This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...) I argue that Bold Physical CT is not relevant to the epistemological concerns that motivate CT and hence not suitable as a physical analog of Mathematical CT. The correct physical analog of Mathematical CT is Modest Physical CT. I propose to explicate the notion of physical computability in terms of a usability constraint, according to which for a process to count as relevant to Physical CT, it must be usable by a finite observer to obtain the desired values of a function. Finally, I suggest that proposed counterexamples to Physical CT are still far from falsifying it because they have not been shown to satisfy the usability constraint. (shrink)

In 'Two Dogmas of Empiricism', Quine attacks the analytic/synthetic distinction and defends a doctrine that I call epistemological holism. Now, almost fifty years after the article's appearance, what are we to make of these ideas? I suggest that the philosophical naturalism that Quine did so much to promote should lead us to reject Quine's brief against the analytic/synthetic distinction; I also argue that Quine misunderstood Carnap's views on analyticity. As for epistemological holism, I claim that this thesis does not follow (...) from the logical point that Duhem and Quine made about the role of auxiliary assumptions in hypothesis testing, and that the thesis should be rejected. \\\ [Peter Hylton] Section I of this essay discusses Quine's views about reference, contrasting them with those of Russell. For the latter, our language and thought succeed in being about the world because of our acquaintance with objects; the relation of reference-roughly, the relation between a name and its bearer-is thus fundamental. For Quine, by contrast, the fundamental relation by which our language comes to be about the world, and to have empirical content, is that between a sentence and stimulations of our sensory surfaces; reference, while important, is a derivative notion. Section II shows how this view of reference as derivative makes possible the notorious Quinean doctrine of ontological relativity. Section III raises the issue of realism. It argues that somewhat different notions of realism are in play for Quine and for Russell-for Russell, objects, and our knowledge of objects, play the fundamental role, while for quine objectivity and truth are fundamental, with ontology being derivative. (shrink)

Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's (...) Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and--in particular--the effectively-computable functions on string representations of numbers. (shrink)

In ‘Two Dogmas of Empiricism’, Quine attacks the analytic/synthetic distinction and defends a doctrine that I call epistemological holism. Now, almost fifty years after the article’s appearance, what are we to make of these ideas? I suggest that the philosophical naturalism that Quine did so much to promote should lead us to reject Quine’s brief against the analytic/synthetic distinction; I also argue that Quine misunderstood Carnap's views on analyticity. As for epistemological holism, I claim that this thesis does not follow (...) from the logical point that Duhem and Quine made about the role of auxiliary assumptions in hypothesis testing, and that the thesis should be rejected. (shrink)