(b) ‡(KP & KyKP) AE ‡(KP & yKP) in the modal logic T, and so (c) ‡(KP & yKP) AE ^ in the minimal modal logic for ‡. Thus, a contradiction has been derived from the assumption P & yKP, and we have shown overall that P implies KP, making truth and knowledge equivalent. Proposed remedies for the paradox fall mainly into two kinds (cf. Brogaard and Salerno 2002; Wansing 2002). Some weaken the logic in the argument still further. This is like turning down the volume on your radio so as not to hear the bad news. You will not hear much good news either. Other remedies leave the logic untouched, but weaken the verification principle itself. This is like censoring the news: you hear things loud and clear, but they may not be so interesting. The proposal made below falls into the latter category, but using a different perspective from mere tinkering with proof rules or premises. We will emphasize positive reasons why VT can, and sometimes should, fail having to do with the ways in which we learn new information.
[1]
Berit Brogaard,et al.
Fitch's Paradox of Knowability
,
2002
.
[2]
H. Wansing.
Diamonds are a Philosopher ’ s Best Friends . The Knowability Paradox and Modal Epistemic Relevance Logic
,
2002
.
[3]
Richard Spencer-Smith,et al.
Modal Logic
,
2007
.
[4]
Lawrence S. Moss,et al.
The Logic of Public Announcements and Common Knowledge and Private Suspicions
,
1998,
TARK.
[5]
Heinrich Wansing,et al.
Diamonds are a Philosopher's Best Friends
,
2002,
J. Philos. Log..
[6]
G. E. Moore,et al.
Commonplace Book: 1919-1953
,
1993
.
[7]
Neil Tennant,et al.
Victor vanquished
,
2002
.