Abstract
The third alternative to universals discussed in this work is theological nominalism. This form of nominalism postulates concepts in the mind of God to replace universals. There are many advantages of this position over regular concept nominalism. Nevertheless, it is argued here that the conception seems unfeasible if one supposes divine simplicity. It is also affected by a problem of regress specific to this form of nominalism. The chapter finally considers if Platonic universals are incompatible with divine aseity. They are not.
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Notes
- 1.
In recent years, all the traditional forms of argumentation for the existence of God have been explored, as well as the problem of evil and the ‘hiddenness of God’. A form of argument that I find especially convincing depends on modal and causal principles. ♠x = df [◊∃y (y = x) ∧ ◊¬∃y (y = x)], i. e., [♠x] is an abbreviation of “x is contingent”. The denial of [♠x] is —strictly— [□∀y (y ≠ x) ∨ □∃y (y = x)], that is, it is either impossible or necessary. Since it does not make any sense to say of something (that has to be in the range of quantification) that is impossible, [¬♠x] will be taken as [□∃y (y = x)], abbreviated [♣x]. ‘x causes y’ will be abbreviated as [x ⇒ y]. ‘|’ designates the mereological connective ‘is disjoint from’. For simplicity, it will be assumed that quantifiers have states of affairs as their range.
-
1.
∃x(♠x ∧ (x = c))
-
2.
∀x ∃ y( ♠ x → ((y| x) ∧ (y ⇒ x))
This principle (2) has been called sometimes as the ‘principle of sufficient reason’. By universal instantiation of (2) and modus ponens with (1), it follows:
-
3.
∃y((y|c) ∧ (y ⇒ c))
-
4.
∀x((x ⇒ c) → ♠ x) ∨ ∃ x((x ⇒ c) ∧ ♣ x))
This statement (4) is simply an instance of the principle of the excluded middle. But:
-
5.
¬ ∀ x((x ⇒ c) → ♠ x)
From (5) and (4), it follows, by modus tollendo ponens:
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6.
∃x((x ⇒ c) ∧ ♣ x))
And, then, by simplification of (6):
-
7.
∃x ♣ x
Why would the premise (5) be accepted? One reason is that [c = (xι) ∀y ((y ◯ x) ↔ ∃z (♠z ∧ (y ◯ z)))], i. e., c is the mereological fusion of all contingent states of affairs. Any disjoint cause of c must be necessary, by definition. Probably the most discussed premise in this argument is (2). For a detailed discussion of the principle of sufficient reason, see Pruss 2006. Note also that what is concluded in (7) is that there is a necessary state of affairs. A necessary state of affairs must have as a component a necessary object if this state of affairs is a causal relatum, so it follows that there is at least one necessary concrete object.
-
1.
- 2.
‘Eternity’ is the absence of temporal distension. As indicated above, some have questioned the coherence of the idea of ‘eternity’ and, therefore, prefer to speak of “omni-temporality” (see Swinburne 1993, 223–229). For what matters here, it is sufficient with the supposition that God exists at all times, which is consistent both with his eternity and with his omni-temporality.
- 3.
More precisely: [□(∃x (God = x) → □(∃x (God = x)))].
- 4.
Several issues arise concerning this response to the problem. For Immutability to work in the mental states of God, it is required that all moments of time —past, present, or future— are equally available to his knowledge. But this does not seem reasonable if there are no future times. Nor does it seem reasonable if the character by which some time is present is perpetually changing. There could not be a ‘static’ knowledge of the entire time series since the entire series would always be in change. These questions cannot be discussed here with all the detail that it would require. It seems that the principles of Immutability and Omniscience work with a tetra-dimensional or eternalist ontology of time in which all times have the same ontological status. We also have to take care of the coherence of Omniscience and the freedom of the will of created persons, if this freedom is incompatible with determinism.
- 5.
Also, it should be noted that there is an entire Augustinian epistemological tradition that understands knowledge as divine illumination. In this tradition, we can develop our superior cognitive abilities precisely because we can assimilate the concepts in the mind of God and interpret perceptual information from the ‘point of view of God’. Again, this may seem epistemologically extravagant, but I do not see that it is more extravagant than knowing infinite merely possible objects or tropes that make up a class of similarity. Certainly, it is no more extravagant than the traditional forms of nominalism, if one admits at the outset that God exists. Illuminating the mind of a finite rational thinker is within his causal powers.
- 6.
It is a conception already defended by the Neo-Platonists. Plato (1982) had maintained in the Timaeus that the demiurge eternally contemplates forms (see Timaeus, 28a-29b). In Middle Platonism ideas are located in the divine mind (see Philo, About the creation of the world according to Moses, 4; Alcinous (1993), Handbook of Platonism IX, 1). Plotinus interprets the Timaeus holding that the act of contemplation and the contemplated form are identified (see Enneads, V, 5). An important background of this thesis is Aristotle (1998) Λ 7, 1072b 19–23 and Aristotle (2010) III 4, 430a 3–6 of Aristotle. Plotinus differentiates between the One and the Intellect-Intelligible. If one were to identify God with the One, it happens, then, that the forms are not identified with concepts of the first hypostasis, but with concepts of the second hypostasis. St. Augustine, on the other hand, identifies the forms with concepts in the mind of God, in such a way that our cognition of forms is produced by divine illumination (see Octoginta trium quaestionum, Q. 46, ML 40, 30). St. Thomas Aquinas later rejects divine enlightenment as a cognitive mechanism but argues that there are ideas that are divine forms in whose likeness the world has been made (see Summa Theologiae, I-II, q. 15). I thank Marcelo Boeri and José Antonio Giménez for illustrating me about this historical background.
- 7.
It has been designated as “narrow content” the type of content of mental states that a rational thinker can possess regardless of whether there is something ‘external’ to the mind that constitutes what that content refers to or on what such content depends. Narrow content corresponds to how mental states have been conceived in the Cartesian tradition. One might think that there are elephants without there being elephants, nor an independent property of being an elephant, nor a chain of causal connections and/or chain of communicative transmission that ultimately is linked with elephants or with the property of being an elephant. For those who propose, instead, “broad content”, nobody could think that there are elephants without elephants or without the property of being an elephant. The content of this concept involves the environment in which that thinker is since it consists of the natural kind of elephants or the property of being an elephant. Without elephants or without the property of being an elephant, there simply would not be such content (see Kim 2006, 254–272).
- 8.
More precisely, keeping the same variables:
□∀S □∀m □∀C1 □∀C2 □((C1 = C2) ↔ ((S believes that [… C1 …] in m) ↔ (S believes that [… C2 …] in m)))
- 9.
In some theories, the identity of a concept is determined by the inferential connections of that concept with others. No concept can here, therefore, exist in isolation without the ‘cluster’ of which it is a part. Similar situations have been adduced to reject the adequacy of other identity conditions. These questions are not going to be discussed here. The identity of concepts must be seen here as fixed in a block for all the concepts that are connected inferentially. In other theories, however, there are ‘atomic’ concepts whose identity is independent of the others. One can then postulate complex concepts constituted from these simple concepts and dependent on them. In any of these cases, the conditions of the identity of a concept can be characterized by a principle like Concepts.
- 10.
God has to be an abstract entity if the only way a property could exist is as a universal. If one admits tropes, however, the problem does not arise. The thesis of divine simplicity must be seen as the thesis that God is a unique trope and that the expressions “the omnipotence of God”, “the wisdom of God” or “the goodness of God” are all designations of it. Olof Page has also pointed out to me that it is difficult for a nominalist of concepts to adduce this argument against divine simplicity since from the perspective of a nominalist there are no abstract properties of any kind.
- 11.
A scenario of God without God understanding the nature of God may seem very strange given our traditional way of understanding him, but we must think of a scenario in which we have a non-personal concept of God or a ‘processual’ conception of God in which God ‘falls in time’ and does, for example, abandon its attributes. Something of this style is what has been defended by the ‘kenotic’ theories of the Incarnation.
- 12.
But it is not the only possible way in which this adjustment could be made. In abstract, it would not be incompatible with divine aseity to postulate tropes and classes of tropes that fulfill the functions of universals. Nor would it be incompatible with divine aseity to postulate immanent universals. God would create these universals by creating their instantiations. Nor would it be incompatible with other forms of nominalism. What has happened, however, since Antiquity, is that these philosophical positions have been considered—correctly—far inferior to the postulation of Platonic universals. A form of nominalism of divine concepts has seemed the most reasonable way to accommodate the advantages of Platonic universals without affecting divine aseity.
- 13.
The thesis (i) of Aseity, that is, that God does not depend on anything, is analysed as: [∀x ((x ≠ God) → ¬□((God exists) → (x exists)))]. From this thesis it follows that [∀x ((x ≠ God) → ◊((God exists) ∧ ¬(x exists)))] The thesis (ii) of Aseity, that is, that everything different from God depends on God, is analysed as: [∀x ((x ≠ God) → □((x exists) → (God exists)))], which is equivalent to [∀x ((x ≠ God) → ¬◊((x exists) ∧ ¬(God exists)))].
- 14.
At least, this has been the supposition made by the Judeo-Christian tradition in which the creation is a contingent and free action of the Will of God. In other traditions, the ‘emanation’ of the creatures from God is a necessary process. Others, additionally, have argued that it is necessary that God creates the best of all possible universes. What is argued here about the Aseity of God applies in any of these conceptions about God and its creatures.
- 15.
A structuralist point of view in the philosophy of mathematics according to which what mathematics deals with are ‘abstract structures’ that can have multiple instantiations has gained a lot of acceptance. These ‘structures’ are transcendent universals (see Shapiro 1997, 84–106).
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Alvarado, J.T. (2020). The Superiority of Universals over Theological Nominalism. In: A Metaphysics of Platonic Universals and their Instantiations. Synthese Library, vol 428. Springer, Cham. https://doi.org/10.1007/978-3-030-53393-9_5
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