A study in philosophical taxonomy

Philosophical Studies

Volumn 83, Issue 2, 1996, Pages 121-169

  Humberstone, I L ^a  

^a MONASH UNIVERSITY   (Australia)

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EID: 35348838314     PISSN: 00318116     EISSN: 15730883     Source Type: Journal    
DOI: 10.1007/BF00354286     Document Type: Article

References (41)

1. 1. (Two worlds agree on a statement when that statement is true in both or true in neither of them.) For discussion of this and related notions, see G. Hellman and F. W. Thompson, 'Physicalism: Ontology, Determination, and Reduction', Journal of Philosophy 72 (1975), 551-564,
2. and J. Kim, 'Concepts of Supervenience', Philosophy and Phenomenological Research 45 (1984), 153-176,
3. and '"Strong" and "Global" Supervenience Revisited', Philosophy and Phenomenological Research ibid. 48 (1987), 315-326.
4. I. L. Humberstone, 'First Steps in Philosophical Taxonomy', Canadian Journal of Philosophy 12 (1982), 467-478.
5. Philosophical Papers 17 (1988), 1-31;
6. see also Lewis' 'Relevant Implication', Theoria 54 ( 1988), 161-174. Lewis himself does not tie down the notion of subject matter either to the equivalence relations introduced below, or to the associated partitions, regarding each as a way of thinking of subject matters, whereas in the interests of definiteness, we specifically make the latter identification.
7. And further, since we want to speak of statements as true or false in worlds without further relativization to features of the context of utterance, statements should be free of indexical expressions (at least until §6 below).
8. 2∥.
9. The above 'Compositional Condition' does not quite correspond to what Lewis calls the Compositional Principle, which makes a special exemption for analytic statements. (This makes no difference to Lewis' discussion: see 'Statements Partly About Observation', p. 21, second paragraph.)
10. The insertion of 'contingent' was suggested by Lewis (in conversation) as the natural repair to make in view of this difficulty. The repair creates a slight further awkwardness, in that being entirely about a subject matter no longer implies being partly about that subject matter, at least when the statement in question is noncontingent. We shall not bother to take remedial action to fix this up, however.
11. A. N. Prior, 'The Autonomy of Ethics', Australasian Journal of Philosophy 38 (1960), 199-206.
12. See 'First Steps', and C. Pigden 'Logic and the Autonomy of Ethics', Australasian Journal of Philosophy 67 (1989), 127-151, for fuller discussion - and references to other discussions - of this material. Pigden's positive remarks pertain to anomalies in inferences violating Hume's Law, describable in terms of the uniform replaceability of occurrences of ethical vocabulary in their conclusions. (Prior, op. cit., had already toyed with the possibility of a reaction along these lines.)
13. A different criterion of anomalousness which similarly falls under this general description has been championed in various works by P. Weingartner and G. Schurz; see especially §§1.5,2.5, and 5.2, in Schurz, 'Relevant Deduction: From Solving Paradoxes Toward a General Theory', Erkenntnis 35 (1991), 391-437. Because these proposals do not connect directly with the project of erecting an inferential barrier between two mutually exclusive and jointly exhaustive classes of statements, we do not discuss them here.
14. A similar usage of the term 'kind' may be found in Geach's presentation of Prior's argument, in his 'Kinds of Statement', pp. 221-235 of C. Diamond and J. Teichman (eds.) Intention and Intentionally: Essays in Honour of G. E. M. Anscombe, Harvester Press 1979. Reference to other discussions by Geach of our topic are listed in note 1 of the paper by Karmo cited in note 24 below.
15. See Part 2 of I. L. Humberstone, 'Zero-Place Operations and Functional Completeness', History and Philosophy of Logic 14 (1993), 39-66.
16. In connexion with intuitionistic logic, we understand by what is usually called intuitionistic negation, i.e., more explicitly, Heyting negation, and not, for example, 'strong' negation or Brouwerian ("dual intuitionistic") negation. In saying that the last step of the argument in the text would be blocked if the underlying logic were taken to be intuitionistic, we do not intend to deny that the result goes through via some other proof in that case, since the properties of other connectives may be appealed to in an alternative argument. Such an alternative argument could run as follows. Take S £C, C a kind. Clearly to show C is a co-kind, it suffices to show that C is universal. As usual, we take an arbitrary S' and show S′ ∈ ℂ. Let S″ be any statement from whose negation, according to
17. intuitionistic logic, S′ follows. (One simple way of doing this is to choose S′ as something, for example, S ∨S, from whose negation everything follows.) Since C is a kind containing 5, we have S ∨ S″ ∈ ℂ, so (S ∨ S″) ∈ ℂ, so S″ ∈ ℂ, so, finally, S′ ∈ ℂ.
18. TE in Appendix B to this paper.
19. This dual form of the argument is given on p. 468 of 'First Steps', in response to R. and V. Routley, 'The Semantics of First-Degree Entailment', Nous 6 (1972), 335-359.
20. w, to comprise those statements which follow from some statements (plural) which belong to ℂ and are true in w, since for the choices of ℂ considered, if two statements belong to ℂ so does their conjunction.
21. See Lewis, 'Extrinsic Properties', Philosophical Studies 44 (1983), 197-200.
22. This line of thought is developed in (especially) Section 2 of my 'Intrinsic/Extrinsic', forthcoming in Synthese.
23. Essentially as given in the final paragraph of 'First Steps'.
24. Since being a coin is arguably a matter of having been minted (officially or otherwise), whether or not a box contains a coin is not strictly speaking a matter entirely about the contents of the box. Ignore this complication for present purposes (or treat 'coin' as an abbreviation for 'metal disc'.)
25. Compare the asymmetry between a priori and a posteriori truths: the former can be known on the basis of reflection, while the latter cannot be known without the aid of observation.
26. eval given, the identity of the other is fixed by the requirement of satisfying (individuation) and the orthogonality condition. Unfortunately this is not the case. From the assumption that M and N are orthogonal partitions relations satisfying (the analysis of) the condition (Individuation), and that the same holds for M, N′ it does not follow that N = N′. For example, consider the upper right-hand quadrant of the cartesian plane, with M-equivalence as the relation (between the points in that quadrant) of having the same -4-coordinate, N-equivalence as the relation of having the same y-coordinate, and N′-equivalence as the relation of subtending the same angle (to the x-axis) at the origin. N-equivalence and M-equivalence are clearly distinct relations, even though each is orthogonal to M-equivalence and every point is uniquely determined by its M-equivalence class together with its N′-equivalence class, no less than by its M-equivalence class together with its W-equivalence class.
27. Shorter's contribution was a brief note, 'Professor Prior on the Autonomy of Ethics', Australasian Journal of Philosophy 39 1961), 286-7.
28. In fact the rather unmemorable terminology of 'g-ish' and 'Z-ish' was used for 'factual' and 'ethical', respectively.
29. Toomas Karmo, 'Some Valid (but no Sound) Argument Trivially Span the "Is'/'Ought" Gap', Mind 97 (1988), 252-257.
30. See note 1 above, and the works of Kim cited therein.
31. This quotation is from Karmo op. cit., note 6, which goes on to mention the possibility of a refinement to cater for the conditional obligation statements of dyadic deontic logic.
32. n is ethical in w." (Op. cit., pp. 256f.)
33. See Chapter 5 of Gibbard's book Wise Choices, Apt Feelings, Harvard University Press, Cambridge, Mass. 1990;
34. further discussion of this device may be found in Simon Blackburn, 'Gibbard on Normative Logic', Philosophy and Phenomenological Research 52 (1992), 947-952, and in Gibbard's reply, ibid., 969-980.
35. Again, on the subjectivist side of the debate, an ethical standard may be taken to be what gets called a 'moral system' in James Dreier, 'Internalism and Speaker Relativism', Ethics 101 (1990), 6-20.
36. Readers familiar with Lewis' 'Relevant Implication' will recognize a strategic similarity here: as Lewis says (p. 172) 'Splattering stars all over the page cannot affect our argument'; likewise in what follows, with splattering "G"s all over the page.
37. 2, above, an additional parameter is needed anyway for the time of evaluation, in view of the role of tense in the examples. While this means that these are not actually examples of statements in the narrow sense introduced in §1 (since they are not indexical-free), one can obviously take the examples 'tenselessly'. On the treatment of ethical standards ('moral systems') in Dreier, op. cit., the parameter e itself records an implicit indexicality, to the speaker's (perhaps better: thinker's) standard, reducing the double-barelled (w + e) determination of a semantic value in the moral case a special case of the more familiar phenomenon of indexicality.
38. Versions of this reasoning may be found in various papers by Kim cited in Kim, op. cit., see also I. G. McFetridge, 'Supervenience, Realism, Necessity', Philosophical Quarterly 35 (1985), 244-258. This tension between strong supervenience and Hume's Law was first drawn to my attention in 1979 by André Gallois.
39. 33 So in the present context, entailmento is a better rendering of the informal idea of entailment than strict implication is; this version of the claim that entailment is not strict implication has nothing to do with the similar sounding claim on the part of relevant logic, of course. It is, rather, of a piece with replacing the necessity of the premisses-to-conclusion conditional with the a priori knowability of that conditional (as McFetridge, in effect, remarks on p. 251, op. cit.). An interesting question is whether entailmentc is indeed to be subsumed under the latter characterization. I am inclined to favour such a subsumption, thinking that even an ethical intuitionist should not regard the process of consulting one's intuitions as pure reflection (ratiocination) of the type relevant to a priori knowledge; the issue is clearly potentially controversial, and we need not take sides on it here.
40. Since Karmo does not relativize ethicality to e, but only to w, this is not strictly Karmo's account, but a slightly more general version of it (abstracting away from a particular ethical standard assumed correct).
41. I am especially grateful to Jamie Dreier for comments on this material which have resulted in numerous improvements. Thanks also to David Lewis and to Thomas Bull for the points attributed to them in note 7 and Appendix C, respectively, and to a referee for Philosophical Studies, whose helpful suggestions have been incorporated.