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First Steps in Philosophical Taxonomy

Published online by Cambridge University Press:  01 January 2020

I.L. Humberstone
I.L. Humberstone*
Affiliation:
Monash University
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Extract

A.N. Prior once showed that on certain apparently reasonable assumptions, a thesis sometimes associated with the name of Hume to the effect that no set of factual statements can ever entail an evaluative statement (call this principle ‘H’), is quite untenable. We assume only that there is at least one statement of each kind, and that the negation of a factual statement (evaluative statement) is factual (evaluative, respectively) — a principle we may call ‘N'. Now consider the disjunction F V E of some factual with some evaluative statement. Since the disjunction is entailed by F, a factual statement, it must, if principle H is correct, be classified as factual. But by N, ∽ F is also factual, and this together with F V E entails E, thus violating H since E was exhypothesi an evaluative statement.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 12 , Issue 3 , September 1982 , pp. 467 - 478
Copyright
Copyright © The Authors 1982

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References

1 ‘The Autonomy of Ethics,’ Australasian Journal of Philosophy, 38 (1960) 199-206. That the classification of all statements into the categories of factual and evaluative in such a way as to respect ‘Hume's Law’ faces difficulties because of truth-functional compounding seems to have been inchoately recognised earlier by Rynin, D. in ‘The Autonomy of Morals,’ Mind, 66 (1957) 308-17.CrossRefGoogle Scholar

2 Much material in this vein is assembled and discussed in Hudson's, W.D. collection The Is/Ought Question (London: MacMillan 1969).Google Scholar The present paper is in no way a contribution to this already voluminous literature; indeed to any reader who thinks that Hudson's book deserves its subtitle ‘A collection of papers on the central problem in moral philosophy,’ I would recommend Peter Singers ‘The Triviality of the Debate over “ls-Ought’ and the Definition of “Moral“', American Philosophical Quarterly, 10 (1973) 51-6.

3 This sentiment is clearly discernible in R. and Routley, V. ‘The Semantics of FirstDegree Entailment,’ Noûs, 6 (1972) 335-59.CrossRefGoogle Scholar

4 The talk of relevant entailment here may be understood as the entailment of the paper cited in note 3.

5 Another common misconception is that it is always possible for a defender of H to save the principle by what his opponent considers an objectionable circularity, classifying as evaluative anything which entails something what has already (perhaps on more appealing grounds) been reckoned evaluative, and as factual, anything else. The defense fails because the suggested criterion makes both F v E and ∼ F factual (even though it counts their conjunction as evaluative).

6 This conclusion is quite well-known to logicians; witness the remarks in the Routleys’ paper cited above, as well as the following comment by Thomason, R.H. (from ‘A Semantical Theory of Sortal Incorrectness; Journal of Philosophical Logic, 1 (1972) 209-58)CrossRefGoogle Scholar: This train of thought shows, I believe, that the notion of sortal incorrectness does not extend very well to complex sentences. In this respect the distinction between sortally correct and sortally incorrect sentences resembles certain other distinctions that philosophers have made, such as those between normative and factual, or theoretical and observation sentences. These too do not extend very well to disjunctions. (239)

7 ‘Professor Prior on the Autonomy of Ethics: Australasian Journal of Philosophy, 39 (1961) 286-7

8 Perhaps the fact that Prior's argument does not touch on these matters is what makes many people whose main interest is in moral philosophy inclined to dismiss it as some sort of ‘trick’ - or at any rate, as irrelevant to their concerns. (I believe that the latter reaction is correct.)

9 We naturally exempt here those formulae which are true on every valuation, because they will trivially (on the conception of entailment with which we are working) end up being entailed by everything. (This sort of exemption is of course precisely the kind of thing those, like the Routleys, sympathetic to the relevance approach regard as unnatural.)

10 An earlier draft has been improved here, and at several other places, as a result of suggestions from two of this Journal's referees.

11 On this more modest proposal, the classification of formulae which are true on a valuation V into those which are Q-ish and those which are Z-ish with respect to Vis mutually exclusive and Jointly exhaustive. On the subject of what can be inferred from what, I am skirting round some interesting difficulties in speaking of the premisses as known to be true. A more thorough investigation would need to look at the subjective probabilities of the premisses for the inferrer. For example, in the original disjunctive syllogism case, I may attach a high probability to F v E and then come to learn ∼ F, but so far from going on to infer E, I may go back and lower my degree of belief in F v E - if my sole reason for believing that dis· Junction was my confidence in the truth of the first disjunct. (What we need to require for disjunctive syllogism inferences to be ‘probabilistically sound’ is that the disjunction in question be two-sidedly robust, in the sense of Jackson, F. ‘On Assertion and Indicative Conditionals,’ Philosophical Review, 88 [1979] 565-89.CrossRefGoogle Scholar)

12 In the possible worlds semantics for deontic logic the relativity represented here as to a valuation instead emerges as: to a world in a model. For instance, ‘Op v q' (no significance here attaching to the choice of ‘p’ and ‘q': there is a single sort of propositional variables) is Z-ish (evaluative) at a world in a model if its second disjunct is false at that world in that model. The situation is similar with the possi· ble worlds semantics for (alethic) modal logic, where there is the additional complication that the relevant analogue of the Barrier Lemma holds only asymmetrically, in view of the inference from necessity to truth. (I am thinking of the taxonomy necessary/contingent. I have gone into some aspects of this case in another paper, ‘Necessary Conclusions.’)

13 The same point could be made with the inference from disjuncts to disjunctions.