Death to metaphysics?

Logical positivism was a philosophical school of thought that was hot during the 1920s. The bedrock of this philosophy was the explicit rejection of metaphysics as a valid mode of inquiry into the nature of reality. The positivists believed that metaphysics was essentially meaningless, and that the only statements that harbored meaning were statements that could be, at least in principle, empirically verifiable. The first fruits of this philosophy could even be seen in the writings of David Hume in his Enquiry Concerning Human Understanding:

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, "Does it contain any abstract reasoning concerning quantity or number?" No. "Does it contain any experimental reasoning concerning matter of fact and existence?" No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.

While logical positivism as an organized philosophy has died out, there still remain many who, along with Hume, would affirm a death sentence to metaphysics. This contemporary school of thought still takes metaphysics as essentially ambiguous and superfluous.

 I myself, as a Scholastic, would disagree with this. The Scholastics—a school of philosophy which is actually increasing in adherents—would claim that not only should metaphysics be utilized, but that it must. It would be claimed by them that metaphysical concepts like identity, essence, form, substance, and act/potency etc., describe fundamental properties of reality, and therefore that such concepts are necessary for a sound framework regarding the nature of reality in the first place.

 However, the contemporary positivist scoffs at such assertions. They would claim that concepts like the ones mentioned above are, even if remotely accurate—of which the positivist would most likely claim they are not—completely superfluous for describing reality. Physics already tells us how one event can, and does, follow another, and thus the need for a description riddled with the act/potency distinction is not necessary. Likewise, physics and chemistry already enlighten us regarding what physically composes and makes up a certain empirical object, so that to add descriptive concepts like identity and essence on top of these physical explanations and descriptions is to upset the principle of parsimony. Science, it is seen by contemporary positivists, already tells us (or will eventually tell us) all we need to know about the objects and phenomena that make up our observable universe. Hence, the need for any metaphysical description is seen as completely superfluous.

 While such a position might seem rational, especially since science has been extremely successful in a pragmatic and predictive sense, I maintain that said position is not only false, but demonstrably so--and for multiple reasons at that. First, the picture that science provides of the material world can only be seen as comprehensively descriptive if one assumes ahead of time that reality can only be described in scientific terms and concepts. Theologian David Bentley Hart, in his amazing book The Experience of God, articulates such fallacious thinking:

And naturalism’s claim that, by confining itself to purely material explanations for all things, it adheres to the only sure path of verifiable knowledge is nothing but a feat of sublimely circular thinking: physics explains everything, which we know because anything physics cannot explain does not exist, which we know because whatever exists must be explicable by physics, which we know because physics explains everything. (p. 77)

The problem here should be obvious. Moreover, the claim that science gives us an exhaustive portrait of reality is itself a claim that only metaphysics, and not science, can make. So, even ignoring the question begging nature of positivism alluded to above, the positivist still has the problem of utilizing the very method they’re attempting to overthrow. They’re basically claiming the following: all metaphysics is meaningless, except for the metaphysical statement I’m making currently.

 The second problem that positivism runs into—as if being subject to question-begging and self-refutation weren’t bad enough—is that the scientific method already a priori rules out the kinds of descriptions that could be considered metaphysical in the first place. You see, the objective of science was to be able to control and predict the world around us using the language of mathematics. This means, and this is crucial here, that science is, already at the outset, only looking for a quantitative description of reality—thereby paying no attention to anything qualitative or metaphysical. This is to say, the scientific method already stipulates what kind of answers and descriptions it’s looking for. It’s not as if science, looking for the quantitative, will somehow stumble upon the metaphysical, because it’s not looking for the metaphysical. To use an example, science will not stumble upon the ‘essence’ of a substance, because science is not looking for ‘essences’ in the first place--precisely because a thing’s essence cannot be modeled by the language of mathematics and prediction. Philosopher Edward Feser, in his (also) amazing book Scholastic Metaphysics, further articulates my point:

The reason qualitative features don’t show up is not that the method has allowed us to discover that they aren’t there but rather that the method has essentially stipulated that they be left out of the description whether they are there or not. (p. 14)

And again, David Bentley Hart reinforces the point:

If we look exclusively for material and efficient processes, then indeed we find them, precisely where everyone, of nearly any metaphysical persuasion, expects them to be found. All this shows is that we can coherently describe physical events in mechanical terms, at least for certain limited practical purposes; it certaintly does not prove that they cannot also be described otherwise with as much or more accuracy. To paraphrase Heisenberg, the sorts of answers that nature provides are determined by the sorts of questions we pose of her. (p.65)

Moreover, there is a third problem for positivism. You see, science, and physics most importantly, only enlightens us regarding how nature tends to behave, or how certain events produce or tend to be produced by others. Atheist Bertrand Russell articulates:

[Physics] lays down certain fundamental equations which enable it to deal with the logical structure of events, while leaving it completely unknown what is the intrinsic character of the events that have the structure[…] All that physics gives us is certain equations giving abstract properties of their changes. But as to what it is that changes, and what it changes from and to—as to this, physics is silent.

 Now, the reader might be inclined to part ways with Russell here. “Surely” one might claim, “physics does tell us the intrinsic nature of things. Physics give us comprehensive knowledge of the physical characteristics of certain objects, and describes how it is possible for these objects to behave the way they do.” But this is only half true. No matter what explanations and descriptions that physics gives of certain characteristics of an object or event, these descriptions themselves will still only boil down to abstract mathematical equations and functions. For example, for physics to describe the behavior of object (x), physics will posit the description that A events follow B events, of which object (x) is a part of. But, A events and B events will also only be subject to further descriptions of certain other objects following certain other sequential events.  So, no matter how many layers of physics one traverses to explain a certain object or event, one will invariably run into nothing but abstract behavioral descriptions dancing to the tune of mathematics—and this, again, only gives structure, and does not enlighten us regarding any sort of intrinsic nature that these objects or events have themselves. I’ll pass the baton once more to Feser:

By the very fact that physics tells us that an abstract structure of such-and-such a mathematically describable character exists, then, physics implies that there is more to reality than structure itself, and thus more to reality than what physics can reveal. (p.18)

These three problems (there are others) articulated above suffice to show that positivism is, quite frankly, vacuous. Nowhere have we uncovered any cogent reason to believe that metaphysical descriptions are superfluous, nor have we seen any reason to believe that science gives an exhaustive description of reality. On the contrary, we’ve seen that metaphysical explanations and concepts are completely necessary, and are required, even in light of, and because of, science. Metaphysics, then, is here to stay. Thus stated, we shouldn’t be worried about utilizing metaphysical inquiry, but rather we should be worried about utilizing it fallaciously, and I think the positivist position is a good example of how this can be done.

 

Thom Stark on faith

Christian Thom Stark--upon answering atheist John Loftus a few years back regarding a review of his great book The Human Faces of God--perfectly articulated what faith is, in a very profound and intriguing manner:


To me, if a Christian is certain that God exists and that everything Christianity teaches (whatever brand of Christianity they think is truest) accurately describes metaphysical and physical reality, then they don’t have faith. To think that you can “know” that these things are true is by my definition of faith precisely to reject faith. What faith is by my definition is action based on hope, and hope is a direct response to profound uncertainty. Let’s put it this way. Loftus and I both agree on what resources we should utilize to figure out what the moral thing to do is in a given situation. But for me (and maybe Loftus doesn’t have this problem, and if not, more power to him), what I’m not sure about is whether being moral is itself morally significant. I see people suffering, I want to try and alleviate their suffering, but I struggle with the question of whether my doing so has any point, beyond the obvious one of the immediate alleviation of their suffering. Why is the alleviation of human suffering the right thing to do? If the universe is a cosmic accident (and it may very well be just that), I can’t figure out why human beings should have impetus to behave morally, other than when it helps us to preserve ourselves or our species or to make us happier in some way. When morality conflicts with self-preservation or self-gratification, I just don’t know why morality should win out.


I really don’t know. This isn’t a hypothetical or an argument for the existence of God from the undesirability of a morally absurd universe. The universe may well be completely amoral. I’m afraid it might be. And because I’m human, that troubles me. (I doubt it troubles raccoons.) That doesn’t mean I believe because I’m emotionally weak. Anyone who’s read my book will know, so it’s really no surprise, that I don’t by a longshot believe everything Christianity says is true. But the question is, when I am faced with human suffering, and I set out to alleviate that suffering, is there a point to it? Does it matter, not just in that moment, but in the long run? Does it ultimately matter whether human beings continue to exist or not? I don’t believe that it does. I don’t believe that it doesn’t. I really don’t know whether it does or not. But here’s the point: I earnestly hope that it matters; and when I act on that hope, that is, when I act as if human suffering matters, I am acting in faith. That to me is what faith is. It is action based on hope, which in turn is a direct response to profound uncertainty. If I weren’t profoundly uncertain, I couldn’t hope that our existence has a profound meaning; and if I didn’t have that hope, then I couldn’t have faith (which is action, not assent to metaphysical propositions).


So, I have faith because I really don’t know if any of this has any meaning. But I act like it does, because I hope that it does. I can’t be “wrong” (about this) because I haven’t made a claim one way or the other. And this isn’t Pascal’s Wager. Another thing I really don’t know about: I don’t know if there is a God that sends unbelievers to hell, but I hope that there isn’t. Not because I don’t want to go to hell, but because it would really suck if God turned out to be less just than most humans. I’m not talking about Pascal’s Wager. I’m simply saying that my uncertainty about the meaning of our existence goes so deep that any time I try to do what is right for right’s sake is an act of faith on my part. Maybe others (maybe Loftus) aren’t as profoundly uncertain as I am. Like I said, that’s great for them.


If somebody could show me beyond doubt that the universe is a cosmic accident and everything is ultimately meaningless, then I’ll accept that and find some way to go on, but it’ll be a different way, most likely. I’m not talking about needing a reason to live by rules. I’m not saying that if the cosmos has no meaning then I’d rather blow off my family and party till I’m dead. I’m not talking about that kind of morality. I’m talking about the very core of human endeavor itself.


It may well be that there is no meaning and that we can only create meaning for ourselves. But if that’s the case, then the best I can do is try to create the best meaning, and that’s what I’m already doing. I’m trying to find out what’s good and true and to pursue that. And I think that when it comes to such truths, the processes of “discovery” and the processes of “creativity” are virtually the same processes. All human beings can do is create their own meaning, and hope they got it right. The Bible is the product of such efforts, as are all cultural artifacts. To create meaning and believe in it is, I am convinced, what it means to be human. It’s when we refuse to acknowledge that our creativity is a response to profound uncertainty that it loses its human quality—that’s when we’re trying to be more than what we are, or rather, other than what we are. To be human is to have faith—to act on our hopes which arise consciously in response to our own ignorance and uncertainty.

The metaphors of theology

Christianity (like other religions) is founded upon centuries of theological doctrine—e.g., the Trinity, the atonement, the virgin birth etc. And many of these doctrines that have been passed down are seen, especially by fundamentalists, to be unquestionable and infallible. Fair enough. But, the question can be posed regarding whether or not some (or many) of these doctrines are necessary, useful, and, more importantly for this specific post, univocal. That is to say, my point in this post is to ask “Can the meaning of these doctrines be pinned down unambiguously?”

Take the doctrine that I so vehemently oppose, namely, the inerrancy of scripture. Christians who adhere to inerrancy believe that God, in some sense, was behind the authorship of scripture and rendered the nature of scripture error-free. Ok, but if you ask an inerrantist exactly in what sense God “authored” scripture you run into problems. Did God himself take up a pen and a paper and write out the Bible? Of course not. But then how did it happen? Did God supersede the consciousness of the writer of scripture and control his mind? Some inerrantists will say yes, and some no. But, therein lies the ambiguity in the doctrine. How can we even promulgate this doctrine with certainty if the means by which it was carried out are extremely obscure?

This example can be multiplied over and over again: Was Jesus literally God, or only metaphorically God? And does Jesus have to be seen as God himself in order to be our Lord? Was the story of the fall really meant to be predicated of an original pair of humans, or is it simply a story that illuminates that humanity as a whole has “fallen”? Is Hell an everlasting torture chamber of fire, or is the language predicated of Hell mostly metaphorical, and Hell is a different place altogether? Etc.

My point regarding these examples is not that people disagree about doctrines, though this is an important periphery here. The point is that the language and concepts usually utilized about these doctrines is ambiguous and obscure. These doctrines are wrapped in so much metaphor, analogy, and mere approximations that it seems difficult to state some of them literally. The question of what exactly we mean when we promulgate a doctrine can always be posed, and clear answers are not always forthcoming. But, if this is the case, then can we really say that some doctrines are unquestionable and infallible? If there is so much semantic wiggle room with regards to a certain doctrine, then I don’t see how questioning or offering radical interpretations of said doctrine can constitute heresy.

Let it also be remembered that the doctrines that we have inherited from the Christian tradition were originally expounded by fellow humans; humans who share the same semantic and cognitive limitations as us. And those doctrines were based on those individual’s own subjective interpretations of scripture—interpretations that we still disagree on today. So, even though most of our doctrines have had a long line of tradition to back them up, this does little to help our confidence in their univocality.

All that being said, I do not mean to insinuate that Christian doctrine is useless and void. Far from it. It is through Christianity that I believe we come into the closest contact with God and Jesus, and I don’t believe that the metaphorical nature of doctrine negates this. What it should do, however, is make us more sensitive to the differences that our doctrinal interpretations produce. We shouldn’t be quick to put our own Christian denomination on a pedestal and proclaim that the other denominations” have it wrong”. We should realize that different interpreters necessitate different interpretations, and that we can still be fellow servants of God while harboring these differences.

Semantics and the mind

Last week I posted an article devoted to articulating the famous Argument from Reason (AfR). This argument attempts (and succeeds, in my opinion) to demonstrate that if naturalism were true, then there would be no such thing as reason. The AfR goes about demonstrating this by first highlighting the nature of reasoning. Reasoning, according to David Bentley Hart, is “to proceed from one premise or proposition or concept to another, in order ideally to arrive at some conclusion, and in a coherent sequence whose connections are determined by the semantic content of each of the steps taken”. The AfR then contrasts this account of reasoning with “reasoning” on a naturalistic worldview. See, for the naturalist all that exists are material processes governed by the laws of physics. But, this means that the cause of “reasoning,” on naturalism, is not semantics and meaning, but only electrochemical properties in the brain—there’s more subtlety to the argument than this, this is simply a quick summarization. Thus, it is argued, there would be no such thing as reason on a naturalistic worldview.

After articulating this argument on the aforementioned post, a frequent and attentive commenter named Ray posted some of his objections in the comment section. One of these objections I found to be quite substantive, and thus I felt the need to write a post addressing it.

His objection was that the AfR makes a hidden assumption that needs to be supported. The AfR contrasts semantics and meaning (the basis of reasoning) with purely material processes, and it claims that the former constitutes reasoning and the latter does not. However, the naturalist believes that semantics and meaning themselves are also the result of purely material processes, and therefore the proponent of AfR is creating a false dichotomy. He makes it seem as if the naturalist must choose between a rational cause—grounded in meaning and semantics—or a non-rational one—both choices leading to a rejection of naturalism. However, if meaning and semantics are themselves the result of material processes then there is no such choice for the naturalist—that is, there is no choice between a process grounded in non-material causes and material causes, since on naturalism all causes are ultimately material in nature. Thus stated, the proponent of AfR needs to demonstrate that semantics and meaning are not reducible to material causes before the AfR can be valid.

I do believe that this is a good and valid objection to the AfR. So let us see if semantics can indeed be reduced to the material. Let’s begin with an example. Take the symbol “2”. What does it stand for? Well, it stands for the concept of “two”, derived from set theory to represent the set containing two elements (II). But, it’s important to point out that the symbol “2” does not contain this meaning intrinsically. If that were true, then the symbol “2” would necessarily have to have represented the concept “two”. But the symbol “2” is completely arbitrary. In fact, it’s quite possible that we humans could have designated “2” to represent the number “five” instead, or it could have represented the concept of “love,” as opposed to a heart, if we so chose to embed it with that meaning.

Another way to demonstrate this is by imagining a primitive tribe that actually does take the symbol “2” to mean “love”. Now, if this were a true state of affairs then we could ask the question, “What does ‘2’ mean?” And the answer would be that it depends. To us it means “two” and to the tribe it means “love”. All this means that the symbol “2” by itself is intrinsically nothing but a meaningless squiggle. Its meaning is only grounded in minds who impart meaning to it. And what’s crucial here is that we can say the same regarding any symbol.

Hence, symbols can only exhibit derived meaning, and thus their semantic value is of a secondary, and borrowed order. But, symbols are the only type of meaning that we’ve seen material things exhibit, and therefore our conclusions regarding the secondary semantic nature of symbols applies to the physical as well. Thus stated, we arrive at the following conclusions regarding the physical. First, the physical and material can only gain meaning from a mind. (This of course demonstrates that naturalism cannot account for the semantic content of the mental, because meaning already presupposes the mental, and it cannot therefore account for it without arguing in a circle.) Second, meaning is not intrinsic to the physical, but is only derived, or borrowed.

I maintain that all this suffices to show that the skeptic’s challenge has been met. It has been demonstrated that semantics and meaning cannot be reduced to the material. Therefore, since semantics cannot be reduced to the material, then the contrast between rational and non-rational causes that the AfR promulgates is valid. Thus stated, the AfR stands and refutes naturalism.

Moreover, even if the above demonstrations didn’t lend validation to the AfR, they would still land a fatal blow to any naturalist theory of mind. For, to reiterate, if the phenomena of the mental cannot be reduced to the material, then naturalism is in jeopardy. And I maintain that we have done just such a thing by demonstrating that semantics cannot be found in the material, but must be predicated of the mental alone. 

The argument from reason

Let us examine the following familiar syllogism: 1) All men are mortal, 2) Socrates is a man, 3) Therefore, Socrates is mortal. This syllogism is logically sound, and it can be reasonably seen why the conclusion follows from the premises. But, how exactly is it the case that we reasonably deduce the conclusion? Well, it’s the case because we understand the semantics behind every proposition in the syllogism. That is, we clearly comprehend what 1) and 2) mean, and we logically deduce the third proposition (the conclusion) based on the meaning of the preceding premises. This is the process of reasoning, namely, making deductions based on the semantic content of previous concepts, propositions or ideas. Thus stated, our deduction from 1) and 2) to 3) is based on meaning, semantics, and reason.

Now what is going on psychologically when we make our way, logically, through this line of reasoning? Well, we have a brain state and a mental state associated with upholding premise 1), and the same with regards to 2) and 3). The brain state is just what is happening electrochemically in my brain when I uphold a certain proposition or thought, and the mental state is the associated with the actual mental apprehension of said proposition or thought. (Note: even if one is an eliminative materialist and therefore doesn’t believe mental states exist, the distinction between brain and mental states is not crucial to my present argument, and would actually make the force of the argument stronger.) It should be obvious that brain states and mental states are different with regards to the different propositions we are upholding. That is to say, the brain state and mental state we have for 1), will be different from the brain and mental state we have for 2), and 3).

However, one immediately encounters a problem with the above promulgations if one is a naturalist. Why? Well, remember that a naturalist believes that all that exists is mindless matter, or energy, governed by the laws of physics. A corollary of this is that any thoughts (and, therefore, any mental states) are ultimately the result of physical processes swinging to the tune of physics. But, this means that the mental states associated with upholding 1), 2) and 3) are ultimately grounded in, and caused by, the electrochemical properties of brain states.  A consequence of this is that when the brain state associated with 3) succeeds 2), which succeeds 1), this succession was the result of only physical laws acting on the matter that makes up these brain states.

But, this completely conflicts with what we expounded above, namely, that is it the meaning and semantics associated with our syllogism that causes us to arrive at such a deduction. On the naturalistic account of the world, when one makes their way down the syllogism, it is not the meaning or semantics that leads one there, but, rather, purely  mindless electrochemical processes. But this means that, on naturalism, it is not reason-- making deductions based on the semantic content of previous concepts, propositions or ideas—that grounds our thinking. In fact, based on what we’ve discovered, there is no room for such a thing as reason on naturalism!

The naturalist position, then, results in a reductio ad absurdum. That is, if naturalism were true, then we could not reason, which means we could not arrive at the conclusion of naturalism, since to do so would require reasoning deductively. Naturalism, therefore, cannot possibly be true.

Meeting the Mormons

A few weeks ago I had two young Mormon boys ride up to my house—you know the picture—prepared to tell me the good news that Joseph Smith had to offer me. I’m actually quite ignorant when it comes to Mormon theology, so I felt it might be interesting to invite them in and see what they had to say. They were very friendly and inviting, and seemed to be genuine “god-fearing” individuals. We proceeded to sit down, whereby the elder began the discussion with a prayer.

After the prayer they began by asking what I knew of Mormonism, and though I knew a little, I asked them to enlighten me as best they could. The novice (unfortunately, I don’t remember his name) decided to demonstrate why and where the Mormon church came from, and began by speaking of the early Christian church. He basically stated that after the apostles were martyred, there was no longer any authoritative appointed leadership in the church. This immediately struck me as blatantly false, since he was only begging the question regarding in what fashion church leadership is constituted as authoritative or divinely appointed. (Also, I’m not sure the Catholic Church would have agreed with such a statement.) Nevertheless, I stayed silent and respectfully listened to this young gentleman—I call him young as if I’m old, heck, I’m only twenty three—finish his point. He continued by claiming that this loss of leadership in the church is what led to the current Christian denominational branching that has taken place lo these past two-thousand years.

The novice continued by telling the story of Joseph Smith. Smith apparently prayed to God and asked him which church was the One True Church. God replied that none of them were, and subsequently arranged it so that Smith could translate some ancient golden tablets—which said that Jesus apparently found it necessary to float over to the Americas and evangelize to the Native Americans--and found Mormonism— which would now be the One True Church. Such is the happy ending of the Church of Latter Day Saints.

After the novice finished with his elucidation, I had several thoughts floating in my head. I knew I could attack the historical credibility of such a story, though I know the Mormons have several “explanations” for the complete lack of historical evidence of said story. But, I decided to take a much more subtle approach. I conceded the fact that Christianity has thousands of denominations, and that this manifests problems regarding whether or not there exists a “One True Church” (I bet it’s my church!). Then I asked them a question of my own, based on pure curiosity: “Does the Church of Latter Day Saints have any denominational splits?” The novice answered (apparently the elders don’t speak as much) that there have been a few splits in the church, but that the church recognizes these as apostates. Well well well, I think my point was made right there. His central argument against the complete validity of Christianity, and for the validity of Mormonism, was that Christianity has too many denominations, and this obviously blurs the lines between what constitutes orthodoxy and heresy. But, here was Mormonism with the same problems. I mean think about it, Christianity has been around for two-thousand years, and Mormonism has only been around for a few centuries. Give them a few more hundred years and you’ll see the same thing happen, namely, dozens and dozens of Mormon denominations.

After making this point I asked them how the unique truth of Mormonism can be validated by the disparity of Christianity churches, when Mormonism is already showing signs of the same. They quickly changed their tune, by then claiming that their leaders are divinely appointed. Well, if you say so! They seemed oblivious to the fact that the same argument could be promulgated by the Catholics regarding the Pope. I asked how I could know that their leaders are divinely inspired, as opposed to, say, my own pastor. They answered that the preaching of their leaders registers with their spirit and that’s how they know. Well…alright. I’m sure the reader can predict what my response was. The discussion ended with them handing me a Book of Mormon (yay!) and suggesting a few passages to read. “Just read it, pray, and let the Spirit lead you” they said, to which I replied “you got it!”

Needless to say, the discussion went just as I had expected. There were objective claims made in order to validate Mormonism, but when these claims were shown to be empty, they resorted to the old “let God lead you there” line. And obviously God has not done so. (Although The Mormon Agnostic might have a better ring to it!)

 

Brute facts and naturalism

Many naturalists are naturalists for the very reason that they believe that talk of God or the supernatural is superfluous. That is, it is seen by them to be unnecessary to posit anything ontologically “outside” the universe. To ask for more and more explanations on top of the material universe is to upset the principle of parsimony. “Why can’t the universe simply be, with no rhyme or reason?” the naturalist wonders.

The nature of this position is that the naturalist is basically calling the universe a brute fact. A brute fact is simply something that admits of no explanation. To ask the “why” question of a brute fact is to receive the answer “it just is that way, for no reason”. Now, this is obviously not a satisfying answer, but whether or not a position is satisfying says nothing regarding its validity. So, the question should be posed regarding whether or not admission of a brute fact is logically valid. My position: it is not.

To illuminate my position, let us take us detour aimed at an explanation of, well, explanation. To ask for an explanation of something is to ask for a reason whereby that thing becomes intelligible. Let me utilize an example from mathematics to illustrate my point. (Warning: nerdy math terms ahead.) In Calculus there is a concept known as a derivative. A derivative basically tells you the rate of change at the exact moment of a function, it’s also known as the instantaneous rate of change. Now, in order to understand instantaneous rate of change, one first needs to understand the average rate of change, because instantaneous rate of change is just the limit, at a specific point, of the average rate of change. But, in order to comprehend the average rate of change, one first needs to understand rate of change itself, also known as slope (remember slope from algebra?). (Ok, the mathematical nerdage is over, go take a walk, or something, and come back.) All this is to say that the concept of a derivative is explained by average rate of change, which is explained by slope. This means that a derivative is made intelligible by average rate of change, which is made intelligible by slope.

This leads us to the conclusion that explanation is somewhat of a transitive relation. That is, if A explains B, and B explains C, then A in turn explains C. This means that the explanation of C is ultimately dependent on A. To return to our math example, this means that the concept of a derivative is ultimately dependent on the concept of slope. This is all to say that explanation, and intelligibility, is imparted by higher members of an explanatory series to the lower members. A imparts explanation and intelligibility to B, and B imparts it to C. So notice that if A does not impart explanation to B, then B has no explanation to impart to C. Taking derivatives into account, if slope is unintelligible, then it has no explanation to give to derivatives, and derivatives would likewise be unintelligible.

So, how does this all affect the position of admitting of brute facts? Well, it means, quite frankly, that brute facts are impossible. Remember that a brute fact admits of no explanation; that is, there is no reason whereby its existence becomes intelligible. But, this means that it has no explanation to give, or impart, which means that it cannot be a participant in an explanatory chain, and certainly cannot be the first member in an explanatory chain. Yet this is exactly what the naturalist wants, namely, explanation to terminate in the brute fact of the existence of the universe. But we’ve seen that this is exactly what cannot be done. That is to say, explanation cannot terminate in the universe, as a brute fact.

Moreover, we can demonstrate this in another facet. If explanation is imparted in an explanatory chain, then we can formulate the following proposition: If (x) is intelligible, then the explanatory chain leading down to (x) contains no brute facts. Why can we say this? Because if (x) is intelligible, then it has a reason whereby it is rendered intelligible—otherwise it is unintelligible. And since explanation and intelligibility are imparted, we can say that for (x) to be intelligible, every member in the explanatory chain leading down to (x) must also be intelligible—again, otherwise intelligibility is not imparted at some point in the chain—and therefore every member is not a brute fact.

So, remember that explanation, for the naturalist, terminates in the universe. That is, all explanations end up leading to the existence of the universe, which admits of no explanation and is a brute fact. But this would mean, per the contrapositive of our above proposition, that if the universe were a brute fact, then any explanation that ultimately ends in the universe—you know, everything contained in the universe, e.g., matter, energy, stars, planets etc.—would be unintelligible. However, these things inside the universe are intelligible, and since they are intelligible, we can assuredly say that the universe is not a brute fact.