In the philosophy of mathematics, he is best known for his book ''Frege's Conception of Numbers as Objects'' (1983), where he argues that
Gottlob Frege's
logicist project could be revived by removing the
axiom schema of unrestricted comprehension (sometimes referred to as
Basic Law V) from the
formal system.
Arithmetic is then derivable in
second-order logic from
Hume's principle. He gives informal
arguments that (i)
Hume's
principle plus second-order logic is
consistent, and (ii) from it one can produce the
Dedekind–Peano axioms. Both results were
proven informally by Frege (
Frege's theorem), and would later be more rigorously proven by
George Boolos and Richard Heck. Wright is one of the major proponents of
neo-logicism, alongside his frequent collaborator
Bob Hale. He has also written
Wittgenstein and the Foundations of Mathematics (1980). In general metaphysics, his most important work is
Truth and Objectivity (Harvard University Press, 1992). He argues in this book that there need be no single, discourse-invariant thing in which
truth consists, making an analogy with
identity. There need only be some
principles regarding how the truth
predicate can be applied to a
sentence, some 'platitudes' about true sentences. Wright also argues that in some contexts, probably including
moral contexts,
superassertibility will effectively function as a truth predicate. He
defines a predicate as superassertible if and only if it is "assertible" in some state of information and then remains so no matter how that state of information is enlarged upon or improved. Assertiveness is
warrant by whatever standards inform the
discourse in question. Many of his most important papers in philosophy of language, epistemology,
philosophical logic, meta-ethics, and the interpretation of Wittgenstein have been collected in the two volumes published by
Harvard University Press in 2001 and 2003. In epistemology, Wright has argued that
G. E. Moore's proof of an
external world ("
Here is one hand") is logically valid but cannot transmit warrant from its premise to the conclusion, as it instantiates a form of epistemic circularity called by him "warrant transmission failure". Wright has also developed a variant of
Ludwig Wittgenstein's hinge epistemology, introduced in Wittgenstein's
On Certainty as a response to radical skepticism. According to hinge epistemology, there are assumptions or presuppositions of any enquiry – called "hinge propositions" – that cannot themselves be rationally doubted, challenged, established or defended. Examples of hinges are the propositions that there are universal regularities in nature, that our sense organs are normally reliable, and that we do not live in a skeptical scenario (such as that in which we are globally hallucinated by a Cartesian
evil demon or the more recent
simulation hypothesis). Wright instead contends that certain hinge propositions can actually be rationally held because there exists a type of non-evidential,
a priori warrant – which Wright calls "epistemic entitlement" – for accepting them as true. In collaboration with epistemologist Luca Moretti, Wright has further developed this theory to the effect that we are entitled to
ignore the possibility that we live in a skeptical scenario. == Awards ==