Logical Constants and Harmony of the Rules of Inference

Mariela Rubin


All through the literatura, the question about what is a logical constant has recieved many answers, from model-theoretic aproaches (Tarski; 1966), (Sher; 1991), (Bonnay; 2007) to answers that focus in the inferential practice as meaning (Dummett; 1991), (Prawitz; 1965), (Lorenzen; 1955). Detractors of the second tradition presented many ineludible incovenients, in particular, the logical constant named ‘tonk’ (Prior; 1960). Inferentialist tryed many solutions, in particular they presented the concept of ‘harmony’. The goal of this paper is to show that the different criteria of ‘harmony’ used in the proof-theoretic semantics to determine what is and what is not a logical constant fail to be necessary or sufficient.  I will show the philosophical reasons that make this concept appear and then i will describe the different ways in wich the literatura understads the concept of ‘harmony’. Then I will show that they subgenerate or overgenerate connectives with some counterexamples. Finaly, I will explain some philosophical reasons that should delimitate where to go towards a satisfactory definition of ‘harmony’.


Harmony; tonk; Inferentialism; Proof-theoretic Semantics


Belnap, Nuel D. (1962). “Tonk, Plonk and Plink”. Analysis, Vol. 22, No. 6 (Jun., 1962), pp. 130-134.

Bonnay, D. (2008). “Logicality and Invariance”. Bulletin of Symbolic Logic, Vol. 14, pp. 29-68.

Buacar, N. (2015). “La justificación de la deducción”. Tesis doctoral sin publicar, UBA.

Cook, R. (2005). “What’s wrong with tonk(?)”, Journal of Philosophical Logic, Vol. 34, Nro. 2, pp. 217-226.

Dummett, M. (1978). “Truth and Other Enigmas”, Cambridge, MA: Harvard University Press.

Dummett, M. (1991). “The Logical Basis of Metaphysics”. Cambridge: Harvard University Press.

Gómez Torrente, M. (2007). “Constantes Lógicas”. En M. J. Frápolli (comp.), Filosofía de la Lógica, Madrid, Tecnos, pp. 179-205.

Prawitz, D. (1965). “Natural Deduction. A Proof-Theoretical Study”, Estocolmo, Almqvist&Wiksell.

Prawitz, D. (1971). “Ideas and Results in Proof Theory”. En Jens E. Fenstad (ed.), Proceedings of the Second Scandinavian Logic Symposium (Oslo 1970). Amsterdam: North-Holland, pp. 235–308.

Prawitz, D. (2007). “Pragmatist and Verificationist Theories of Meaning” En Randall E. Auxier and Lewis Edwin Hahn (eds.), The Philosophy of Michael Dummett. La Salle: Open Court, pp. 455–481.

Prior, N. (1960). “The Runabout Inference-Ticket”. Analysis, Vol. 21, No. 2, (Dec., 1960), pp. 38-39.

Rahman, S. & Redmond, J. (2016). “Armonía Dialógica: tonk, Teoría Constructiva de Tipos y Reglas para Jugadores Anónimos”, THEORIA. Revista de Teoría, Historia y Fundamentos de la Ciencia, vol. 31, núm. 1, pp. 27-53.

Read, S. (2009). “General-Elimination Harmony and the Meaning of the Logical Constants”. Springer Science+Business. Media B.V. 2010.

Sher, G. (2011). “Is Logic in the Mind or in the World?”. Synthese, Vol. 18, pp. 353-65.

Sher, G. (2013). “The foundational problem of logic”. The Bulletin of Symbolic Logic, Vol. 19, Nro. 2, pp. 145-198. Las citas corresponden a la versión digital disponible en: http://philosophyfaculty.ucsd.edu/faculty/gsher/the_foundational_problem_of_log ic_bsl.pdf

Steiberger, F. (2011). “What Harmony Could and Could Not Be.” Australasian Journal of Philosophy, Volume 89, - Issue 4, pp. 617-639.

Tajer, D. (2014). “Dialeteismo: una teoría contradictoria de la verdad”. En E. A. Barrio (dir.), La lógica de la verdad, EUDEBA, Buenos Aires, Argentina, pp. 249-292.

Tarski, A. (1933). “The concept of truth in the languages of the deductive sciences” (Polish), PraceTowarzystwaNaukowegoWarszawskiego, Wydzial III NaukMatematyczno-Fizycznych 34, Warsaw; reprinted in Zygmunt 1995, pp. 13–172; expanded English translation in Tarski 1983, pp. 152–278.

Tarski, A. (1966). “What Are Logical Notions?”. En J. Corcoran (ed.), History and Philosophy of Logic 7 (1986), pp. 143-54.

DOI: http://dx.doi.org/10.22370/rhv.2017.9.852


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