In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press (2009)
|Abstract||(T5) ϕ → ◊Kϕ |-- ϕ → Kϕ where ◊ is possibility, and ‘Kϕ’ is to be read as ϕ is known by someone at some time. Let us call the premise the knowability principle and the conclusion near-omniscience.2 Here is a way of formulating Fitch’s proof of (T5). Suppose the knowability principle is true. Then the following instance of it is true: (p & ~Kp) → ◊K(p & ~Kp). But the consequent is false, it is not possible to know p & ~Kp. That is because the supposition that it is known is provably inconsistent.3 The inconsistency requires us to deny the possibility of the supposition, yielding ~◊K(p & ~Kp). This, together with the above instance of the knowability principle, entails ~(p & ~Kp), which is (classically) equivalent to p → Kp. Since p occurs in none of our undischarged assumptions, we may generalize to get near-omniscience, ϕ → Kϕ. QED.|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Neil Tennant (2009). Revamping the Restriction Strategy. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
Michael Fara (2010). Knowability and the Capacity to Know. Synthese 173 (1).
Bernhard Weiss (2007). Truth and the Enigma of Knowability. Dialectica 61 (4):521–537.
Rafał Palczewski (2007). Distributed Knowability and Fitch's Paradox. Studia Logica 86 (3):455--478.
Salvatore Florio & Julien Murzi (2009). The Paradox of Idealization. Analysis 69 (3):461-469.
Greg Restall (2009). Not Every Truth Can Be Known (at Least, Not All at Once). In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
Berit Brogaard & Joe Salerno, Fitch's Paradox of Knowability. The Stanford Encyclopedia of Philosophy.
Joe Salerno (ed.) (2009). New Essays on the Knowability Paradox. Oxford University Press.
Added to index2009-01-28
Total downloads24 ( #52,493 of 556,914 )
Recent downloads (6 months)5 ( #16,193 of 556,914 )
How can I increase my downloads?