Abstract
The paper is motivated by the need of accounting for the practical syllogism as a piece of defeasible reasoning. To meet the need, the paper first refers to ranking theory as an account of defeasible descriptive reasoning. It then argues that two kinds of ought need to be distinguished, purely normative and fact-regarding obligations (in analogy to intrinsic and extrinsic utilities). It continues arguing that both kinds of ought can be iteratively revised and should hence be represented by ranking functions, too, just as iteratively revisable beliefs. Its central proposal will then be that the fact-regarding normative ranking function must be conceived as the sum of a purely normative ranking function and an epistemic ranking function (as suggested in qualitative decision theory). The distinctions defends this proposal with a comparative discussion of some critical examples and some other distinctions made in the literature. It gives a more rigorous justification of this proposal. Finally, it starts developing the logic of purely normative and of fact-regarding normative defeasible reasoning, points to the difficulties of completing the logic of the fact-regarding side, but reaches the initial aim of accounting for the defeasible nature of the practical syllogism.
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Notes
Aristotle actually takes the conclusion of a practical syllogism to be the action itself and not a sentence saying that that action ought to be performed. Many interpreters take this to be significant. Here, however, I neglect this point in order to treat the practical syllogism as an ordinary inference between sentences.
Pigden (2010) is an up-to-date collection of papers on Hume’s Thesis, in which, however, defeasibility issues play no significant role.
See, however, the criticism of Fuhrmann (2017).
A short note about the history of this paper: In my master thesis 1973 I presented a sound and complete calculus for Hansson’s (1969) semantics of conditional deontic logic, unaware of the fact that Lewis (1973) had contemporaneously and more elegantly done the very same. My result is published in Spohn (1975). At that time I felt the strong urge that conditional deontic logic needs to be extended to an alethic-deontic logic, e.g., in order to represent the practical syllogism. I did not see, though, how this could be done; the only way to account for the interaction of norms and facts, or rather of beliefs and desires, seemed to be to turn to quantitative decision theory. That’s what I did then in my dissertation. However, I never made whole peace with this move. Reading Schurz (1997), which is still the most thorough-going investigation into Hume’s thesis and into alethic-deontic logic, inspired me to think again about this issue and to find a way to fill the old lacuna with ranking theoretic means (whence this paper is well placed in this collection in honor of Gerhard Schurz). The defeasible aspect is not well belabored in his book (as he would be the first to agree). That’s where I hope to make progress.
Well, perhaps not in the form originally found in Aristotle, but in a form as it is discussed today.
This point is fully elaborated in Huber (2007). There are various other justifications of ranking theory.
Goldszmidt and Pearl (1991) develop system Z into system Z+, which allows default rules to have varying strength. This is similar to endowing arguments with varying strength, as done by Mogdil and Prakken (2013). Kern-Isberner (2004) has proposed an alternative algorithm applying a different notion of minimality.
The latter condition makes conditionals with impossible antecedents vacuously true. For a full treatment of those exceptional antecedents see Raidl (2018).
Carmo and Jones (2002), e.g., try to avoid deductive closure, although they accept substitutivity of logical equivalents. Concerning moral dilemmas, see the excellent overview of Goble (2013), who discusses in Sects. 5 and 6 how revisions of standard deontic logic might encompass normative conflicts. In Sect. 4, however, he explains how normative conflicts may be treated without such revisions—a line of thought which I definitely prefer and will take up again in Sect. 6.
See the references in the previous footnote. We find this idea also in Schurz (1997, p. 41, footnote 31).
At this point I may add a remark on my own behalf. In formal epistemology, Bayesianism is the dominating conception. Bayesians think that other conceptions of epistemic states must be reducible to the basic conception of subjective probabilities. I have always argued that ranking functions are not so reducible; prima facie, at least, we should accept ranking theory as an independent epistemological theory. I think the above ranking-theoretic construal of normative conceptions strengthens my case. In the case of epistemology, Bayesianism is quite plausible, no doubt. However, its normative counterpart has no plausibility at all. Probabilities should then be interpreted as degrees of obligation or prohibition or value. But how? I don’t see how a normative reinterpretation of Bayesianism could make sense. For an opposing view see, however, Merin (1996, ch. 4), who gives Aristotle’s endoxastic conception of probability a normative twist by interpreting endoxastic probability as ‘approvability’. Bayesians must judge whether they welcome this support.
That’s the so-called Harper identity translated into our present context. Cf. Gärdenfors (1988, p. 70).
These are the familiar contraction postulates (K-7) and (K-(8) translated into our context. Cf. Gärdenfors (1988, p. 64).
I am grateful to two reviewers demanding that clarification.
Instead of conditional and unconditional obligations (whether in the pure or the fact-regarding sense) I am tempted to speak of hypothetical and categorical imperatives. These terms should be released from their Kantian grip.
This formal translation works almost perfectly. However, I should emphasize that it does not help interpreting ranking theory. Its interpretation as an account of belief stands by its own and is orthogonal to that of probability theory.
In July 2015, Franz Huber has suggested essentially the same formula to me in personal communication. His term for νκ(A) is ‘anticipated regret’—‘regret’ because ν expresses only negative utilities, as it were, and ‘anticipated’ because he thinks that ‘expected’ is too firmly associated with probability.
Observe that Definition 3 of epistemic conditionalization essentially refers to the arithmetics of ranks.
This distinction was introduced already by Ross (1930). It has become common to speak of pro tanto duties instead of prima facie duties (or moral reasons, etc.).
This point also reflects my above remarks about facts and beliefs. In our context, “all facts considered” can only mean “all beliefs considered”.
Hence, all-things-considered obligations may conform to standard deontic logic. Normative ranking functions do so as well, and hence they must be understood in this way, too.
See also my extensive ranking-theoretic account of ceteris paribus conditions in Spohn (2014).
There may even be a direct relation between facts and norms blurring their distinction. (I am grateful to a reviewer for raising this issue.) We expect people to conform to the norms. That is, we expect that only permissible things happen; and the more strictly something is forbidden, the more firmly we disbelieve that it takes place. In the dogs example, e.g., the condition that there is a dog seems epistemically deviant only because it is normatively deviant and hence unexpected. The inference may be even reversed. When something occurs, it was presumably admissible, and when something doesn’t occur, maybe that is so because it is inadmissible. Now, the latter is dangerously close to a rejection of Hume’s Thesis and to Leibniz’ claim that the actual world is the best of all worlds (according to God’s proper standards). I admit that both inferences have some justification. However, they clearly are defeasible inferences, and the second is much weaker than the first. And they are relatively plausible only with respect to human actions, and the less plausible, the farther we move away from human influence. If it ought to rain, there is no way to infer that it will rain; the reverse would be even worse. There is a general simple explanation why the inference is sometimes plausible. We simply expect our fellows to respect the norms (at least if the norms are publicly known and not my idiosyncratic ones), and reversely, if we observe a behavioral regularity within our community without natural explanation, then it is presumably a normative rule. However, this does not reflect a general logical point, as we pursue it here. It is rather based on a special empirical claim, namely the human receptivity for norms. Therefore, the issue is besides our present interests, even though it would deserve getting developed.
Note that the fact that ψ is a necessary condition of φ could as well be formalized by ¬ψ ⊳d ¬φ. As is well known, the two formalizations are not equivalent. Only our choice yields a promising inference.
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I am indebted to three fortunately very critical reviewers for many most helpful commentaries and suggestions.
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Spohn, W. Defeasible normative reasoning. Synthese 197, 1391–1428 (2020). https://doi.org/10.1007/s11229-019-02083-2
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DOI: https://doi.org/10.1007/s11229-019-02083-2