This paper tries to unleash the nature of the paradox of nonexistence or non-being or negative singular existentials by using a General Metalogical Theory. In the first section, this paper explains in detail the paradox of negative singular eixistentials and explains how Alexius Meinong and Bertrand Russell respond to this paradox. Russell resolves the paradox using quantification method which Quine extends to formulate a criterion of ontological commitments. In the second section, a General Metalogical Theory is explained, and it is shown that how the developed General Metalogical Theory is useful in unleashing the paradox of nonexistence. The principles of General Metalogical Theory is developed from Quine’s criterion: to be is to be the value of bound variable. In Quine’s criterion, the notion of the bound variable is significant. The General Metalogical Theory in unleashing the nature of the paradox mainly focuses on the question: from where does the binding of the bound variable come? The paper argues that it is not enough to say that the binding of the bound variable comes from the existentially loaded use of the particular quantifier. General Metalogical Theory attempts to show that the binding of the bound variable comes from somewhere else, so that we attach the particular quantifier to the variable and use the particular quantifier in an existentially loaded sense. Explaining the binding nature of the bound variable in the above-mentioned manner will unleash the nature of the paradox.
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This is known as the referential theory of meaning.
Marek, Johann. Fall (2013) Edition. “Alexius Meinong,” The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.) < http://plato.stanford.edu/archives/fall2013/entries/meinong/ > .
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The notion of functionally isomorphic quantifier (FIQ) does not have any application to the issues discussed in this paper. The chief purpose of developing FIQ was to express the ontological disagreements between the metaphysical systems that have apparently similar ontological commitments.
To be is to be the value of bound variable.
First formulation: I cannot admit that there are some things which McX countenances and I do not, for in admitting that there are such things I should be contradicting my own rejection of them.
Second formulation: So long as I adhere to my ontology, as opposed to McX’s, I cannot allow my bound variables to refer to entities which belong to McX’s ontology and not to mine. See for details: Quine, W. V. (1948). “On What There Is,” p.35.
According to David Lewis’ Modal Realism, there are spatiotemporally isolated possible worlds which exist concretely. All actual and possible entities exist within a world. Lewis, David. 1986. On the Plurality of Worlds. Oxford: Blackwell.
According to Quine’s naturalism or Quinean ontology, our ontology is provided by our best scientific theories.
One could expand the notion of robust sense of reality by enumerating different assumptions associated with this notion: that the entity should be concrete, should be spatiotemporally located, etc.
Lewis, D. (1986). On the plurality of worlds. Blackwell.
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Thomas, J. (2018). Developing metalogic to formalize ontological disputes of the systems in metaphysics by introducing the notion of functionally isomorphic quantifiers. Logica Universalis, 12(3–4), 461–492.
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Thomas, J. Unleashing the Nature of the Paradox of Nonexistence. J. Indian Counc. Philos. Res. 39, 263–278 (2022). https://doi.org/10.1007/s40961-023-00289-x