Philosophical Method and Galileo's Paradox of Infinity

Philosophy, and especially metaphysics, has often been attacked on either epistemic or semantic grounds. Anything outside of experience and the laws of logic is said to be unknowable, and according to Wittgenstein and the logical positivists, there are no such things to know; metaphysical disputes are either meaningless or merely verbal. This was thought to explain philosophy’s supposed lack of progress: philosophers argue endlessly and fruitlessly precisely because they are not really saying anything about matters of fact (Wittgenstein,1 Remark 402; Carnap2 ). Since the mid-twentieth century, the tide has been against such views, and metaphysics has re-established itself within the analytic tradition. Ontology, essentialism, and de re necessity have regained credibility in many eyes and are often investigated by excavating intuitions of obscure origin. Relatedly, externalist semantic theories have claimed that meaning or reference has a secret life of its own, largely unfettered by our understanding and intentions (Kripke;3,4 Putnam5,6). ‘Water’, it is claimed, would denote H2O even if we had never discovered that particular molecular structure, and this is allied with the view that such structure is metaphysically essential to water — that water could not have been otherwise (Kripke3,4).