Results 1 
3 of
3
Diamonds are a Philosopher's Best Friends. The Knowability Paradox and Modal Epistemic Relevance Logic (Extended Abstract)
 Journal of Philosophical Logic
, 2002
"... Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution o#ered is in the spirit of the constructivist attitude usually maintained by defenders of the antirealist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.
Knowability from a Logical Point of View
, 2010
"... The wellknown ChurchFitch paradox shows that the verificationist knowability principle all truths are knowable, yields an unacceptable omniscience property. Our semantic analysis establishes that the knowability principle fails because it misses the stability assumption ‘the proposition in questio ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
The wellknown ChurchFitch paradox shows that the verificationist knowability principle all truths are knowable, yields an unacceptable omniscience property. Our semantic analysis establishes that the knowability principle fails because it misses the stability assumption ‘the proposition in question does not change from true to false in the process of discovery, ’ hidden in the verificationist approach. Once stability is made explicit, the resulting stable knowability principle accurately represents verificationist knowability, does not yield the omniscience property, and can be offered as a resolution of the knowability paradox. Two more principles are considered: total knowability stating that it is possible to know whether a proposition holds or not, and monotonic knowability stemming from the intrinsically intuitionistic reading of knowability. The study of these four principles yields a “knowability diamond ” describing their logical strength. These results are obtained within a logical framework which opens the door to the systematic study of knowability from a logical point of view. 1
unknown title
, 2008
"... A wellknown proof by Alonzo Church, first published in 1963 by Frederic Fitch, shows that all truths are knowable only if all truths are known.1 This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines com ..."
Abstract
 Add to MetaCart
A wellknown proof by Alonzo Church, first published in 1963 by Frederic Fitch, shows that all truths are knowable only if all truths are known.1 This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic antirealism. Since its rediscovery by Colin McGinn and William Hart in 1976,2 many solutions to the Paradox have been offered. In this paper, we show that some of them do not have the resources to block a problem we raise. We present a new proof to the effect that not all truths are knowable, resting on different assumptions from the original argument published by Fitch. In light of this proof, antirealists who favour either a hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up antirealism or opt for a highly controversial interpretation of their original tenet. 1