A brief survey of evolutionary explanations for why math works

Space has been given on this blog for Plantinga's argument about the difficulty natural selection has in explaining higher functions. My naturalist friends have dismissed such arguments, and this post is meant to explore that perspective. The perspective, to restate, is that natural selection is sufficient to explain the existence of higher-order cognition, such as mathematics. I will be summarizing from a paper given by Russel W. Howell, who was professor of Mathematics at Westmont College.

Recall that what I'm after are evolutionary explanations for rationality, and the first of these that Howell mentions is that natural selection selected for meaning. Evolutionary process selected for survival forms whose inner models of reality best matched reality itself. A variant of this, argued by Geoffrey Miller in his book The Mating Mind, says that any greater capacity can be sexualized. Therefore, rational operations such as logic or math may set one apart from the herd and increase one's chances for sex. Howell says of these, "These speculations, while certainly not disprovable, seem to have no good evidence in their support."

Stephen Mithin is next, with a module approach to rationality. Specialized psychological processes for this or that, once brought into contact with one another, create emergent psychological domains. Plantinga's criticism is leveled at this pillar.

And finally, the author mentions work by Pascal Boyer, whose theory he calls the byproduct hypothesis. The idea is that many higher functions of mind are not evolutionary adaptations in themselves, but are byproducts of the same. They piggyback on adaptedness. Howell writes, "If one if going to argue for something using an evolutionary framework, it behooves that person to supply a detailed model or story that will support it."

Perhaps, going forward, I can flesh out these criticisms and competing arguments with greater depth. But I hadn't had them in the blog yet, and this at least gives me a place to begin. Also, let me say this: natural selection has to have played a great role in human cognition and the existential fact of higher thinking in human beings. To deny this is to deny that matter matters and that natural processes and law have meaning and truly affect a true world. But there does not have to be an either/or. I deny sufficiency without cutting out the bone. And so I retain my Chalcedonian anthropology.

Penciling in a gesture toward providence, determinism, and liberty

What follows is embarrassing in its lack of precision. Let's call it what it is: sloppy. As a matter of fact, it is so bad that I've edited it four times since the original publish. So come back and check it later and it will probably (hopefully) be better. Nevertheless, William Hasker's little survey of metaphysics keeps me blurting out what I think about his subjects. And today, his subject is the impassible way between determinism and libertarianism. (Libertarianism here is not to be confused with the quasi-economic position assumed by many of the Rand-loving, conservative, twenty-something males that I know. It is, rather, a technical term for what is popularly called free will.)

A Reformed Protestant, I begin every thought in this area with a confession of God's providence, for "he himself is before all things, and in him all things hold together (συνεστηκεν)" so that "he sustains (φερων) all things by his powerful word" (Col 1.17; Heb 1.3b NRSV). "The will of God," said Augustine, "is the necessity of all things." Not only, but the first, stated pattern of my theological pattern language is simply, God leads out.[1] But this beginning throws me and similar theists into a certain bind. I like the way Hasker sums it up:

It is quite clear that the doctrine of predestination entails determinism: specifically, theological determinism. God has effectively determined everything that shall happen, and no creature has the power to act otherwise than God has decreed. It is clear, furthermore, that the theological determinist, at least if he is a Christian, must be a soft determinist, for the view that humans are responsible for their actions is central to Christian belief. Thus one has the very difficult problem . . . of explaining how a person is responsible for his actions when he was unable to act otherwise. And there is the additional problem of explaining how God himself is not responsible for human wrongdoing, even though it is God's decrees which necessitate that the wrongdoing occurs. (51)

So the Christian may confess providence, which is a scripture-affirming thing to do, yet providence creates fundamental ethical problems on the human and divine sides. This is why the free will question is unavoidable even if it tires you--as it does me. If humans do not have free will, can they be held responsible for wrongdoing? Is there meaning to human action? Should we trust or value or include as evidence the experience we all have of decision making? Is there a way to avoid Calvin's abhorrent second predestination of the wicked to destruction which, it can and has been argued, makes God unjust, the author of evil, and responsible for the suffering of innocents?[6]

I am not going to discuss the divine side of the equation, but I am going to talk about the rest.[5] Taking up the first question: I believe that people do act with a kind of qualified freedom (a soft libertarianism.) We are embedded (thrown) into layer upon layer of historical and cultural context, and these deeply shape who we are as actors (see the card "Every Action a Reaction.") Because all human beings are made in the image of God, they can freely act within the bounds of nature, and those actions are meaningful--even moral actions--in their context (though compromised). By God's grace, the imago can be restored, which gives greater agency to human beings. Jesus's freedom is, in renewed humanity, proleptically restored, now and now-yet. The regenerate, therefore, begin a struggle for freedom illuminated by God's eschatological promise in Christ to the church. I expect this struggle will continue as long as people do. Human beings, no matter how free, will only ever reflect the freedom of God.

Going back to the conflict between determinism and libertarianism, I think the frame of reference makes a big difference in understanding. If one is looking out of human eyes, actions are messy but still, in a way, free. But if one imagines oneself into a divine state, determined providence seems only natural. The thing is, human beings think about things from both angles, theory and praxis, the vertical and the horizontal, theology proper and ethics. We cannot eliminate one. We must, instead, choose which we will emphasize.

To the problem of settling these two perspectives, God's timelessness comes to the rescue (though it too, Hasker says, is qualified and disputed).[2] Because God is timeless, tensed words like now, tomorrow, yesterday, or talk of the future or past do not apply. As Hasker says, God "believes things timelessly, entirely out side our time sequence . . . And what it is that God timelessly believes depends, in part, on what I will freely choose to do tomorrow morning." (55) God's timelessness allows for human free action. And it tells us that providence must effect itself in a manner much different than the two-dimensional before-then-after of Aristotelian sufficient causation. Something like what I'm getting at I find in this bit from Reformed theologian Paul Helm:

"In creating, God does not add to his reality. The creation does not distend God’s boundaries, for he has no bounds. So thinking of God as if has he has boundaries would be inconceivable. The contrast between God’s ways and ours is not one of degree, but one of kind. For this reason the decree of God may be considered as the eternal aspect of his mind."

To summarize: I take my cue from physics which, at present, talks out of both sides of its mouth. It affirms Einstein's standard model, and it affirms the quantum. The two are irreconcilable. Nevertheless, we affirm them and use them properly depending on our need. Using the analogy, I think the human mind is incapable of reconciling determinism and libertarian free will. But the nature of thought makes one favor one or the other. I favor determinism. I'm a determinist that simultaneously affirms a qualified or soft libertarian free will. The latter is made possible because God is timeless. His tenselessness creates a horizon in which tense can exist.[3] Yes, I shamelessly use two different grammars according to whether the subject is theology proper or ethics. So the Spirit regenerates AND people should repent and believe.[4]

But perhaps some one will say, If all that the Father gives, and whomsoever He shall draw, comes unto You, if none can come unto You except it be given him from above, then those to whom the Father gives not are free from any blame or charges. These are mere words and pretenses. For we require our own deliberate choice also, because whether we will be taught is a matter of choice, and also whether we will believe. (John Chrysostom.Homily 45 on the Gospel of John, Jn. 6.37)

There is another way, of course: the way of the process theologians and the panentheists. Going that way, God limits himself, opening up a space of some kind (logical or spiritual or metaphysical or metaphorical) from which his divine power is removed. That process they call creation, and in it, evil and choice have their temporary arena.

And, finally, meandering to an end, allow me to say this about discussions of providence and free will or, if you like, determinism and libertarianism. A friend today asked me whether this wasn't majoring on the minors. I don't think he knows how much I dislike the whole of it myself. I would much rather talk about other aspects of dogma. Nevertheless, I said to him that though there is no ultimate resolution to these questions in our present state, they have persisted and will persist as long as thinking and confessing persist. And joining in that argument means laboring alongside some of the best minds humanity has ever produced. It is a labor they found valuable because it connects so many other portions of real thinking and living. And shouldn't we, with the life and the minds given to us, be part of this human work? I would look askance at someone who beginning at the door of thought did not eventually arrive at this chamber. And I would doubt the abilities of anyone who found a way to move further in without discomfort at the choice they had to make. Either choice means pain and ongoing discomfort and shouldering the unreasonableness of reason.

----------

[1] "God leads out" does not suggest the lure-theory of the process theologians but a kind of strong pull where the future and the God of the future providentially pull all things to their appointed end. Another way of saying this is that the doctrine of creation is not a static doctrine but an ongoing one. The creation is not yet in the state to which its creator desired it. It is advancing toward that state according to his providence and promises.

[2] Scientific discussion of the non-locality of quantum entanglement suggests that time is not part of the infrastructure of reality but is its result. The engine of reality must work outside of space-time. And the non-locality/non-temporality of quantum events, then, means that there is no need to wait for any cause to produce any state.

[3] It occurred to me at some point that I was thinking of providence as either (a) an organizing force of matter or events in space-time or (b) as a soteriological act whereby God saves sinners. What I haven't considered is that providence provides a horizon of meaning. Because of providence, truth, justice, and beauty have a horizon from which they derive significance. Tracing the philosophy, here: Charles Taylor has usefully distinguished between self-referentiality of content and manner. Self-referentiality of content sees nothing in discourse except the self and its desires. Self-referentiality of manner recognizes a horizon against which the self finds significance. (Ethics of Authenticity [Cambridge, MA: Harvard University Press, 1991], 81-82.) In Michael Polanyi's terms, the self-referential is subsidiary to the focus of education: the pursuit of justice and truth. (Personal Knowledge: Towards a Post-Critical Philosophy [Chicago: University of Chicago Press, 1962], 55-57). // this copied from Hasker pp 490-491n64.

[4] It is of vital importance to remember Luther's warning that a peek at God's determinism is not supposed to give the Christian a window into guessing at reality. Instead, it is meant to provide comfort to the believer that God is well able to do what he has promised to do. Luther strongly urged those interested in this "arrived doctrine" to run from the metaphysical temptation. Providence, he said, falls under soteriology and needs to stay there. Consider, in the spirit of this idea, the following:

"When its content is not specifically defined in relationship to the incarnation of the Jewish human being Jesus of Nazareth, the doctrine of providence becomes vulnerable to ideological colonization. Reflection on providence, therefore, must proceed in light of the fact that there is only ever one divine Subject of the doctrine: the particular God revealed in the covenant with Israel and the incarnation of Jesus Christ. Providence is not primarily about abstract concepts like omnipotence, sovereignty, or causality, but about how the God who brought Israel out of slavery in Egypt, became a Jewish human being, and was crucified and resurrected continues to be in an active relationship to creation. Contemporary reflection on the doctrine of providence begins by affirming that God never acts otherwise than God has acted in Israel and Jesus. Theological accounts of providence must fix their vision on the concrete particularity of Jesus Christ. (Matt R. Jantzen,God, Race, and History: Liberating Providence (Lanham, MD: Lexington Books, 2021), pp. 145–146)

[5] I am going to copy this insight that someone named Nick Prendes-Brizuela wrote on a theology forum regarding Molinism and middle knowledge.

My main contention with Molinism and mere Molinism is the foundation of the theological belief that God's knowledge of counterfactuals (the Would Be's of reality) stem from God's middle knowledge. It seems to me that God knows all the counterfactuals based in his natural and free knowledge rather than this invention of middle knowledge in the 16th century. In other words, I believe that God's knowledge of counterfactuals stems from his intimate knowledge of his creation and what they would do in any given circumstance. Middle knowledge by definition states that God's knowledge of counterfactuals isn't due to his intimate knowledge of his creation, but instead middle knowledge states that God knows the counterfactuals of his creation based upon their possible actions prior to God's decision to create. I do not believe that middle knowledge is required for God to know all counterfactuals."

Middle knowledge is independent of the divine will. That is absurd because how can something be or do apart from the divine will? Arminius doesn't answer how free will etc can exist, and neither does Molinus.

[6] Arminians say yes and argue for an understanding of God's eternal exhaustive foreknowledge as the only alternative that leaves genuine human freedom, called libertarian freedom, intact.

a brainy argument against determinism (and also materialism)

For some beach reading, I picked up a two-dollar paperback survey of metaphysics by William Hasker, part of the IVP series Contours of Christian Philosophy. My goal was pure curiosity: I wanted to see what topics the author included under this heading. I will probably blog something in dialogue with this book again in the near future. But, for now, it includes an argument against determinism (and, by extension, against materialism) worthy of reproduction against future forgetting. From pages 47-48, italics rendered as in the text:

----------

"It is clear . . . that rational thinking must be guided by rational insight in the light or principles of sound reasoning. That is to say, one must "see," rationally, that the conclusion is justified by the evidence--and one is helped to see this by principles of reasoning, such as the laws of inductive and deductive logic and the like. Furthermore, and this point is crucial, one accepts the conclusion because one recognizes that it is justified by the evidence. It is this recognition which brings about the acceptance.

"Now let us suppose that all human thinking is physically determined in the following sense: (1) Every thought or belief accepted by a person is a result of that person's brain being in a corresponding state. (2) We assume, provisionally, that the physical indeterminacy which exists at the quantum level makes no perceptible difference in the overall functioning of the brain. So that (3) every brain state, and therefore every thought and belief of the person, is fully determined by the physical functioning of the brain in accordance with the deterministic laws of physics.

"Is it not evident, on this supposition, that rational thinking is an impossibility? It cannot be true, on this assumption, that anyone's thinking is guided by rational insight; rather, it is guided entirely by the physical laws which govern the brain's functioning, which proceed with no regard to whether the thought processes they generate correspond to principles of sound reasoning. Occasionally, to be sure, it may happen that the thought processes generated by the physically determined functioning of the brain will arrive at a conclusion which is correct. But this, when it happens, is simply a fortunate accident--and to say that a conclusion is reached by accident is incompatible with the claim that that conclusion was reached by rational thinking .Therefore, if all human thought is physically determined, then no one ever thinks rationally.

"Nor is the situation changed if we modify our assumptions (and our definitions of "physically determined") so as to allow that sometimes random, physically undetermined events within the brain have a perceptible effect, so that a different conclusion is reached than would have been the case without the random event. For such a random event is no more responsible to rational insight than was the physically determined brain process of the previous model. What is needed for rationality is not simply an injection of randomness into the physically deterministic brain functioning, but rather an infusion of rational insight as a factor which guides and directs the thought processes. But to accept this is to give up physical determinism altogether. And so our conclusion: If physical determinism is true, no one ever thinks rationally."

----------

The summary of the above is simply this: that a car, acting according to its own structure, cannot take you where you want to go. Even should it, somehow and by your good fortune, deliver you safely to a desired address, the result says nothing about the cause. Rational insight, one's reason, and in this metaphor the driver, must come from elsewhere.

What this means for emergence, I'm not wholly sure. Emergence theorist assert that the driver emerges from the complex and perhaps ineffable workings of the machinery, subject as it is to physical laws. If that is the case, doesn't this but shift the problem? In that case, the emergent property becomes our metaphorical car, and we are left asking how it knows where to go.

Some time ago, I wrote a post akin to this one called "Plantinga Pulls a Sampson." In it, Alvin Plantinga invokes natural selection, whereas William Hasker, who wrote the above, was addressing the debate between free will and determinism.

As I consider both posts, I can begin to see my own outline. I see a skepticism of reductive materialism, scientism, and "nothing but" physics--no surprise there. What is embraced is more interesting: a qualified dualism:

• the mind as not the same as the brain but connected, perhaps as an emergent property
• the self as a (qualified) free agent [not theologically free, but naturally so]
• a humanity that, though subject to material laws, transcends them
• reason/ethical judgment, the derivation of which could be the community or someplace altogether mysterious in origin

Note: this post does not well address the point of the quotation itself which is epistemology, which is about determining what is true.