In my ongoing debate about God’s existence with biologist Jerry Coyne, who writes at Why Evolution Is True, frequent reference is made to Aquinas’ Five Ways, particularly to his Prime Mover argument. It is the most popular formal argument for the existence of God, and it is often misunderstood and, when understood, often misrepresented. Atheists, in my experience, never get it right. If they did, they wouldn’t be atheists.

The first three of Aquinas’ Five Ways share a similar logical structure, and are called the cosmological arguments. More precisely, these arguments probably ought to be called the cosmogonical arguments, because they are proofs based on origins of things. I’ll stick with habit and call them cosmological, but keep in mind that what ties them together is that they are proofs of God’s existence based on the beginnings in nature. 

In this post I’ll lay out the logical structure, and in coming posts I hope to apply the structure to three kinds of beginnings in nature: the beginning of change, the beginning of causes, and the beginning of existence itself. 

The cosmological arguments have two cornerstones: the law of non-contradiction, and the metaphysics of potency and act. Both principles are Aristotelian, developed in fullest form by St. Thomas Aquinas. 

Simple but Profound

The law of non-contradiction is simple but profound. It is the principle that it is not possible for a thing to be and not be at the same time in the same respect. If my coffee cup is full, it cannot also be empty at the same time. If I am alive, I cannot be dead at the same time (for readers thinking “What about Schrödinger’s cat?”, I’ll address that later). 

Succinctly, A is not not-A, and not-A is not A. An interesting side-note is that, contra Descartes, it is the law of non-contradiction, not “Cogito ergo sum,” that is the most certain thing we know. This is because if the law of contradiction were not true, I could “think” without “I am.” “I think therefore I am” has a logical structure, and it’s not valid unless “therefore” is always true.  “Cogito ergo sum” presupposes the law of non-contradiction. Without the law of non-contradiction, nature is Alice-in-Wonderland, where I could think without existing. Reality must make sense first, before I can draw conclusions from it. 

The First Thing We Learn

Notably, Aquinas observed that the law of non-contradiction is the first thing we learn as infants, even before we are aware of our own existence. We come to understand existence first: milk and Mom and colic are either there, or not there, not both. Our own existence can only be apprehended if reality makes sense. If reality makes no sense (if A and not-A are compatible), we can apprehend nothing. Expressed another way, sense is the precondition of truth. We can’t know any truth unless the world makes sense. 

The second cornerstone of the cosmological arguments is Aristotle’s principle of potency and act. The principle is the solution to a problem that obsessed pre-Socratic philosophers: what is change? 

Understanding Change

One school of philosophers, following Parmenides, insisted that change was impossible. Parmenides argued that a thing cannot change itself, and can only be changed by another. However this means that being — all that exists — can’t change itself and can only be changed by another. The only “other” to being is non-being, so being could only be changed by non-being, but that means that change cannot happen, because non-being doesn’t exist. Change isn’t real — it’s an illusion.

Another school of philosophers, following Heraclitus, argued that everything was change all the time. Heraclitus asserted, “No man ever steps into the same river twice.” Nothing was exactly the same from moment-to-moment. At every moment, I’m a moment older, at every moment something moving is in a different location. The world is always in flux. It is stability, not change, that Heraclitus denied. For Heraclitus, nature is change, and nothing else. 

A Solution from Aristotle

Aristotle’s solution to this conundrum of change is, along with his law of non-contradiction, the cornerstone of all metaphysics and of natural science. Aristotle observed that in contrast to non-being, there were two manifestations of being — potentiality and actuality. 

Potentiality (or potency) is an intermediate state between non-being and being. It is the capacity to receive form — the capacity to become a defined existing thing. It is not the thing itself, however, it is only capacity. Potency is not actual. 

Actuality (or act) is the state of actually being in a defined way — full reality. 

The classic example of potency and act is a sculptor sculpting a statue. The marble is in potency to be a statue until the sculptor sculpts it, at which time it becomes actually a statue. The bare marble isn’t nothing, but it isn’t a statue yet either. It is something intermediate — it is potentially a statue. The same states of potency and act are ubiquitous in nature. An acorn is in potency to be an oak tree. A kitten is in potency to be a cat. A green leaf is in potency to be red (in autumn). 

Aristotle’s principle of potency and act solves the pre-Socratic dilemma of change. A substance (i.e. an existing thing) exists in two senses: it is actually something (act), and it is potentially something else (potency). So there is something that is actual and persists — substance; and there is something (in a lesser sense) that mediates change — potency. In Aquinas’ famous dictum (I paraphrase), all of nature is divided between potency and act. When something changes, one of its potencies is elevated to act. The underlying substance remains throughout the change (contra Heraclitus), but change is real (contra Parmenides) because a potency is not non-being, but rather an attenuated kind of being in its own right. 

In Thomistic metaphysics, the principle of potency and act are what define the natural world. Nature is that which is in potency to act. 

Aquinas (following Aristotle) pointed out that the law of non-contradiction applies to the principle of potency and act in a fundamentally important way. A thing may not be in potency and in act in the same respect at the same time. Potency and act for the same thing are mutually exclusive at any moment in time. If something is possible, it is not yet actual, and if something is actual, it is no longer just possible. There is no middle state between potency and act and there is no state of simultaneous potency and act for the same thing. To assert “I am in Las Vegas  (in potency to being in Detroit)” and “I am in Detroit (actually)” at the same moment is nonsense. I can be either at any moment in time, but not both. A or not-A, never both. 

Beginnings in Nature

The logical structure of the cosmological proofs for God’s existence applies the law of non-contradiction and the principle of potency and act to beginnings in nature. In nature we find chains of cause and effect — chains of change, chains of causes, and chains of existence. These chains work by potency and act — individual links in the causal chains activate the potency of the next link in the chain. 

I intend to apply this logical framework to Aquinas’ specific Ways in a future post. There are three provisos I need to mention here, which involve common errors of understanding about the Cosmological arguments.

Causes in Priority

1) The causal chains are causes in priority, not in time. That is, it is assumed that the causes can occur simultaneously, and do not necessarily imply temporal sequence. This means that the cosmological argument is valid regardless of whether the universe has a beginning or it is eternal in the past. In fact, Aristotle, who first developed the argument for the existence of God, thought the universe was eternal in the past. Aquinas developed the cosmological arguments on the assumption of an eternal past — not because he believed it eternal, but because it made the argument harder to prove, and he took the challenge. Time and again Thomas chose premises that made his proofs as difficult as possible, and then proved them. Aquinas was his own harshest critic — I love the guy. An example of a causal chain in priority but not in time is a stable stack of books. Each book in the stack supports the book above, and is in turn supported by the book below it. In this sense, the position of each book in the stack is caused by the one below it, and each book causes the position of the book above. The stack is static — time is irrelevant to it. This kind of time-irrelevant causal chain is called (by Aristotle) an essential chain of causation. It is distinguished by an accidental chain of causation, in which time is relevant (and example of an accidental chain is a family tree, with grandfather causing father causing son and so on.) Both kinds of causal chains are common in nature. The cosmological argument only applies to essential causal chains, not to accidental causal chains. 

A Posteriori Arguments

2) It is essential to note that the cosmological arguments, and all arguments for God’s existence, are a posteriori arguments. They are inductive: they begin with an observation about nature (change, cause, and existence) and proceed logically to prove God’s existence. A priori arguments for God’s existence are impossible (as Aquinas points out), which is a topic I’ll discuss in a later post. The importance of the fact that the cosmological arguments are all a posteriori arguments is that they share that structure with theories in natural science, which are also a posteriori. A common objection by atheists to the cosmological arguments is that they are “a priori” — they assume God’s existence rather than proving it, and thus are not scientific. That is a complete misunderstanding of the arguments. The cosmological arguments begin with observations of nature, exactly as natural science does, and then proceed with logical arguments to the conclusion, exactly as arguments in natural science do. The cosmological arguments are no more or less inductive than the theory of relativity or quantum mechanics or Darwinian evolution. The logical framework is the same: cite an observation in nature, and apply logic to draw valid conclusions from it. In this sense, the existence of God is a scientific conclusion — as scientific as any theory in natural science. I’ll discuss this more in a future post. 

And Now for Schrödinger’s Cat

3) There is a common atheist objection to the Aristotelian principle of non-contradiction, using a famous paradox in quantum indeterminacy.  The argument is that the principle of non-contradiction is disproven by the paradox of Schrödinger’s cat, in which a cat in a box with poison that can be released by a radioactive emission can be simultaneously alive and dead — in a suspended state between life and death — until the box is opened and it is observed. This would seem to be a situation in which A is not-A simultaneously. Before observation, the cat is both dead and alive. This, however, is a misunderstanding of the metaphysics. In fact the paradox of Schrödinger’s cat is better understood in an Aristotelian framework. There is obviously no materialist mechanistic framework in which it is comprehensible. In the Aristotelian framework, one possible perspective is that until observed, the cat is in potency for life and death, not in actuality for either. It is only on observation that the cat is alive or dead. That is, it is only with observation that potency is raised to act and the law of non-contradiction apples. Only the Aristotelian principle that potency is not actuality makes sense of the cat’s indeterminate state. The paradox of Schrödinger’s cat raises profound questions about quantum mechanics, about nature and about metaphysics. Of all of the metaphysical perspectives on tap, the least acceptable is the materialist mechanical perspective — i.e. “nature is atoms in the void, and nothing more.” The most acceptable, in light of the indeterminacy inherent to the quantum state, is Aristotelian potency and act. How the principle of non-contradiction applies to quantum indeterminacy is not clear, although it is difficult to envision a metaphysical perspective of any sort without non-contradiction as a cornerstone. If the law of non-contradiction is cast aside, then any theory of metaphysics may be true and false at the same time. That is, you can’t even talk coherently about metaphysics without the law of non-contradiction. Making any sense of reality at all presupposes the law of non-contradiction. Werner Heisenberg, who worked from an Aristotelian perspective, understood this, and noted that the strangeness of quantum mechanics is largely an artifact of our materialist mechanical philosophy. Quantum indeterminacy (exemplified by Schrödinger’s cat) is a striking example of Aristotelian potency, and collapse of the quantum waveform is an example of reduction of potency to act, and the law of non-contradiction is necessary to even talk about metaphysics or science meaningfully. It is materialist mechanical philosophy, not Aristotelian metaphysics, that is incompatible with quantum mechanics. 

In an ensuing post, I’ll apply Aristotle’s law of non-contradiction and principle of potency and act to change in nature. This is Aquinas’ First Way — the Prime Mover argument.

Editor’s note: For more on Aquinas, intelligent design, and evolution, see the website of Father Michael Chaberek, Aquinas.Design.

Image: Thomas Aquinas, via Aquinas.Design.