Abstract
In this paper my primary aim is to present a logical system of practical reasoning that can be used to assess the validity of practical arguments, that is, arguments with a practical judgment as conclusion. I begin with a critical evaluation of other approaches to this issue and argue that they are inadequate. On the basis of these considerations, I explain in Sect. 2 the informal conception of practical validity and introduce in Sect. 3 the logical system P, which is an extension of propositional logic and can be used to assess the validity of a wide range of practical arguments. In the last section, I apply this system to some examples of practical reasoning in order to demonstrate how it can be used in practice.
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Notes
By claiming this, I do not deny the valuable contributions of so-called decision theory and deontic logic (both kinds of practical logic) to the theory of practical reasoning. However, the logical system I am going to present here is different, even though naturally related, to both of them.
This does, however, not mean that the conclusion of a practical argument must be a value judgement (i.e., a judgement expressing a valuation); it can also be a statement about what should be done without expressing any valuation at all.
Anscombe (1963) is a case in point, if I understand her correctly.
Among them are Davidson (2001), Piller (2001), and von Wright (1997a). Dreier (1997, 96) claims that if this kind of reasoning does not count as a reason, then the request for reasons is empty, and Broome (2002) seems to regret that his account of correct practical reasoning cannot show the validity of a sufficient condition schema. Also Audi (2004, 128–9) accepts the validity of sufficient condition schemata if the conclusion is only a prima facie judgement.
See also von Wright (1977b).
Broome reserves the term ‘valid’ to the propositional content of practical reasoning and calls the reasoning itself only ‘correct.’ He holds that, given some constraints are met, practical reasoning is ‘correct’ if the propositional content gives a valid practical syllogism (see 2001, 177–8; 2002).
It seems that this was the opinion of Aristotle (see, e.g., NE 1147a25–35). This view has been criticized by Audi (1982, 29)–among others.
See Davidson (2004). However, ‘value judgement’ is too broad and too narrow because some value judgements do not refer to actions and not all conclusions are evaluative.
Also this view has been criticized by Audi (1982, 29).
This requires that the ordering is (i) connected. If we choose the symbol ‘≥’ for a valuer’s preference relation, this relation is connected, if, for any two distinct consequences (x, y), either x ≥ y or y ≥ x (or both). It requires (ii) transitivity. The valuer’s preference relation is transitive, if, for all triplets of consequences (x, y, z), x ≥ y and y ≥ z entail x ≥ z. Furthermore, as an anonymous referee has pointed out, if ‘most valued’ means ‘uniquely most valued’ (as is indeed meant here), it requires (iii) that (∃x)(∀y) (x ≠ y → x > y), where ‘>’ stands for the irreflexive relation ‘x is more valued than y,’ That is, there must be a consequence that is more valued than any other.
I use the term ‘implicate’ in the technical sense it has been given especially by H. P. Grice (Studies in the Way of Words, 1989).
The symbols φ and ψ are here used as metavariables ranging over formulae of P.
I use ‘+’ as the symbol for exclusive disjunctions.
At this stage I can reply to the concern, expressed by an anonymous referee, that my criterion of practical validity implies contradictions. Let ‘b’ mean ‘I am taking a bottle of mineral water’ (where ‘a bottle’ means any of the available ones) and ‘b 1 ’ and ‘b 2 ’ mean ‘I am taking the first (second) bottle of mineral water.’ According to my criterion of validity, it is not the case that an agent who wants to take a bottle of mineral water should take the first bottle and it is not the case that he should take the second bottle also. (For the sake of simplicity, we assume that there are only two bottles the agent can choose from.) It seems, therefore, that the agent should not take any bottle. On the other hand, Vb ⊧ Ob is a valid argument, according to my criterion, and from this it seems to follow that the agent should do both, taking a bottle and not taking one.
I do not think, however, that this example causes problems because what follows from my view is that the agent should take any bottle. This can be seen when we symbolize the argument as follows: (b 1 → b), (b 2 → b), ¬(b 1 b 2) → ¬b, Vb ╞ O(b 1 b 2). That is, the agent should take any bottle, and this is here tantamount to saying that he should take ‘a bottle’ (Ob).
The examples are taken, but adapted, from Hurley, P.J. (1994). A concise introduction to logic (5th edn.). Belmont/Cal.: Wadsworth.
Please note that even though the conclusion is of the form O¬φ, doing the conclusion means here doing ¬a because from (a ∧ ¬a) ∨ ¬a follows ¬a.
Even though the argument has apparently only one alternative, it contains in fact two, ‘l’ and ‘¬l’, because ‘f ↔ l’ is, of course, equivalent to ‘l → f’ and ‘¬l → ¬f’. Therefore, not doing the conclusion is tantamount to doing ‘¬l’. The analogous remark applies to the consequence ‘i.’
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Spielthenner, G. A Logic of Practical Reasoning. Acta Anal 22, 139–153 (2007). https://doi.org/10.1007/s12136-007-0005-x
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DOI: https://doi.org/10.1007/s12136-007-0005-x