Abstract
We come back to the question why the logical method of rigorous logical inferences that works so well in geometry cannot be used in philosophy. Philosophical concepts are already in place before we begin philosophising, so that any attempt at defining them ends up in concept-swapping, i.e. replacing the original concept with a different and arbitrary one. Whenever philosophers do that, they equivocate. This fallacy is often compounded with circular definitions.
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Notes
- 1.
Today we would say that the commutative law is provable by mathematical induction.
- 2.
The term used by the Schoolmen was ens universale, ens commune, and occasionally ens generale. Behind all these terms lurks Aristotle’s ‘being qua being’ (Metaphysics Γ).
- 3.
- 4.
See Nelson (1908, Chap. VI).
- 5.
- 6.
Nelson has Bergson (1903) in mind here. On p. 9 Bergson says that metaphysics only deserves its name ‘when it overcomes concepts, or at least when it frees itself from stiff and ready-made concepts in order to create concepts quite different from the usual ones, I mean flexible, loose, almost fluid, always ready to mould themselves upon the elusive shapes of intuition’. For a more thorough treatment of this view, see Chapter “Lecture XIII”. Bencivenga (2000) develops a very interesting argument to the effect that there has been a struggle between two kinds of logic going on ever since Hegel modified Kant’s philosophy and consisting precisely in the acceptance or rejection of ‘fluid concepts’. The reader might be aware of a huge literature on this very topic starting with Wittgenstein (1953) in philosophy and Rosch (1973) in cognitive science. This is no place to tackle what is a rather complex issue, but it may be interesting for the reader to consider Bencivenga’s proposal jointly with the logical diagnosis Nelson presents in his Chapter “Lecture XXII”, when he distinguishes between an Aristotelian-Kantian and a Neoplatonic-Fichtean logic.
- 7.
Examples of such philosophers will be given in Chapter “Lecture XIII”.
- 8.
In Kant’s original scheme the logical form of the conditional corresponds to the category of causality. Today this idea has been modified by having the antecedent and consequent of the causal conditional connected to each other by a counterfactual link. This modified analysis of causality was initiated by Reichenbach (1947, 1954) and has become more or less standard in discussions of causality within analytic philosophy and, after deeper modifications, in computational science (see Pearl 2000).
References
Bencivenga, Ermanno. 2000. Hegel’s dialectical logic. New York: Oxford University Press.
Bergson, Henri. 1903. Introduction à la métaphysique. Revue de métaphysique et de morale 11: 1–36. [English translation: Introduction to metaphysics, New York, Putnam, 1912].
Berkeley, George. 1710. A treatise concerning the principles of human knowledge, Part I. Dublin: Aaron Rhames for Jeremy Pepyat.
Grelling, Kurt, and Leonard Nelson. 1908. Bemerkungen zu den Paradoxien von Russell und Burali-Forti [Remarks on the paradoxes of Russell and Burali-Forti]. Abhandlungen der Fries’schen Schule (N.F.) 2: 301–334. [Reprinted in Nelson (1971–1977), vol. III, pp. 95–129].
Locke, John. 1690. An essay concerning humane understanding. London: The Basset.
Nelson, Leonard. 1908. Über das sogenannte Erkenntnisproblem [On the so-called problem of knowledge]. Abhandlungen der Fries’schen Schule (N.F.) 2(4): 413–818. [Reprinted in Nelson (1971–1977), vol. II, pp. 59–393].
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.
Pearl, Judea. 2000. Causality: Models, reasoning, and inference. New York: Oxford University Press.
Reichenbach, Hans. 1947. Elements of formal logic. New York: Macmillan.
Reichenbach, Hans. 1954. Nomological statements and admissible operations. Amsterdam: North-Holland.
Rosch, Eleanor H. 1973. Natural categories. Cognitive Psychology 4(3): 328–350.
Russell, Bertrand. 1903. The principles of mathematics, vol. I. Cambridge: University Press. [No second volume was ever published].
Wittgenstein, Ludwig. 1953. Philosophische untersuchungen. Philosophical Investigations. German text and English translation by G.E.M. Anscombe. Oxford: Blackwell.
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Nelson, L. (2016). Lecture XII. In: A Theory of Philosophical Fallacies. Argumentation Library, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-20783-4_13
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