Maitzen_Knower

Maitzen_Knower - STEPHEN MAITZEN THE KNOWER PARADOX AND...

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Unformatted text preview: STEPHEN MAITZEN THE KNOWER PARADOX AND EPISTEMIC CLOSURE * ABSTRACT. The Knower Paradox has had a brief but eventful history, and principles of epistemic closure (which say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows) have been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard arguments for and against skepticism seems to turn on the fate of closure. As far as I can tell, however, no one working in either area has emphasized the result I emphasize in this paper: the Knower Paradox just falsifies even the most widely accepted general principles of epistemic closure. After establishing that result, I discuss five of its more important consequences. 1. INTRODUCTION This paper tries to bring together two things that ought to have met but seem not to have made each others acquaintance: (a) the Paradox of the Knower, the focus of a small number of impressive technical discussions, 1 and (b) the debate over epistemic closure, the subject of an enormous, usually less technical, literature. 2 The Knower Paradox, like the much older Liar Paradox, uses seemingly correct inferences to derive an unwelcome conclusion from seemingly cor- rect premises. 3 Principles of epistemic closure say that knowledge is closed under such operations as known material implication and known logical entailment they say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows. (I distinguish such principles from principles of doxas- tic closure, which say that belief or justified belief is closed under similar operations.) The Knower Paradox has had a brief but eventful history, and epistemic closure has been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard argu- ments for and against skepticism seems to turn on the fate of closure. 4 As far as I can tell, however, no one working on either topic has emphasized the fact I emphasize in this paper: the Knower Paradox just falsifies even Synthese 114: 337354, 1998. 1998 Kluwer Academic Publishers. Printed in the Netherlands. 338 STEPHEN MAITZEN the most widely accepted general principles of epistemic closure. After es- tablishing that fact, I will discuss five of its more important consequences. 2. THE KNOWER PARADOX One version of the (Strengthened) Knower Paradox 5 starts with the follow- ing plausible assumptions: (A sentence S is true) (S expresses a true proposition) (A1) (A sentence S is false) (S expresses a false proposition) (A2) (A sentence S is known to be true) (S expresses a proposition which is known to be true) (A3) (A proposition P is known to be true) (P is true) (A4) These assumptions seem innocent enough, although later on I will con- sider some reasons one might have for rejecting the first three assump-...
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Maitzen_Knower - STEPHEN MAITZEN THE KNOWER PARADOX AND...

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