Probability Operators

Yalcin, Seth

doi:10.1111/j.1747-9991.2010.00360.x

“…Steps in this direction have been taken by Portner (2009) and Yalcin (2010b). The present paper is a contribution to this small but growing literature, focusing on the gradable epistemic modals (GEMs) possible, probable, likely, and certain.…”

Section: B Comparisonmentioning

confidence: 99%

Gradable epistemic modals, probability, and scale structure

Lassiter

¹

2015

SALT

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The epistemic modals possible, probable, likely, and certain require a semantics which explains their behavior both as modal operators and as gradable adjectives. An analysis of these items in terms of Kennedy & McNally's (2005) theory of gradability suggests that they are associated with a single, fully closed scale of possibility. An implementation using the standard theory of modality due to Kratzer is shown to make incorrect predictions in several domains. However, identifying the scale of possibility with standard numerical probability explains the facts about gradability and avoids the undesirable predictions of Kratzer's theory.Keywords: gradability, comparison, epistemic modals, probability Gradable modalsMost discussion of the semantics of English modals has focused on the meanings of modal auxiliaries such as must, should, and can, illustrated in (1).(1) a. Harry should be in Sacramento by now.b. My brother can bench press 250 pounds.c. All cameras must be checked at the door.However, English also has a substantial number of adjectival modals such as likely, obligatory, able, and evident. These items are readily gradable, just like the large and well-studied class of gradable adjectives. Some examples are given in (2a)-(2d). * Special thanks to Chris Barker and Seth Yalcin, both of whom have been enormously helpful and inspiring regarding this project. Thanks also to Anna Szabolcsi, Philippe Schlenker, Chris Kennedy, Larry Horn, Angelika Kratzer, Paul Portner, Pauline Jacobson, Julien Dutant, Chris Collins, Bob Frank, Tom Leu, Eytan Zweig, Tricia Irwin, Salvador Mascarenhas, Tim Leffel, Simon Charlow, and Mike Solomon for inspiration, discussion, copies of unpublished work, data, ideas, and/or help. My initial exposure to the idea of thinking about modality and gradability together came in Seth Yalcin's philosophy of language seminar at NYU in 2008, where he floated the idea that possible and probable were instances of minimum-and relative-standard adjectives in K&M's theory and that probability provided the relevant scale. Though most of our subsequent work was done independently, we have reached similar conclusions, as can be seen by comparing the present paper to the forthcoming Yalcin 2010b.

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“…However, the damaging consequences of the Disjunctive Inference for Kratzer's theory do not seem to have been noted in the literature until they were independently discovered by me (Lassiter 2010) and by Seth Yalcin (Yalcin 2010b). As Halpern notes, this property is shared by several other representations of uncertainty, e.g.…”

Section: Problems With the Degree-based Extensionmentioning

confidence: 89%

“…However, I argue this approach makes incorrect predictions about ratio and proportional modifiers and about the interaction of disjunction with equatives. An alternative is to suppose with Yalcin (2010b) that GEMs are associated with the scale of standard numerical probabilities. I show that this assumption explains the behavior of GEMs with respect to tests for scale structure, and avoids Kratzer's problems with quantitative expressions of likelihood and with disjunction.…”

Section: B Comparisonmentioning

confidence: 99%

Gradable epistemic modals, probability, and scale structure

Lassiter

¹

2010

SALT

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The epistemic modals possible, probable, likely, and certain require a semantics which explains their behavior both as modal operators and as gradable adjectives. An analysis of these items in terms of Kennedy & McNally's (2005) theory of gradability suggests that they are associated with a single, fully closed scale of possibility. An implementation using the standard theory of modality due to Kratzer is shown to make incorrect predictions in several domains. However, identifying the scale of possibility with standard numerical probability explains the facts about gradability and avoids the undesirable predictions of Kratzer's theory.Keywords: gradability, comparison, epistemic modals, probability Gradable modalsMost discussion of the semantics of English modals has focused on the meanings of modal auxiliaries such as must, should, and can, illustrated in (1).(1) a. Harry should be in Sacramento by now.b. My brother can bench press 250 pounds.c. All cameras must be checked at the door.However, English also has a substantial number of adjectival modals such as likely, obligatory, able, and evident. These items are readily gradable, just like the large and well-studied class of gradable adjectives. Some examples are given in (2a)-(2d). * Special thanks to Chris Barker and Seth Yalcin, both of whom have been enormously helpful and inspiring regarding this project. Thanks also to Anna Szabolcsi, Philippe Schlenker, Chris Kennedy, Larry Horn, Angelika Kratzer, Paul Portner, Pauline Jacobson, Julien Dutant, Chris Collins, Bob Frank, Tom Leu, Eytan Zweig, Tricia Irwin, Salvador Mascarenhas, Tim Leffel, Simon Charlow, and Mike Solomon for inspiration, discussion, copies of unpublished work, data, ideas, and/or help. My initial exposure to the idea of thinking about modality and gradability together came in Seth Yalcin's philosophy of language seminar at NYU in 2008, where he floated the idea that possible and probable were instances of minimum-and relative-standard adjectives in K&M's theory and that probability provided the relevant scale. Though most of our subsequent work was done independently, we have reached similar conclusions, as can be seen by comparing the present paper to the forthcoming Yalcin 2010b.

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“…Recently, the viability of this ordering-based approach has been called into question (Portner 2009;Yalcin 2010;Lassiter 2011), partially on the basis of a number of puzzles which concern GMEs (Goble 1996;Jackson & Pargetter 1986;Levinson 2003;Kolodny & MacFarlane 2010). These puzzles have often been articulated in the context of discussions of practical reasoning-discussions of what ought to be done or what the best course of action is-and have the character that the optimal outcome does not necessarily determine what the most advisable course of action is.…”

Section: Introductionmentioning

confidence: 99%

“…They also show properties of various classes of gradable predicates: certain but not probable, for example, can be modified by completely, suggesting that the former is a "maximum standard" predicate in Kennedy & McNally's (2005) terms. In order to properly understand GMEs, we must integrate the semantics of modal expressions with a theory of gradability (Yalcin 2006(Yalcin , 2010Portner 2009;Lassiter 2010Lassiter , 2011Klecha to appear). In this paper, we take some initial steps towards this goal.…”

Section: Introductionmentioning

confidence: 99%

Ordering combination for modal comparison

Katz¹,

Pörtner²,

Rubinstein³

2015

SALT

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The well-known ordering semantics for modality has recently been challenged by a number of puzzles which may cast doubt on the viability of this approach. We investigate the properties of the ordering relations used in ordering semantics with a focus on how to derive appropriate orderings based on intuitively correct premises. We use these tools to propose solutions to two of the puzzles and discuss how they relate to other puzzles that have been raised in the literature, and to modal semantics more generally.

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Probability Operators

Cited by 97 publications

References 35 publications

Gradable epistemic modals, probability, and scale structure

Gradable epistemic modals, probability, and scale structure

Gradable epistemic modals, probability, and scale structure

Ordering combination for modal comparison

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