¹ Frege, , Foundations of Arithmetic (Blackwell, Oxford, 1959)Google Scholar, §3.

² Of course, that does not mean that they contain no a priori propositions. But these belong to the method of representation and do not describe what is represented.

³ Russell, B., The Problems of Philosophy (Oxford University Press, Oxford, 1967), 90Google Scholar; for a similar view, see Austin, J. L., ‘Ifs and Cans’, Philosophical Papers (Clarendon Press, Oxford, 1961), 180Google Scholar.

⁴ Dummett, M. A. E., ‘Can analytic philosophy be systematic and ought it to be?’, repr. in Truth and Other Enigmas (Duckworth, London, 1978), 457Google Scholar. Frege died in 1925. Half a century later is 1975, two years after the publication of Dummett, 's, Frege's Philosophy of Language (Duckworth, London, 1973)Google Scholar.

⁵ Williamson, T., ‘Must Do Better’, in Greenough, P. and Lynch, M., (eds.) Truth and Realism (Oxford University Press, Oxford, 2005), 187Google Scholar.

⁶ This radical move was made by the later Wittgenstein and, following him, by many of his distinguished pupils; in a somewhat different form, by the Vienna Circle; and subsequently by many members of the Oxford group of philosophers between 1945 and 1970.

⁷ As G. E. Moore attempted to do in his famous proof of the existence of the external world.

⁸ Williamson, recently declared (The Philosophy of Philosophy (Blackwell, Oxford, 2007), 19)CrossRefGoogle Scholar that the task of metaphysics is to discover ‘what fundamental kinds of things there are’, for example ‘substances and essences, universals and particulars’. Physicists, it seems, discover the existence of fundamental particles such as neutrinos or mesons, meta-physicists discover the existence (or non-existence) of fundamental things such as universals or essences.

⁹ Davidson, Donald, in ‘Causal Relations’, Journal of Philosophy 64 (1967)CrossRefGoogle Scholar offered a proof that events exist. As Waismann remarked apropos Moore's attempt to prove the existence of the external world: ‘What can one say to this – save perhaps that he is a great prover before the Lord’ (‘How I see Philosophy’, in How I see Philosophy and Other Essays (Macmillan, London, 1968), 1).

¹⁰ Wittgenstein was told of Hilbert's remark that no one would drive him out of Cantor's paradise, to which he replied that he would not dream of driving anyone out of paradise, he would just get them to open their eyes and look around – then they would leave of their own accord.

¹¹ Note that even where a philosophically relevant feature is picked out by reference to an aspect of a given language not shared by some other language, it does not follow that the distinction thus marked is not capable of being drawn in the second language and demonstrated by features of its use. Whether a verb has a progressive form or not is often an important clue to the character of the concept expressed, e.g. that ‘to know’ lacks a progressive form shows that it does not signify an activity or process. But German does not have a progressive tense! Nevertheless, that knowledge is no process can be made clear in German too, for there is no such thing as interrupting someone in the middle of knowing, and it makes no sense to ask someone whether he has finished knowing something.

¹² But it would be mistaken to suppose that there are not sometimes philosophically important differences between different languages and cultures. An investigation into the use of ‘mind’, for example, will differ interestingly from investigations into the use of ‘Geist’ and ‘Seele’, or ‘anima’, or ‘psuche’, or ‘nephesh’ and ‘ruach’ – which betokens differences in the way different languages and different cultures articulate characteristic human powers. It is important to note too that a philosophical enquiry into a categorial concept need not be an investigation of the use of the category-word in question. An investigation of the nature of substances (i.e. persistent things of a kind) is not an investigation of the use of the word ‘substance’ (‘substantia’ or ‘ousia’) – which is a term of art in philosophy – but rather an investigation into common features of usage of a large subclass of concrete count nouns, the common form of which is signified by the formal concept of substance.

¹³ To avert misunderstanding, I am not suggesting that such rules for the use of words typically or even commonly take the form of analytic definitions that specify necessary and sufficient conditions for the application of their definienda. Things may have a nature, even though they have no essence – as in the case of propositions, numbers or games (the concepts of which are family-resemblance concepts).

¹⁴ Of course, philosophers sometimes engage in what they misleadingly call ‘thought-experiments’. But a thought-experiment is no more an experiment than monopoly money is money.

¹⁵ To be sure, if the concept of god as an omnipotent, omniscient and benevolent creator of the universe (the god of the philosophers) is coherent, and if the ontological argument for the existence of such a god is invalid, then whether there is such a god is an empirical question, not a conceptual one.

¹⁶ See Wittgenstein, , Remarks on the Foundations of Mathematics, 3rd ed. (Blackwell, Oxford, 1978), 99Google Scholar. For elaboration, see Baker, G. P. and Hacker, P. M. S., ‘Grammar and Necessity’ in Wittgenstein: Rules, Grammar and Necessity (Blackwell, Oxford, corrected edition, 1992), 263–349Google Scholar.

¹⁷ I use the term ‘normative’ to signify what pertains to a rule (a norm), expresses a rule or is rule-governed.

¹⁸ That, I believe, is what Wittgenstein meant by his obscure remark in Investigations §599 ‘In philosophy no inferences are drawn [werden kein Schlüsse gezogen]. “But it must be like this!” is not a philosophical proposition.’ He did not mean that there are no inferences in philosophical discussion and argument, but that in philosophy one cannot infer the existence of entities on the model of inferences to the best explanation in the empirical sciences. Hence it is illegitimate in philosophy to infer that simple objects, or noumena, or universals, must exist on the grounds that if they did not exist then we wouldn't be able to …

¹⁹ I should like to be able to add a fourth form of progress, namely in moral, political and legal philosophy. But that is a question that requires separate detailed treatment.

²⁰ For the confusion, see Kripke, S., Naming and Necessity (Harvard University Press, Cambridge, Mass., 1972). 54–6Google Scholar. For its eradication, see Baker, G. P. and Hacker, P. M. S., Wittgenstein: Understanding and Meaning, Part 1 – the Essays (Blackwell, Oxford, 2005)Google Scholar, ‘The standard metre’, 189–99.

²¹ I am grateful to Hanoch Ben Yami, Jonathan Dancy, Anthony Kenny, Hans Oberdiek, Herman Philipse and David Wiggins for their comments on earlier drafts of this paper.