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Imperatives and Logic

Published online by Cambridge University Press:  14 March 2022

Alf Ross
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Extract

The existing literature treats of several investigations with a certain bearing on the question which is roughly indicated by the title “Imperatives and Logic.” Some of those investigations, however, are entirely outside the scope of the present work.

Mally sets himself the task of developing a “Logik des Willens” constituting a parallel to the usual logic, the “Logik des Denkens". In order to emphasize its independence, the author also calls this “Logik des Willens” “Deontik”, and he conceives it as being based on the “Wesensgesetze” of will in the same way as the usual logic is conceived as being based on the “Wesensgesetze” of thought. The author develops a formalistic deductive system on the basis of 5 axioms of demands (Grundsatze des Bollen), including the axiom that there is at least one fact which is unconditionally demanded, and through a lengthy series of theorems he arrives at the sentence that what is unconditionally demanded is identical with what is actually the case: “was sein soll, ist Tatsache”. Similarly, the author develops a system of axioms for “right” volition, including the axiom that right volition is non-contradictory.

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Type
Research Article
Information
Philosophy of Science , Volume 11 , Issue 1 , January 1944, pp. 30 - 46
Copyright
Copyright © The Philosophy of Science Association 1944

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References

1 Ernst Mally, Grundgesetze des Sollens, Elemente der Logik des Willens, 1926.

2 Karl Menger, Moral, Wille und Weltgestaltung. Grundlegung zur Logik der Sitten. 1934.

3 J⊘rgen J⊘rgensen, Imperativer og Logik, Theoria 1938, p. 183 f.; Imperatives and Logic, Erkenntnis, Volume VII. p. 288 f.; Kurt Grelling, Zur Logik der Sollsätze, Unity of Science Forum, 1939, p. 44 f.; Grue-S⊘rensen, Imperativsätze und Logik, Theoria, 1939, p. 195 f.; Hofstadter & McKinsey, On the Logic of Imperatives, Philosophy of Science, 1939, p. 446 f.; Rose Rand, Logik der Forderungssätze, Revue Internationale de la theorie du Droit, 1939, p. 308 f. See also Karl Menger, A Logic of the Doubtful. On Optative and Imperative Logic, Reports of Mathematical Colloquium, 1939, p. 53.

4 J⊘rgen J⊘rgensen, Erkenntnis, Volume VII, p. 288.

5 Compare Alf Ross, Kritik der sogenannten praktischen Erkenntnis, 1933.

6 In the following a practical inference means an inference of which one or more imperatives form part.

7 Rose Rand does not give an exhaustive treatment of the meaning of the transformation. “Bei Forderungssätzen kann von Wahrheit bzw. Falschheit nicht gesprochen werden. Doch können diese Axiome (i.e. die logische) im übertragenen Sinn in die Logik der Forderungssätze aufgenommen werden, wenn sie sich als zweckmässig für die Handhabung der Forderungssätze erweisen würden” (in note 3 op. cit. p. 317). This is much too vague.

8 P. 198 op. cit. in note 3. It seems as if the author's inquiries lead to the consequence that only impersonal norms can be constituent parts of inferences, a consequence which seems to be at variance with the immediately evident illustrations which may well include imperatives as individual statements of will. Ex. the parents demand: Do as the teacher tells you! the teacher says: Prepare your lessons. From this follows as a demand from the parents, that the lessons are to be prepared.

9 Alf Ross, Kritik der sogenannten praktischen Erkenntnis, 1933.

10 P. 447 op. cit. in note 3: “Roughly, we understand an imperative to be satisfied if what is commanded is the case. Thus the fiat ”Let the door be closed!“ is satisfied if the door is closed. It will be seen that the satisfaction of an imperative is analogous to the truth of a sentence. The connective symbols which we introduce later may, on their analogy with the truth-functions of the calculus of sentences, be thought of as satisfaction-functions of imperatives.” (The italics are mine). It is important to emphasize this. For, as we shall see, the satisfaction of the imperative is not the only and presumably not even the most “natural” analogy to the truth of the indicative. Serious mistakes may therefore result if it is overlooked that the logic of imperatives developed by the authors can be interpreted solely as a logic of satisfaction.

11 Walter Dubislav, Zur Unbegründbarkeit der Forderungssätze, Theoria, 1937, p. 341.

12 It would perhaps be appropriate to explain further the fact that the example stated illustrates in a right way the formula I (x → y). This formula denotes a demand for the realisation of a state so that S (x → y) is true. That is to say, you are to realise the state that love of yourself implies love of others, or the truth of the sentence that if you love yourself, then you also love others. To this corresponds the imperative as stated in the text.

13 By Rose Rand (p. 318 op. cit. in note 3) the inference occurs in the form, Alle Bürger dieses Staates sollen ehrlich sein! Alle Bewohner dieser Insel sollen Bürger dieses Staats sein! Alle Bewohner dieser Insel sollen ehrlich sein! the falsity of which, immediately conceived, seems particularly evident. The conclusion is only warranted in case the minor premise were in the indicative mood. It may be the case that not all the inhabitants of the island have become citizens of the state. If so, the demand for honesty does not apply to all of them.

14 Menger, Moral, Wille, Weltgestaltung, (1934), p. 52 f., and in Reports of a Mathematical Colloquium, 1939, p. 59. Menger makes in this connection a distinction between commands and wishes which I find no reason to dwell on.

15 Compare Alf Ross, Virkelighed og Gyldighed i Retslaeren (1934), p. 132.