Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the (...) philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

It seems that the Truth-teller is either true or false, but there is no accepted principle determining which it is. From this point of view, the Truth-teller is a hypodox. A hypodox is a conundrum like a paradox, but consistent. Sometimes, accepting an additional principle will convert a hypodox into a paradox. Conversely, in some cases, retracting or restricting a principle will convert a paradox to a hypodox. This last point suggests a new method of avoiding inconsistency. This article provides (...) a significant example. The Liar paradox can be defused to a hypodox by relatively minimally restricting three principles: the T-schema, substitution of identicals and universal instantiation. These restrictions are not arbitrary. For each, I identify the source of a contradiction given some presumptions. Then I propose each restriction as a reasonable way to deal with that source of contradiction. (shrink)

Kremer presented three approaches of comparing fixed-point and revision theories of truth in Kremer, 363–403, 2009). Using these approaches, he established the relationships among ten fixed-point theories suggested by Kripke in, 690–716, 1975) and three revision theories presented by Gupta and Belnap in. This paper continues Kremer’s work. We add five other revision theories to the comparisons, including the theory proposed by Gupta in, 1–60, 1982), the theory proposed by Herzberger in, 61–102, 1982), the theory based on fully-varied revision sequences (...) proposed by Gupta and Belnap in, the theory proposed by Yaqūb in, and the theory based on weakly consistent revision sequences. We show that, the notion of Thomason model defined by Belnap’s limit rule is not equivalent to the one defined by Gupta’s limit rule, and that the theory based on fully-varied revision sequences is ≤2-equivalent to the one based on the greatest intrinsic fixed point of σ. (shrink)

The liar paradox is widely conceived as a problem for logic and semantics. On the basis of empirical studies presented here, we suggest that there is an underappreciated psychological dimension to the liar paradox and related problems, conceived as a problem for human thinkers. Specific findings suggest that how one interprets the liar sentence and similar paradoxes can vary in relation to one’s capacity for logical and reflective thought, acceptance of certain logical principles, and degree of philosophical training, but also (...) as a function of factors such as religious belief, gender, and whether the problem is treated as theoretical or practical. Though preliminary, these findings suggest that one reason the liar paradox resists a final resolution is that it engages both aspects described by so-called dual process accounts of human cognition. (shrink)

Several philosophers have recently developed accounts of relative truth. Given that logical consequence is often characterized in terms of truth preservation, notions of truth are often associated with corresponding notions of logical consequence. Accordingly, in his Assessment Sensitivity: Relative Truth and Its Applications, John MacFarlane provides two different definitions of logical consequence that incorapte assessment context-sensitive truth. One motivation for adopting an assessment context-sensitive account of truth for judgements about taste is to explain how conflicting taste claims can be true (...) relative to different contexts of assessment. However, in the midst of dialogues in which conflicting taste claims are made, it is also possible for the participants in the dialogue to make conflicting claims about what inferences are and are not logically valid. This paper accomplishes two objectives. First, I argue that MacFarlane’s notions of logical consequence do not adequately account for important features of some dialogues in which conflicting logical claims are made. In particular, I argue that MacFarlane’s accounts of logical consequence do not explain how logical claims made about inferences in taste-discourse could be assessment context-sensitive. Second, I propose a consequence relation that can be incorporated into an assessment context-sensitive account of logical claims made about inferences in taste discourse. (shrink)