There is an area of causal inquiry that allows for logical deduction - culpability. The tracing back from effects to a person or persons who are the cause is often a logical process that forms the basis of legal and historical inquiry. When considering this kind of causality, the degree of responsibility, blame, or praise is determined by a person's degree of freedom and their intentions or negligence. The intention is the cause. A cause-and-effect relation of persons is necessary when determining responsibility, blame, justice, and, by extension, grace and love. 

The logical (ie. a priori) element in cause and effect has to do with the intention of a person. The fundamental presupposition of legal/historical causality is, of course, the person - the moral agent. A person is the locus of a cause. If we cannot find a human or perhaps animal cause, then we must blame or praise a divine one, ultimately getting back to the Logos, God. Therefore, some destructive event that is completely outside of human responsibility is called an "act of God." 

Once we are aware of the personification and remove it, we are left with the banal historical fact that "people have used guns to kill people." It's those people that are the problem. Removing intent, the shortcut "guns kill people" has been essentially flattened to "occasionally a death is correlated with an object of the group commonly called 'gun'."

The concern of modern science is to determine cause-and-effect as a relation of things rather than persons. In doing so, it borrowed the paradigm of culpability and so routinely personifies the thing as being causal. Each statement of cause is invoking a thing as a tiny god, and then afterward, denying that the thing is in fact of minuscule divinity. This procedure is merely a harmless shortcut for the theist. By whatever circuitous route, which might include angels and demons, all order ultimately flows from the Logos, God - and God is indeed intentional. For the 'secularist', this is an utter embarrassment. Hume's skepticism of induction emphatically points his finger and calls out the shortcut without appealing to the Logos. Philosophically, the effect of this on 'secular' science is brutal. 

One of the most strident atheists in the world is the evolutionary biologist Richard Dawkins. Ironically, one of the things he is most famous for is introducing "selfish genes" to the evolutionary literature. Genes are strands of DNA code that code for a certain protein or trait. DNA is not in and of itself a living thing and has no intent, but in the operation of a cell, a gene provides a recipe that cell mechanisms put to use. Dawkins, of course, knows this but personifies the gene to efficiently get across his overarching idea of the locus of natural selection. He is so aware of the shortcut, he knows that any scientist will deny the intent when seeking to understand the idea, thus we have science by irony. In Selfish Genes, the intentional shortcut is on neon display. 

SELFISH GENE – selfish to persist (2020) - biologyonline.com 

The literature on evolutionary theory, in particular, is filled with this kind of intent and design language, which brings an even bigger irony and absurdity - we understand the gene by declaring it a person, but the human, the actual person, is a mere vessel or mechanism of the gene. Frankly, Dawkins made even a few 'secular' scientists flinch with how unabashedly this ironic procedure was presented. 

The Two Languages of Science (2020) by Yanai, I., & Lercher, M. - ncbi.nlm.nih.gov 

Dawkin's intentional language is sometimes misrepresented as being merely anthropomorphic. We have every reason to believe that any animal with a central nervous system and senses enough to detect others takes an intentional stance. What is truly anthropomorphic is then denying the intention and replacing it with abstruse language concealing a different kind of intent. Is there any other animal that does this without being deceptive? Is there any other animal that is so deceived? 

That's right, deceived. The verb 'cause' and any approximate synonym is intentional: bring about, lead, generate, spawn, create, produce, purpose, incite, instigate, determine, begin, motivate, etc. The most that a denier of intention can say about a 'cause' is that it is a metaphor. Hume's skepticism allows no other option because all that connects a cause to an effect is our habits and jumps of extrapolation. The most that can be said of the abstruse supposedly metaphor-free language used in science is that it might shift the intending cause from the lifeless object to the Logos or at least a higher-order intermediary of intent, such as perhaps the Wave Function or General Relativity. This is not necessarily so, as seen in the contrasting "Night Science" and "Day Science" that Itai Yanai and Martin Lercher (2020) defend as informal and formal science language: 

On the one hand, Yanai and Lercher have made their point well - Night Science such as Dawkin's "selfish genes" can be translated into the more precise and testable Day Science language. On the other hand, as the bolded causal words show, metaphysically nothing has changed, at least not with these examples. Except for Aristotle's "Nature" invoking a powerful god, both night and day statements are invoking tiny gods. The evidence is in. These are all sound statements of knowledge if one can believe in tiny gods; delete the gods through unexamined habit; delete them after accepting that science is fundamentally an ironic endeavor; or see this kind of causal language as a shortcut pointing back to the underlying cause of everything - the Logos, God. 

So what of Aristotle's totalizing generality Nature? 

Nature, according to Aristotle, is an inner principle of change and being at rest (Physics 2.1, 192b20–23). This means that when an entity moves or is at rest according to its nature reference to its nature may serve as an explanation of the event. We have to describe how—to what extent, through what other processes, and due to what agency—the preconditions for the process of change or of being at rest are present, but once we have provided an account of these preconditions, we have given a complete account of the process. The nature of the entity is in and of itself sufficient to induce and to explain the process once the relevant circumstances do not preempt it.

- "Aristotle’s Natural Philosophy" (2023) by Istvan Bodnar - plato.stanford.edu 

Thereby Aristotle reasons four required causes in increasing hierarchy: matter, form, efficient, and ultimate. Matter of a suitable nature can be given a suitable form by efficient causes towards the ultimate intention of an agent. Internally or externally, all four causes in the chain of causation are required for an explanation. Having (inadequately) dispensed with the Logos after rejecting the "Heraclitean doctrine" of the unity of opposites (Physics 1.2), Aristotle had to conceive of the Unmoved Mover to make his Physics work. Needing an ultimate cause for all motion, it must be the Unmoved Mover that Aristotle is intending when talking of Nature in total. 

But maybe not. Aristotle's method is not that of experimental modern science. He is using what is commonly known to explain the unknowns of Nature. 

Plainly... in the science of Nature, as in other branches of study, our first task will be to try to determine what relates to its principles. 

The natural way of doing this is to start from the things which are more knowable and obvious to us and proceed towards those which are clearer and more knowable by nature; for the same things are not ‘knowable relatively to us’ and ‘knowable’ without qualification. So in the present inquiry we must follow this method and advance from what is more obscure by nature, but clearer to us, towards what is more clear and more knowable by nature. 

Now what is to us plain and obvious at first is rather confused masses, the elements and principles of which become known to us later by analysis. Thus we must advance from generalities to particulars; for it is a whole that is best known to sense-perception, and a generality is a kind of whole, comprehending many things within it, like parts. Much the same thing happens in the relation of the name to the formula. A name, e.g. ‘round’, means vaguely a sort of whole: its definition analyses this into its particular senses. Similarly a child begins by calling all men ‘father’, and all women ‘mother’, but later on distinguishes each of them. 

- Aristotle Physics Book 1.1 

The very nature of using a generality is to treat it as an agent - a god - who has messages - an angel. The generality of all Nature then is treated by Aristotle as a hugely influential angel, regardless of whether he conceived of the Unmoved Mover or not. And the angel Nature abhors a vacuum, the meaning of which is clear - "vacuums suck."

Turtles All the Way

Even if the mind were declared "fully determined," any physicalist explanation that invokes concepts and terms such as probability, chance, or randomness in that explanation is begging the question. An untold number of outliers and counterfactuals are shaded over in the probabilities. 

Each of the 30-40 trillion cells in a human body has around 100 trillion atoms. Every human body produces highly improbable events at the atomic level every single second. And yet, the instantaneous probability of any event is 0. 

Taking time out of it, there is the problem of the single case - the event so rare that it only happens once or twice in the universe. To deny there is such a single event is to posit an infinite universe, and yet at the atomic and sub-atomic level we know of no single cases. And yet at our macroscopic level, we can group, define, and discuss all sorts of single cases such as the Mona Lisa by Leonardo Davinci. The existence and history of every mind is a single case. 

Quantum Mechanics has been repeatedly described as "a wildly successful theory." This wild success has been due to the precision of its observable probabilities. And yet, the philosophy of probability yields a host of unresolvable questions and diverse answers to what it all means. It seems only a humble use of the art combined with an intention toward truth is all that keeps us from lies, damn lies, and statistics. 

"Interpretations of Probability", The Stanford Encyclopedia of Philosophy - plato.stanford.edu 

Arguments of Chance are wallowing deep in the mud of metaphysics. It can't possibly be considered the proper end of a physicalist explanation. And yet, Chance can easily be taken as an epithet of God. 

Make Physics Real Again (2019) by David Guaspari - www.thenewatlantis.com 

And yet we can go further. Let's say that Quantum Mechanics has somehow returned to a Newtonian certainty no longer strongly beholden to statistical probability and chance. >>