Abstract
Ontological arguments for the existence of God highlight classical logic’s problematic treatment of the existential entailments of true propositions. Is existence implicitly assumed to hold of the logical subject (i.e., argument) of a true proposition? Or must existence be explicitly predicated? To allow for assertions about non-existent objects, modern non-classical approaches from Meinong to Berto, reject the classical approach traceable to Kant and Frege that associates existence with the logical subjects of true propositions. Yet, in overcoming the acknowledged problems with logical subject-based existential entailment (as exemplified by the existential quantifier) these newer predicate-based approaches have only re-opened the door to the problems created by the ontological argument (e.g., from Anselm, Descartes, Leibniz) which were what originally had motivated Kant to delegitimize existential predicates in the first place. Classical logic’s approach to the ontological argument appears to be running in circles.
In this paper, I attempt to simultaneously resolve the problems in both the predicate-based and logical subject-based approaches to the ontological argument (and to the characterization principle-based approaches which are closely related to predicate-based ones) by replacing the notion of existential entailment with the notion of ‘sequenced evaluation’ as the fundamental entailment that applies to both the logical subject and predicate of a proposition. Towards that end, I use a logic consistent with the principles laid out in Wittgenstein’s Tractatus. The recasting of ontological arguments in Tractarian terms appears to show a foundational mistake made by all approaches and how it can be resolved.
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Notes
- 1.
“And certainly that greater than which cannot be understood cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater”. From Chapter 2 ‘That God really exists’ in Anslem https://sourcebooks.fordham.edu/source/anselm.asp.
- 2.
Leibniz’s shoring up of Anselm’s argument by more precisely justifying the ability to conceive of a perfect being is interesting but outside the scope of this paper which focuses on those aspects of the Ontological argument directly impacted by logic’s approach to existence.
- 3.
Descartes also thought that whatever could be clearly and distinctly perceived to be contained in the idea of something was true of that thing.
- 4.
In On Denoting (Russell 1905) p. 491, Russell also criticized Descartes’s argument. But his criticism stating that Descartes’s ontological argument fails for “want of a proof of the premise” was unfair because Descartes treated God’s perfection as analytic (coming from ‘the storehouse of my mind’).
- 5.
Though not an ontological argument in the sense of an argument widely discussed in the literature, the EG argument is a way of exemplifying the problems that arise from associating the quantification of a variable with any kind of existential entailment which is a significant problem as described elsewhere in this essay.
- 6.
Some authors who follow in the wake of Meinong (e.g., Routley (1980), Paoletti (2013), Priest (2016), and Bacigalupo (2017)) debate the issue of existential entailments using the term characterization instead of ‘predications assumed to be true of, or that are part of the identity of, an object’. Priest (2016), for example, asserts on p xviii (and then in chapter 4 beginning p. 83 under the heading ‘characterization principle’ or CP) that “an object has those properties that it is characterized as having”. On closer examination, however, this characterization principle reduces to the circular and trivial assertion that an object for which certain predicates are assumed true (i.e., the properties the object is characterized as having) may be assumed to be truthfully predicated with those predicates (i.e., the object has those properties it is characterized as having).
Priest himself criticizes CP as being too general, but when it comes to discussing non-existent objects, for example on page 13, he uses the more traditional language of predicates and refers to existence as a special predicate. Regardless whether he eventually recasts the notion of predicatable existence in suitably restricted CP terms, it is clear that he treats existence as something that may or may not be predicated of an object. (E.g., Sherlock Holmes is characterized as a detective which is to say that it is assumed that the predicate ‘is a detective’ is true of the object Sherlock Holmes. But this characterization is independent of whether Sherlock Holmes exists). So, although Priest and others use, at times, different terminology, they adhere to the notion that existence is not entailed by the logical subject of a true proposition but rather that existence is associated with an object through predication. Their arguments thus fit into the existence-as-predicate group described in this paper and so are a part of the train of logical approaches to existence that have come full circle.
- 7.
Independent of the metaphysical status one may wish to ascribe to Descartes’s postulation of a supreme being having all perfections e.g., whether one wishes to treat it as a clear and distinct idea—namely the idea of a supreme being having all perfections or as simply a definition of same, Descartes needs to link these premises that are not empirical (regardless whether ideas or a priori or analytic definitions) with something that one might call real or ‘in the world’ or ‘empirical’ or ‘synthetic a posteriori’. His method of linking was his second premise that existence (in the world) is a perfection. Since there are no epistemically neutral terms that can be used to describe definitions/ideas or empirical/synthetic statements, the author made every attempt to use extent terms in non-controversial ways so as to support the major thesis in the paper on the value of a Tractarian style logic to resolving ontological arguments without entering into epistemic debates that are beyond the scope of this paper.
- 8.
Whether in conjunction with an existential quantifier (e.g., “There exists an X such that f(x)”), or a universal quantifier, (e.g., “For all ‘x’ f(x)”), Hilbert, Peano, Russell, Carnap, Quine and Putnam to name but a few, all used a symbolism based on the notion of a predicate ‘f’ and N-adic logical subject ‘(a)’ to formally denote and reason about propositions.
- 9.
The complexity of the fact, what Wittgenstein calls “logical multiplicity” (4.04) governs the number of distinct propositions that can be generated for a single fact/complex.
- 10.
Wittgenstein’s views on the multiplicity of propositions that can be generated from a single complex fact can be traced back to Aristotle’s (n.d-a, n.d-b) original dialectic (De Interp. (20b 22–31), Categoriae, 2a 4–10, 13b 10–12) which begins by looking at an assertion as the answer to a question; not simply as a declarative statement. Aristotle situated logic within the context of an affirming/denying game (the “dialectic”, in its original sense), and defined assertions (i.e., propositions) as the primitive units of this game. He further diagnosed a certain compositeness of type as their defining character, distinguishing that which an assertion was asserting from that of which the assertion was being made.
- 11.
The presence of a name (“Sheep”) where a predicate generally occurs, and the presence of a predicate (“white”) where a name generally occurs in “Sheep(white)” will be dealt with soon.
- 12.
See sections 3.314–3.317: “And the only thing essential to the stipulation is that it is merely a description of symbols and states nothing about what is signified” (3.317).
- 13.
There are numerous ways one could modify Descartes’s argument to highlight an empirical interpretation for premise #2. The specific way is not important to the argument.
References
Anselm, St. 1965. In Proslogion, in St. Anselm’s Proslogion, ed. M. Charlesworth. Oxford: OUP. [Available online, in the Internet medieval sourcebook, ed. Paul Halsall. Fordham University Center for Medieval Studies. Trans. David Burr].
Aristotle. n.d-a. Categories, 350 BCE. Translated by E. M. Edgehill at http://classics.mit.edu/Aristotle/categories.1.1.html.
Aristotle. n.d-b. On interpretation, 350 BCE. Translated by E. M. Edgehill at http://classics.mit.edu/Aristotle/interpretation.html.
Aristotle. On Interpretation, 350 BCE. Translated by E. M. Edgehill at http://classics.mit.edu/Aristotle/interpretation.html.
Bacigalupo, G. 2017. A study on existence. Newcastle upon Tyne: Cambridge Scholars Publishing.
Bacigalupo, G. 2017. A study on existence. Newcastle upon Tyne: Cambridge Scholars Publishing.
Berto, F. 2013. Existence as a real property: The ontology of meingongianism. Vol. 356. Dordrecht: Springer.
Boole. 1854. An investigation of the laws of thought: On which are founded the mathematical theories of logic and probabilities. Mineola, NY: Dover Publications.
Descartes, R. 1968. Discourse on method and the meditations, translated with an introduction by F Sutcliffe. Harmondsworth: Penguin. [Translation of The Meditations by John Veitch, LL.D. available online].
Frege, G. 1980. The foundations of arithmetic. Trans. J. L. Austin; 2nd ed. Evanston, IL: Northwestern University Press.
Kant, I. 1933. Critique of pure reason, 1787, 2nd ed. Trans. N. Kemp-Smith, London: Macmillan.
Kleene, S.C. 1952. Two papers on the predicate calculus. Providence: American Mathematical Society.
Lambert, K. 2003. Free logic: Selected essays. Cambridge: The Press Syndicate of the University of Cambridge. Copyright Karel lambert.
Leibniz, G. 1896. New essay concerning human understanding, 1709, Trans. A. Langley, New York: Macmillan.
Lewis, D. 1970. Anselm and actuality. Noûs 4: 175–188.
Lukasiewicz, J. 1970. Selected works. Studies in logic and the foundations of mathmatics. Amsterdam: North–Holland Publishing Company. Translated by O. Wojtasiewicz.
Mion, G. 2018. On Kant’s ambivalence toward existence in his critique of the ontological argument. Journal of Applied Logic 5: 7.
Modenato, F. 1995. Meinong’s theory of objects. In Grazer Philosophische Studien, vol. 50. Amsterdam: Rodopi.
Nagasawa, Y. 2011. The existence of god. Oxford: Routledge.
Oppenheimer, P., and E. Zalta. 1991. On the logic of the ontological argument. In Philosophical perspectives 5: The philosophy of religion, ed. J. Tomberlin, 509–529. Ridgeview: Atascadero.
Oppy, G. 1995. Ontological arguments and belief in god. New York: Cambridge University Press.
Paoletti, M. 2013. Meinong strikes again, Humana. Mente Journal of Philosophical Studies 25: I–XIV.
Plantinga, A. 1974. The nature of necessity. Oxford: Oxford University Press.
Priest, G. 2008. The closing of the mind: How the particular quantifier became existentially loaded behind our backs. The Review of Symbolic Logic 1(1): 42–55.
———. 2016. Towards non-being. 2nd ed. Oxford: Oxford University Press.
———. 2017. Logic: A very short introduction. 2nd ed. Oxford: Oxford University Press.
Routley, R. 1980. Exploring Meinong’s jungle and beyond. An investigation of noneism and the theory of items. Canberra: Research School of Social Sciences, Australian National University.
Russell, B. 1905. On denoting mind. Vol. 14, 479–493. Oxford: Oxford University Press.
———. 1946. History of western philosophy. New York: Routledge.
Sobel, J. 2004. Logic and theism. New York: Cambridge University Press.
Spinoza, B. 1955. The ethics, 1677, translation of 1883 by R. Elwes. New York: Dover. [Available online, prepared by R. Bombardi, for the Philosophy Web Works project, Middle Tennessee State University].
Thomsen, E. 1990. A tractarian approach to information modeling. In Wittgenstein-towards a re-evaluation. Wien: Verlag Holder-Pichler-Tempsky.
Thomsen, E. 2002. OLAP solutions: building multidimensional information systems, 2nd ed. New York: Wiley.
Wittgenstein, L. 1977. Tractatus Logico-Philosophicus. Trans. D. F. Pears and McGuinness. London: Routledge & Kegan Paul.
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Thomsen, E. (2020). A Tractarian Resolution to the Ontological Argument. In: Silvestre, R.S., Göcke, B.P., Béziau, JY., Bilimoria, P. (eds) Beyond Faith and Rationality. Sophia Studies in Cross-cultural Philosophy of Traditions and Cultures, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-43535-6_7
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