In this paper, we use algebra-valued models to study cardinal numbers in a class of non-classical set theories. The algebra-valued models of these non-classical set theories validate the Axiom of Choice, if the ground model validates it. Though the models are non-classical, the foundations of cardinal numbers in these models are similar to those in classical set theory. For example, we show that mathematical induction, Cantor’s theorem, and the Schröder–Bernstein theorem hold in these models. We also study a few basic (...) properties of cardinal arithmetic. In addition, the generalized continuum hypothesis is proved to be independent of these non-classical set theories. (shrink)

In this paper, we argue for an instrumental form of existence, inspired by Hilbert’s method of ideal elements. As a case study, we consider the existence of contradictory objects in models of non-classical set theories. Based on this discussion, we argue for a very liberal notion of existence in mathematics.

In this paper we extend to non-classical set theories the standard strategy of proving independence using Boolean-valued models. This extension is provided by means of a new technique that, combining algebras (by taking their product), is able to provide product-algebra-valued models of set theories. In this paper we also provide applications of this new technique by showing that: (1) we can import the classical independence results to non-classical set theory (as an example we prove the independence of $\mathsf {CH}$ ); (...) and (2) we can provide new independence results. We end by discussing the role of non-classical algebra-valued models for the debate between universists and multiversists and by arguing that non-classical models should be included as legitimate members of the multiverse. (shrink)

We present a generalization of the algebra-valued models of \ where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get intermediate values, in a set of designated values. Under this generalization there are many algebras which are neither Boolean, nor Heyting, but that still validate \.

We generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.

The question that this paper tries to answer is Q: “Can good academic bioethics be done without commitment to moral theory?” It is argued that the answer to Q is an unequivocal “Yes” for most of what we could call “critical bioethics,” that is, the kind of bioethics work that primarily criticizes positions or arguments already in the literature or put forward by policymakers. The answer is also “Yes” for much of empirical bioethics. The second part of the paper then (...) provides an analysis of Q in relation to “constructive bioethics,” that is, bioethics work aimed at providing an argument for a particular position. In this part, it is argued that a number of the approaches or methods used that initially look like they involve no commitment to moral theory, nevertheless, involve such a commitment. This is shown to be the case for reflective equilibrium, mid-level theory, the use of theory fragments, and argument by analogy. (shrink)

In this book, S. A. Lloyd offers a radically new interpretation of Hobbes's laws of nature, revealing them to be not egoistic precepts of personal prudence but rather moral instructions for obtaining the common good.

The status quo: dogmatism, the biopsychosocial model, and alternatives -- What there is: of mind and brain -- How we know: understanding the mind -- What is scientific method? -- Reading Karl Jaspers's General Psychopathology -- What is scientific method in psychiatry? -- Darwin's dangerous method: the essentialist fallacy -- What we value: the ethics of psychiatry -- Desire and self: Hellenistic and Islamic approaches -- On the nature of mental illness: disease or myth? -- Order out of chaos: from (...) insanity to DSM-III to a pluralistic nosology -- A theory of DSM-IV: ideal types -- Dimensions versus categories -- The perils of belief: psychosis -- The slings and arrows of outrageous fortune: depression -- Life's rollercoaster: mania -- Being self-aware: insight -- Calvinism or hedonism? -- Truth and statistics: problems of empirical psychiatry -- A climate of opinion: what remains of psychoanalysis -- Being there: existential psychotherapy -- Beyond eclecticism: teaching psychotherapy in the twenty-first century -- Bridging the biology/psychology dichotomy: the hopes of integrationism -- Why it is hard to be pluralist. (shrink)

Study of Hans-Georg Gadamer's and Julius Stenzel's interpretations of Plato.

This chapter develops a perceptual solution to the epistemological problem of other minds, relying on central ideas from Maurice Merleau-Ponty's phenomenology. The Merleau-Pontian account is contrasted with another attempted perceptual solution to the other minds problem, and it is argued that only the former meets the phenomenologists' desideratum of providing an alternative to inferential solutions. The chapter also provides responses to various objections to the perceptual solution, including a pair of objections recently put forward by Alec Hyslop.

Conduct of Muslim women in Turkey in the age of globelization; 20th century.

The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to (...) term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning. (shrink)

pt. 1. Collection of Sastri's writings and a kavya on him -- pt. 2. Select research papers presented at the birth centenary seminars.

Can philosophy offer reasonable grounds for the existence of a God possessing genuine religious significance and not proposed simply as the solution to a purely intellectual philosophical problem? Certainly many contemporary thinkers have insisted that no genuine religion could be based upon metaphysics. In this book, however, T. L. S. Sprigge examines sympathetically the most notable metaphysical systems of the last four centuries which purport to put religion on a rational footing and, after a thorough examination of their claims, considers (...) what kind of religious outlook they might support and how they actually affected the lives of their proponents. The thinkers studied include Spinoza, Hegel, T. H. Green, Bernard Bosanquet, Josiah Royce, A. N. Whitehead, and Charles Hartshorne, concluding with an exposition of the author's own viewpoint and a general discussion on the relation between metaphysics and religion. There is also a chapter on Kierkegaard as the most important critic of metaphysical religion. (shrink)

This paper is a technical study of the systematic observations and computations made by Muḥyī al-Dīn al-Maghribī (d. 1283) at the Maragha observatory (north-western Iran, c. 1259–1320) in order to newly determine the parameters of the Ptolemaic lunar model, as explained in his Talkhīṣ al-majisṭī, “Compendium of the Almagest.” He used three lunar eclipses on March 7, 1262, April 7, 1270, and January 24, 1274, in order to measure the lunar epicycle radius and mean motions; an observation on April 20, (...) 1264, to determine the lunar eccentricity; an observation on August 29, 1264, to test the model; and another on March 15, 1262, for measuring the lunar parallax. In the second period of activity at the Maragha observatory, Shams al-Dīn Muḥammad al-Wābkanawī (c. 1254–1320) adopted all of al-Maghribī’s parameter values in his Zīj, but decreased his value for the mean longitude of the moon at epoch by 0;13,11∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}. By comparing the times of the new moons and lunar eclipses in the period of 1270–1320 as computed from the astronomical tables of the Maragha tradition with the true modern ones, it is argued that this correction was very probably the result of actual observations. (shrink)

The elephant in the room -- Crabs and octopuses -- The central intelligence of a frog -- The cerebral cortex and consciousness -- Social consciousness -- Yoda and Darth: how can we find -- Consciousness in the brain? -- The hard problem and other perspectives on consciousness -- Conscious machines -- Uploading minds -- How to build visual consciousness.

Treatise, with commentaries, on Navya-Nyāya philosophy.

Commentary on Tarkasaṅgraha of Annambhaṭṭa, 17th cent., work on Nyaya and Vaiśeṣika philosophy; critical edition with complete text.

Seminar papers on Dvaitadvaita philosophy with reference to Advaitabrahmasiddhi of Madhusūdana Sarasvatī and Nyāyāmr̥ta of Vyāsatīrtha, 1460-1539.

Professor Toynbee observes in his Study of History that as he walked down Whitehall one day in the spring of 1918, and passed the Board of Education offices which had been commandeered for a new department of the War Office, “improvised in order to make an intensive study of trench warfare,” he found himself repeating the passage from St. Matthew's Gospel.