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Logical Organization of Philosophical Concepts

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Abstract

It is argued that the theory of opposition is in position to contribute as a formal method of conceptual engineering, by means of an increasing dichotomy-making process that augments the number of elements into any structured lexical field. After recalling the roots of this theory and its logical tenets, it is shown how the processes of expansion and contraction of discourse can modify a lexical field and, with it, our collective representation of ideas. This theory can also bring some order to the question of disagreement in philosophical discourse: what do philosophers disagree about; how can we clarify the distinction between verbal disagreement (focused on words) and substantive disagreement (focused on things)? The ensuing construction of conceptual systems will be exemplified through three case studies of philosophy: desire, truth judgment, and the left–right political divide. The construction rules of such systems resort to the theory of opposition, which intends to improve our understanding of what entails either agreement or disagreement about the meaning of concepts. Such a better understanding of philosophical discourse relies on its formalization in terms of closed lexical fields, thereby leading to a comparative analysis of concepts in light of logical relations between their definitions.

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Notes

  1. For an introduction about the traditional theory of opposition (based on Aristotle’s categorical statements), see e.g. Terence Parsons’ entry in Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/square/. For more details about its broader application to philosophical concepts and issues, see especially Blanché (1966).

  2. The theory of logical opposition has been accused of not being valid in any model and requiring the existence of subject terms (in any proposition of subject-predicate form: “S is P”). The literature on the issue is considerable (see e.g. the related literature in Chatti & Schang 2013), and the solutions to this problem have mixed comments that go beyond the realm of pure logic (see Horn 1989).

  3. Blanché (1966) gave a large number of lexical fields that illustrate logical oppositions, far beyond the sole case of Aristotle’s categorical sentences: modalities (necessity, possibility, contingency), temporality (always, sometimes, never), arithmetics (greater than, equal, lesser than), and the like. In a nutshell, Blanché purported to show that the theory of opposition contributes to a better understanding of lexical fields once these can be defined in terms of truth-conditional properties.

  4. The corresponding writings stem from a series of lectures delivered from April to July 1921.

  5. Paraconsistent logic is the set of logical systems in which the so-called “explosion” rule (admitting the truth of two contradictory propositions entails the truth of any proposition within a closed language) is not valid.

  6. According to Priest (1979), there exist propositions which are true and false at the same time (“paradoxical” propositions, such as “This statement is false)”. A contradiction can therefore be true in the sense that the conjunction of a paradoxical proposition (neither true nor false) and its negation (neither false nor true) gives a value which includes truth in both cases. This semantic debate on the interpretation of truth values goes beyond our scope here; but it is crucial in Slater’s refutation of paraconsistency, according to which a contradiction cannot be “true” by definition.

  7. For examples of sites devoted to research on logical oppositions, see in particular the site Oppositional Geometry by Alessio Moretti: https://oppositionalgeometryblog.wordpress.com/, together with the site Logical Geometry by Lorenz Demey: https://logicalgeometry.org/.

  8. True a priori judgments were qualified as “truths of reason”, as opposed to true a posteriori judgments which were qualified as “truths of fact”.

  9. This is Buridan’s negatio infinitans (see Correia 2017). A suggested formalization of this infinite negation in term logic consists of translating “not-A” as “not A, but B” (where A and B are arbitrary predicates) (see Schang 2024b).

  10. The dating of this divide goes back to the meeting of September 11, 1789, relating to the debate on the royal veto; but the use of these terms took time to become effective in popular vocabulary, and cases of political opposition between a “left” and a “right” can be cited well before the date of this historic event. On the distinction between the meaning of the left-right divide and its use, see in particular Fabry & Portal (2021), Gauchet (2021) and Schang (2022).

  11. This new category of truths is the one that allows Kant (2007) to first reconcile empiricism and rationalism in philosophy, but also to rehabilitate metaphysical truths by situating them in the domain of mathematics and geometry. It is therefore a specifically Kantian questioning which justifies this classification and explains why the previous classifications, those of the empiricist Hume and the rationalist Leibniz, could not have anticipated it.

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Acknowledgements

I am especially grateful to the reviewers for their very helpful comments and to Mlika Hamdi, editor of the philosophical journal Al Mukhatabat, for inviting me to a special talk on the present issue. The recording is available in the following URL link: https://www.youtube.com/watch?v=Gpxx8gEorIA.

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Schang, F. Logical Organization of Philosophical Concepts. Topoi 43, 1593–1605 (2024). https://doi.org/10.1007/s11245-024-10111-1

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