Famous examples of conceivability arguments include: (i) Descartes' argument for mind-body dualism; (ii) Kripke's 'modal argument' against psychophysical identity theory; (iii) Chalmers' 'zombie argument' against materialism; and (iv) modal versions of the ontological argument for theism. In this paper we show that for any such conceivability argument, C, there is a corresponding 'mirror argument', M. M is deductively valid and has a conclusion that contradicts C's conclusion. Hence a proponent of C-henceforth, a 'conceivabilist'-can be warranted in holding that C's premises are conjointly true only if she can find fault with one of M's premises. But M's premises-of which there are just two-are modeled on a pair of C's premises. The same reasoning that supports the latter supports the former. For this reason a conceivabilist can repudiate M's premises only on pain of severely undermining C's premises. We conclude on this basis that all conceivability arguments, including each of (i)-(iv), are fallacious.

Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose ([41], p. 644) goes one step further and asserts that: a radical new theory is indeed needed, and I am suggesting, moreover, that this theory, when it is found, will be of an essentially non-computational character. The aim of this paper is three fold: 1) to examine the incompatibility between the hypothesis of strong determinism and computability, 2) to give new examples of uncomputable physical laws, and 3) to discuss the relevance of Gödel's Incompleteness Theorem in refuting the claim that an algorithmic theory-like strong AI-can provide an adequate theory of mind. Finally, we question the adequacy of the theory of computation to discuss physical laws and thought processes.

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