2016
DOI: 10.1007/978-3-319-45980-6_2
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What Is the Benacerraf Problem?

Abstract: In "Mathematical Truth," Paul Benacerraf presented an epistemological problem for mathematical realism. " [S]omething must be said to bridge the chasm, created by […] [a] realistic […] interpretation of mathematical propositions… and the human knower," he writes. 1 For prima facie "the connection between the truth conditions for the statements of [our mathematical theories] and […] the people who are supposed to have mathematical knowledge cannot be made out." 2 The problem presented by Benacerraf-variously… Show more

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Cited by 38 publications
(14 citation statements)
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“…As many authors have pointed out, these strong conclusions do not follow: beliefs may be justified even if we can't explain their reliability, and we may psychologically hold onto such beliefs even if we know we cannot explain their reliability (for relevant discussion, see Enoch ; Setiya , chap. 2; Clarke‐Doane ; Tersman ). But the force of Field's Nepalese village analogy does not depend on these overly strong conclusions.…”
Section: The Generalized Integration Challengementioning
confidence: 99%
See 1 more Smart Citation
“…As many authors have pointed out, these strong conclusions do not follow: beliefs may be justified even if we can't explain their reliability, and we may psychologically hold onto such beliefs even if we know we cannot explain their reliability (for relevant discussion, see Enoch ; Setiya , chap. 2; Clarke‐Doane ; Tersman ). But the force of Field's Nepalese village analogy does not depend on these overly strong conclusions.…”
Section: The Generalized Integration Challengementioning
confidence: 99%
“…Focusing on subjects’ reliability about the instantiation of properties helps sidestep a puzzle highlighted by Justin Clarke‐Doane (; ). Clarke‐Doane focuses on the reliability of beliefs about necessary moral truths such as ‘torturing toddlers for fun is morally wrong’.…”
mentioning
confidence: 99%
“…See Clarke‐Doane (). Clarke‐Doane's view is a sophisticated version of an idea that is sometimes attributed to Lewis (), pp.…”
mentioning
confidence: 99%
“…If believing P is a defeasible reason for S to believe Q, M * is an undercutting defeater for this reason if and only if M * is a defeater (for believing P as a reason for S to believe Q) and M * is a reason for S to doubt or deny that P would not be true unless Q were true" (Pollock 1986: 196). 7 Cf. Lewis: "[I]f it is a necessary truth that so-and-so, then believing that so-and-so is an infallible method of being right.…”
mentioning
confidence: 99%