Abstract
The concept-swapping fallacy produces circular definitions and infinite regresses. It is found in theoretical disciplines, as shows the case of Poincaré and Le Roy in the philosophy of mathematics. But it is also found in practical ones. Thus in ethics we find it in the repeated attempts to define the good, by authors as different as Bentham and Mill, on the one hand, or Brentano on the other. And in the philosophy of law we find it in the convoluted ways in which legal positivists attempt to define what is lawful. In all these and many other cases, what is at work is the replacement of a real synthetic judgment by an apparent analytic one.
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Notes
- 1.
The most relevant parts of Le Roy’s argument are probably his ‘criticism of scientific facts’ (1899, pp. 514–518), his ‘criticism of the laws of nature’ (ibid 518–526) and his ‘criticism of physical theories’ (ibid 526–534). It is also remarkable that the author, when talking about the experimental method, says that truth is no more than ‘the inner joy’ of the scientist (ibid 512).
- 2.
See Mill (1861, Chap. II).
- 3.
See Brentano (1889, §23).
- 4.
The German phrase ‘practical discipline’ (praktische Wissenschaft), at least as used in Kantian philosophy, means more or less the same as ‘normative discipline’. Thus both ethics and the philosophy of law would be ‘practical disciplines’ in this sense.
- 5.
The following argument relies to a considerable extent on the double meaning of the German word Recht, which means both ‘law’ and ‘right’.
- 6.
Legal positivists, however, have notoriously made statements much to that effect, e.g. Jellinek (1914, p. 333). A detailed discussion of Jellinek can be found in Nelson (1917, Chap. 1). Nonetheless, it is only fair to say that Jellinek (1914, p. 334, n. 2) admits that enforceability has to meet serious objections.
- 7.
The German text is somewhat opaque at this point. It seems possible, if a bit stretched, to translate it as follows, ‘Enforcing a rule of conduct makes that rule a law only if the enforcement is lawful.’ However, the translation given above, even if freer, reflects Nelson’s argument better.
- 8.
Nelson did not take advantage of the logical method of definition by means of variables which Russell (1905) used to so much effect. If he had, his argument would have been less convoluted. He would have started with ‘x is legal iff x is enforceable’. Then under exclusion of mere physical enforceability we would get ‘x is legal iff x is legally enforceable’. The meaning of the adverb ‘legally’ would obviously become unreachable after an endless substitution of the definiens: ‘x is legal iff x is … enforceably enforceably enforceably enforceable’.
- 9.
- 10.
The phrase ‘conviction of lawfulness’ translates German Rechtsüberzeugung, which refers to the feeling most citizens have about the legitimacy of laws, decrees or government policies. The somewhat inelegant translation chosen helps make Nelson’s argument clear. See Jellinek (1914, pp. 333–334, 355) and Nelson (1917, p. 16).
- 11.
Nelson touches here the difficult question of how a definition can actually produce results. This question was first adumbrated by Kant, who believed that this was only possible in the case of mathematics, where we were able to construct the mathematical object corresponding to the concept defined, because the definition gave us the relevant instructions. Frege (1884) was concerned with this question in all his work, starting with his Principles of Arithmetic. Nelson’s point is that this works in mathematics but can and will never work in philosophy.
- 12.
This problem arose from Newton’s theory of universal gravitation. For a historical overview of the conceptual difficulties of action at a distance, see Hesse (1962).
References
Bentham, Jeremy. 1789. An Introduction to the Principles of Morals and Legislation. London: Payne.
Brentano, Franz. 1889. Vom Ursprung sittlicher Erkenntnis. Leipzig: Duncker & Humblot. [English translation: The Origin of the Knowledge of Right and Wrong, Westminster, Archibald Constable & Co., 1902].
Frege, Gottlob. 1884. Die Grundlagen der Arithmetik: eine logisch-arithmetische Untersuchung über den Begriff der Zahl. Wrocław: Wilhelm Koebner. [English translation by J.L. Austin: The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Oxford, Blackwell, 1950. New translation by Dale Jacquette: The foundations of arithmetic. New York: Pearson, 2007].
Hesse, Mary B. 1962. Forces and Fields: The Concept of Action at a Distance in the History of Physics. London and New York: T. Nelson.
Jellinek, Georg. 1914. Allgemeine Staatslehre [General theory of the state], 3rd ed. Berlin: Oscar Häring. [First edition 1900, second edition 1905].
Le Roy, Édouard. 1899, 1900. Science et philosophie [Science and philosophy]. Revue de métaphysique et de morale, VII, 375–425, 503–562, 708–731; VIII, 37–72.
Mill, John Stuart. 1861. Utilitarianism. Fraser’s Magazine 64: 391–406, 525–534, 658–673 [Reprinted many times].
Nelson, Leonard. 1917. Die Rechtswissenschaft ohne Recht: kritische Betrachtungen über die Grundlagen des Staats- und Völkerrechts, insbesondere über die Lehre von der Souveranität [Law without justice: critical reflections on the foundations of public and international law, in particular on the theory of sovereignty]. Leipzig: Veit & Comp. [Reprinted in Nelson (1971–1977), vol. IX, pp. 123–324].
Nelson, Leonard. 1971–1977. Gesammelte Schriften, 9 vols. Edited by Paul Bernays, Willy Eichler, Arnold Gysin, Gustav Heckmann, Grete Henry-Hermann, Fritz von Hippel, Stephan Körner, Werner Kroebel, and Gerhard Weisser. Hamburg: Felix Meiner.
Poincaré, Henri. 1902. La science et l’hypothèse. Paris: Flammarion. [English translation: The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method, New York, The Science Press, 1929, pp. 27–197].
Russell, Bertrand. 1905. On Denoting. Mind 14(56): 479–493.
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Nelson, L. (2016). Lecture XIV. In: A Theory of Philosophical Fallacies. Argumentation Library, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-20783-4_15
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