Some New Arguments for a First Cause

I’m going to start a new series of posts in which I present some of my most recent thoughts on the classic First Cause arguments.

In this post, I will lay out some explications and definitions for some key terms that will appear in my arguments. Some of the terms are so fundamental that they cannot be defined. In those cases, I will explicate the terms by contrasting their meanings with others with which they may be confused.

Possibility. Throughout this series of posts, I will use ‘possibility’ to refer to fundamental, metaphysical possibility. This is a notion that cannot be defined. It means possibility in the broadest sense, an unconditional possibility. It is to be contrasted with logical notions like consistency and with epistemological notions like conceivability or imaginability. We can use possibility to define impossibility and necessity: something is impossible if it is not possible, and something is necessary if it is impossible that it not be the case.

Actuality. Like ‘possibility’, ‘actuality’ is too fundamental a notion to be defined. I will assume that there is a real and absolute (non-perspectival) distinction between what is actual and what is merely possible. The actual world is unified, complete, and consistent. If two facts F₁ and F₂ are both actual, then so is their conjunction (F₁ & F₂). A proposition p is actually true if and only if its negation ~p is not actually true.

Existence. When I speak of ‘existence’, I will mean actual existence. Only things that are actually existent can act on other actual things. Actual relations of causation must relate actually existing things.

Causation. I will assume that causation is a binary relation between things: between existing entities or between states or conditions of existing things. I have in mind causation as a kind of production: making something to be the case. Causation is more fundamental than time and more fundamental than truth of subjunctive conditionals. The order of time depends on the order of causation (earlier times are earlier because they contain causes of things occurring later), and the truth of subjunctive conditionals (e.g., if p had been the case, q would have been the case) depends on causal powers and capacities of things.  I assume, therefore, that it makes sense to hypothesize causal relations that involve items that are non-temporal (“outside” of time). Causal explanation is to be defined in terms of causation, and not vice versa: to explain something causally is simply to describe accurately its causal history. I also assume that causation is asymmetric and transitive: if x causes y, then y does not cause x (asymmetry). And, if x causes y and y causes z, then x causes z (transitivity).[1] There is therefore no self-causation or circles of causation. Finally, I will not assume that a cause necessitates its effects. I allow for chancy or probabilistic causation, in which a cause makes its effect probable (or, at least, possible in the circumstances).

A priori knowledge. We know something a priori when we know it in a way that does not depend for its status as knowledge (its warrant) on any reliance on experience (including both sense experience and introspection). When I know something a priori, reason itself demands that I believe it, regardless of what I know or fail to know by way of experience. A priori knowledge encompasses such things as logic, mathematics, and the basic principles of philosophy.

Real essence (kind-essence). To give the real essence of a kind of thing is to state clearly what it is to be that kind of thing. Everything belongs to a unique most specific kind, whose kind-essence is also the essence of that thing. Real essences belong to things in and of themselves, independently of how we conceive of them or what we know of them. Nothing can exist except by exhibiting in actuality its own real essence.

Conceivability. By ‘conceivable’, I will mean what David Chalmers defines as ideal, negative, secondary conceivability (Chalmers 2002). Some state of affairs is conceivable if and only if we cannot know a priori that it is impossible, even given complete knowledge of the real essences of the things involved. This kind of conceivability is ideal because it concerns what we cannot in principle and not merely what we do not know a priori. It is negative because it is defined in terms of the impossibility of the knowledge of what is impossible, not in terms of the possible knowledge of what is possible. And it is secondary, because we are allowed to consider what we would know, given complete knowledge of the real essences of things. So, for example, if the real essence of water is to be composed of H₂O molecules, then it is inconceivable that water not be composed of such molecules.

Pluralities. A plurality is not a single entity but a multiplicity of things (Boolos 1984). To speak of a plurality is to speak of “them” rather than of an “it”. Something belongs to a plurality if it is one of them. Pluralities exist whenever their members exist, and philosophers can accept talk about a certain plurality, even if the members of the plurality do not collectively compose a single thing or even belong to a single set. A plurality can be jointly caused by a single thing or by another plurality. I will assume that if x causes plurality P, then x does not belong to P, and if plurality P₁ jointly causes plurality P₂, then P₁ and P₂ have no members in common.

Broadly Causable. A thing is broadly causable if it is conceivable that it be caused. Similarly, a plurality is broadly causable if it is conceivable that something cause them (collectively).

Strictly Uncausable. A thing or plurality of things is strictly uncausable if and only if it is not broadly causable. So, it is inconceivable that a strictly uncausable thing or plurality be caused.

Infinite Regress. An infinite regress is a series of actually existing things, each of which is caused by its successor in the series.

The Universe. The Universe is the plurality of actually existing, broadly causable things.

I claim that the Universe has a cause, in the sense that the Universe is caused by some thing or plurality of things. By definition, no strictly uncausable thing belongs to the Universe. Since the Universe contains, by definition, all the broadly causable things, if it has a cause, it must have a strictly uncausable cause.

My arguments will depend on the following principles of Universal Causation, which I will defend in section 5:

Universal Causation (Simple). Every actually existing, broadly causable thing has an actual cause.

Universal Causation (Pluralized). Every actually existing, broadly causable plurality of things has an actual cause (either a single thing or a plurality of things).

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[1] If it turns out that causation is not transitive, then we can use the transitive closure of causation instead—causation*. The transitive closure R* of a relation R is the smallest transitive relation that contains R. The transitive closure is by definition transitive. I will assume that the transitive closure of causation is asymmetric, ruling out any cycles of causation.