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axiom

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Journal Article
The Philosophical Review (2014) 123 (2): 173–204.
Published: 01 April 2014
...Robert Shaver Sidgwick gives various tests for highest certainty. When he applies these tests to commonsense morality, he finds nothing of highest certainty. In contrast, when he applies these tests to his own axioms, he finds these axioms to have highest certainty. The axioms culminate...
Journal Article
The Philosophical Review (2012) 121 (2): 241–275.
Published: 01 April 2012
...Richard Pettigrew In “A Nonpragmatic Vindication of Probabilism,” James M. Joyce attempts to “depragmatize” de Finetti’s prevision argument for the claim that our credences ought to satisfy the axioms of the probability calculus. This article adapts Joyce’s argument to give nonpragmatic...
Journal Article
The Philosophical Review (2014) 123 (2): 131–171.
Published: 01 April 2014
...Hannes Leitgeb This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which...
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Journal Article
The Philosophical Review (2017) 126 (1): 123–126.
Published: 01 January 2017
... and casually cite definitions, axioms, and demonstration by number alone without elaboration. This can make them resemble prisoners who have lived together for so long in a single cell that they can crack each other up merely by citing, for example, joke #12, in lieu of actually telling the joke. It's...
Journal Article
The Philosophical Review (2023) 132 (2): 329–333.
Published: 01 April 2023
... is that primitive plurals are needed to ‘give an account of sets’ (62) (section 4.4, chap. 12). The first half of Florio and Linnebo’s account comprises two elegant axioms that characterize the ‘singularization’ that maps each plurality to its set. These axioms are to be justified via the liberal view...
Journal Article
The Philosophical Review (2003) 112 (3): 425–427.
Published: 01 July 2003
... (that is, propositions such as the continuum hypothesis that can be neither proved nor disproved from the standard ZFC axioms), and on attempts to set- tle them by searching for new axioms. The book is in three parts. Part 1, “The Problem,” gives historical and technical background. Various sorts of candi- date new...
Journal Article
The Philosophical Review (2001) 110 (2): 296–300.
Published: 01 April 2001
... preferences over, respectively, gambles and propositions describing uncertain states of the world (of the form “Pprefers x to y and each derives a “representation theorem,” stating that preferences satisfying the axioms are indistinguishable from preferences formed to maximize expected utility...
Journal Article
The Philosophical Review (2014) 123 (1): 1–41.
Published: 01 January 2014
... not defined in terms of unconditional probability, but freestanding. Popper's axioms guarantee that whenever P ( B ) ≠ 0, the standard relations still hold, but just add the claim that P ( A | B ) is always defined. Instead of having , we just have , as I originally stated in the introduction, which...
Journal Article
The Philosophical Review (2004) 113 (2): 157–201.
Published: 01 April 2004
... . The Point of Kant's Axioms of Intuition.” Pacific Philosophical Quarterly 86 : 135 -59. ____. 2005b . Kant on Fundamental Geometrical Relations. Archiv für Geschichte der Philosophie 87 : 117 --58. ____. Forthcoming. Kant on Arithmetic, Algebra, and the Theory of Proportions.” Journal...
Journal Article
The Philosophical Review (2008) 117 (3): 385–443.
Published: 01 July 2008
.... φ’s universal Ramseyfication is the universal closure of (A → φ ) ,whereA is the conjunction of a suitable list of axioms, and ψ∗ is the result of uniformly replacing 398 xxx pr08-003 June 10, 2008 10:55...
Journal Article
The Philosophical Review (2021) 130 (4): 623–627.
Published: 01 October 2021
... formula by its dual ♢. It is shown that the modalizations of all axioms of ZF can be derived from MST p , with the exception of the axioms of infinity and replacement. However, the latter two follow by a modal reflection principle, which can also be given a motivation in terms of the intended...
Journal Article
The Philosophical Review (2022) 131 (1): 1–49.
Published: 01 January 2022
... Fundamental Laws For any world w , fundamental laws of nature in w are the non-mathematical axioms (basic postulates) of the complete fundamental physical theory of w . 10 Examples of physical theories include classical mechanics and quantum mechanics. 11 For a physical theory to be complete...
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Journal Article
The Philosophical Review (2000) 109 (2): 277–281.
Published: 01 April 2000
... REVlEWS abilities (called €-semantics in the literature) (Pearl 1989)-that are all characterized by the same axioms, ones originally introduced by Adams (1966, 19’75) for conditional logic.* In retrospect, this should not be sur- prising. A defeasible statement like “birds typically fly” can...
Journal Article
The Philosophical Review (2001) 110 (1): 138–141.
Published: 01 January 2001
... could eliminate such paradoxes by denying that there are any gen- eral propositions. However, to sustain logicism, he introduced a “mitigating axiom”-similar to his later axiom of reducibility-according to which for any general statement, there is an equivalent nongeneral proposition...
Journal Article
The Philosophical Review (2020) 129 (3): 469–473.
Published: 01 July 2020
... is possible, there is a possible world w in which s is instantiated. Assuming that the definitions and axioms of part 1 of the Ethics are necessary, 2 they are all true in w . Insofar as E1p7 follows necessarily from these definitions and axioms, E1p7 too is true in w . Therefore, were s...
Journal Article
The Philosophical Review (2015) 124 (3): 299–352.
Published: 01 July 2015
... axiom of classical logic, does not contain some axiom of Peano arithmetic, or is not closed under the classical rules of inference. T does not contain every instance of the schema H ( ⌜ φ ⌝ ) → ( T r ( ⌜ φ ⌝ ) ↔ φ ) . There is a sentence γ belonging to T...
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Journal Article
The Philosophical Review (2000) 109 (1): 101–103.
Published: 01 January 2000
... the criticism of the axiom of reducibility leveled by Ramsey, Godel, and Quine. He argues that the axiom is neither ad hoc nor in conflict with other aspects of Russell’s logical system. Finally, Hylton ex- amines Wittgenstein’s puzzling remarks on the distinction between func- tions and operations...
Journal Article
The Philosophical Review (2014) 123 (4): 485–531.
Published: 01 October 2014
.... By means of several examples, I will argue that two mathematical proofs may prove the same theorem from the same axioms, though only one of these proofs is explanatory. My goal in this essay will be to identify the ground of this distinction. Accordingly, my focus will be on the course that a given proof...
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Journal Article
The Philosophical Review (2002) 111 (1): 1–23.
Published: 01 January 2002
...—that is, such that no alternative has a higher expected-value. This is the formal representation of the optimality pre- scription.1 Different approaches to decision theory arrive at the optimality pre- scription in different ways. Savage lays down axioms governing rational choice, and derives the optimality prescription...
Journal Article
The Philosophical Review (2000) 109 (1): 98–101.
Published: 01 January 2000
... flawed. He locates the source of their misreading of Mill in one 100 BOOK REVIEWS of their greatest philosophical foes, namely Bradley. Linsky’s paper defends Russell against the criticism of the axiom of reducibility leveled by Ramsey...