An Axiomatic Study of God

A Defence of the Rationality of Religion

Paul Weingartner

• Publisher: De Gruyter
• Year: 2021
• ISBN:
  9783110718058
• Edition: 1
• Topic: Philosophie
• Subtopic: Philosophie de la religion

Weingartner shows that an essential part of natural or philosophical theology and even a part of theology can be treated axiomatically. God's essence, omniscience, omnipotence, creating activity, and all-goodness are described by axioms and by theorems proved from them.

1 Existence and General Attributes

1.1 Definition D1 and Axiom A1: God

God is defined as being triune, actual, omniscient, omnipotent, all-good, and as creator. The first attribute, being triune, holds especially for the Christian Religion. It also holds to some extent for Judaism, in the sense that in the Old Testament at least Christ is announced and predicted with his birth, life, suffering, death, and resurrection. According to the New Testament, these announcements and predictions have been fulfilled by the life of Christ.

The subsequent axioms, definitions, and theorems about God, however, can be easily applied to monotheistic religions in general. In that case, one would only have to drop g∈Tr (the attribute of being triune) in D1, A1, and T1 and to drop A2 altogether.

D 1. b = g ↔ (b∈TR ∧ b∈AC ∧ b∈OS ∧ b∈OM ∧ b∈AG ∧ b∈CT)

A 1. (E!b)(b∈TR ∧ b∈AC ∧ b∈OS ∧ b∈OM ∧ b∈AG ∧ b∈CT)

T 1. g∈TR ∧ g∈AC ∧ g∈OS ∧ g∈OM ∧ g∈AG ∧ g∈CT A1, D1

A 2. g∈TR → [(∃a)(a = ft) ∧ (∃a)(a = sn) ∧ (∃a)(a = hs) ∧ (∀a)(a = ft ∨ a = sn ∨ a = hs) ∧ (ft ≠ sn ≠ hs) ∧ ¬(ft ∈ cr) ∧ ¬(sn ∈ cr) ∧ ¬(hs ∈ cr) ∧ (∃R₁R₂)(R₁(ft : sn)∧ R₂(ft, sn : hs)) ∧ (ft∈DPers ∧ sn∈DPers ∧ hs∈DPers) ∧ (Ess(ft) = Ess(sn) = Ess(hs))]

If God is triune then there exist father, son, and holy spirit such that they are not identical and they are not creatures; they stand in two relations to each other: father to son (paternity, R₁) and father and son to holy spirit (procession, R ₂); each of the three is a divine person, and all three agree in their essence.

As has been said in the Introduction 1, 1. above, the universes of discourse of the variables ‘a’ and ‘b’ are allowed to be empty. Therefore, it is necessary to postulate the existence of the three divine persons in the consequent of axiom A2, which leads to theorem T4 with the help of theorem T1. More accurately, since the universe of discourse of the variable ‘a’ is allowed to be empty, the inferential principle (or rule) of Existential Generalisation cannot be generally applied, such that (∃a)(a = ft) does not follow logically from ft = ft, although the latter is of course true. Consequently, theorem T4 is not a logical truth. For the same reason, theorem T2 is not a truth of logic because the universe of discourse for the variable ‘b’ is allowed to be empty (see section 1.11 below).

A 3. (∀a)[a∈DPers → (a∈Ind ∧ ¬(a∈cr) ∧ (∃p)aKp ∧ (∃p)aWp ∧ (∃p)aLp)]

D 2. x∈HPers ↔ (x∈cr ∧ x∈Ind ∧ (∃p)xKp ∧ (∃p)xWp ∧ (∃p)xLp)

g ...God, OM ...omnipotent, OS ...omniscient, AG ...all-good, AC ...actual, CT ...creator, TR ...triune, cr ...created, creature Ind ...individual, DPers ...divine person, HPers ...human person R₁ ...paternity, R₂ ...procession

Ess(ft) ...the essence of God the Father

1.1.1 Justification of D1 and A1

1. We begin with God’s being creator (g∈CT). As has been said in the introduction, we have two sources for our knowledge about God. The first one – accessible to everyone – is the world (the universe) which we (believers) interpret as an effect of an intelligent cause. Therefore, to deny God as a creator would be certainly absurd for those who believe in God at all.¹ For the others, several options can be considered: (a) The world is everlasting. (b) The world is “self-contained” in the sense that it contains its own cause. (c) The world is “self-contained” in the sense that it does not need an initial state as a cause for later states. (d) The world is “self-contained” in the sense that it contains its intelligent observer and cause. The last option (d) can be rigorously refuted.² For the other options, we refer to a detailed discussion³ since this treatment is not a book on the existence of God. God as a creator will be treated in chapter 4 (theorems T121-227).
2. Omniscience: Assume that God is not omniscient. (see A6 below). Then, his knowledge could be greater than man’s knowledge, but not in an essential way. However, the assumption of God as creator already suggests that his knowledge must exceed man’s knowledge in an immense way. This is manifest of man’s present knowledge of the universe with its differentiated and complex structure.⁴ But in addition to the fact that he must know everything about his universe and his creation in general (which might also incorporate entities that do not belong to the universe, like angels), we have to assume that he must know everything about logic and mathematics and everything about himself. This strongly supports that God’s knowledge must essentially exceed man’s knowledge in the sense of being omniscient.⁵ God’s Omniscience will be treated in chapter 2 (theorems 36-80).
3. Omnipotence: Assuming that God is not omnipotent (see A9 below) would either mean that his will is not always fulfilled or that he cannot will or cause things other than those that he in fact wills or causes. That his will is not always fulfilled – though frequently a fact for man’s will – is impossible for God’s will (see however the commentary to A9 below). If he could not have created an alternative world, at least in some sense of “alternative”, we would not speak of omnipotence.⁶ God’s Omnipotence will be treated in ch. 3 (theorems T81-T120).
4. All-good: Assume that God is not all-good (see A21 ch. 5 below). Then, he would either contradict his commands (for example the Ten Commandments) or will something bad, or his will would not be “moved” by his love. The first is impossible since, then, his actions would be inconsistent which is impossible for a perfect being. Concerning the second, it has to be observed that God cannot will something bad unconditionally, although in some cases he wills the absence of some special good in order to achieve another higher good. Concerning the third: Since love is an essential feature of God’s essence as is his will, they are one w.r.t. himself but may differ concerning his relation to creation (cf. 5.5.6). God’s All-goodness will be treated in ch. 5 (theorems T228-T350).
5. Actual: Assume that God is not actual (see A4 below). Then, he would not be pure actuality but also potency (i.e. something possible which is not realized) or he would not be permanently active by knowing, loving, and causing, but sometimes inactive. The first is impossible because there is no unrealized potency of God. From the second, it follows that God is not eternal but in time. Therefore, if God is eternal (see D9 below) and not in time, he must be purely actual. Observe Introduction 3 for all parts 1.-5. derived from A1-T1.

1.2 Axiom A1: Existence of God

Axiom A1 says that there is one God that is triune, actual, omniscient, omnipotent, all-good, and creator. This is the confession of one special type of monotheism: one God, undivided according to its common essence or nature and distinct according to the proper characteristics of the three persons. This type of monotheism fits only the Christian Religion, although there are some small hints at trinity in the Old Testament (Ge 18).

If we drop triune, then axiom A1 is a clear confession of monotheism which holds at least for the three Abrahamic religions: Judaism, Christianity, and Islam.

1.2.1 Biblical...