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Quantifiers and Conceptual Existence

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Mario Bunge: A Centenary Festschrift

Abstract

This chapter examines Bunge’s distinction between the logical concept of existence and the ontological one. We introduce a new conceptual existence predicate in an intensional environment that depends on the evaluation world. So that we can investigate restricted areas (worlds) where the different kinds of concepts might exist. We hope this new predicate would encompass Bunge’s philosophical position which he designates as conceptualist and fictional materialism. The basic hybridization (adding nominals and @ operators) acts as a bridge between intensions and extensions because @ works as a useful rigidifier. In hybrid logic, the accessibility relation and many properties this relation might have can be easily expressed in the formal language. The initial hypothesis is that hybridization and intensionality can serve as unifying tools in the areas involved in this research; namely, Logic, Philosophy of Science and Linguistics.

This research has been possible thanks to the research projects sustained by Ministerio de Economía y Competitividad of Spain with reference FFI2013-47126-P and FFI2017-82554-P.

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Notes

  1. 1.

    Nowadays, to discriminate object language from metalanguage we make a distinction between predicates (of the object language) and properties of the metalanguage.

  2. 2.

    In spite of this conclusion, Kant allows existence to be a logical predicate for “anything we please can be made to serve as a logical predicate”(Kant 1787/1929, B626).

  3. 3.

    In the standard hierarchy, each \(\mathcal {D}_{\left \langle a,b\right \rangle } \) contains the whole \(\mathcal {D}_{a}^{\mathcal {D}_{b}}\) while in the general models, \(\mathcal {D}_{\left \langle a,b\right \rangle }\) is a subset of \(\mathcal {D}_{a}^{\mathcal {D}_{b}}\) closed under definability. General models were first introduced by Henkin (1950) to prove the completeness of type theory.

  4. 4.

    For a longer explanation, see section 1.2: “Paradoxes and their solution in4 type theory” in Manzano (1996, pp. 182–186).

  5. 5.

    The definition was first done by Henkin (1963) and improved by Andrews (1963).

  6. 6.

    This is our translation of the Spanish original: “Si x es un objeto, entonces:

    1. a]

      xexiste conceptualmente = df Algún conjunto no vac ío C de constructos es tal que EC(x);

    2. b]

      xexiste físicamente = df Algún conjunto no vac ío F de entes físicos es tal que EF(x).” (Bunge 1980, p. 62).

  7. 7.

    By a “rigid interpretation” we understand one that does not change from world to world.

  8. 8.

    “Tanto en ciencias formales como en ciencias fácticas las afirmaciones de existencia son responsables: se tiene algún motivo razonable y no se pierde el tiempo inventando postulados o conjeturas de existencia de objetos ociosos que no desempeñan función alguna tales como mundos posibles.” (Bunge 1980, p. 64).

  9. 9.

    “En este trabajo exploraremos una alternativa, que llamaremos materialismo conceptualista y ficcionista” (Bunge 1980, p. 54).

  10. 10.

    The example is based on Tichy (1979).

  11. 11.

    “In order to describe what the members of each type are to be, it will be convenient to introduce the term concept in a sense which is entirely different from that of Frege’s Begriff, but which corresponds approximately to the use of the word by Russell and others in the phrase ‘class concept’ and rather closely to the recent use of the word by Carnap, in Meaning and Necessity. Namely anything which is capable of being the sense of a name of x is called a concept of x.” (Church 1951, p. 11).

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Acknowledgements

To Mario Bunge, with gratitude.

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Correspondence to María Manzano .

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Manzano, M., Moreno, M.C. (2019). Quantifiers and Conceptual Existence. In: Matthews, M.R. (eds) Mario Bunge: A Centenary Festschrift. Springer, Cham. https://doi.org/10.1007/978-3-030-16673-1_7

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