Abstract
The purpose of the paper is to show that axiomatic thinking can also be applied to religion provided a part of the language used in religion (here called: Religious Discourse) consists of propositions or norms. Although David Hilbert was not concerned with religion when he gave his famous talk “Axiomatisches Denken” in 1917, his published essay (in 1918) treats this topic in such a broad sense that such an application seems appropriate.
This application is done in the following way: The first part discusses the possibility of applying axiomatic thinking to religion by considering the necessary preconditions to be satisfied for a successful application. The second part discusses the specific logical language that will be used in the application. The third part offers two concrete examples of such an application: a short and preliminary axiomatic theory of omniscience and omnipotence.
This paper has been given in Lisbon in 2017; meanwhile the author has written an extensive study (going beyond the third part of this essay). It is published by De Gruyter with the title “An axiomatic study of God. A defence of the rationality of religion” (2021). The author is indebted to the members of the 2018 Bergseminar for valuable suggestions.
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Notes
- 1.
Bochenski stresses only the Creed (Bochenski [4], p. 10). However, in a private conversation with him, where I told him that one has to add the specific Commands as the second important component for demarcating the religious discourse and a religious believer, he agreed.
- 2.
Thomas Aquinas (CGJn) 1285 [1].
- 3.
See Weingartner [15], ch. 9, pp.183–202.
- 4.
If the logically valid principles are not restricted for applying the operator O, this leads to the well-known paradoxes of Deontic Logic. Possible restrictions are by incorporation of action-operators (see Vanderveken [13]) or by restricting the logically valid principles to logically valid and relevant principles (see Weingartner [19]).
- 5.
Gödel [7].
- 6.
v. Neumann [12] in: Bulloff, J.J./Holyoke, Th.C./Hahn, S.W. (1969).
The “Tribute to Dr. Gödel” from which the passage is cited was given by v. Neumann in March 1951 on the occasion of the presentation of the Albert Einstein Award to Gödel. It appeared in print in the volume Foundations of Mathematics (ed. Bulloff et al.), a collection of papers given at a symposium commemorating the sixtieth birthday of Kurt Gödel.
- 7.
- 8.
Some examples are discussed in ch. 10 of Weingartner [20].
- 9.
For proofs see Kreisel/Krivine [10].
- 10.
- 11.
Weingartner [17].
- 12.
G: “One could establish an exact postulate-system with concepts that are usually called metaphysical: “God”, “Soul”, “Ideas”. If this is done in an exact way nothing could be said against it.” Ich: “Certainly not, as a calculus. Or do you mean with interpretation?” G: Not mere calculus, but theory. From it something follows about observations: but this does not exhaust the theory.” (My translation)—This is the first part of the discussion which is recorded in: Köhler et al. (eds.) [9]. Kurt Gödel. Wahrheit und Beweisbarkeit, p.127.
- 13.
“die prinzipielle Forderung der Axiomenlehre muß vielmehr weitergehen, nämlich dahin, zu erkennen, daß jedesmal innerhalb eines Wissensgebietes auf Grund des aufgestellten Axiomensy-stems Widersprüche überhaupt unmöglich sind”. Hilbert [8], p. 411.
- 14.
To this point cf. Weingartner [16] ch. 3 (Whether God knows something at some time).
- 15.
- 16.
- 17.
MPL 40, 276.
- 18.
(STh) I, 25, 5 and ad 1 [2].
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Weingartner, P. (2022). Axiomatic Thinking—Applied to Religion. In: Ferreira, F., Kahle, R., Sommaruga, G. (eds) Axiomatic Thinking II. Springer, Cham. https://doi.org/10.1007/978-3-030-77799-9_11
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