Argument against infinite causal regress

Last revised: 05/11/25

These are in progress and subject to revision. Feedback welcomed.
The subpoints provide further clarifying thoughts or definitions.
I offer an argument against a regression of contingent facts and an argument against an infinite hierarchical regression of contingent conjunctive causes.

Argument against a regression of contingent facts

Presuppositions

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

2. The argument adopts the principle that all contingent states of affair have an explanation in principle or a sufficient reason for existence, although I have posted arguments in favor of the PSR.

3. The argument uses the S5 axiom of modal logic. In S5, all possible worlds are accessible from each other. If something is possible, then it is possible in all possible worlds. If something is necessary, then it is necessary in all possible worlds.

   S5 also includes the principle that if something is possibly necessary, then it is necessary. This follows from the idea that possibility and necessity apply across all possible worlds without restriction.

   The modality used is metaphysical possibility. A proposition is metaphysically possible if it is not logically contradictory and follows from necessary truths and nature of things. For example, “a triangle has three sides” is necessarily true in all possible worlds, while “a triangle has four sides” is not possible in any.

Premises

1. Either a regression of only grounded contingent facts can be infinite or not.

   1. “Contingent” refers to a thing’s mode of existence to exists in some possible worlds but not in all. It means the thing does not have to exist and could have failed to exist.

2. Assume for reductio that a regression of only grounded contingent facts can be infinite.

3. If true, then the fact that the plurality of all contingent facts are numerous is not explained by any contingent fact (including the contingent fact that the plurality of all contingent facts are numerous).

   1. The idea that there are tons of contingent facts (like “It’s raining” or “I ate pizza”) can’t be explained by just looking at those facts themselves. Imagine a giant playlist of all these facts, labeled the plurality, and the “numerosity” is the fact that this playlist has a ton of songs. You can’t explain why there are so many songs by pointing to each song individually, because no single song is a plurality on its own (since it’s just one song). This doesn’t work with a rule like G-HEP, which says each part needs to share the property you’re explaining, like numerosity. Also, saying all the songs together explain why the playlist is huge is circular is like saying, “The playlist is big because it has all these songs.” That breaks a rule called the irreflexivity of ground, which says something can’t explain itself. So, to explain why there are so many contingent facts, you need a reason outside the playlist, not just the songs in it.

      1. The Hume-Edwards Principle (HEP) is a philosophical principle that states since each fact in the infinite series is explained by its antecedents, they are all thereby explained. The ground theoretic version of the Hume-Edwards Principle (G-HEP) states that if each member of a plurality has a ground, then the plurality has a ground as well. Even if the G-HEP is true, the fact that the plurality of contingent facts is numerous cannot be explained distributively by its individual members, as required by a principle like G-HEP, because no single contingent fact possesses the property of numerosity. Because no single contingent fact can explain why the plurality of all contingent facts is numerous, this numerosity fact itself is a contingent fact within the plurality that requires an explanation.

      2. Saying each contingent fact “contributes” to numerosity because it’s one of many is misleading: each member is merely being a member, not explaining why there are many members. Since no individual fact has numerosity or a property that explains why the plurality has many members, the explanation cannot be built up from the members individually.

         It’s like trying to explain why a playlist has so many songs by saying each song contributes to the series. A single song isn’t “series-ness” in any meaningful way. Listing each song just describes the contents but not explain why the playlist has many songs.

      3. “Grounding” refers to what makes something true or real. For example, the fact that the ground is wet might be grounded in the fact that it’s raining.

      4. “Irreflexivity” means that something can’t ground (or explain) itself. The explanations has to come from something more basic or outside the thing being explained.

   2. The “numerosity” is the idea that there are lots of these facts under consideration. The question is: Why are there so many contingent facts in the first place? That’s what needs explaining.

      1. For example, you can’t explain why a backpack is full of lots of books (numerosity) by just pointing to the facts inside the backpack (the members of the plurality). Why not? Because that would be circular, like saying, “The reason I have a lot of books is because I have a lot of books.” It doesn’t actually explain anything, and it just repeats the problem.

4. The fact that contingent facts are numerous is not a necessary fact.

   1. The numerosity fact is not a necessary fact because its truth depends on the existence of the plurality, which is itself contingent. It is possible for there to be a world with just one or no contingent facts at all. For instance, consider a "minimal" possible world containing only necessary facts (e.g., mathematical truths, logical truths) and no contingent facts (no physical objects, events, or states of affairs). In such a world, the plurality would be empty or non-existent because there are no contingent facts to include.

   2. Modal rigidity states that if the plurality exists, it necessarily has the members it has (all contingent facts). However, this is a conditional necessity: the necessity applies only if the plurality exists. It does not entail that the plurality exists in all possible worlds or that the numerosity fact is true in all possible worlds. Since the plurality existence is contingent, the numerosity fact remains contingent. Compare the numerosity fact to a necessary fact like "All triangles have three sides." This is true in all possible worlds because the concept of a triangle inherently requires three sides, regardless of what contingent facts exist. In contrast, the numerosity fact depends on the existence of contingent facts. If no contingent facts exist, there is no plurality to be numerous, so the numerosity fact is false. This dependence on contingent conditions makes the numerosity fact contingent.
      It is a necessary fact that if the plurality exists, then the plurality of all contingent facts are numerous. This is the necessary fact that grounds why plurality of all contingent facts are numerous in every possible world.

5. If true, the fact that contingent facts are numerous has an explanation.

   1. This is true in virtue of the presupposition that all contingent states of affair have an explanation in principle.

6. Therefore, assuming a regression of only grounded 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. (Definitional Substitution and Hypothetical Syllogism on #2-5)

7. If true, then the fact that the plurality of all contingent facts are numerous is explained by a necessary fact.

   1. Since its explanation is not contingent, then that only leaves a necessary explanation.

8. If true, then not every fact in the grounding series of a regression of only grounded contingent facts is contingent.

9. A regression of only grounded contingent facts is infinite if and only if every fact in its grounding series is contingent.

   1. If every fact in the grounding series is contingent, each fact requires another contingent fact as its ground (per the Principle of Sufficient Reason). This creates an unending chain, as no necessary fact exists to halt the regression, and brute facts are ruled out if all contingent facts need grounds. Thus, the regression must be infinite.

   2. Both directions hold in all cases, as the conditional explicitly includes all grounding facts (internal and external), eliminating finite chains with necessary or brute grounds.

10. Therefore, assuming a regression of only grounded contingent facts can be infinite, then every fact and not every fact in the grounding series of a regression of only grounded contingent facts is contingent, which is a contradiction. (Definition Substitution and Hypothetical Syllogism on #6-9)

11. Therefore, the assumption that a regression of only grounded contingent facts can be infinite is false. (Reductio ad Absurdum on #2 & #10)

12. Therefore, a regression of only grounded contingent facts cannot be infinite. (Disjunctive Syllogism on #1 & #11)

Argument against an infinite hierarchical regression of contingent conjunctive causes

Presupposition

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

Premises

1. An infinite hierarchical regression of contingent conjunctive causes is a chain or series of dependent causes and contains no conjunctive cause with actuality of its own.

   1. The premise asserts that in this infinite series, no cause has independent existence.

   2. A “hierarchical regression” refers to a chain or series of causes arranged in a dependent, essentially ordered structure, where each cause depends on a prior cause. Each member derives its causal power mediately from a prior member (e.g., a hand moves a stick, which moves a stone; the stick’s power to move the stone is borrowed from the hand).

   3. “Contingent” refers dependence contingency, not modal contingency. The existent depends on something else for either coming, remaining or going out of existence.

   4. “Conjunctive causes” are causes that rely on other factors for their existence and work in combination to produce effects, but none of them are independently sufficient or self-existent.

   5. “Actuality of its own” refers to a cause that exists independently.

2. A chain or series of causes can be actual only if and only if it contains a conjunctive cause with actuality of its own unless it is supplied with actuality external to itself.

   1. For any contingent cause in the series to actualize an effect, it must already possess the causal power to do so (e.g., the stick cannot move the stone unless the hand first imparts motion to the stick).

   2. For analogy to illustrate the concept of a hierarchical series of causes and the necessity of a primary source to account for a derived effect, think of how the moon’s light (a contingent effect) depends on the sun (a primary source) because the moon cannot generate light independently. An infinite series of contingent reflectors cannot account for the light without a non-contingent source. The light we see from the moon here and now depends on a hierarchical causal chain: the moon reflects light from the sun, which generates light through its own actuality. If we trace the cause of moonlight backward, we arrive at the sun as the ultimate source in this chain. The moon’s light depends on the sun’s light being actualized, and an infinite regress of reflective bodies fails because no conjunction in the series provides independent actuality.

3. Therefore, no conjunctive cause in an infinite hierarchical regression of contingent conjunctive causes can be actual unless it is supplied with actuality external to itself. (Definitional Substitution and Modus Tollens on #1-2)

4. A hierarchical regression of contingent conjunctive causes can take place if and only if it can be actual.

5. Therefore, no infinite hierarchical regression of contingent conjunctive causes can take place unless it is supplied with actuality external to itself. (Modus Tollens on #3-4)

Argument against an infinite regress of dependent conditional causes

Presupposition

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

2. A causal power is responsible for bringing about the current state of reality.

Premises

1. If there is an infinite regression of dependent "only if" members (R), then no member in the regression has an inherent causal power.

2. If true, then an R has no inherent causal power in bringing about the current state of reality.

3. If true, then a causal power external to R is responsible for bringing about the current state of reality.

4. Therefore, if there is an R, then a causal power external to R is responsible for bringing about the current state of reality. (Hypothetical Syllogism on #1-3)