The Knower Paradox Revisited

Philosophical Studies -     

The Knower Paradox and Epistemic Closure

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.     

Truth,omniscience, and the Knower

Conclusion Let us sum up.The paradox of the Knower poses a direct and formal challenge to the coherence of common notions of knowledge and truth. We've considered a number of ways one might try to meet that challenge: propositional views of truth and knowledge, redundancy or operator views, and appeal to hierarchy of various sorts. Mere appeal to propositions or operators, however, seems to be inadequate to the task of the Knower, at least if unsupplemented by an auxiliary recourse to hierarchy. But the cost of hierarchy appears to be an abandonment of any notion of all truth or of omniscience. What the contradictions of the Knower seem to demand, then, is at least an abandonment of these.As noted in the introduction, the argument is complicated enough that one must be wary of dogmatic and precipitate conclusions. One may legitimately wonder whether some new response, or some variation on an old one, will yet offer a way out.Far too often, however, it is asked what has gone wrong with paradox rather than what paradox may have to teach us. What the Knower may have to teach us, I think, is that there really can be no coherent notion of all truth and really can be no coherent notion of omniscience. In its own way that conclusion is perhaps as humbling as is any traditional notion of God.I am grateful to C. Anthony Anderson, Robert F. Barnes, David Boyer, Tyler Burge, Evan W. Conyers, and Allen Hazen for correspondence and discussion regarding basic ideas, and owe a special debt to David Boyer and Evan W. Conyers for careful criticism of earlier drafts.     

The No-No Paradox Is a Paradox

The No-No Paradox consists of a pair of statements, each of which ‘says’ the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ‘paradox’ must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view is mistaken: situated within an appropriate background theory of truth, the statements comprising the No-No Paradox are genuinely paradoxical in the same sense as is the Liar (and thus, on Sorensen's view, must fail to have truth values). This result has consequences beyond Sorensen's semantic framework. In particular, the No-No Paradox, properly understood, is not only a new paradox, but also provides us with a new type of paradox, one which depends upon a general background theory of the truth predicate in a way that the Liar Paradox and similar constructions do not.     

道德悖论视阈中的德福悖论

德行与幸福的关系问题是道德哲学的重要问题.德行是否与幸福保持一致直接影响到人们对某种道德理论的判断和评价.运用道德悖论理论可以帮助我们从一种新的视角来分析、理解二者之间的关系.现代德性伦理所追求的提升道德主体的整体德性,对于克服功利主义和单纯义务论对德福关系的简单理解.正确理解德福悖论具有借鉴意义.     

The Cookie Paradox

We’ve all been at parties where there's one cookie left on what was once a plate full of cookies, a cookie no one will eat simply because everyone is following a rule of etiquette, according to which you’re not supposed to eat the last cookie. Or at least we think everyone is following this rule, but maybe not. In this paper I present a new paradox, the Cookie Paradox, which is an argument that seems to prove that in any situation in which everyone is truly following the rule, no one eats any cookies at all, no matter how many there are to be eaten. The ‘Cookie Argument’ resembles the more familiar argument that surprise exams are impossible, but it's not exactly the same. I argue that the biggest difference is that, unlike the surprise exam argument, the Cookie Argument is actually sound! I conclude the paper by explaining how it could be possible for a group of people to engage in behavior (eating cookies) that guarantees that at least one of the members of the group will violate a rule, even when it's common knowledge in the group that everyone is committed to following that very rule.

Sometimes me think, “What is friend?” and then me say, “Friend is someone to share the last cookie with.” ‐ Cookie Monster, http://youtu.be/LHh0A_bH5ig 1 1 I’m grateful to Eric Carter for this quote.

     

The Apology Paradox

Some leaders and citizens think it appropriate to apologize for historical injustices like slavery or the dispossession of indigenous people. But can we sincerely say 'Sorry' for the deeds of our forebears? By making an apology we are expressing regrets for what they did: we are saying that we prefer that these deeds had not been done. However, if these deeds had not been done, history would have been different, and probably we would not exist. Since most of us are glad to be alive, it seems that our apologies must be insincere. I discuss a number of proposed solutions to this paradox.     

The Train Paradox

When two omnipotent beings are randomly and sequentially selecting positive integers, the being who selects second is almost certain to select a larger number. I then use the relativity of simultaneity to create a paradox by having omnipotent beings select positive integers in different orders for different observers.

The Abridgement Paradox

When axiomatizing a body of truths, one first concentrates on obtaining a set of axioms that entail all and only those truths. The theorist expects that this complete system will have some needlessly strong axioms that can later be weakened or even deleted. What happens if the theorist includes in his system recognition of this superfluity? Contradiction! Even admitting the possibility of superfluity dashes all hope of consistency. Any suspicion of superfluous information must be voiced from outside the system.     

The Self in Pain: The Paradox of Memory. The Paradox of Testimony

Using the 7-year psychotherapy of a Holocaust survivor, this paper explores the sometimes contradictory aspects of approaches to trauma. Conceptualizing a “self in pain” as an alternative to contemporary conceptualizations of the traumatized person as having a damaged, dissociated or collapsed self leads to a corresponding alternative clinical approach. The paradoxes of traumatic memory and testimony necessitate an adaptational emphasis and the emergence of a “doubled” in contrast to a dissociated self. The decision to respect this “doubled” self involves a privileging of “reality” over “psychic reality” which then, paradoxically enables this patient to develop a phantasy life.