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Logica Universalis

Erschienen in:

06.11.2019

Knowability and Other Onto-theological Paradoxes

verfasst von: Franca D’Agostini

Erschienen in: Logica Universalis | Ausgabe 4/2019

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Abstract

In virtue of Fitch-Church proof, also known as the knowability paradox, we are able to prove that if everything is knowable, then everything is known. I present two ‘onto-theological’ versions of the proof, one concerning collective omniscience and another concerning omnificence. I claim these arguments suggest new ways of exploring the intersection between logical and ontological givens that is a grounding theme of religious thought. What is more, they are good examples of what I call semi-paradoxes: apparently sound arguments whose conclusion is not properly unacceptable, but simply arguable.

Vorheriger Artikel Metalanguage and Revelation: Rethinking Theology’s Language and Relevance

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Hegel [14, pp. 124–128].

Here and hereafter I omit quotation marks, but it is intended that what is true is the proposition ‘p’ and not the fact that p.

As to the proposals to reject the premise, Edgington [8] was the first to suggest relieving verificationism (« anti-realism ») of the commitment to KP. For discussion, and « restrictive »approaches in general, see Kvanvig [16, pp. 56–88].

In fact, one may say there are more than one mistake. Williamson [24, 25] also notes arguable use of modal operator and distribution [25, pp. 270–301]. He accepts \(\lnot \)K(p \(\wedge \lnot \)Kp) as an expression of the « protective belt »that surrounds « cases in which p is true but unknown », so that ignorance is not « luminous »: « [t]hat belt has the peculiarity that one cannot know that one is in it »[25, p. 18].

In this respect, Beall’s ‘changing logic’ strategy is similar to the one adopted by Dummett [7], who notes in intuitionistic logic the classical inference from \(\lnot \)(p \(\wedge \lnot \)Kp) to p \(\rightarrow \) Kp does not hold. In Beall’s account the conclusion (in the version of the FC I have given) is unacceptable: evidently, Beall’s argument stops at 9, so avoiding omniscience.

There might be positive suggestions in this regard. For instance, in the second book of the Metaphysics, Aristotle stresses that it is impossible for one man or woman to capture perfectly complete truths, though our collective knowledge, gathered in form of science, can give us absolute truth. The Hegelian idea of absolute Geist is similar. Note that these intuitions are not so far from the notion of « total science »typical of David Armstrong’s naturalism [1, p. 19].

Guigon [13] discusses this point, but, keeping to the notion of truth-making that I am endorsing here (in Armstrong’s version [1]), and the account of the argument here proposed, that there is a fact CB3 makes sense.

A similar approach for K-arguments (with different aims and conclusions) is provided by Cozzo [6].

Armstrong, D.M.: Sketch for a Systematic Metaphysics. Oxford University Press, Oxford (2010)CrossRef

Beall, J.C.: Fitch’s proof, verificationism and the knower paradox. Aust. J. Philos. 78, 241–247 (2000) CrossRef

Beall, J.C.: Knowability and odd epistemic possibilities. In: Salerno, J. (ed.) New Essays on the Knowability Paradox. Oxford University Press, Oxford (2009)

Bigelow, J.: Omnificence. Analysis 65, 187–96 (2005)CrossRef

Brogaard, B., Salerno J.: Fitch’s paradox of knowability. In: Zalta, E. (ed.) Stanford Encyclopedia. https://plato.stanford.edu/archives/win2013/entries/fitch-paradox/ (2013)

Cozzo, C.: What we can learn from the paradox of knowability. Topoi 13, 71–78 (1996)MathSciNetCrossRef

Dummett, M.: Victor’s error. Analysis 61, 1–2 (2001)MathSciNetCrossRef

Edgington, D.: The paradox of knowability. Mind 94, 557–68 (1985)MathSciNetCrossRef

Edgington, D.: On conditionals. Mind 104, 235–329 (1995)MathSciNetCrossRef

10.

Edgington, D.: Conditionals. In: Goble, L. (ed.) The Blackwell Guide to Philosophical Logic, pp. 385–413. Blackwell, Oxford (2001)

11.

Fitch, F.B.: A logical analysis of some value concepts. J. Symb. Log. 28, 135–42 (1963)MathSciNetCrossRef

12.

Goldstein, L.: ‘This statement is not true’ is not true. Analysis 52, 1–5 (1992)MathSciNetMATH

13.

Guigon, G.: Bringing about and conjunction: a reply to Bigelow on omnificence. Analysis 69, 452–458 (2009)CrossRef

14.

Hegel, G.W.F.: Wissenschaft der Logik (1813), Moldenhauer, E., Michel, K.M. (eds.), Werke, vol. 5. Frankfurt a. M.: Suhrkamp (1986)

15.

Humberstone, I.: The formalities of collective omniscience. Philos. Stud. 48, 401–23 (1985)MathSciNetCrossRef

16.

Kvanvig, J.L.: The Knowability Paradox. Clarendon Press, Oxford (2006)CrossRef

17.

Oppy, G.: Ontological Arguments and Belief in God. Cambridge University Press, New York (1995)

18.

Oppy, G.: Ontological arguments. In: Zalta, E. (ed.) Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/win2016/entries/ontological-arguments/ (2016)

19.

Priest, G.: Doubt Truth to Be a Liar. Oxford University Press, Oxford (2006)MATH

20.

Quine, W.V.O.: The ways of paradox. In: Quine, W.V.O. (ed.) The Ways of Paradox and Other Essays, pp. 1–18. Random House, New York (1962)

21.

Sainsbury, R.M.: Paradoxes, 3rd edn. Cambridge University Press, Cambridge (1987)

22.

Salerno, J.: Knowability Noir: 1945–1963. In: Salerno, J. (ed.) New Essays on the Knowability Paradox. Oxford University Press, Oxford (2009)CrossRef

23.

Tennant, N.: The Taming of the True. Oxford University Press, Oxford (1997)MATH

24.

Williamson, T.: On the paradox of knowability. Mind 96, 256–261 (1987)MathSciNetCrossRef

25.

Williamson, T.: Knowledge and Its Limits. Oxford University Press, Oxford (2000)

Titel: Knowability and Other Onto-theological Paradoxes
verfasst von: Franca D’Agostini
Publikationsdatum: 06.11.2019
Verlag: Springer International Publishing
Erschienen in: Logica Universalis / Ausgabe 4/2019
Print ISSN: 1661-8297
Elektronische ISSN: 1661-8300
DOI: https://doi.org/10.1007/s11787-019-00237-x

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