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Logic and Logical Philosophy

Mereology with Super-Supplementation Axioms. A Reconstruction of the Unpublished Manuscript of Jan F. Drewnowski
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  • Mereology with Super-Supplementation Axioms. A Reconstruction of the Unpublished Manuscript of Jan F. Drewnowski
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Mereology with Super-Supplementation Axioms. A Reconstruction of the Unpublished Manuscript of Jan F. Drewnowski

Authors

  • Kordula Świętorzecka Cardinal Stefan Wyszyński University in Warsaw, Institute of Philosophy
  • Marcin Łyczak Cardinal Stefan Wyszyński University in Warsaw, Institute of Philosophy

DOI:

https://doi.org/10.12775/LLP.2019.034

Keywords

mereology, axiomatics for classical mereology, supplementation principles, super-supplementation principles, Stanisław Leśniewski, Jan F. Drewnowski

Abstract

We present a study of unpublished fragments of Jan F. Drewnowski’s manuscript from the years 1922–1928, which contains his own axiomatics for mereology. The sources are transcribed and two versions of mereology are reconstructed from them. The first one is given by Drewnowski. The second comes from Leśniewski and was known to Drewnowski from Leśniewski’s lectures. Drewnowski’s version is expressed in the language of ontology enriched with the primitive concept of a (proper) part, and its key axiom expresses the so-called weak super-supplementation principle, which was named by Drewnowski “the postulate of the existence of subtractions”. Leśniewski’s axiomatics with the primitive concept of an ingrediens contains the axiom expressing the strong super-supplementation principle. In both systems the collective class of objects from the range of a given non-empty concept is defined as the upper bound of that range. From a historical point of view it is interesting to notice that the presented version of Leśniewski’s axiomatics has not been published yet. The same applies to Drewnowski’s approach. We reconstruct the proof of the equivalence of these two systems. Finally, we discuss questions stemming from their equivalence in frame of elementary mereology formulated in a modern way.

References

Cotnoir, A.J., and A. Varzi, “Natural axioms for classical mereology”, Review of Symbolic Logic 12, 1 (2018): 201–208. DOI: http://dx.doi.org/10.1017/S1755020318000412

Drewnowski, J.F., “Personal file from archives of the University of Warsaw”, file number RP 7327, 1921.

Drewnowski, J.F., the manuscript on mereology, 1922 (from the collection of Jacek Drewnowski).

Drewnowski, J.F., “Zarys programu filozoficznego” (Outline of the philosophical program), in S. Majdański and S. Zalewski (eds.), Filozofia I precyzja. Zarys programu filozoficznego i inne pisma (Philosophy and precision. Outline of the philosophical program and other writings), Tow. Nauk. KUL, Lublin, 1996.

Leśniewski, S., “O podstawach matematyki”, Przegląd Filozoficzny XXXII (1930): 77–105. Eng. trans. by D.I. Barnett (referenced): “On the foundations of mathematics”, pages 174–382 in S.J. Surma et al. (eds.), Stanisław Leśniewski, Collected Works, vol. 4, Kluwer, Dordrecht, 1992.

Łyczak, M., and A. Pietruszczak, “On the definability of Leśniewski’s copula ‘is’ in some ontology-like theories”, Bulletin of the Section of Logic 47, 4 (2018): 233–263. DOI: http://dx.doi.org/10.18778/0138-0680.47.4.02

Pietruszczak, A., Metamereologia, Wydawnictwo Naukowe Uniwersytetu Mikołaja Kopernika, Toruń, 2000. Revised and extended Eng. trans.: Metamereology, Nicolaus Copernicus University Scientific Publishing House, Toruń, 2018. DOI: http://dx.doi.org/10.12775/3961-4

Pietruszczak, A., “O teoriach pierwszego rzędu zwiąnych z elementarnym fragmentem ontologii Leśniewskiego” (About first-order theories connected with elementary fragment of Leśniewski’s ontology), pages 127–168 in J. Perzanowski and A. Pietruszczak (eds.), Logika & Filozofia Logiczna, 1996–1998 (Logic & Logical Philosophy, 1996–1998), Wydawnictwo Naukowe Uniwersytetu Mikołaja Kopernika, Toruń, 2000.

Pietruszczak A., Podstawy teorii części, Wydawnictwo UMK, Toruń 2013. Revised and extended Eng. trans.: Foundations of the Theory of Parthood. A Study of Mereology, Springer, 2019 (in press).

Sobociński, B., “Studies in Leśniewski’s mereology”, pages 34–48 in Yearbook for 1954–1955 of the Polish Society of Arts and Sciences Abroad, PhilPapers, London, 1954.

Urbaniak, R., Leśniewski’s Systems of Logic and Foundation of Mathematics, part of the Trends in Logic book series, vol. 37, Springer, Basel, 2014. DOI: http://dx.doi.org/10.1007/978-3-319-00482-2

Varzi, A.C., “On three axiom systems for classical mereology”, Logic and Logical Philosophy 28, 2 (2019): 203–207. DOI: http://dx.doi.org/10.12775/LLP.2018.014

Logic and Logical Philosophy

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Published

2019-09-28

How to Cite

1.
ŚWIĘTORZECKA, Kordula and ŁYCZAK, Marcin. Mereology with Super-Supplementation Axioms. A Reconstruction of the Unpublished Manuscript of Jan F. Drewnowski. Logic and Logical Philosophy. Online. 28 September 2019. Vol. 29, no. 2, pp. 189-211. [Accessed 17 May 2025]. DOI 10.12775/LLP.2019.034.
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