Mind of God

Reconciling Theism and Atheism

In his Dialogues Concerning Natural Religion, David Hume presents Philo as arguing that the disagreement between theists and atheists is merely verbal:

All men of sound reason are disgusted with verbal disputes, which abound so much in philosophical and theological inquiries; and it is found, that the only remedy for this abuse must arise from clear definitions, from the precision of those ideas which enter into any argument, and from the strict and uniform use of those terms which are employed. But there is a species of controversy, which, from the very nature of language and of human ideas, is involved in perpetual ambiguity, and can never, by any precaution or any definitions, be able to reach a reasonable certainty or precision. These are the controversies concerning the degrees of any quality or circumstance. Men may argue to all eternity, whether HANNIBAL be a great, or a very great, or a superlatively great man, what degree of beauty CLEOPATRA possessed, what epithet of praise LIVY or THUCYDIDES is entitled to, without bringing the controversy to any determination. The disputants may here agree in their sense, and differ in the terms, or vice versa; yet never be able to define their terms, so as to enter into each other’s meaning: Because the degrees of these qualities are not, like quantity or number, susceptible of any exact mensuration, which may be the standard in the controversy. That the dispute concerning Theism is of this nature, and consequently is merely verbal, or perhaps, if possible, still more incurably ambiguous, will appear upon the slightest inquiry. I ask the Theist, if he does not allow, that there is a great and immeasurable, because incomprehensible difference between the human and the divine mind: The more pious he is, the more readily will he assent to the affirmative, and the more will he be disposed to magnify the difference: He will even assert, that the difference is of a nature which cannot be too much magnified. I next turn to the Atheist, who, I assert, is only nominally so, and can never possibly be in earnest; and I ask him, whether, from the coherence and apparent sympathy in all the parts of this world, there be not a certain degree of analogy among all the operations of Nature, in every situation and in every age; whether the rotting of a turnip, the generation of an animal, and the structure of human thought, be not energies that probably bear some remote analogy to each other: It is impossible he can deny it: He will readily acknowledge it. Having obtained this concession, I push him still further in his retreat; and I ask him, if it be not probable, that the principle which first arranged, and still maintains order in this universe, bears not also some remote inconceivable analogy to the other operations of nature, and, among the rest, to the economy of human mind and thought. However reluctant, he must give his assent. Where then, cry I to both these antagonists, is the subject of your dispute? The Theist allows, that the original intelligence is very different from human reason: The Atheist allows, that the original principle of order bears some remote analogy to it. Will you quarrel, Gentlemen, about the degrees, and enter into a controversy, which admits not of any precise meaning, nor consequently of any determination? If you should be so obstinate, I should not be surprised to find you insensibly change sides; while the Theist, on the one hand, exaggerates the dissimilarity between the Supreme Being, and frail, imperfect, variable, fleeting, and mortal creatures; and the Atheist, on the other, magnifies the analogy among all the operations of Nature, in every period, every situation, and every position. Consider then, where the real point of controversy lies; and if you cannot lay aside your disputes, endeavour, at least, to cure yourselves of your animosity.

To what extent Hume actually agrees with this argument is not clear, and whether or not a dispute is verbal or real is itself like Hume’s questions about greatness or beauty, that is, it is a matter of degree. Few disagreements are entirely verbal. In any case, I largely agree with the claim that there is little real disagreement here. In response to a question on the about page of this blog, I referred to some remarks about God by Roderick Long:

Since my blog has wandered into theological territory lately, I thought it might be worth saying something about the existence of God.

When I’m asked whether I believe in God, I usually don’t know what to say – not because I’m unsure of my view, but because I’m unsure how to describe my view. But here’s a try.

I think the disagreement between theism and atheism is in a certain sense illusory – that when one tries to sort out precisely what theists are committed to and precisely what atheists are committed to, the two positions come to essentially the same thing, and their respective proponents have been fighting over two sides of the same shield.

Let’s start with the atheist. Is there any sense in which even the atheist is committed to recognising the existence of some sort of supreme, eternal, non-material reality that transcends and underlies everything else? Yes, there is: namely, the logical structure of reality itself.

Thus so long as the theist means no more than this by “God,” the theist and the atheist don’t really disagree.

Now the theist may think that by God she means something more than this. But likewise, before people knew that whales were mammals they thought that by “whale” they meant a kind of fish. What is the theist actually committed to meaning?

Well, suppose that God is not the logical structure of the universe. Then we may ask: in what relation does God stand to that structure, if not identity? There would seem to be two possibilities.

One is that God stands outside that structure, as its creator. But this “possibility” is unintelligible. Logic is a necessary condition of significant discourse; thus one cannot meaningfully speak of a being unconstrained by logic, or a time when logic’s constraints were not yet in place.

The other is that God stands within that structure, along with everything else. But this option, as Wittgenstein observed, would downgrade God to the status of being merely one object among others, one more fragment of contingency – and he would no longer be the greatest of all beings, since there would be something greater: the logical structure itself. (This may be part of what Plato meant in describing the Form of the Good as “beyond being.”)

The only viable option for the theist, then, is to identify God with the logical structure of reality. (Call this “theological logicism.”) But in that case the disagreement between the theist and the atheist dissolves.

It may be objected that the “reconciliation” I offer really favours the atheist over the theist. After all, what theist could be satisfied with a deity who is merely the logical structure of the universe? Yet in fact there is a venerable tradition of theists who proclaim precisely this. Thomas Aquinas, for example, proposed to solve the age-old questions “could God violate the laws of logic?” and “could God command something immoral?” by identifying God with Being and Goodness personified. Thus God is constrained by the laws of logic and morality, not because he is subject to them as to a higher power, but because they express his own nature, and he could not violate or alter them without ceasing to be God. Aquinas’ solution is, essentially, theological logicism; yet few would accuse Aquinas of having a watered-down or crypto-atheistic conception of deity. Why, then, shouldn’t theological logicism be acceptable to the theist?

A further objection may be raised: Aquinas of course did not stop at the identification of God with Being and Goodness, but went on to attribute to God various attributes not obviously compatible with this identification, such as personality and will. But if the logical structure of reality has personality and will, it will not be acceptable to the atheist; and if it does not have personality and will, then it will not be acceptable to the theist. So doesn’t my reconciliation collapse?

I don’t think so. After all, Aquinas always took care to insist that in attributing these qualities to God we are speaking analogically. God does not literally possess personality and will, at least if by those attributes we mean the same attributes that we humans possess; rather he possesses attributes analogous to ours. The atheist too can grant that the logical structure of reality possesses properties analogous to personality and will. It is only at the literal ascription of those attributes that the atheist must balk. No conflict here.

Yet doesn’t God, as understood by theists, have to create and sustain the universe? Perhaps so. But atheists too can grant that the existence of the universe depends on its logical structure and couldn’t exist for so much as an instant without it. So where’s the disagreement?

But doesn’t God have to be worthy of worship? Sure. But atheists, while they cannot conceive of worshipping a person, are generally much more open to the idea of worshipping a principle. Again theological logicism allows us to transcend the opposition between theists and atheists.

But what about prayer? Is the logical structure of reality something one could sensibly pray to? If so, it might seem, victory goes to the theist; and if not, to the atheist. Yet it depends what counts as prayer. Obviously it makes no sense to petition the logical structure of reality for favours; but this is not the only conception of prayer extant. In Science and Health, for example, theologian M. B. Eddy describes the activity of praying not as petitioning a principle but as applying a principle:

“Who would stand before a blackboard, and pray the principle of mathematics to solve the problem? The rule is already established, and it is our task to work out the solution. Shall we ask the divine Principle of all goodness to do His own work? His work is done, and we have only to avail ourselves of God’s rule in order to receive His blessing, which enables us to work out our own salvation.”

Is this a watered-down or “naturalistic” conception of prayer? It need hardly be so; as the founder of Christian Science, Eddy could scarcely be accused of underestimating the power of prayer! And similar conceptions of prayer are found in many eastern religions. Once again, theological logicism’s theistic credentials are as impeccable as its atheistic credentials.

Another possible objection is that whether identifying God with the logical structure of reality favours the atheist or the theist depends on how metaphysically robust a conception of “logical structure” one appeals to. If one thinks of reality’s logical structure in realist terms, as an independent reality in its own right, then the identification favours the theist; but if one instead thinks, in nominalist terms, that there’s nothing to logical structure over and above what it structures, then the identification favours the atheist.

This argument assumes, however, that the distinction between realism and nominalism is a coherent one. I’ve argued elsewhere (see here and here) that it isn’t; conceptual realism pictures logical structure as something imposed by the world on an inherently structureless mind (and so involves the incoherent notion of a structureless mind), while nominalism pictures logical structure as something imposed by the mind on an inherently structureless world (and so involves the equally incoherent notion of a structureless world). If the realism/antirealism dichotomy represents a false opposition, then the theist/atheist dichotomy does so as well. The difference between the two positions will then be only, as Wittgenstein says in another context, “one of battle cry.”

Long is trying too hard, perhaps. As I stated above, few disagreements are entirely verbal, so it would be strange to find no disagreement at all, and we could question some points here. Are atheists really open to worshiping a principle? Respecting, perhaps, but worshiping? A defender of Long, however, might say that “respect” and “worship” do not necessarily have any relevant difference here, and this is itself a merely verbal difference signifying a cultural difference. The theist uses “worship” to indicate that they belong to a religious culture, while the atheist uses “respect” to indicate that they do not. But it would not be easy to find a distinct difference in the actual meaning of the terms.

In any case, there is no need to prove that there is no difference at all, since without a doubt individual theists will disagree on various matters with individual atheists. The point made by both David Hume and Roderick Long stands at least in a general way: there is far less difference between the positions than people typically assume.

In an earlier post I discussed, among other things, whether the first cause should be called a “mind” or not, discussing St. Thomas’s position that it should be, and Plotinus’s position that it should not be. Along the lines of the argument in this post, perhaps this is really an argument about whether or not you should use a certain analogy, and the correct answer may be that it depends on your purposes.

But what if your purpose is simply to understand reality? Even if it is, it is often the case that you can understand various aspects of reality with various analogies, so this will not necessarily provide you with a definite answer. Still, someone might argue that you should not use a mental analogy with regard to the first cause because it will lead people astray. Thus, in a similar way, Richard Dawkins argued that one should not call the first cause “God” because it would mislead people:

Yes, I said, but it must have been simple and therefore, whatever else we call it, God is not an appropriate name (unless we very explicitly divest it of all the baggage that the word ‘God’ carries in the minds of most religious believers). The first cause that we seek must have been the simple basis for a self-bootstrapping crane which eventually raised the world as we know it into its present complex existence.

I will argue shortly that Dawkins was roughly speaking right about the way that the first cause works, although as I said in that earlier post, he did not have a strong argument for it other than his aesthetic sense and the kinds of explanation that he prefers. In any case, his concern with the name “God” is the “baggage” that it “carries in the minds of most religious believers.” That is, if we say, “There is a first cause, therefore God exists,” believers will assume that their concrete beliefs about God are correct.

In a similar way, someone could reasonably argue that speaking of God as a “mind” would tend to lead people into error by leading them to suppose that God would do the kinds of the things that other minds, namely human ones, do. And this definitely happens. Thus for example, in his book Who Designed the Designer?, Michael Augros argues for the existence of God as a mind, and near the end of the book speculates about divine revelation:

I once heard of a certain philosopher who, on his deathbed, when asked whether he would become a Christian, admitted his belief in Aristotle’s “prime mover”, but not in Jesus Christ as the Son of God. This sort of acknowledgment of the prime mover, of some sort of god, still leaves most of our chief concerns unaddressed. Will X ever see her son again, now that the poor boy has died of cancer at age six? Will miserable and contrite Y ever be forgiven, somehow reconciled to the universe and made whole, after having killed a family while driving drunk? Will Z ever be brought to justice, having lived out his whole life laughing at the law while another person rotted in jail for the atrocities he committed? That there is a prime mover does not tell us with sufficient clarity. Even the existence of an all-powerful, all-knowing, all-good god does not enable us to fill in much detail. And so it seems reasonable to suppose that god has something more to say to us, in explicit words, and not only in the mute signs of creation. Perhaps he is waiting to talk to us, biding his time for the right moment. Perhaps he has already spoken, but we have not recognized his voice.

When we cast our eye about by the light of reason in his way, it seems there is room for faith in general, even if no particular faith can be “proved” true in precisely the same way that it can be “proved” that there is a god.

The idea is that given that God is a mind, it follows that it is fairly plausible that he would wish to speak to people. And perhaps that he would wish to establish justice through extraordinary methods, and that he might wish to raise people from the dead.

I think this is “baggage” carried over from Augros’s personal religious views. It is an anthropomorphic mistake, not merely in the sense that he does not have a good reason for such speculation, but in the sense that such a thing is demonstrably implausible. It is not that the divine motives are necessarily unknown to us, but that we can actually discover them, at least to some extent, and we will discover that they are not what he supposes.

Divine Motives

How might one know the divine motives? How does one read the mind of God?

Anything that acts at all does it what it does ultimately because of what it is. This is an obvious point, like the point that the existence of something rather than nothing could not have some reason outside of being. In a similar way, “what is” is the only possible explanation for what is done, since there is nothing else there to be an explanation. And in every action, whether or not we are speaking of the subject in explicitly mental terms or not, we can always use the analogy of desires and goals. In the linked post, I quote St. Thomas as speaking of the human will as the “rational appetite,” and the natural tendency of other things as a “natural appetite.” If we break down the term “rational appetite,” the meaning is “the tendency to do something, because of having a reason to do it.” And this fits with my discussion of human will in various places, such as in this earlier post.

But where do those reasons come from? I gave an account of this here, arguing that rational goals are a secondary effect of the mind’s attempt to understand itself. Of course human goals are complex and have many factors, but this happens because what the mind is trying to understand is complicated and multifaceted. In particular, there is a large amount of pre-existing human behavior that it needs to understand before it can attribute goals: behavior that results from life as a particular kind of animal, behavior that results from being a particular living thing, and behavior that results from having a body of such and such a sort.

In particular, human social behavior results from these things. There was some discussion of this here, when we looked at Alexander Pruss’s discussion of hypothetical rational sharks.

You might already see where this is going. God as the first cause does not have any of the properties that generate human social behavior, so we cannot expect his behavior to resemble human social behavior in any way, as for example by having any desire to speak with people. Indeed, this is the argument I am making, but let us look at the issue more carefully.

I responded to the “dark room” objection to predictive processing here and here. My response depends both the biological history of humans and animals in general, and to some extent on the history of each individual. But the response does not merely explain why people do not typically enter dark rooms and simply stay there until they die. It also explains why occasionally people do do such things, to a greater or lesser approximation, as with suicidal or extremely depressed people.

If we consider the first cause as a mind, as we are doing here, it is an abstract immaterial mind without any history, without any pre-existing behaviors, without any of the sorts of things that allow people to avoid the dark room. So while people will no doubt be offended by the analogy, and while I will try to give a more pleasant interpretation later, one could argue that God is necessarily subject to his own dark room problem: there is no reason for him to have any motives at all, except the one which is intrinsic to minds, namely the motive of understanding. And so he should not be expected to do anything with the world, except to make sure that it is intelligible, since it must be intelligible for him to understand it.

The thoughtful reader will object: on this account, why does God create the world at all? Surely doing and making nothing at all would be even better, by that standard. So God does seem to have a “dark room” problem that he does manage to avoid, namely the temptation to nothing at all. This is a reasonable objection, but I think it would lead us on a tangent, so I will not address it at this time. I will simply take it for granted that God makes something rather than nothing, and discuss what he does with the world given that fact.

In the previous post, I pointed out that David Hume takes for granted that the world has stable natural laws, and uses that to argue that an orderly world can result from applying those laws to “random” configurations over a long enough time. I said that one might accuse him of “cheating” here, but that would only be the case if he intended to maintain a strictly atheistic position which would say that there is no first cause at all, or that if there is, it does not even have a remote analogy with a mind. Thus his attempted reconciliation of theism and atheism is relevant, since it seems from this that he is aware that such a strict atheism cannot be maintained.

St. Thomas makes a similar connection between God as a mind and a stable order of things in his fifth way:

The fifth way is taken from the governance of the world. We see that things which lack intelligence, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that not fortuitously, but designedly, do they achieve their end. Now whatever lacks intelligence cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is shot to its mark by the archer. Therefore some intelligent being exists by whom all natural things are directed to their end; and this being we call God.

What are we are to make of the claim that things act “always, or nearly always, in the same way, so as to obtain the best result?” Certainly acting in the same way would be likely to lead to similar results. But why would you think it was the best result?

If we consider where we get the idea of desire and good, the answer will be clear. We don’t have an idea of good which is completely independent from “what actually tends to happen”, even though this is not quite a definition of the term either. So ultimately St. Thomas’s argument here is based on the fact that things act in similar ways and achieve similar results. The idea that it is “best” is not an additional contribution.

But now consider the alternative. Suppose that things did not act in similar ways, or that doing so did not lead to similar results. We would live in David Hume’s non-inductive world. The result is likely to be mathematically and logically impossible. If someone says, “look, the world works in a coherent way,” and then attempts to describe how it would look if it worked in an incoherent way, they will discover that the latter “possibility” cannot be described. Any description must be coherent in order to be a description, so the incoherent “option” was never a real option in the first place.

This argument might suggest that the position of Plotinus, that mind should not be attributed to God at all, is the more reasonable one. But since we are exploring the situation where we do make that attribution, let us consider the consequences.

We argued above that the sole divine motive for the world is intelligibility. This requires coherence and consistency. It also requires a tendency towards the good, for the above mentioned reasons. Having a coherent tendency at all is ultimately not something different from tending towards good.

The world described is arguably a deist world, one in which the laws of nature are consistently followed, but God does nothing else in the world. The Enlightenment deists presumably had various reasons for their position: criticism of specific religious doctrines, doubts about miracles, and an aesthetic attraction to a perfectly consistent world. But like Dawkins with his argument about God’s simplicity, they do not seem (to me at least) to have had very strong arguments. That does not prove that their position was wrong, and even their weaker arguments may have had some relationship with the truth; even an aesthetic attraction to a perfectly consistent world has some connection with intelligibility, which is the actual reason for the world to be that way.

Once again, as with the objection about creating a world at all, a careful reader might object that this argument is not conclusive. If you have a first cause at all, then it seems that you must have one or more first effects, and even if those effects are simple, they cannot be infinitely simple. And given that they are not infinitely simple, who is to set the threshold? What is to prevent one or more of those effects from being “miraculous” relative to anything else, or even from being something like a voice giving someone a divine revelation?

There is something to this argument, but as with the previous objection, I will not be giving my response here. I will simply note for the moment that it is a little bit strained to suggest that such a thing could happen without God having an explicit motive of “talking to people,” and as argued above, such a motive cannot exist in God. That said, I will go on to some other issues.

As the Heavens are Higher

Apart from my arguments, it has long been noticed in the actual world that God seems much more interested in acting consistently than in bringing about any specific results in human affairs.

Someone like Richard Dawkins, or perhaps Job, if he had taken the counsel of his wife, might respond to the situation in the following way. “God” is not an appropriate name for a first cause that acts like this. If anything is more important to God than being personal, it would be being good. But the God described here is not good at all, since he doesn’t seem to care a bit about human affairs. And he inflicts horrible suffering on people just for the sake of consistency with physical laws. Instead of calling such a cause “God,” why don’t we call it “the Evil Demon” or something like that?

There is a lot that could be said about this. Some of it I have already said elsewhere. Some of it I will perhaps say at other times. For now I will make three brief points.

First, ensuring that the world is intelligible and that it behaves consistently is no small thing. In fact it is a prerequisite for any good thing that might happen anywhere and any time. We would not even arrive at the idea of “good” things if we did not strive consistently for similar results, nor would we get the idea of “striving” if we did did not often obtain them. Thus it is not really true that God has no interest in human affairs: rather, he is concerned with the affairs of all things, including humans.

Second, along similar lines, consider what the supposed alternative would be. If God were “good” in the way you wish, his behavior would be ultimately unintelligible. This is not merely because some physical law might not be followed if there were a miracle. It would be unintelligible behavior in the strict sense, that is, in the sense that no explanation could be given for why God is doing this. The ordinary proposal would be that it is because “this is good,” but when this statement is a human judgement made according to human motives, there would need to be an explanation for why a human judgement is guiding divine behavior. “God is a mind” does not adequately explain this. And it is not clear that an ultimately unintelligible world is a good one.

Third, to extend the point about God’s concern with all things, I suggest that the answer is roughly speaking the one that Scott Alexander gives non-seriously here, except taken seriously. This answer depends on an assumption of some sort of modal realism, a topic which I was slowly approaching for some time, but which merits a far more detailed discussion, and I am not sure when I will get around to it, if ever. The reader might note however that this answer probably resolves the question about “why didn’t God do nothing at all” by claiming that this was never an option anyway.

Anticipations of Darwin

I noted here that long before Darwin, there was fairly decent evidence for some sort of theory of evolution, even evidence available from the general human experience of plant and animal life, without deep scientific study.

As said in the earlier post, Aristotle notes that Empedocles hypothesized something along the lines of natural selection:

Wherever then all the parts came about just what they would have been if they had come to be for an end, such things survived, being organized spontaneously in a fitting way; whereas those which grew otherwise perished and continue to perish, as Empedocles says his ‘man-faced ox-progeny’ did.

Since Aristotle is arguing against Empedocles, we should be cautious in assuming that the characterization of his position is entirely accurate. But as presented by Aristotle, the position is an argument against the existence of final causes: since things can be “organized spontaneously” in the way “they would have been if they had come to be for an end,” there is no reason to think they in fact came to be for an end.

This particular conclusion, namely that in such a process nothing comes to be for an end, is a mistake, based on the assumption that different kinds of causes are mutually exclusive, rather than recognizing that different kinds of causes are different ways of explaining one and the same thing. But the general idea regarding what happened historically is correct: good conditions are more capable of persisting, bad conditions less so, and thus over time good conditions tend to predominate.

Other interesting anticipations may be found in Ibn Khaldun‘s book, The Muqaddimah, published in 1377. For example we find this passage:

It should be known that we — may God guide you and us — notice that this world with all the created things in it has a certain order and solid construction. It shows nexuses between causes and things caused, combinations of some parts of creation with others, and transformations of some existent things into others, in a pattern that is both remarkable and endless. Beginning with the world of the body and sensual perception, and therein first with the world of the visible elements, (one notices) how these elements are arranged gradually and continually in an ascending order, from earth to water, (from water) to air, and (from air) to fire. Each one of the elements is prepared to be transformed into the next higher or lower one, and sometimes is transformed. The higher one is always finer than the one preceding it. Eventually, the world of the spheres is reached. They are finer than anything else. They are in layers which are inter­connected, in a shape which the senses are able to perceive only through the existence of motions. These motions provide some people with knowledge of the measurements and positions of the spheres, and also with knowledge of the existence of the essences beyond, the influence of which is noticeable in the spheres through the fact (that they have motion).

One should then look at the world of creation. It started out from the minerals and progressed, in an ingenious, gradual manner, to plants and animals. The last stage of minerals is connected with the first stage of plants, such as herbs and seedless plants. The last stage of plants, such as palms and vines, is connected with the first stage of animals, such as snails and shellfish which have only the power of touch. The word “connection” with regard to these created things means that the last stage of each group is fully prepared to become the first stage of the next group.

The animal world then widens, its species become numerous, and, in a gradual process of creation, it finally leads to man, who is able to think and to reflect. The higher stage of man is reached from the world of the monkeys, in which both sagacity and perception are found, but which has not reached the stage of actual reflection and thinking. At this point we come to the first stage of man after (the world of monkeys). This is as far as our (physical) observation extends.

It is possible that he makes his position clearer elsewhere (I have not read the entire work.) The passage here does not explicitly assert that humans arose from lower animals, but does suggest it, correctly associating human beings with monkeys in particular, even if some of his other connections are somewhat strange. In other words, both here and elsewhere, he speaks of one stage of things being “prepared to become” another stage, and says that this transition sometimes happens: “Each one of the elements is prepared to be transformed into the next higher or lower one, and sometimes is transformed.”

While Ibn Khaldun is at least suggesting that we notice a biological order that corresponds to some degree to an actual historical order, we do not see in this text any indication of what the mechanism is supposed to be. In contrast, Empedocles gives us a mechanism but no clarity regarding historical order. Admittedly, this may be an artifact of the fact that I have not read more of Ibn Khaldun and the fact that we have only fragments from Empedocles.

One of the strongest anticipations of all, although put in very general terms, can be found in David Hume’s Dialogues Concerning Natural Religion, in the following passage:

Besides, why may not motion have been propagated by impulse through all eternity, and the same stock of it, or nearly the same, be still upheld in the universe? As much is lost by the composition of motion, as much is gained by its resolution. And whatever the causes are, the fact is certain, that matter is, and always has been, in continual agitation, as far as human experience or tradition reaches. There is not probably, at present, in the whole universe, one particle of matter at absolute rest.

And this very consideration too, continued PHILO, which we have stumbled on in the course of the argument, suggests a new hypothesis of cosmogony, that is not absolutely absurd and improbable. Is there a system, an order, an economy of things, by which matter can preserve that perpetual agitation which seems essential to it, and yet maintain a constancy in the forms which it produces? There certainly is such an economy; for this is actually the case with the present world. The continual motion of matter, therefore, in less than infinite transpositions, must produce this economy or order; and by its very nature, that order, when once established, supports itself, for many ages, if not to eternity. But wherever matter is so poised, arranged, and adjusted, as to continue in perpetual motion, and yet preserve a constancy in the forms, its situation must, of necessity, have all the same appearance of art and contrivance which we observe at present. All the parts of each form must have a relation to each other, and to the whole; and the whole itself must have a relation to the other parts of the universe; to the element in which the form subsists; to the materials with which it repairs its waste and decay; and to every other form which is hostile or friendly. A defect in any of these particulars destroys the form; and the matter of which it is composed is again set loose, and is thrown into irregular motions and fermentations, till it unite itself to some other regular form. If no such form be prepared to receive it, and if there be a great quantity of this corrupted matter in the universe, the universe itself is entirely disordered; whether it be the feeble embryo of a world in its first beginnings that is thus destroyed, or the rotten carcass of one languishing in old age and infirmity. In either case, a chaos ensues; till finite, though innumerable revolutions produce at last some forms, whose parts and organs are so adjusted as to support the forms amidst a continued succession of matter.

Suppose (for we shall endeavour to vary the expression), that matter were thrown into any position, by a blind, unguided force; it is evident that this first position must, in all probability, be the most confused and most disorderly imaginable, without any resemblance to those works of human contrivance, which, along with a symmetry of parts, discover an adjustment of means to ends, and a tendency to self-preservation. If the actuating force cease after this operation, matter must remain for ever in disorder, and continue an immense chaos, without any proportion or activity. But suppose that the actuating force, whatever it be, still continues in matter, this first position will immediately give place to a second, which will likewise in all probability be as disorderly as the first, and so on through many successions of changes and revolutions. No particular order or position ever continues a moment unaltered. The original force, still remaining in activity, gives a perpetual restlessness to matter. Every possible situation is produced, and instantly destroyed. If a glimpse or dawn of order appears for a moment, it is instantly hurried away, and confounded, by that never-ceasing force which actuates every part of matter.

Thus the universe goes on for many ages in a continued succession of chaos and disorder. But is it not possible that it may settle at last, so as not to lose its motion and active force (for that we have supposed inherent in it), yet so as to preserve an uniformity of appearance, amidst the continual motion and fluctuation of its parts? This we find to be the case with the universe at present. Every individual is perpetually changing, and every part of every individual; and yet the whole remains, in appearance, the same. May we not hope for such a position, or rather be assured of it, from the eternal revolutions of unguided matter; and may not this account for all the appearing wisdom and contrivance which is in the universe? Let us contemplate the subject a little, and we shall find, that this adjustment, if attained by matter of a seeming stability in the forms, with a real and perpetual revolution or motion of parts, affords a plausible, if not a true solution of the difficulty.

It is in vain, therefore, to insist upon the uses of the parts in animals or vegetables, and their curious adjustment to each other. I would fain know, how an animal could subsist, unless its parts were so adjusted? Do we not find, that it immediately perishes whenever this adjustment ceases, and that its matter corrupting tries some new form? It happens indeed, that the parts of the world are so well adjusted, that some regular form immediately lays claim to this corrupted matter: and if it were not so, could the world subsist? Must it not dissolve as well as the animal, and pass through new positions and situations, till in great, but finite succession, it falls at last into the present or some such order?

Although extremely general, Hume is suggesting both a history and a mechanism. Hume posits conservation of motion or other similar laws of nature, presumably mathematical, and describes what will happen when you apply such laws to a world. Most situations are unstable, and precisely because they are unstable, they will not last, and other situations will come to be. But some situations are stable, and when such situations occur, they will last.

The need for conservation of motion or similar natural laws is not accidental here. This is why I included the first paragraph above, rather than beginning the quotation where Hume begins to describe his “new hypothesis of cosmogony.” Without motion, the situation could not change, so a new situation could not come to be, and the very ideas of stable and unstable situations would not make sense. Likewise, if motion existed but did not follow any law, all situations should be unstable, so no amount of change could lead to a stable situation. Thus since things always fall downwards instead of in random directions, things stabilize near a center, while merely random motion could not be expected to have this effect. Thus a critic might argue that Hume seems to be positing randomness as the origin of things, but is cheating, so to speak, by positing original stabilities like natural laws, which are not random at all. Whatever might be said of this, it is an important point, and I will be returning to it later.

Since his description is more general than a description of living things in particular, Hume does not mention anything like the theory of the common descent of living things. But there is no huge gulf here: this would simply be a particular application. In fact, some people have suggested that Hume may have had textual influence on Darwin.

While there are other anticipations (there is one in Immanuel Kant that I am not currently inclined to seek out), I will skip to Philip Gosse, who published two years before Darwin. As described in the linked post, while Gosse denies the historicity of evolution in a temporal sense, he posits that the geological evidence was deliberately constructed (by God) to be evidence of common descent.

What was Darwin’s own role, then, if all the elements of his theory were known to various people years, centuries, or even millennia in advance? If we look at this in terms of Thomas Kuhn’s account of scientific progress, it is not so much that Darwin invented new ideas, as that he brought the evidence and arguments together in such a way as to produce — extremely quickly after the publication of his work — a newly formed consensus on those ideas.

Infinity

I discussed this topic previously, but without coming to a definite conclusion. Here I will give what I think is the correct explanation.

In his book Infinity, Causation, and Paradox, Alexander Pruss argues for what he calls “causal finitism,” or the principle that nothing can be affected by infinitely many causes:

In this volume, I will present a number of paradoxes of infinity, some old like Thomson’s Lamp and some new, and offer a unified metaphysical response to all of them by means of the hypothesis of causal finitism, which roughly says that nothing can be affected by infinitely many causes. In particular, Thomson’s Lamp story is ruled out since the final state of the lamp would be affected by infinitely many switch togglings. And in addition to arguing for the hypothesis as the best unified resolution to the paradoxes I shall offer some direct arguments against infinite regresses.

Thomson’s Lamp, if the reader is not familiar with it, is the question of what happens to a lamp if you switch it on and off an infinite number of times in a finite interval, doubling your velocity after each switch. At the end of the interval, is it on or off?

I think Pruss’s account is roughly speaking correct. I say “roughly speaking” because I would be hesitant to claim that nothing can be “affected” by infinitely many causes. Rather I would say that nothing is one effect simultaneously of infinitely many causes, and this is true for the same reason that there cannot be an infinite causal regress. That is, an infinite causal regress removes the notion of cause by removing the possibility of explanation, which is an intrinsic part of the idea of a cause. Similarly, it is impossible to explain anything using an infinite number of causes, because that infinity as such cannot be comprehended, and thus cannot be used to understand the thing which is the supposed effect. And since the infinity cannot explain the thing, neither can it be the cause of the thing.

What does this imply about the sorts of questions that were raised in my previous discussion, as for example about an infinite past or an infinite future, or a spatially infinite universe?

I presented an argument there, without necessarily claiming it to be correct, that such things are impossible precisely because they seem to imply an infinite causal regress. If there an infinite number of stars in the universe, for example, there seems to be an infinite regress of material causes: the universe seems to be composed of this local portion plus the rest, with the rest composed in a similar way, ad infinitum.

Unfortunately, there is an error in this argument against a spatially infinite world, and in similar arguments against a temporally infinite world, whether past or future. This can be seen in my response to Bertrand Russell when I discuss the material causes of water. Even if it is possible to break every portion of water down into smaller portions, it does not follow that this is an infinite sequence of material causes, or that it helps to explain water. In a similar way, even if the universe can be broken down into an infinite number of pieces in the above way, it does not follow that the universe has an infinite number of material causes: rather, this breakdown fails to explain, and fails to give causes at all.

St. Thomas gives a different argument against an infinite multitude, roughly speaking that it would lack a formal cause:

This, however, is impossible; since every kind of multitude must belong to a species of multitude. Now the species of multitude are to be reckoned by the species of numbers. But no species of number is infinite; for every number is multitude measured by one. Hence it is impossible for there to be an actually infinite multitude, either absolute or accidental.

By this argument, it would be impossible for there to be “an infinite number of stars” because the collection would lack “a species of multitude.” Unfortunately there is a problem with this argument as well, namely that it presupposes that the number is inherently fixed before it is considered by human beings. In reality, counting depends on someone who counts and a method they use for counting; to talk about the “number of stars” is a choice to break down the world in that particular way. There are other ways to think of it, as for example when we use the word “universe”, we count everything at once as a unit.

According to my account here, are some sorts of infinity actually impossible? Yes, namely those which demand an infinite sequence of explanation, or which demand an infinite number of things in order to explain something. Thus for example consider this story from Pruss about shuffling an infinite deck of cards:

Suppose I have an infinitely deep deck of cards, numbered with the positive integers. Can I shuffle it?

Given an infinite past, here is a procedure: n days ago, I perfectly fairly shuffle the top n cards in the deck.

This procedure is impossible because it makes the current state of the deck the direct effect of what I did n days ago, for all n. And the effect is a paradox: it is mathematically impossible for the integers to be randomly shuffled, because any series of integers will be biased towards lower numbers. Note that the existence of an infinite past is not the problem so much as assuming that one could have carried out such a procedure during an infinite past; in reality, if there was an infinite past, its contents are equally “infinite,” that is, they do not have such a definable, definite, “finite” relationship with the present.

Counterfactuals and Causality

People have frequently noted some connection between counterfactuals and causation. While it seems backwards to suggest that causation should be defined in terms of counterfactuals, it is reasonable to connect the two concepts, and explains why some counterfactuals are more reasonable than others, as we noted in the last post.

For example, “If I dropped this cup, it would fall to the floor,” is more reasonable than “If I dropped this cup, it would fly up to the moon,” because we are considering the operation of causes like gravity which could cause falling to the floor, and which could not cause (merely by dropping) an object to fly to the moon. In particular, since causes eliminate alternatives, they give us a reason to say “this would have happened rather than that.”

Nonetheless, we cannot get any sort of absolute determination out of this. One would attempt to get a determinate outcome by specifying the counterfactual as clearly as possible: “If I dropped this cup, and everything else was the same.” The “nearest possible world” idea is trying to get at this. However, this is not in fact completely determinate because “everything else” can’t be entirely the same, and what else needs to change is not determinate. In order to drop the cup, there would need to be a course of events that led up to the dropping, and there are many different courses that could have done that. The same thing will happen if you to specify exactly what led to the dropping of the cup; there will need to be something that led to your specification. Thus, at the very least, you will not typically be able to get absolute determination in this way.

Naturally, there is nothing to prevent us from coming up particular examples where we can get complete determination by using something which is always true anyway, or by using logical implication from the counterfactual, e.g. “If I dropped this cup, 2 and 2 would still be 4,” or “If I dropped the cup, it would have been dropped.” But these are not typical cases.

Structure of Explanation

When we explain a thing, we give a cause; we assign the thing an origin that explains it.

We can go into a little more detail here. When we ask “why” something is the case, there is always an implication of possible alternatives. At the very least, the question implies, “Why is this the case rather than not being the case?” Thus “being the case” and “not being the case” are two possible alternatives.

The alternatives can be seen as possibilities in the sense explained in an earlier post. There may or may not be any actual matter involved, but again, the idea is that reality (or more specifically some part of reality) seems like something that would be open to being formed in one way or another, and we are asking why it is formed in one particular way rather than the other way. “Why is it raining?” In principle, the sky is open to being clear, or being filled with clouds and a thunderstorm, and to many other possibilities.

A successful explanation will be a complete explanation when it says “once you take the origin into account, the apparent alternatives were only apparent, and not really possible.” It will be a partial explanation when it says, “once you take the origin into account, the other alternatives were less sensible (i.e. made less sense as possibilities) than the actual thing.”

Let’s consider some examples in the form of “why” questions and answers.

Q1. Why do rocks fall? (e.g. instead of the alternatives of hovering in the air, going upwards, or anything else.)

A1. Gravity pulls things downwards, and rocks are heavier than air.

The answer gives an efficient cause, and once this cause is taken into account, it can be seen that hovering in the air or going upwards were not possibilities relative to that cause.

Obviously there is not meant to be a deep explanation here; the point here is to discuss the structure of explanation. The given answer is in fact basically Newton’s answer (although he provided more mathematical detail), while with general relativity Einstein provided a better explanation.

The explanation is incomplete in several ways. It is not a first cause; someone can now ask, “Why does gravity pull things downwards, instead of upwards or to the side?” Similarly, while it is in fact the cause of falling rocks, someone can still ask, “Why didn’t anything else prevent gravity from making the rocks fall?” This is a different question, and would require a different answer, but it seems to reopen the possibility of the rocks hovering or moving upwards, from a more general point of view. David Hume was in part appealing to the possibility of such additional questions when he said that we can see no necessary connection between cause and effect.

Q2. Why is 7 prime? (i.e. instead of the alternative of not being prime.)

A2. 7/2 = 3.5, so 7 is not divisible by 2. 7/3 = 2.333…, so 7 is not divisible by 3. In a similar way, it is not divisible by 4, 5, or 6. Thus in general it is not divisible by any number except 1 and itself, which is what it means to be prime.

If we assumed that the questioner did not know what being prime means, we could have given a purely formal response simply by noting that it is not divisible by numbers between 1 and itself, and explaining that this is what it is to be prime. As it is, the response gives a sufficient material disposition. Relative to this explanation, “not being prime,” was never a real possibility for 7 in the first place. The explanation is complete in that it completely excludes the apparent alternative.

Q3. Why did Peter go to the store? (e.g. instead of going to the park or the museum, or instead of staying home.)

A3. He went to the store in order to buy groceries.

The answer gives a final cause. In view of this cause the alternatives were merely apparent. Going to the park or the museum, or even staying home, were not possible since there were no groceries there.

As in the case of the rock, the explanation is partial in several ways. Someone can still ask, “Why did he want groceries?” And again someone can ask why he didn’t go to some other store, or why something didn’t hinder him, and so on. Such questions seem to reopen various possibilities, and thus the explanation is not an ultimately complete one.

Suppose, however, that someone brings up the possibility that instead of going to the store, he could have gone to his neighbor and offered money for groceries in his neighbor’s refrigerator. This possibility is not excluded simply by the purpose of buying groceries. Nonetheless, the possibility seems less sensible than getting them from the store, for multiple reasons. Again, the implication is that our explanation is only partial: it does not completely exclude alternatives, but it makes them less sensible.

Let’s consider a weirder question: Why is there something rather than nothing?

Now the alternatives are explicit, namely there being something, and there being nothing.

It can be seen that in one sense, as I said in the linked post, the question cannot have an answer, since there cannot be a cause or origin for “there is something” which would itself not be something. Nonetheless, if we consider the idea of possible alternatives, it is possible to see that the question does not need an answer; one of the alternatives was only an apparent alternative all along.

In other words, the sky can be open to being clear or cloudy. But there cannot be something which is open both to “there is something” and “there is nothing”, since any possibility of that kind would be “something which is open…”, which would already be something rather than nothing. The “nothing” alternative was merely apparent. Nothing was ever open to there being nothing.

Let’s consider another weird question. Suppose we throw a ball, and in the middle of the path we ask, Why is the ball in the middle of the path instead of at the end of the path?

We could respond in terms of a sufficient material disposition: it is in the middle of the path because you are asking your question at the middle, instead of waiting until the end.

Suppose the questioner responds: Look, I asked my question at the middle of the path. But that was just chance. I could have asked at any moment, including at the end. So I want to know why it was in the middle without considering when I am asking the question.

If we look at the question in this way, it can be seen in one way that no cause or origin can be given. Asked in this way, being at the end cannot be excluded, since they could have asked their question at the end. But like the question about something rather than nothing, the question does not need an answer. In this case, this is not because the alternatives were merely apparent in the sense that one was possible and the other not. But they were merely apparent in the sense that they were not alternatives. The ball goes both goes through the middle, and reaches the end. With the stipulation that we not consider the time of the question, the two possibilities are not mutually exclusive.

Additional Considerations

The above considerations about the nature of “explanation” lead to various conclusions, but also to various new questions. For example, one commenter suggested that “explanation” is merely subjective. Now as I said there, all experience is subjective experience (what would “objective experience” even mean, except that someone truly had a subjective experience?), including the experience of having an explanation. Nonetheless, the thing experienced is not subjective: the origins that we call explanations objectively exclude the apparent possibilities, or objectively make them less intelligible. The explanation of explanation here, however, provides an answer to what was perhaps the implicit question. Namely, why are we so interested in explanations in the first place, so that the experience of understanding something becomes a particularly special type of experience? Why, as Aristotle puts it, do “all men desire to know,” and why is that desire particularly satisfied by explanations?

In one sense it is sufficient simply to say that understanding is good in itself. Nonetheless, there is something particular about the structure of a human being that makes knowledge good for us, and which makes explanation a particularly desirable form of knowledge. In my employer and employee model of human psychology, I said that “the whole company is functioning well overall when the CEO’s goal of accurate prediction is regularly being achieved.” This very obviously requires knowledge, and explanation is especially beneficial because it excludes alternatives, which reduces uncertainty and therefore tends to make prediction more accurate.

However, my account also raises new questions. If explanation eliminates alternatives, what would happen if everything was explained? We could respond that “explaining everything” is not possible in the first place, but this is probably an inadequate response, because (from the linked argument) we only know that we cannot explain everything all at once, the way the person in the room cannot draw everything at once; we do not know that there is any particular thing that cannot be explained, just as there is no particular aspect of the room that cannot be drawn. So there can still be a question about what would happen if every particular thing in fact has an explanation, even if we cannot know all the explanations at once. In particular, since explanation eliminates alternatives, does the existence of explanations imply that there are not really any alternatives? This would suggest something like Leibniz’s argument that the actual world is the best possible world. It is easy to see that such an idea implies that there was only one “possibility” in the first place: Leibniz’s “best possible world” would be rather “the only possible world,” since the apparent alternatives, given that they would have been worse, were not real alternatives in the first place.

On the other hand, if we suppose that this is not the case, and there are ultimately many possibilities, does this imply the existence of “brute facts,” things that could have been otherwise, but which simply have no explanation? Or at least things that have no complete explanation?

Let the reader understand. I have already implicitly answered these questions. However, I will not link here to the implicit answers because if one finds it unclear when and where this was done, one would probably also find those answers unclear and inconclusive. Of course it is also possible that the reader does see when this was done, but still believes those responses inadequate. In any case, it is possible to provide the answers in a form which is much clearer and more conclusive, but this will likely not be a short or simple project.

Words, Meaning, and Formal Copies

There is quick way to respond to the implicit questions at the end of the last post. I noted in an earlier discussion of form that form is not only copied into the mind; it is also copied into language itself. Any time you describe something in words, you are to some degree copying its form into your description.

This implies that Aristotle’s objection that a mind using an organ would not be able to know all things could equally be made against the possibility of describing all things in words. There simply are not enough combinations of words to relate them to all possible combinations of things; thus, just as a black and white image cannot imitate every aspect of a colored scene, so words cannot possibly describe every aspect of reality.

Two things are evident from this comparison:

First, the objection fails overall. There is nothing that cannot be described in words because words are flexible. If we don’t have a word for something, then we can make up a name. Similarly, the meaning of a single word depends on context.  The word “this” can refer to pretty much anything, depending on the context in which it is used. Likewise meaning can be affected by the particular situation of the person using the word, or by broader cultural contexts, and so on.

Second, there is some truth in the objection. It is indeed impossible to describe every aspect of reality at the same time and in complete detail, and the objection gives a very good reason for this: there are simply not enough linguistic combinations to represent all possible combinations of things. The fact that language is not prime matter does mean that language cannot express every detail of reality at once: the determination that is already there does exclude this possibility. But the flexibility of language prevents there from being any particular aspect of things that cannot be described.

My claim about the mind is the same. There is nothing that cannot be understood by the mind, despite the fact that the mind uses the brain, because the relationship between the brain, mind, and world is a flexible one. Just as the word “this” can refer to pretty much anything, so also the corresponding thought. But on the other hand, the limitations of the brain do mean that a perfectly detailed knowledge of everything is excluded.

Our Interlocutor Insists

In a sense, the above account is sufficient to respond to the objection. There does not seem to be a reason to hold Aristotle’s account of the immateriality of the mind, unless there is also a reason to hold that language cannot be used to describe some things, and this does not seem like a reasonable position. Nonetheless, this response will give rise to a new and more detailed objection.

A black and white scene, it will be said, really and truly copies some aspects of a colored scene, and fails to copy others. Thus right angles in the black and white scene may be identical to right angles in the colored scene. The angles are really copied, and the angles are not. But language seems different: since it is conventional, it does not really copy anything. We just pretend, as it were, that we are copying the thing. “Let the word ‘cat’ stand for a cat,” we say, but there is nothing catlike about the word in reality. The form of the cat is not really copied into the word, or so it will be argued. And since we are not really copying anything, this is why language has the flexibility to be able to describe all things. The meaning of thoughts, however, is presumably not conventional. So it seems that we need to copy things in a real way into the mind, the way we copy aspects of a colored scene into a black and white image. And thus, meaning in the mind should not be flexible in this way, and a particular material medium (such as the brain) would still impede knowing all things, the way the black and white image excludes color.

Formal Copies

The above objection is similar to Hilary Lawson’s argument that words cannot really refer to things. In the post linked above on form and reality, we quoted his argument that cause and effect do not have anything in common. I will reproduce that argument here; for the purpose of the following discussion it might be useful to the reader to refer to the remainder of that post.

For a system of closure to provide a means of intervention in openness and thus to function as a closure machine, it requires a means of converting the flux of openness into an array of particularities. This initial layer of closure will be identified as ‘preliminary closure’. As with closure generally, preliminary closure consists in the realisation of particularity as a consequence of holding that which is different as the same. This is achieved through the realisation of material in response to openness. The most minimal example of a system of closure consists of a single preliminary closure. Such a system requires two discrete states, or at least states that can be held as if they were discrete. It is not difficult to provide mechanical examples of such systems which allow for a single preliminary closure. A mousetrap for example, can be regarded as having two discrete states: it is either set, it is ready, or it has sprung, it has gone off. Many different causes may have led to it being in one state or another: it may have been sprung by a mouse, but it could also have been knocked by someone or something, or someone could have deliberately set it off. In the context of the mechanism all of these variations are of no consequence, it is either set or it has sprung. The diversity of the immediate environment is thereby reduced to single state and its absence: it is either set or it is not set. Any mechanical arrangement that enables a system to alternate between two or more discrete states is thereby capable of providing the basis for preliminary closure. For example, a bell or a gate could function as the basis for preliminary closure. The bell can either ring or not ring, the gate can be closed or not closed. The bell may ring as the result of the wind, or a person or animal shaking it, but the cause of the response is in the context of system of no consequence. The bell either rings or it doesn’t. Similarly, the gate may be in one state or another because it has been deliberately moved, or because something or someone has dislodged it accidentally, but these variations are not relevant in the context of the state of system, which in this case is the position of the gate. In either case the cause of the bell ringing or the gate closing is infinitely varied, but in the context of the system the variety of inputs is not accessible to the system and thus of no consequence.

Lawson’s basic argument is that any particular effect could result from any of an infinite number of different causes, and the cause and effect might be entirely different: the effect might be ringing of a bell, but the cause was not bell-like at all, and did not have a ringing sound. So the effect, he says, tells you nothing at all about the cause. In a similar way, he claims, our thoughts cause our words, but our words and our thoughts have nothing in common, and thus our words tell us nothing about our thoughts; and in that sense they do not refer to anything, not even to our thoughts. Likewise, he says, the world causes our thoughts, but since the cause and effect have nothing in common, our thoughts tell us nothing about the world, and do not even refer to it.

As I responded at the time, this account is mistaken from the very first step. Cause and effect always have something in common, namely the cause-effect relationship, although they each have different ends of that relationship. They will also have other things in common depending on the particular nature of the cause and effect in question. Similarly, the causes that are supposedly utterly diverse, in Lawson’s account, have something in common themselves: every situation that rings the bell has “aptness to ring the bell” in common. And when the bell is rung, it “refers” to these situations by the implication that we are in a situation that has aptness to ring the bell, rather than in one of the other situations.

It is not accidental here that “refer” and “relate” are taken from forms of the same verb. Lawson’s claim that words do not “refer” to things is basically the same as the claim that they are not really related to things. And the real problem is that he is looking at matter (in this case the bell) without considering form (in this case the bell’s relationship with the world.)

In a similar way, to say that the word “cat” is not catlike is to look at the sound or at the text as matter, without considering its form, namely the relationship it has with the surrounding context which causes that word to be used. But that relationship is real; the fact that the word is conventional does not prevent it from being true that human experience of cats is the cause of thoughts of cats, and that thoughts of cats are concretely the cause of the usage of the word “cat,” even if they could in some other situation have caused some other word to be used.

I argued in the post on the nature of form (following the one with the discussion of Lawson) that form is a network of relationships apt to make something one. Insofar as an effect really receives form from a cause in the above way, words really receive meaning from the context that gives rise to their use. And in this way, it is not true that form in language is unlike form in a black and white scene, such that one could say that form in the scene is “real” and form in language is not. Both are real.

Thus the objection fails. Nonetheless, it is true that it is easier to see why it is possible to describe anything in words, than it is to see why anything can be known. And this happens simply because “anything is describable in words” precisely because “anything can be known.” So the fact that anything can be known is the more remote cause, and thus harder to know.

 

Tautologies Not Trivial

In mathematics and logic, one sometimes speaks of a “trivial truth” or “trivial theorem”, referring to a tautology. Thus for example in this Quora question, Daniil Kozhemiachenko gives this example:

The fact that all groups of order 2 are isomorphic to one another and commutative entails that there are no non-Abelian groups of order 2.

This statement is a tautology because “Abelian group” here just means one that is commutative: the statement is like the customary example of asserting that “all bachelors are unmarried.”

Some extend this usage of “trivial” to refer to all statements that are true in virtue of the meaning of the terms, sometimes called “analytic.” The effect of this is to say that all statements that are logically necessary are trivial truths. An example of this usage can be seen in this paper by Carin Robinson. Robinson says at the end of the summary:

Firstly, I do not ask us to abandon any of the linguistic practises discussed; merely to adopt the correct attitude towards them. For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game. And, secondly, once we pass sentence on knowing, a priori, anything but trivial truths we shall have at our disposal the sharpest of philosophical tools. A tool which can only proffer a better brand of empiricism.

While the word “trivial” does have a corresponding Latin form that means ordinary or commonplace, the English word seems to be taken mainly from the “trivium” of grammar, rhetoric, and logic. This would seem to make some sense of calling logical necessities “trivial,” in the sense that they pertain to logic. Still, even here something is missing, since Robinson wants to include the truths of mathematics as trivial, and classically these did not pertain to the aforesaid trivium.

Nonetheless, overall Robinson’s intention, and presumably that of others who speak this way, is to suggest that such things are trivial in the English sense of “unimportant.” That is, they may be important tools, but they are not important for understanding. This is clear at least in our example: Robinson calls them trivial because “there are no known/knowable facts about logic.” Logical necessities tell us nothing about reality, and therefore they provide us with no knowledge. They are true by the meaning of the words, and therefore they cannot be true by reason of facts about reality.

Things that are logically necessary are not trivial in this sense. They are important, both in a practical way and directly for understanding the world.

Consider the failure of the Mars Climate Orbiter:

On November 10, 1999, the Mars Climate Orbiter Mishap Investigation Board released a Phase I report, detailing the suspected issues encountered with the loss of the spacecraft. Previously, on September 8, 1999, Trajectory Correction Maneuver-4 was computed and then executed on September 15, 1999. It was intended to place the spacecraft at an optimal position for an orbital insertion maneuver that would bring the spacecraft around Mars at an altitude of 226 km (140 mi) on September 23, 1999. However, during the week between TCM-4 and the orbital insertion maneuver, the navigation team indicated the altitude may be much lower than intended at 150 to 170 km (93 to 106 mi). Twenty-four hours prior to orbital insertion, calculations placed the orbiter at an altitude of 110 kilometers; 80 kilometers is the minimum altitude that Mars Climate Orbiter was thought to be capable of surviving during this maneuver. Post-failure calculations showed that the spacecraft was on a trajectory that would have taken the orbiter within 57 kilometers of the surface, where the spacecraft likely skipped violently on the uppermost atmosphere and was either destroyed in the atmosphere or re-entered heliocentric space.[1]

The primary cause of this discrepancy was that one piece of ground software supplied by Lockheed Martin produced results in a United States customary unit, contrary to its Software Interface Specification (SIS), while a second system, supplied by NASA, expected those results to be in SI units, in accordance with the SIS. Specifically, software that calculated the total impulse produced by thruster firings produced results in pound-force seconds. The trajectory calculation software then used these results – expected to be in newton seconds – to update the predicted position of the spacecraft.

It is presumably an analytic truth that the units defined in one way are unequal to the units defined in the other. But it was ignoring this analytic truth that was the primary cause of the space probe’s failure. So it is evident that analytic truths can be extremely important for practical purposes.

Such truths can also be important for understanding reality. In fact, they are typically more important for understanding than other truths. The argument against this is that if something is necessary in virtue of the meaning of the words, it cannot be telling us something about reality. But this argument is wrong for one simple reason: words and meaning themselves are both elements of reality, and so they do tell us something about reality, even when the truth is fully determinate given the meaning.

If one accepts the mistaken argument, in fact, sometimes one is led even further. Logically necessary truths cannot tell us anything important for understanding reality, since they are simply facts about the meaning of words. On the other hand, anything which is not logically necessary is in some sense accidental: it might have been otherwise. But accidental things that might have been otherwise cannot help us to understand reality in any deep way: it tells us nothing deep about reality to note that there is a tree outside my window at this moment, when this merely happens to be the case, and could easily have been otherwise. Therefore, since neither logically necessary things, nor logically contingent things, can help us to understand reality in any deep or important way, such understanding must be impossible.

It is fairly rare to make such an argument explicitly, but it is a common implication of many arguments that are actually made or suggested, or it at least influences the way people feel about arguments and understanding.  For example, consider this comment on an earlier post. Timocrates suggests that (1) if you have a first cause, it would have to be a brute fact, since it doesn’t have any other cause, and (2) describing reality can’t tell us any reasons but is “simply another description of how things are.” The suggestion behind these objections is that the very idea of understanding is incoherent. As I said there in response, it is true that every true statement is in some sense “just a description of how things are,” but that was what a true statement was meant to be in any case. It surely was not meant to be a description of how things are not.

That “analytic” or “tautologous” statements can indeed provide a non-trivial understanding of reality can also easily be seen by example. Some examples from this blog:

Good and being. The convertibility of being and goodness is “analytic,” in the sense that carefully thinking about the meaning of desire and the good reveals that a universe where existence as such was bad, or even failed to be good, is logically impossible. In particular, it would require a universe where there is no tendency to exist, and this is impossible given that it is posited that something exists.

Natural selection. One of the most important elements of Darwin’s theory of evolution is the following logically necessary statement: the things that have survived are more likely to be the things that were more likely to survive, and less likely to be the things that were less likely to survive.

Limits of discursive knowledge. Knowledge that uses distinct thoughts and concepts is necessarily limited by issues relating to self-reference. It is clear that this is both logically necessary, and tells us important things about our understanding and its limits.

Knowledge and being. Kant rightly recognized a sense in which it is logically impossible to “know things as they are in themselves,” as explained in this post. But as I said elsewhere, the logically impossible assertion that knowledge demands an identity between the mode of knowing and the mode of being is the basis for virtually every sort of philosophical error. So a grasp on the opposite “tautology” is extremely useful for understanding.