and has since been teaching in the Philosophy Department of the University of Pennsylvania. He spent a year as Visiting Professor at the American School of Classical Studies in Athens, and had additional Visiting Fellowships at Balliol College, Oxford and Clare Hall, Cambridge, and a term as Visiting Professor at Harvard. He is the recipient of several prestigious research grants, from the American Council of Learned Societies, the National Endowment for the Humanities, and the Guggenheim Foundation. In 2000 he was elected Fellow of the National Academy of Arts and Sciences. He is the author of _Anaximander and the Origins of Greek Cosmology, The Verb “Be” in Ancient Greek, The Art and Thought of Heraclitus, Plato and the Socratic Dialogue, Pythagoras and the Pythagoreans, and Essays on Being_. His latest book,_Plato and the Post-Socratic Dialogue_, is forthcoming from Cambridge University Press. _ Contributors: Julia Annas Sarah Broadie Lesley Brown Tomás Calvo-Martínez Diskin Clay John M. Dillon Dorothea Frede Arnold Hermann Carl A. Huffman Enrique Hülsz Piccone D. M. Hutchinson Paul Kalligas Vassilis Karasmanis Aryeh Kosman Anthony A. Long Richard McKirahan Susan Sauvé Meyer Alexander P.D.Mourelatos Satoshi Ogihara Richard Patterson Christopher J. Rowe David Sedley Richard Sorabji. (shrink)

The ninth edition of Media Ethics: Issues and Cases has been updated to reflect the most pressing ethical issues in media. Featuring 25 new cases on hot topic issues from fake news to drones and a new chapter on social justice, this authoritative case book gives students the tools to make ethical decisions in an increasingly complex environment.

In this book, Newell makes the case for unified theories by setting forth a candidate.

Contrary to Vaesen's argument that humans are unique with respect to nine cognitive capacities essential for tool use, we suggest that although such cognitive processes contribute to variation in tool use, it does not follow that these capacities arenecessaryfor tool use, nor that tool use shaped cognition per se, given the available data in cognitive neuroscience and behavioral biology.

Obtaining informed consent from patients prior to a medical or surgical procedure is a fundamental part of safe and ethical clinical practice. Currently, it is routine for a significant part of the consent process to be delegated to members of the clinical team not performing the procedure (eg, junior doctors). However, it is common for consent-taking delegates to lack sufficient time and clinical knowledge to adequately promote patient autonomy and informed decision-making. Such problems might be addressed in a number of (...) ways. One possible solution to this clinical dilemma is through the use of conversational artificial intelligence using large language models (LLMs). There is considerable interest in the potential benefits of such models in medicine. For delegated procedural consent, LLM could improve patients’ access to the relevant procedural information and therefore enhance informed decision-making.In this paper, we first outline a hypothetical example of delegation of consent to LLMs prior to surgery. We then discuss existing clinical guidelines for consent delegation and some of the ways in which current practice may fail to meet the ethical purposes of informed consent. We outline and discuss the ethical implications of delegating consent to LLMs in medicine concluding that at least in certain clinical situations, the benefits of LLMs potentially far outweigh those of current practices. (shrink)

This masterful work on Kant's Religion within the Boundaries of Mere Reason explores Kant's treatment of the Idea of God, his views concerning evil, and the moral grounds for faith in God. Kant and Religion works to deepen our understanding of religion's place and meaning within the history of human culture, touching on Kant's philosophical stance regarding theoretical, moral, political, and religious matters. Wood's breadth of knowledge of Kant's corpus, philosophical sharpness, and depth of reflection sheds light not only on (...) Kant, but also on the fate of religion and its relation to philosophy in the modern world. (shrink)