1 Hume, David, A Treatise of Human Nature. Selby-Bigge edition. Oxford: Clarendon Press, 1958. III-I-i. Though it appears in this passage that Hume's criticism is directed only at the moral theories of moral philosophers, it is obvious that what Hume says applies to anyone using an argument involving is-statements and ought-statements.
2 Hare, R. M., The Language of Morals. Oxford: Clarendon Press, 1952. p. 29ff.Prior, A. N., Logic and the Basic Of Ethics. Oxford: Clarendon Press, 1949. pp. 32–33.Nowell-Smith, P. H., Ethics. Pelican, 1959. pp. 36–38.
3 MacIntyre, A. C., “Hume On ‘Is’ And ‘Ought’,” Philosophical Review. 1959. pp. 451–468.Hampshire, S., “Fallacies in Moral Philosophy”, Mind. 1949. p. 466ff.
4 I have purposely chosen not to define such words as belief and statement, for I am content with their ordinary usage. I should point out, however, that I am not using belief in Hume's technical sense, (Treatise, I-3-vii, passim).
5 Kant, Critique Of Pure Reason. Norman Kemp Smith, trans. B375.
6 See Kant, , Foundations of the Metaphysics of Morals. Beck, trans. New York: Liberal Arts, 1959. p. 59ff.
7 Moore, G. E., Principia Ethica. Cambridge: University Press, 1960. p. 9ff.
8 Other Intuitionists, like Sir W. David Ross and A. C. Ewing, follow Moore in asserting Hume's hurdle. The word intuition itself is usually used to mean that we cannot or do not reason in arriving at moral decisions.
9 The school of meta-ethics often referred to as ‘Emotivism’, represented by such philosophers as Stevenson and Ayer, is also asserting the unbridgeable gap when it refers to ought-statements as solely or primarily emotive.
10 De Morgan, Augustus, A Budget of Paradoxes. London: Longmans, Green, 1872. p. 2.
11 I should, perhaps, point out that in this paper I am concerned with ought-statements expressing ends (rather than means). I am concerned with what Kant called categorical imperatives, as distinct from hypothetical imperatives. Statements like If you want to be happy, you ought not to commit adultery are, so far as I can see, purely factual, and their truth-values are discoverable empirically. But people do say ϒou ought not to commit adultery, regarding abstention from adultery as an end in itself.
12 I think, though the philosophers concerned may not agree, that Nowell-Smith argues in this way, especially in passages about “logical oddness”, and that Stephen Toulmin tries to do the same thing when talking about “limiting questions”. Toulmin, , The Place of Reason in Ethics. Cambridge: University Press, 1960.
13 Mandelbaum, M., “On the Use of Moral Principles”, Journal of Philosophy. 1956. pp. 662–670.Demos, R., “Is Moral Reasoning Deductive?”, Journal of Philosophy. 1958. pp. 153–159. By the end of his paper, Demos is virtually admitting that moral reasoning does not fit the inductive pattern.