Factive knowability and the problem of possible omniscience

Abstract

Famously, the Church-Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In this argument, knowability is analyzed in terms of having the possibility to know. Several philosophers have objected to this analysis, because it turns knowability into a nonfactive notion. In addition, they claim that, if the knowability thesis is reformulated with the help of factive concepts of knowability, then omniscience can be avoided. In this article we will look closer at two proposals along these lines (Edgington 1985; Fuhrmann 2014a), because there are formal models available for each. It will be argued that, even though the problem of omniscience can be averted, the problem of possible or potential omniscience cannot: there is an accessible state at which all (actual) truths are known. Furthermore, it will be argued that possible or potential omniscience is a price that is too high to pay. Others who have proposed to solve the paradox with the help of a factive concept of knowability should take note (Fara 2010; Spencer 2017).Keywords Factive knowability; Actuality Potential knowledge; Knowability thesis; Church-Fitch paradox of knowability Possible omniscience Potential omniscience How to conceptualise knowability? In the philosophical literature the most common conceptualisation of knowability is in terms of having the possibility to know, i.e. there being an accessible possible world in which one knows. This * Earlier versions of this paper have been presented at the Leuven-Paris Analytic Workshop in Epistemology (Leuven, 19/01/2018), The Ninth Congress of Analytic Philosophy (Munich, 25/08/2017), and a CLAW Seminar (Leuven, 04/10/2016). I would like to thank all the audiences for their helpful feedback. In addition, I would like to thank Lorenz Demey and Davide Fassio for commenting on earlier versions of the paper. Last but not least, I would like to thank the two anonymous reviewers, who have given very detailed and extensive comments and suggestions for improvement.

Counterfactual Knowledge, Factivity, and the Overgeneration of Knowledge

“…2 Schlöder on knowability and antirealism Schlöder (2019) thinks that a further development of Edgington's idea will lead to a version of the knowability thesis that avoids the Church-Fitch paradox of knowability and also the triviality issues raised by Rabinowicz and Segerberg (1994), Williamson (1987) and Heylen (2020). The guiding idea for reformulating the knowability thesis is in Schlöder (2019, Section 2.3)'s own words the following:…”

“…The antirealist thesis ART' does not succumb to the problem of possible omniscience (Heylen, 2020) either. There is an important preliminary point to be made here, to wit, there are plausibly no "super" procedures that can impart knowledge about everything.…”

“…A final remark is that the arguments for possible omniscience advanced by Heylen (2020) all make use of properties of the frame conditions of knowability theses such as Edgington (1985)'s AK. However, as Schlöder (2019, Section 2.3), points out: his knowability thesis is formulated with the help of counterfactuals, which do not have frame conditions.…”

“…There is a technical solution for this problem: make use of a particular kind of twodimensional semantics (Rabinowicz and Segerberg, 1994). Heylen (2020) argues that, even with this solution, there is another trivialisation issue lurking around the corner. One can derive in two-dimensional semantics from the hypothetical validity of AK and via the frame condition for AK that possibly every actual truth is known to be actually true.…”

Counterfactual knowability revisited

“…Finally, an anonymous reviewer points out to me another kind of triviality argument that has recently been developed by Heylen (2018). He argues that even if Edgington's principle (AK), repeated below, is interpreted in a suitable semantics for actuality that avoids the derivations of every truth is known, it still follows that possibly, every truth is known which is equally unwelcome (or so Heylen argues).…”