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Displaying: 51-60 of 11835 documents

51. The Journal of Philosophy: Volume > 113 > Issue: 5/6
W. Sieg, On Tait on Kant and Finitism
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In his “Kant and Finitism” Tait attempts to connect his analysis of finitist arithmetic with Kant’s perspective on arithmetic. The examination of this attempt is the basis for a distinctive view on the dramatic methodological shift from Kant to Dedekind and Hilbert. Dedekind’s 1888 essay “Was sind und was sollen die Zahlen?” gives a logical analysis of arithmetic, whereas Hilbert’s 1899 book “Grundlagen der Geometrie” presents such an analysis of geometry or, as Hilbert puts it, of our spatial intuition. This shift in the late ninteenth century required a radical expansion of logic: first by the inclusion of principles for “systems” (sets) and “mappings” (functions), but second by a structuralist broadening of axioms and inferential principles. The interaction of mathematics and logic in mathematical logic opened, around 1920, fields of investigation with enormous impact on the philosophy of mathematics, promoting a deeper integration of mathematical practice and philosophical reflection.
52. The Journal of Philosophy: Volume > 113 > Issue: 5/6
Charles Parsons, Reply to Feferman, Koellner, Tait, and Sieg
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I comment on Feferman’s views on set theory, in particular criticizing a priori arguments claiming that the continuum hypothesis has no determinate truth value and commenting on his responses to my paper on his skepticism about set theory. I respond to criticisms of his of the structuralism that I have advocated and comment on his view of proof theory. On Koellner’s paper, I register little disagreement but note a difference of sympathy about views such as constructivism. On Tait’s paper, I note that Kant gives more play to the notion of whole number than Tait seems to allow and that Kant’s conception of real numbers is unclear. Responding to Sieg’s paper, I note his emphasis on how much mathematics and its foundations changed from Kant’s time to that of Dedekind and Hilbert and mention my effort to find a limited role for an intuition distantly descended from Kant’s.
53. The Journal of Philosophy: Volume > 113 > Issue: 5/6
New Books: Anthologies
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54. The Journal of Philosophy: Volume > 113 > Issue: 4
Jared Warren, Internal and External Questions Revisited
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Rudolf Carnap famously distinguished between the external meanings that existence questions have when asked by philosophers and the internal meanings they have when asked by non-philosophers. Carnap’s overall position involved various controversial commitments, but relatively uncontroversial interpretative principles also lead to a Carnap-style distinction between internal and external questions. In section 1 of this paper I offer arguments for such a distinction in several particular cases; in section 2 I defend my arguments from numerous objections and motivate them by using points drawn from the general theory of interpretation; and in section 3 I discuss the meanings of external questions, ultimately arguing that they are best understood as involving primitive metaphysical notions, and that when so understood, it is natural to adopt a general error theory about philosophical ontology.
55. The Journal of Philosophy: Volume > 113 > Issue: 4
Yael Loewenstein, Why the Direct Argument Does Not Shift the Burden of Proof
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Peter van Inwagen's Direct Argument (DA) makes use of an inference rule he calls "Rule B." Michael McKenna has argued that van Inwagen's defense of this rule is dialectically inappropriate because it is based entirely on alleged “confirming” cases that are not of the right kind to justify the use of Rule B in DA. Here I argue that McKenna’s objection is on the right track but more must be said if we are to see why. To fill in the gaps I consider a recent attempt by Ira M. Schnall and David Widerker to defend DA against McKenna’s objection. I argue that neither prong of their attack is successful against a variation on McKenna’s basic argument. In the course of responding to Schnall and Widerker’s objections to McKenna, I identify what is, as I argue, the real reason DA fails in its purpose to shift the burden of proof.
review essays
56. The Journal of Philosophy: Volume > 113 > Issue: 4
James M. Joyce, Arif Ahmed: Evidence, Decision and Causality
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57. The Journal of Philosophy: Volume > 113 > Issue: 3
Shieva Kleinschmidt, Placement Permissivism and Logics of Location
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All of the current leading theories of location are parsimonious: they have at most one locative primitive, and the definitions of all of the other locative relations appeal to nothing beyond that primitive, mereological properties and relations, and basic logic. I argue that if we believe there can be extended, mereologically simple regions, we can construct cases that are incompatible with every possible parsimonious theory of location. In these cases, an object is contained within a simple region that is larger than the object; that is, there is some region, r, and some object, x, are such that every subregion of r fails to be completely free of x, yet x fails to fill r. I argue that we ought to respond to this incompatibility by rejecting the analytic possibility of extended, simple regions.
58. The Journal of Philosophy: Volume > 113 > Issue: 3
Bryan Pickel, Brian Rabern, The Antinomy of the Variable: A Tarskian Resolution
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Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics.
59. The Journal of Philosophy: Volume > 113 > Issue: 3
In Memoriam: Hilary Putnam
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60. The Journal of Philosophy: Volume > 113 > Issue: 3
New Books
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