Argument against nominalism

Last revised: 03/12/25

These are in progress and subject to revision. Feedback welcomed.
The subpoints provide further clarifying thoughts or definitions.

Presupposition of each argument

1. Self-contradictions cannot take place or be true.

2. Potentiality does exist, although I have separate argument for the existence of potentiality linked here.

Against nominalism with regard to immaterial objects

Definition: Concrete nominalism (or spatiotemporal nominalism) is the view that all things that exist or have causal relations are located within spacetime.

1. If nothing exists or can be in causal relations outside of spacetime, then all things that exist or have causal relations must be temporal and consist of matter.

2. Anything this is temporal or consists of matter has potentiality (the capacity to change or be otherwise than what it is).

3. Therefore, if nothing exists or can be in causal relations outside of spacetime, then all things that exist or have causal relations have potentiality. (Definitional Modus Ponens on #1-2)

4. If true, then all things that exist or have causal relations are either ontologically contingent (dependent on external factors or subsists through its parts) or brute.

5. If true, then all things that exist or have causal relations, if ontologically contingent, depend on an infinite regress or chain of prior reasons or causes or, if brute, have no reasons or causes at all for their existence.

6. An infinite regress or chain of reasons or causes doesn't ultimately explain the existence of the infinite regress or chain itself, whether it’s an ontologically necessary existent or modally contingent state of affairs.

   1. I offer an argument against a regression of contingent facts. See step #6, which concludes “Therefore, if we assume a regression of contingent facts can be infinite, then the fact that the plurality of all contingent facts are numerous, which has an explanation, is not explained by any contingent fact.”

7. If true, then there is at least one ontologically necessary existent or modally contingent state of affairs without an explanation for its existence.

8. Therefore, if nothing exists or can be in causal relations outside of spacetime, then there is at least one ontologically necessary existent or modally contingent state of affairs without an explanation for its existence. (Hypothetical Syllogism on #3-7)

9. All ontologically necessary existents and modally contingent states of affairs have an explanation for their existence.

   1. PSR argument for ontologically necessary existents linked here.

   2. PSR argument for modally contingent states of affairs linked here.

   3. The inference is that existents and state of affairs are in principle explainable, whether or not the explanation is currently known. The explanation does not necessarily have to be entailing of the existent or state of affairs.

10. Therefore, some thing (at least one) exists or can be in causal relations outside of spacetime. (Modus Tollens on #8-9)

Against nominalism with regard to universals (in progress)

Definition: Predicate nominalism (or class nominalism) is the view that universals do not exist independently of the language we use. Instead, "red" or "triangular" are just linguistic or conceptual groupings of particular things, without any real shared property.

1. If universals do not exist independently of language, then the meanings of particular things are determined by linguistic or conceptual conventions rather than by real shared properties or by intrinsic features of reality.

   1. For example, trilaterals and triangulars refer to the same object.

2. If true, then the boundaries of events or sequences of events are also established by convention rather than by real shared properties or by intrinsic features of reality.

3. If true, then distinctions between different states of affairs (such as something existing vs. not existing or changing vs. not changing) are linguistic or conceptual conventions.

4. If true, then there is no real fact of the matter about when or why something changes rather than remains the same.

   1. Real refers to existing independently of any created mind.

5. If true, then there is no necessary and sufficient reason why one state of affairs follows another.

6. Therefore, if universals do not exist independently of language, then there is no necessary and sufficient reason why one state of affairs follows another. (Hypothetical Syllogism on #1-5)

7. It must be the case that change occurs due to some reason.

   1. PSR argument for change linked here.

8. Therefore, universals do exist independently of language. (Modus Tollens on #6-7)