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set theory

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Journal Article
The Philosophical Review (2017) 126 (1): 81–122.
Published: 01 January 2017
...Jared Warren This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration...
Journal Article
The Philosophical Review (2020) 129 (4): 537–589.
Published: 01 October 2020
... necessarily had antecedently, and any pretheoretic judgments we have about how it should behave ought to be taken with that in mind. My attitude is that it is better to set these untutored intuitions aside and follow the theory where it leads, judging the result by its fruits, familiarizing oneself...
Journal Article
The Philosophical Review (2010) 119 (1): 1–30.
Published: 01 January 2010
..., are analogues of voting situations in which the voters unanimously adopt the same set of preferences. In such situations, all plausible voting rules and all plausible decision rules agree. 1. Background Assumptions The decision theories I’ll discuss all rest on a common conceptual frame- work. All three...
Journal Article
The Philosophical Review (2020) 129 (1): 1–51.
Published: 01 January 2020
... for the latter to secure in a principled way. Section 2 presents Epistemic Kantianism. Section 3 argues that it is uniquely poised to satisfy the desiderata set out in section 1 on an ideal theory of epistemic justification. Section 4 gives three further arguments, suggesting that it (1) best explains...
Journal Article
The Philosophical Review (2020) 129 (3): 395–431.
Published: 01 July 2020
... the new cases elicit can be explained away by a compelling error theory. Having set out this new challenge to internalism, I will proceed in the remainder of this paper as follows. In section 2 I offer a diagnosis as to why our intuitive verdicts diverge between these two sets of cases, old and new...
Journal Article
The Philosophical Review (2012) 121 (4): 539–571.
Published: 01 October 2012
.... Concluding Remarks The crucial modification to standard theory proposed in this essay is the representation of semantic content by ordered sets of possible worlds 566 Multidimensional Possible-World Semantics for Conditionals rather than just sets of worlds. Up...
Journal Article
The Philosophical Review (2009) 118 (4): 501–532.
Published: 01 October 2009
... to both problems, setting out from the continuity between Kant's early and mature views on sensibility and mind-world relations. Kant's early writings subscribe to an interactionist cosmology opposed to both Leibniz's preestablished harmony and Malebranche's occasionalism. The modern debate on mind-world...
Journal Article
The Philosophical Review (2018) 127 (3): 371–398.
Published: 01 July 2018
...Jan Sprenger This article develops axiomatic foundations for a probabilistic theory of causal strength as difference-making. I proceed in three steps: First, I motivate the choice of causal Bayes nets as an adequate framework for defining and comparing measures of causal strength. Second, I prove...
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Journal Article
The Philosophical Review (2016) 125 (3): 397–430.
Published: 01 July 2016
... divulge information from another world not obtainable by any other means. —T. E. Forster, Set Theory with a Universal Set The Principle of Sufficient Reason, PSR, says that for any truth there is a sufficient reason. Although it has lost much of its luster over the years, lately there has been...
Journal Article
The Philosophical Review (2023) 132 (2): 329–333.
Published: 01 April 2023
... of plural logic. Salvatore Florio and Øystein Linnebo advocate a set theory based on a ‘critical plural logic’ that refutes many instances of plural comprehension. In particular, they deny that there are one or more things that include everything. Instead, they argue, when it comes to resolving...
Journal Article
The Philosophical Review (2003) 112 (3): 425–427.
Published: 01 July 2003
... to believe mathematics is true, and how it is that we come to know these truths. In the later work, a radical position is adopted according to which mathematics stands in no need of justification external to mathematics itself. The main focus of the discussion is on undecidable questions in set theory...
Journal Article
The Philosophical Review (2021) 130 (4): 623–627.
Published: 01 October 2021
... admissibly be interpreted in an even wider sense. The modal formulation of (interpretationalist expansionist) relativism allows for a beautiful recovery of standard set-theoretic principles from modal principles of expansion. A basic modal theory MST p is proposed, which consists...
Journal Article
The Philosophical Review (2014) 123 (1): 1–41.
Published: 01 January 2014
... real number. Because these structures satisfy the complete first-order theory of the real numbers, much of our standard reasoning carries over to them. But it is important to note that this is only the first-order theory—we must be careful about statements involving sets of real numbers...
Journal Article
The Philosophical Review (2021) 130 (2): 335–338.
Published: 01 April 2021
... to be skippable by less formally inclined readers, as well as a few appendices. Nevertheless, this is not a book for beginners. Knowledge of basic set theory is required, especially for the discussion in sections 4–6. Some knowledge of probability theory is likewise required. For the researchers in metaphysics...
Journal Article
The Philosophical Review (2007) 116 (3): 401–425.
Published: 01 July 2007
...- guage on all predicates. To see the problem here, suppose that our theory T includes just a little bit of set theory. (Of course, it can’t include very much set theory since it’s not committed to the existence of infi nitely many sets. Still, we can assume that it thinks...
Journal Article
The Philosophical Review (2018) 127 (2): 240–247.
Published: 01 April 2018
... on Putnam's ground-breaking work in the philosophy of mathematics, which “recast mathematics in a framework of modal logic” instead of set theory, and goes on to stress that Putnam's recasting was only one alternative among others: “mathematics can survive perfectly without any particular foundation , set...
Journal Article
The Philosophical Review (2021) 130 (4): 628–632.
Published: 01 October 2021
... is decomposed into 1,476 cases, each of which is algorithmic and can be checked by a computer. This is clearly not an explanation of what is proved, and there is presently no other proof. For all we know, none will ever be found. We could just have a brute combinatorial fact. Or again, in a moment, set theory...
Journal Article
The Philosophical Review (2001) 110 (1): 77–79.
Published: 01 January 2001
... about resemblance and sorting, something more than set-theory is need- ed for an account of properties. Some of these classes are better than, more natural than, others. In virtue of membership in such classes, objects can be said to have more, or less, natural properties. (He also calls...
Journal Article
The Philosophical Review (2000) 109 (1): 115–118.
Published: 01 January 2000
... relating one place in a pattern to another. For example, the natural numbers are the places in the pattern exhibited by infinitely many collinear points. Set theory is the theory of certain kinds of tree structures. There is no “fact of the matter,” therefore, whether numbers are sets...
Journal Article
The Philosophical Review (2016) 125 (2): 298–302.
Published: 01 April 2016
... the borders of conventional set theory. Simultaneously, the ontology of mathematics—in the second sense—saw alteration and variation equally profound. Influential philosophical studies of the stuff of mathematics went forward under the banners of neo-Kantian psychologism ( Sigwart 1895 ), post-Husserlian...