Amherst Lecture in Philosophy (2009)

What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge . Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma between scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are known. Safety is modal, not probabilistic, in structure, with closure and factiveness conditions. It is modelled using closeness of worlds. Safety is analogous to knowledge. It suggests an interpretation of possible worlds semantics for epistemic logic. To avoid logical omniscience, a relation of epistemic counterparthood between formulas is introduced. This supports a safety conception of knowledge and formalizes how extending knowledge by deduction depends on logical competence.
Keywords lottery paradox  preface paradox  multi-premise closure
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References found in this work BETA

Knowledge and its Limits.Timothy Williamson - 2000 - Oxford University Press.
Knowledge and Practical Interests.Jason Stanley - 2005 - Oxford University Press.
Vagueness.Timothy Williamson - 1994 - London and New York: Routledge.
Elusive Knowledge.David K. Lewis - 1996 - Australasian Journal of Philosophy 74 (4):549 – 567.

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Taking a Chance on KK.Jeremy Goodman & Bernhard Salow - 2018 - Philosophical Studies 175 (1):183-196.
Skill in Epistemology I: Skill and Knowledge.Carlotta Pavese - 2016 - Philosophy Compass 11 (11):642-649.

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