Online research in philosophy

Der Aufsatz schildert den platonisierenden Antipsychologismus welchen Bolzano, der junge Brentano, Twardowski, Meinong, der Husserl der Logischen Untersuchungen, Frege, der Russell der Jahrhundertwende und der junge Wittgenstein (...) philosophisch vertraten, und versucht eine soziologische und ideologiekritische Interpretation sowohl dieser Einstellung als auch derjenigen des traditionellen Psychologismus des achtzehnten Jahrhunderts. Der Platonismus des neunzehnten und zwanzigsten Jahrhunderts wird als ein Ausdruck fiir - oder vielmehr als eine Reaktion gegen - den Verfall der klassischen burgerlichen Werte aufgefaBt. In Wittgensteins Tractatus spielen Elemente sowohl eines platonisierenden Antipsychologismus wie auch eines relativistischen, verhaltensphanomenologisch orientierten Antipsychologismus eine Rolle: dieses Werk wird also als eine grelle Manifestation des Uberganges von der klassischen zur spatbiirgerlichen Weltanschauung, als ein Obergang vom Glauben an ewige Wahrheiten zur Hinnahme einer Gebrauchs-Theorie der Bedeutung und deren Konsequenzen interpretiert. (shrink)

One recursively enumerable real α dominates another one β if there are nondecreasing recursive sequences of rational numbers (a[n] : n ∈ ω) approximating α and (b[n] (...) : n ∈ ω) approximating β and a positive constant C such that for all n, C(α − a[n]) ≥ (β − b[n]). See [R. M. Solovay, Draft of a Paper (or Series of Papers) on Chaitin’s Work, manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1974, p. 215] and [G. J. Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. We show that every recursively enumerable random real dominates all other recursively enumerable reals. We conclude that the recursively enumerable random reals are exactly the Ω-numbers [G. J. Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. Second, we show that the sets in a universal Martin-Lof test for randomness have random measure, and every recursively enumerable random number is the sum of the measures represented in a universal Martin-Lof test. (shrink)

Metaethics is a perennially popular subject, but one that can be challenging to study and teach. As it consists in an array of questions about ethics, it (...) is really a mix of (at least) applied metaphysics, epistemology, philosophy of language, and mind. The seminal texts therefore arise out of, and often assume competence with, a variety of different literatures. It can be taught thematically, but this sample syllabus offers a dialectical approach, focused on metaphysical debate over moral realism, which spans the century of debate launched and framed by G. E. Moore's Principia Ethica. The territory and literature are, however, vast. So, this syllabus is highly selective. A thorough metaethics course might also include more topical examination of moral supervenience, moral motivation, moral epistemology, and the rational authority of morality. Authors Recommend: Alexander Miller, An Introduction to Contemporary Metaethics (Cambridge: Polity Press, 2003). This is one of the few clear, accessible, and comprehensive surveys of the subject, written by someone sympathetic with moral naturalism. David Brink, Moral Realism and the Foundations of Ethics (Cambridge: Cambridge University Press, 1989). Brink rehabilitates naturalism about moral facts by employing a causal semantics and natural kinds model of moral thought and discourse. Michael Smith, The Moral Problem (Oxford: Blackwell, 1994). Smith's book frames the debate as driven by a tension between the objectivity of morality and its practical role, offering a solution in terms of a response-dependent account of practical rationality. Gilbert Harman and Judith Jarvis Thomson, Moral Relativism & Moral Objectivity (Cambridge, MA: Blackwell, 1996). Harman argues against the objectivity of moral value, while Thomson defends it. Each then responds to the other. Frank Jackson, From Metaphysics to Ethics (Oxford: Clarendon Press, 1998). Jackson argues that reductive conceptual analysis is possible in ethics, offering a unique naturalistic account of moral properties and facts. Mark Timmons, Morality without Foundations (Oxford: Oxford University Press, 1999). Timmons distinguishes moral cognitivism from moral realism, interpreting moral judgments as beliefs that have cognitive content but do not describe moral reality. He also provides a particularly illuminating discussion of nonanalytic naturalism. Philippa Foot, Natural Goodness (New York, NY: Oxford University Press, 2001). A Neo-Aristotelian perspective: moral facts are natural facts about the proper functioning of human beings. Russ Shafer-Landau, Moral Realism: A Defence (New York, NY: Oxford University Press, 2003). In this recent defense of a Moorean, nonnaturalist position, Shafer-Landau engages rival positions in a remarkably thorough manner. Terence Cuneo, The Normative Web (New York, NY: Oxford University Press, 2007). Cuneo argues for a robust version of moral realism, developing a parity argument based on the similarities between epistemic and moral facts. Mark Schroeder, Slaves of the Passions (New York, NY: Oxford University Press, 2007). Schroeder defends a reductive form of naturalism in the tradition of Hume, identifying moral and normative facts with natural facts about agents' desires. Online Materials: PEA Soup: http://peasoup.typepad.com A blog devoted to philosophy, ethics, and academia. Its contributors include many active and prominent metaethicists, who regularly post about the moral realism and naturalism debates. Metaethics Bibliography: http://www.lenmanethicsbibliography.group.shef.ac.uk/Bib.htm Maintained by James Lenman, professor of philosophy at the University of Sheffield, this online resource provides a selective list of published research in metaethics. Stanford Encyclopedia of Philosophy: http://plato.stanford.edu See especially the entries under 'metaethics'. Sample Syllabus: Topics for Lecture & Discussion Note: unless indicated otherwise, all the readings are found in R. Shafer-Landau and T. Cuneo, eds., Foundations of Ethics: An Anthology (Malden: Blackwell, 2007). (FE) Week 1: Realism I (Classic Nonnaturalism) G. E. Moore, Principia Ethica, 2nd ed. (FE ch. 35). W. K. Frankena, 'The Naturalistic Fallacy,'Mind 48 (1939): 464–77. S. Finlay, 'Four Faces of Moral Realism', Philosophy Compass 2/6 (2007): 820–49 [DOI: [DOI link]]. Week 2: Antirealism I (Classic Expressivism) A. J. Ayer, 'Critique of Ethics and Theology' (1952) (FE ch. 3). C. Stevenson, 'The Nature of Ethical Disagreement' (1963) (FE ch. 28). Week 3: Antirealism II (Error Theory) J. L. Mackie, 'The Subjectivity of Values' (1977) (FE ch. 1). R. Joyce, Excerpt from The Myth of Morality (2001) (FE ch. 2). Week 4: Realism II (Nonanalytic Naturalism) R. Boyd, 'How to be a Moral Realist' (1988) (FE ch. 13). P. Railton, 'Moral Realism' (1986) (FE ch. 14). T. Horgan and M. Timmons, 'New Wave Moral Realism Meets Moral Twin Earth' (1991) (FE ch. 38). Week 5: Antirealism III (Contemporary Expressivism) A. Gibbard, 'The Reasons of a Living Being' (2002) (FE ch. 6). S. Blackburn, 'How To Be an Ethical Anti-Realist' (1993) (FE ch. 4). T. Horgan and M. Timmons, 'Nondescriptivist Cognitivism' (2000) (FE ch. 5). W. Sinnott-Armstrong, 'Expressivism and Embedding' (2000) (FE ch. 37). Week 6: Realism III (Sensibility Theory) J. McDowell, 'Values and Secondary Qualities' (1985) (FE ch. 11). D. Wiggins, 'A Sensible Subjectivism' (1991) (FE ch. 12). Week 7: Realism IV (Subjectivism) & Antirealism IV (Constructivism) R. Firth, 'Ethical Absolutism and the Ideal Observer' (1952) (FE ch. 9). G. Harman, 'Moral Relativism Defended' (1975) (FE ch. 7). C. Korsgaard, 'The Authority of Reflection' (1996) (FE ch. 8). Week 8: Realism V (Contemporary Nonnaturalism) R. Shafer-Landau, 'Ethics as Philosophy' (2006) (FE ch. 16). T. M. Scanlon, What We Owe to Each Other (Cambridge, MA: Harvard University Press, 1998), ch. 1. T, Cuneo, 'Recent Faces of Moral Nonnaturalism', Philosophy Compass 2/6 (2007): 850–79 [DOI: [DOI link]]. (shrink)

The early twentieth century witnessed a shift in the way philosophers of science thought about traditional 'problems of induction'. Keynes championed the idea that Hume's Problem (...) class='Hi'>was not a problem about causation (which had been the traditional reading of Hume) but rather a problem about induction. Moreover, Keynes (and later Nicod) viewed such problems as having both logical and epistemological components. Hempel picked up where Keynes and Nicod left off, by formulating a rigorous formal theory of inductive logic. This spawned a new branch of philosophy of science called confirmation theory. Hempel's theory of confirmation was based on a few very simple (and seemingly plausible) assumptions about (instantial) 'inductive-logical support'. However, as Hempel himself was keenly aware, even such simple and seemingly plausible assumptions give rise to various puzzles and paradoxes. The two most famous paradoxes of confirmation were discovered by Hempel and Goodman. This article discusses Hempel's paradox (which is known as 'the' paradox of confirmation, since it was discovered first). However, many of the historical developments surrounding Hempel's paradox (also known as the 'raven paradox') are also crucial for understanding Goodman's later ('grue') paradox. Author Recommends: Branden Fitelson, 'The Paradox of Confirmation', Philosophy Compass 1/1 (2006): 95–113, doi: [DOI link]. In this article, I explain how the inconsistency between Hempel's intuitive resolution and his official theory of confirmation affects the historical dialectic about the paradox and how it illuminates the nature of confirmation. After the survey, I argue that Hempel's intuitions about the paradox of confirmation were basically correct, and that it is his theory that should be rejected, in favor of a (broadly) Bayesian account of confirmation. C. G. Hempel, 'Studies in the Logic of Confirmation' (I and II), Mind 54 (1945): 1–26, 97–121, dois: [DOI link]; [DOI link]. This is the locus classicus of traditional (instantial) confirmation theory. It is here that original motivations for, traditional approaches to, and paradoxes of confirmation are discussed in depth for the first time, under the rubric 'confirmation theory'. Hempel's discussion (which picks up where Keynes and Nicod left off) is chock full of crucial historical, logical, and epistemological insights. J. M. Keynes, A Treatise on Probability (London: Macmillan, 1921). Keynes does not get enough credit in this context. But, basically, chapters 18 to 23 of this classic book planted the seeds for almost all of modern confirmation theory. Nicod and Hempel (as well as Hosiasson-Lindenbaum, Carnap, and others) were, basically, just picking-up where Keynes left off. J. Nicod, The Logical Problem of Induction (1923), reprinted in Foundations of Geometry and Induction (London: Routledge, 2000). Nicod's essay expands upon Keynes's work. Nicod is the first to use the term 'confirmation', in connection with a relation of 'inductive-logical support'. Nicod endorses several key confirmation-theoretic principles (which were already advanced by Keynes). In the hands of Hempel, Nicod's work later becomes an important historical foil. J. Hosiasson–Lindenbaum, 'On Confirmation', Journal of Symbolic Logic 5 (1940): 133–48. This essay contains most (if not all) of the basic ingredients of the 'Bayesian' approaches to the paradox of confirmation that appeared later. It also sheds much light on an important dispute between Keynes and Nicod concerning one of the claims Keynes makes (in his Treatise) about 'long-run convergence' in certain (instantial) confirmation-theoretic problems. This paper also contains one of the earliest rigorous axiomatizations of conditional (subjective or logical) probability. R. Carnap, Logical Foundations of Probability (Chicago, IL: University of Chicago, 1950). This is Carnap's encyclopaedic work on inductive logic and probability. There is a tremendous amount of wisdom in here. For present purposes, the sections on Hempel's theory of confirmation (in contrast to probabilistic approaches to confirmation, such as Hosiasson–Lindenbaum's and Carnap's) are probably most important and salient (see §§87–8). I. J. Good, 'The Paradox of Confirmation', British Journal for the Philosophy of Science 11 (1960): 145–9. C. Chihara, 'Quine and the Confirmational Paradoxes', in Midwest Studies in Philosophy. Vol. 6: The Foundations of Analytic Philosophy, eds. Peter A. French, Theodore E. Uehling, Jr., and Howard K. Wettstein (Minneapolis, MN: University of Minnesota Press, 1981), 425–52. J. Earman, Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory (Cambridge, MA: MIT Press, 1992), specifically: pp. 63–73. R. M. Royall, Statistical Evidence: A Likelihood Paradigm (New York, NY: Chapman & Hall, 1997), specifically: the Appendix on 'The Paradox of the Ravens'. C. McKenzie and L. Mikkelsen, 'The Psychological Side of Hempel's Paradox of Confirmation', Psychonomic Bulletin & Review 7 (2000): 360–6. P. Maher, 'Probability Captures the Logic of Scientific Confirmation', in Contemporary Debates in the Philosophy of Science, ed. Christopher <span class='Hi'>Hitchcockspan> (Oxford: Blackwell, 2004), 69–93. P. Vranas, 'Hempel's Raven Paradox: A Lacuna in the Standard Bayesian Solution', British Journal for the Philosophy of Science 55 (2004): 545–60. This is a list of seven of my favourite papers on the paradox of confirmation, since 1950 (listed in chronological order). Most of these are coming from a broadly 'Bayesian' perspective. In particular, I recommend Vranas as a good starting point here. Online Materials: http://fitelson.org/probability/ Probability & Induction (PHIL 148, UC-Berkeley, Spring 2008) This is the Web site for an undergraduate course on probability and induction that I taught at UC-Berkeley in Spring 2008. Much of the course focuses on confirmation theory (including the paradoxes of confirmation). There are many links there to lecture notes, papers, books and other salient online resources. http://fitelson.org/confirmation/ Confirmation (graduate seminar, UC-Berkeley, Fall 2007) This is the Web site for a graduate seminar on confirmation that I taught at UC-Berkeley in Fall 2007. This seminar is a historical trace of induction/confirmation, from Aristotle to Goodman (mostly, focusing on the 20th century and the paradoxes of confirmation). Sample Syllabus: See the online syllabi for Confirmation and/or Probability & Induction (above). Note: those online syllabi contain electronic copies of many of the salient readings. (shrink)

Three clusters of philosophically significant issues arise from Frege's discussions of definitions. First, Frege criticizes the definitions of mathematicians of his day, especially those of Weierstrass (...) class='Hi'>and Hilbert. Second, central to Frege's philosophical discussion and technical execution of logicism is the so-called Hume's Principle, considered in The Foundations of Arithmetic . Some varieties of neo-Fregean logicism are based on taking this principle as a contextual definition of the operator 'the number of …', and criticisms of such neo-Fregean programs sometimes appeal to Frege's objections to contextual definitions in later writings. Finally, a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend is whether the logical structures of the definientia reflect our pre-Fregean understanding of arithmetical terms. It seems that unless they do, it is unclear how Frege's proofs demonstrate the analyticity of the arithmetic in use before logicism. Yet, especially in late writings, Frege characterizes the definitions as arbitrary stipulations of the senses or references of expressions unrelated to pre-definitional understanding. One or more of these topics may be studied in a survey course in the philosophy of mathematics or a course on Frege's philosophy. The latter two topics are obviously central in a seminar in the philosophy of mathematics in general or more specialized seminars on logicism, or on mathematical definitions and concept formation. Author Recommends: 1. Kant, Immanuel. Critique of Pure Reason . Trans. P. Guyer and A. Wood. Cambridge: Cambridge University Press, 1999 [1781, 1787], A7-10/B11-14, A151/B190. In the first Critique , Kant appears to give four distinct accounts of analytic judgments. The initial famous account explains analyticity in terms of the predicate-concept belonging to the subject-concept (A6–7/B11). In this passage, we also find an account of establishing analytic judgments on the basis of conceptual containments and the principle of non-contradiction. (The other accounts are in terms of 'identity' (A7/B1l), in terms of the explicative–ampliative contrast (A7/B11), and by reference to the notion of 'cognizability in accordance with the principle of contradiction' (A151/B190).) 2. Frege, Gottlob. The Foundations of Arithmetic . Trans. J. L. Austin. 2nd ed. Evanston, IL: Northwestern University Press, 1980 [1884], especially sections 1–4, 87–91. Frege here criticizes and reformulates Kant's account of analyticity. Central to Frege's account is the provability of an analytic statement on the basis of (Frege's) logic and definitions that express analyses of (mathematical, especially arithmetical) concepts. 3. Frege, Gottlob. Review of E. G. Husserl. 'Philosophie der Arithmetik I [1894],' in Frege, Collected Papers . Ed. B. McGuinness. Trans. M. Black et al. Oxford: Blackwell, 1984. 195–209. In this review, Frege responds to Husserl's charge that Frege's definitions fail to capture our intuitive pre-analytic arithmetical concepts by claiming that the adequacy of mathematical definitions is measured, not by their expressing the same senses, but merely by their having the same references, as pre-definitional vocabulary. It follows not only that Husserl's criticism is unfounded, but also that there can be alternative, equally legitimate, definitions of mathematical terms. 4. Frege, 'Logic in Mathematics,' in Frege, Posthumous Writings . Trans. P. Long and R. White. Oxford: Blackwell, 1979 [1914]. 203–50. These are a set of lecture notes including, among other things, an account of proper definitions as mere abbreviation of complex signs by simple ones, in contrast to definitions which purport to express the analyses of existing concepts. Frege here claims that if there is any doubt whether a definition purporting to express an analysis succeeds in capturing the senses of the pre-definitional expressions, then the definition fails as an analysis, and should be regarded as the introduction of an entirely new expression abbreviating the definiens . 5. Picardi, Eva. 'Frege on Definition and Logical Proof,' Temi e Prospettive della Logica e della Filosofia della Scienza Contemporanee . i vol. Eds. C. Cellucci and G. Sambin. Bologna: Cooperativa Libraria Universitaria Editrice Bologna, 1988. 227–30. Picardi sets out forcefully the view that unless Frege's definitions capture the meanings of existing arithmetical terms, his logicism cannot have the epistemological significance he takes it to have. 6. Dummett, Michael. 'Frege and the Paradox of Analysis,' in Dummett, Frege and other Philosophers . Oxford: Oxford University Press, 1991. 17–52. Dummett agrees with Picardi's view and analyzes the philosophical pressures that led Frege to the account of definition in 'Logic in Mathematics.' Especially significant is Dummett's claim of the centrality of the transparency of sense – that if one grasps the senses of any two expressions, one must know whether they have the same sense – in Frege's account. 7. Benacerraf, Paul. 'Frege: The Last Logicist,' Midwest Studies in Philosophy . vol. 6. Eds. P. French, T. Uehling, and H. Wettstein. Minneapolis: University of Minnesota Press, 1981. 17–35. Frege's aims, on Benacerraf's reading, are primarily mathematical. Frege was interested in traditional philosophical issues such as the analyticity of arithmetic only to the extent that they can be exploited for the mathematical goal of proving previously unproven arithmetical statements. Hence, Frege never had any serious interest in or need for showing that his definitions of arithmetical terms reflect existing arithmetical conceptions. 8. Weiner, Joan. 'The Philosopher Behind the Last Logicist,' in Frege: Tradition and Influence . Ed. C. Wright. Oxford: Blackwell, 1984. 57–79. Weiner argues that on Frege's view, prior to his definitions of arithmetical terms the references of such expressions are in fact not known by those who use arithmetical vocabulary. Thus, in Foundations , Frege operated with a 'hidden agenda' (263) namely, replacing existing arithmetic with a new science based on stipulative definitions that assign new senses to key arithmetical terms. 9. Tappenden, Jamie. 'Extending Knowledge and 'Fruitful Concepts': Fregean Themes in the Foundations of Mathematics.' Noûs 29 (1995): 427–67. Tappenden argues that Frege takes his crucial innovation over previous practices and accounts of mathematical concept formation to be the role of quantificational structure made possible by his logical discoveries. 10. Horty, John. Frege on Definitions: A Case Study of Semantic Content . Oxford: Oxford University Press, 2007. A useful interpretation of Frege's views of definition, together with suggestive extensions for resolving the issues framing Frege's views. 11. Shieh, Sanford. 'Frege on Definitions,' Philosophy Compass 3/5 (2008): 992–1012. A more detailed account of Frege's views on definition and the philosophical issues they raise, surveying and discussing critically the main substantive and interpretive issues. Online Materials On Frege http://plato.stanford.edu/entries/frege/ On the Paradox of Analysis http://plato.stanford.edu/entries/analysis/ Sample Syllabus The following is a 3-week module that can be incorporated into fairly focused historically oriented graduate-level seminars on logicism or on the paradox of analysis. It is also possible to compress the material into 2 weeks in an undergraduate or graduate class Frege's thought in general. Week I: Background, Kant on Analyticity; Definition in Foundations , Review of Husserl, and 'Logic in Mathematics' Readings Kant, Immanuel. Critique of Pure Reason , A7–10/B11–14. Frege, Gottlob. The Foundations of Arithmetic , sections 1–4, 87–91. Frege, Gottlob. Review of E. G. Husserl, Philosophie der Arithmetik I. Frege, Gottlob. 'Logic in Mathematics.' Optional Proops, Ian. 'Kant's Conception of Analytic Judgment,' Philosophy and Phenomenological Research LXX, 3 (2005): 588–612. Week II: The Supposed Paradox of Analysis, Picardi and Dummett; Bypassing Traditional Epistemological Issues About Mathematics, Benacerraf Readings Picardi, Eva. 'Frege on Definition and Logical Proof.' Dummett, Michael. 'Frege and the Paradox of Analysis.' Benacerraf, Paul. 'Frege: The Last Logicist.' Optional Tappenden, Jamie. 'Extending Knowledge and 'Fruitful Concepts': Fregean Themes in the Foundations of Mathematics.' Week III: Weiner's Hidden Agenda Interpretation Readings Weiner, Joan. 'The Philosopher Behind the Last Logicist.' Optional Weiner, Joan. Frege in Perspective . Ithaca, NY: Cornell University Press, 1990. Focus Questions 1. To what extent is Frege's account of analyticity in Foundations a rejection, and to what extent an updating, of Kant's view of analyticity? 2. According to Picardi it 'would be incomprehensible' how Frege's proofs tells us anything about the arithmetic we already have unless his 'definitions [are] somehow responsible to the meaning of [arithmetical] sentences as these are understood' (228). Why does she hold this? Why does Dummett agree with her? Do you think Frege's logicism needs to address this worry? 3. What are the major differences and continuities in Frege's discussions of definition in mathematics in Foundations , the review of Husserl and 'Logic in Mathematics'? 4. Frege writes that definitions must prove their worth by being fruitful. He also says that nothing can be proven using a proper definition that cannot be proven without it. Are these claims consistent? Why or why not? 5. Weiner held that in Foundations Frege had 'hidden agenda.' What, according to her, is this agenda? How does this fit with Frege's later views of definition? 6. What are Frege's main complaints about Weierstrass's definitions in 'Logic in Mathematics'? Are these criticisms consistent with Frege's account of 'definition proper' in the same text? Seminar/Project Ideas What, if anything, is the relation between Frege's critique of Hilbert's use of definitions and Frege's later views of definitions? (shrink)