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Developing Metalogic to Formalize Ontological Disputes of the Systems in Metaphysics by Introducing the Notion of Functionally Isomorphic Quantifiers

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Abstract

A general meta-logical theory is developed by considering ontological disputes in the systems of metaphysics. The usefulness of this general meta-logical theory is demonstrated by considering the case of the ontological dispute between the metaphysical systems of Lewis’ Modal Realism and Terence Parsons’ Meinongianism. Using Quine’s criterion of ontological commitments and his views on ontological disagreement, three principles of metalogic is formulated. Based on the three principles of metalogic, the notions of independent variable and dependent variable are introduced. Then, the ontological dispute between Lewis’ Modal Realism and Terence Parsons’ Meinongianism are restated in the light of the principles of metalogic. After the restatement, Independent variable and dependent variables are fixed in both Lewis’ Modal Realism and Terence Parsons’ Meinongianism to resolve the dispute. Subsequently, a new variety of quantifiers are introduced which is known as functionally isomorphic quantifiers to provide a formal representation of the resolution of the dispute. The specific functionally isomorphic quantifier which is developed in this work is known as st-quantifier. It is indicated that how st-quantifier which is one of the functionally isomorphic quantifiers can function like existential quantifier. It is also shown that there is some kind of inconsistency which is unavoidable in stating the ontological disagreement and therefore, paraconsistent logic is a requirement in stating the ontological disputes.

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Acknowledgements

I am very grateful to Prof. Prajit K. Basu (Department of Philosophy, University of Hyderabad) for supervising the entire research. I thank Don Wallace F. Dcruz (University of Hyderabad) for the valuable comments and suggestions. I also thank Shinod N K (IIT Delhi), R Venkata Raghavan (Chinmaya University) and Sreejith K K (BITS Goa) for the valuable suggestions and very pleasant discussions. I thank Martin Vacek (Slovak Academy of Sciences, Slovakia) for the suggestions and comments. I thank Prof. Mihir K. Chakraborty (Jadavpur University) and Prof. Raja Natarajan (TIFR, Mumbai) for the suggestions and comments during UNILOG’18. I thank Prof. Michele Friend (George Washington University) and Prof. Graham Priest (City University of New York) for the suggestions and discussions during UNILOG’18.

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  1. International Institute of Information Technology, Hyderabad, India

    Jolly Thomas

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  1. Jolly Thomas
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Correspondence to Jolly Thomas.

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This paper was the recipient of the 1st Bimal Krishna Matilal Logic Prize (India) and was presented at the Universal Logic contest at UNILOG’2018 in Vichy, France. For details, see http://www.uni-log.org/logic-prize-world.

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Thomas, J. Developing Metalogic to Formalize Ontological Disputes of the Systems in Metaphysics by Introducing the Notion of Functionally Isomorphic Quantifiers. Log. Univers. 12, 461–492 (2018). https://doi.org/10.1007/s11787-018-0213-8

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  • DOI: https://doi.org/10.1007/s11787-018-0213-8

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