497 research outputs found
The paradox of idealization
A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. 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 Hart and McGinn (1976), many solutions to the paradox have been offered. In this article, we present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists
who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable
Inferentialism
This article offers an overview of inferential role semantics. We aim
to provide a map of the terrain as well as challenging some of the inferentialistâs
standard commitments. We begin by introducing inferentialism and
placing it into the wider context of contemporary philosophy of language. §2
focuses on what is standardly considered both the most important test case
for and the most natural application of inferential role semantics: the case
of the logical constants. We discuss some of the (alleged) benefits of logical
inferentialism, chiefly with regards to the epistemology of logic, and consider
a number of objections. §3 introduces and critically examines the most influential
and most fully developed form of global inferentialism: Robert Brandomâs
inferentialism about linguistic and conceptual content in general. Finally, in
§4 we consider a number of general objections to IRS and consider possible
responses on the inferentialistâs behalf
Inferentialism without VeriïŹcationism: Reply to Prawitz
I discuss Prawitzâs claim that a non-reliabilist answer to the question âWhat is a proof?â compels us to reject the standard Bolzano-Tarski account of validity, andto account for the meaning of a sentence in broadly veriïŹcationist terms. I sketch what I take to be a possible way of resisting Prawitzâs claim---one that concedes the anti-reliabilist assumption from which Prawitzâs argument proceeds
Maximally Consistent Sets of Instances of Naive Comprehension
Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that NaĂŻve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that NaĂŻve Comprehension embodies the only really intuitive conception of set and should be restricted as little as possible. The view might even have been held by Ernst Zermelo (1908), who,according to Penelope Maddy (1988), subscribed to a âone step back from disasterâ rule of thumb: if a natural principle leads to contra-diction, the principle should be weakened just enough to block the contradiction. We prove a generalization of McGeeâs Theorem, anduse it to show that the situation for set theory is the same as that for truth: there are multiple incompatible sets of instances of NaĂŻve Comprehension, none of which, given minimal assumptions, is recursively axiomatizable. This shows that the view adumbrated by Goldstein, Quine and perhaps Zermelo is untenable
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