The Knowability Paradox is a logical argument that, starting from the plainly innocent assumption that every true proposition is knowable, reaches the strong conclusion that every true proposition is known. The same conclusion could also be put as follows: if there are unknown truths, there are unknowable truths. The paradox has been considered a problem for every theory assuming the Knowability Principle, according to which all truths are knowable and, in particular, for semantic anti-realist theories. A well-known criticism of the Knowability Paradox is the so-called restriction strategy. This bounds the scope of the universal quantification in (KP) to a set of formulae, whose logical form avoids the paradoxical conclusion. Specifically, Tennant suggests restricting the quantifier in (KP) to propositions whose knowledge is provably consistent. He calls them Cartesian propositions. They are distinguished from Anti-Cartesian propositions, which are propositions whose knowledge is provably inconsistent, and which are responsible for the paradox. Tennant distinguished Anti-Cartesian propositions in three kinds. In this paper, we will not be concerned with the soundness of the restriction proposal. Rather, we are interested in analyzing the proposed distinction. We argue that Tennant’s distinction is problematic because it is not grounded on an adequate, logical analysis, and because it is incomplete. We suggest an alternative distinction, and give the following reasons for accepting it: it is logically grounded and more complete than Tennant’s one; is inclusive of Tennant’s distinction; and is independent from non-epistemic notions.
Logically Unknowable Propositions: a criticism to Tennant's three-partition of Anti-Cartesian propositions
CARRARA, MASSIMILIANO;
2009
Abstract
The Knowability Paradox is a logical argument that, starting from the plainly innocent assumption that every true proposition is knowable, reaches the strong conclusion that every true proposition is known. The same conclusion could also be put as follows: if there are unknown truths, there are unknowable truths. The paradox has been considered a problem for every theory assuming the Knowability Principle, according to which all truths are knowable and, in particular, for semantic anti-realist theories. A well-known criticism of the Knowability Paradox is the so-called restriction strategy. This bounds the scope of the universal quantification in (KP) to a set of formulae, whose logical form avoids the paradoxical conclusion. Specifically, Tennant suggests restricting the quantifier in (KP) to propositions whose knowledge is provably consistent. He calls them Cartesian propositions. They are distinguished from Anti-Cartesian propositions, which are propositions whose knowledge is provably inconsistent, and which are responsible for the paradox. Tennant distinguished Anti-Cartesian propositions in three kinds. In this paper, we will not be concerned with the soundness of the restriction proposal. Rather, we are interested in analyzing the proposed distinction. We argue that Tennant’s distinction is problematic because it is not grounded on an adequate, logical analysis, and because it is incomplete. We suggest an alternative distinction, and give the following reasons for accepting it: it is logically grounded and more complete than Tennant’s one; is inclusive of Tennant’s distinction; and is independent from non-epistemic notions.File | Dimensione | Formato | |
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