Abstract
Logic, in one of the many sense of that term, is a theory about what follows from what and why. Arguably, the correct theory has to be determined by abduction. Over recent years, so called logical anti-exceptionalists have investigated this matter. Current discussions have been restricted to deductive logic. However, there are also, of course, various forms of non-deductive reasoning. Indeed, abduction itself is one of these. What is to be said about the way of choosing the best theory of non-deductive inferences? It would seem clear that an anti-exceptionalist should hold that essentially the same method of choice should apply to non-deductive logic. A number of issues need to be faced in the process, not the least of which is the circularity involved in an abductive justification for a theory of abduction. This paper discusses matters.
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Notes
On the many senses of the word ‘logic’, see Priest (2014).
Again, see Priest (2014).
Though see Priest (2006b), Sect. 12.12.
Logical abductivism is not, nota bene, committed to either logical monism or logical pluralism logic itself. See Priest (202+).
Priest (2006b), Sect. 12.12, suggests a general format for all non-deductive inferences.
For a first look at abduction, see Douven (2017). There are certainly a number of ticklish issues concerning abduction—and in particular, the exact way in which the making of (successful or unsuccessful) predictions figures into an account of what the best explanation is. But what follows in not committed to any particular position on this matter, so we need not go into it here. I discuss it briefly in Priest (202+), fn 6.
I note, as did a referee of a previous draft of this essay, that there may be some dispute about what the relevant data are. As an example from the history of science: should a theory of motion on Earth explain the motions of heavenly bodies? For what it is worth, my view is this. The moot data is at least potential data, and the more of it a theory explains is better. So its relevance is captured under the criterion of theoretical power. And if a theory claims that the data is not relevant, there had better be a decent explanation of why not, or writing it off will be ad hoc.
Here is a sketch of one way. (The germ of this idea is to be found in Priest (2006a), Sect. 7.6.) Take a finite Routley/Meyer model for a relevant logic. (I am not assuming that this is the correct logic, merely that its models can deliver a probability theory with the necessary properties.) In such a model we may distinguish between the possible (normal) and the impossible (non-normal) worlds. And we can arrange things such that, for any sentence A, there is world (maybe impossible) where A holds, and a world (maybe impossible) where A fails. (See Priest 2008, esp. 10.11, ex. 11). Now let \(\mu \) be a measure on subsets of worlds. We may then define Pr(A) as \(\mu \{w\in W:A\) holds at w}. Clearly, for any A, Pr(A) will be neither 1 not 0. Of course, not all of the usual Kolmogorov axioms of probability theory—notably, those for negation—are going to hold. But it remains the case that if \(A\rightarrow B\) is a logical truth, \(Pr(A)\le Pr(B)\).
I note, in this context, a very interesting paper by Millson and Straßer (2019) . They give a theory of the formal properties of the connective ‘that A is the best explanation that B’. As such, it provides a constraint on what any account of the relationship delivered by a theory of abduction must satisfy. As they point out, however (p. 5), this in not a theory of abduction, but, if correct, something which provides a necessary condition for any adequate theory.
For a general discussion of this, see Henderson (2018).
Dummett (1978).
Haack (1982).
In the case of deductive logic there has been a well articulated received theory since Aristotle—though what this is has changed over time. In the case of non-deductive logic, I think it fair to say that this is not the case. Articulating a theory of non-deductive inference is a much more recent phenomenon. However, one might say that we have always had some inchoate theory of abduction, embedded in our inferential practices. Call it a “folk theory”, if you like.
For a discussion, see Priest (2016), §3.4.
See Woods (2019). Woods notes that the problem can be solved by enforcing conservativity (p. 322), though he suggests that this applies to certain kinds of what he calls ‘whole theory’ comparison.
On voting theory, see Pacuit (2019)
An example of a quite different kind is the following. Most sports are divided into men’s and women’s competitions. There have recently been a number of cases concerning whether, after transgender surgery, a person can compete in a sport of their new gender. Prior to a ruling by the appropriate body, there is no determinate answer to the question. (The International Olympics Committee ruled on the matter in 2003). Such rulings are necessary precisely because the notions of male and female are open textured, in the sense of Waismann. That is, the old concepts have no clear application in quite novel situations. See, e.g., Shapiro and Roberts (2019).
This paper is a descendent of talks given at the University of Sydney, August 2019, and at the CUNY/Bergen Workshop on Anti-Exceptionalism about Logic, New York, September 2019. Many thanks go to those present on these occasions for their very helpful comments and suggestions, which helped me to see a number of things more clearly. Thanks also go to two anonymous referees of this journal for similar reasons.
References
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Priest, G. Logical abductivism and non-deductive inference. Synthese 199, 3207–3217 (2021). https://doi.org/10.1007/s11229-020-02932-5
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DOI: https://doi.org/10.1007/s11229-020-02932-5