Aristotle

Fire, Water, and Numbers

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Fire vs. Water

“All things are water,” says Thales.

“All things are fire,” says Heraclitus.

“Wait,” says David Hume’s Philo. “You both agree that all things are made up of one substance. Thales, you prefer to call it water, and Heraclitus, you prefer to call it fire. But isn’t that merely a verbal dispute? According to both of you, whatever you point at is fundamentally the same fundamental stuff. So whether you point at water or fire, or anything else, for that matter, you are always pointing at the same fundamental stuff. Where is the real disagreement?”

Philo has a somewhat valid point here, and I mentioned the same thing in the linked post referring to Thales. Nonetheless, as I also said in the same post, as well as in the discussion of the disagreement about God, while there is some common ground, there are also likely remaining points of disagreement. It might depend on context, and perhaps the disagreement is more about the best way of thinking about things than about the things themselves, somewhat like discussing whether the earth or the universe is the thing spinning, but Heraclitus could respond, for example, by saying that thinking of the fundamental stuff as fire is more valid because fire is constantly changing, while water often appears to be completely still, and (Heraclitus claims) everything is in fact constantly changing. This could represent a real disagreement, but it is not a large one, and Thales could simply respond: “Ok, everything is flowing water. Problem fixed.”

Numbers

It is said that Pythagoras and his followers held that “all things are numbers.” To what degree and in what sense this attribution is accurate is unclear, but in any case, some people hold this very position today, even if they would not call themselves Pythagoreans. Thus for example in a recent episode of Sean Carroll’s podcast, Carroll speaks with Max Tegmark, who seems to adopt this position:

0:23:37 MT: It’s squishy a little bit blue and moose like. [laughter] Those properties, I just described don’t sound very mathematical at all. But when we look at it, Sean through our physics eyes, we see that it’s actually a blob of quarks and electrons. And what properties does an electron have? It has the property, minus one, one half, one, and so on. We, physicists have made up these nerdy names for these properties like electric charge, spin, lepton number. But it’s just we humans who invented that language of calling them that, they are really just numbers. And you know as well as I do that the only difference between an electron and a top quark is what numbers its properties are. We have not discovered any other properties that they actually have. So that’s the stuff in space, all the different particles, in the Standard Model, you’ve written so much nice stuff about in your books are all described by just by sets of numbers. What about the space that they’re in? What property does the space have? I think I actually have your old nerdy non-popular, right?

0:24:50 SC: My unpopular book, yes.

0:24:52 MT: Space has, for example, the property three, that’s a number and we have a nerdy name for that too. We call it the dimensionality of space. It’s the maximum number of fingers I can put in space that are all perpendicular to each other. The name dimensionality is just the human language thing, the property is three. We also discovered that it has some other properties, like curvature and topology that Einstein was interested in. But those are all mathematical properties too. And as far as we know today in physics, we have never discovered any properties of either space or the stuff in space yet that are actually non-mathematical. And then it starts to feel a little bit less insane that maybe we are living in a mathematical object. It’s not so different from if you were a character living in a video game. And you started to analyze how your world worked. You would secretly be discovering just the mathematical workings of the code, right?

Tegmark presumably would believe that by saying that things “are really just numbers,” he would disagree with Thales and Heraclitus about the nature of things. But does he? Philo might well be skeptical that there is any meaningful disagreement here, just as between Thales and Heraclitus. As soon as you begin to say, “all things are this particular kind of thing,” the same issues will arise to hinder your disagreement with others who characterize things in a different way.

The discussion might be clearer if I put my cards on the table in advance:

First, there is some validity to the objection, just as there is to the objection concerning the difference between Thales and Heraclitus.

Second, there is nonetheless some residual disagreement, and on that basis it turns out that Tegmark and Pythagoras are more correct than Thales and Heraclitus.

Third, Tegmark most likely does not understand the sense in which he might be correct, rather supposing himself correct the way Thales might suppose himself correct in insisting, “No, things are really not fire, they are really water.”

Mathematical and non-mathematical properties

As an approach to these issues, consider the statement by Tegmark, “We have never discovered any properties of either space or the stuff in space yet that are actually non-mathematical.”

What would it look like if we found a property that was “actually non-mathematical?” Well, what about the property of being blue? As Tegmark remarks, that does not sound very mathematical. But it turns out that color is a certain property of a surface regarding how it reflects flight, and this is much more of a “mathematical” property, at least in the sense that we can give it a mathematical description, which we would have a hard time doing if we simply took the word “blue.”

So presumably we would find a non-mathematical property by seeing some property of things, then investigating it, and then concluding, “We have fully investigated this property and there is no mathematical description of it.” This did not happen with the color blue, nor has it yet happened with any other property; either we can say that we have not yet fully investigated it, or we can give some sort of mathematical description.

Tegmark appears to take the above situation to be surprising. Wow, we might have found reality to be non-mathematical, but it actually turns out to be entirely mathematical! I suggest something different. As hinted by connection with the linked post, things could not have turned out differently. A sufficiently detailed analysis of anything will be a mathematical analysis or something very like it. But this is not because things “are actually just numbers,” as though this were some deep discovery about the essence of things, but because of what it is for people to engage in “a detailed analysis” of anything.

Suppose you want to investigate some thing or some property. The first thing you need to do is to distinguish it from other things or other properties. The color blue is not the color red, the color yellow, or the color green.

Numbers are involved right here at the very first step. There are at least three colors, namely red, yellow, and blue.

Of course we can find more colors, but what if it turns out there seems to be no definite number of them, but we can always find more? Even in this situation, in order to “analyze” them, we need some way of distinguishing and comparing them. We will put them in some sort of order: one color is brighter than another, or one length is greater than another, or one sound is higher pitched than another.

As soon as you find some ordering of that sort (brightness, or greatness of length, or pitch), it will become possible to give a mathematical analysis in terms of the real numbers, as we discussed in relation to “good” and “better.” Now someone defending Tegmark might respond: there was no guarantee we would find any such measure or any such method to compare them. Without such a measure, you could perhaps count your property along with other properties. But you could not give a mathematical analysis of the property itself. So it is surprising that it turned out this way.

But you distinguished your property from other properties, and that must have involved recognizing some things in common with other properties, at least that it was something rather than nothing and that it was a property, and some ways in which it was different from other properties. Thus for example blue, like red, can be seen, while a musical note can be heard but not seen (at least by most people.) Red and blue have in common that they are colors. But what is the difference between them? If we are to respond in any way to this question, except perhaps, “it looks different,” we must find some comparison. And if we find a comparison, we are well on the way to a mathematical account. If we don’t find a comparison, people might rightly complain that we have not yet done any detailed investigation.

But to make the point stronger, let’s assume the best we can do is “it looks different.” Even if this is the case, this very thing will allow us to construct a comparison that will ultimately allow us to construct a mathematical measure. For “it looks different” is itself something that comes in degrees. Blue looks different from red, but orange does so as well, just less different. Insofar as this judgment is somewhat subjective, it might be hard to get a great deal of accuracy with this method. But it would indeed begin to supply us with a kind of sliding scale of colors, and we would be able to number this scale with the real numbers.

From a historical point of view, it took a while for people to realize that this would always be possible. Thus for example Isidore of Seville said that “unless sounds are held by the memory of man, they perish, because they cannot be written down.” It was not, however, so much ignorance of sound that caused this, as ignorance of “detailed analysis.”

This is closely connected to what we said about names. A mathematical analysis is a detailed system of naming, where we name not only individual items, but also various groups, using names like “two,” “three,” and “four.” If we find that we cannot simply count the thing, but we can always find more examples, we look for comparative ways to name them. And when we find a comparison, we note that some things are more distant from one end of the scale and other things are less distant. This allows us to analyze the property using real numbers or some similar mathematical concept. This is also related to our discussion of technical terminology; in an advanced stage any science will begin to use somewhat mathematical methods. Unfortunately, this can also result in people adopting mathematical language in order to look like their understanding has reached an advanced stage, when it has not.

It should be sufficiently clear from this why I suggested that things could not have turned out otherwise. A “non-mathematical” property, in Tegmark’s sense, can only be a property you haven’t analyzed, or one that you haven’t succeeded in analyzing if you did attempt it.

The three consequences

Above, I made three claims about Tegmark’s position. The reasons for them may already be somewhat clarified by the above, but nonetheless I will look at this in a bit more detail.

First, I said there was some truth in the objection that “everything is numbers” is not much different from “everything is water,” or “everything is fire.” One notices some “hand-waving,” so to speak, in Tegmark’s claim that “We, physicists have made up these nerdy names for these properties like electric charge, spin, lepton number. But it’s just we humans who invented that language of calling them that, they are really just numbers.” A measure of charge or spin or whatever may be a number. But who is to say the thing being measured is a number? Nonetheless, there is a reasonable point there. If you are to give an account at all, it will in some way express the form of the thing, which implies explaining relationships, which depends on the distinction of various related things, which entails the possibility of counting the things that are related. In other words, someone could say, “You have a mathematical account of a thing. But the thing itself is non-mathematical.” But if you then ask them to explain that non-mathematical thing, the new explanation will be just as mathematical as the original explanation.

Given this fact, namely that the “mathematical” aspect is a question of how detailed explanations work, what is the difference between saying “we can give a mathematical explanation, but apart from explanations, the things are numbers,” and “we can give a mathematical explanation, but apart from explanations, the things are fires?”

Exactly. There isn’t much difference. Nonetheless, I made the second claim that there is some residual disagreement and that by this measure, the mathematical claim is better than the one about fire or water. Of course we don’t really know what Thales or Heraclitus thought in detail. But Aristotle, at any rate, claimed that Thales intended to assert that material causes alone exist. And this would be at least a reasonable understanding of the claim that all things are water, or fire. Just as Heraclitus could say that fire is a better term than water because fire is always changing, Thales, if he really wanted to exclude other causes, could say that water is a better term than “numbers” because water seems to be material and numbers do not. But since other causes do exist, the opposite is the case: the mathematical claim is better than the materialistic ones.

Many people say that Tegmark’s account is flawed in a similar way, but with respect to another cause; that is, that mathematical accounts exclude final causes. But this is a lot like Ed Feser’s claim that a mathematical account of color implies that colors don’t really exist; namely they are like in just being wrong. A mathematical account of color does not imply that things are not colored, and a mathematical account of the world does not imply that final causes do not exist. As I said early on, a final causes explains why an efficient cause does what it does, and there is nothing about a mathematical explanation that prevents you from saying why the efficient cause does what it does.

My third point, that Tegmark does not understand the sense in which he is right, should be plain enough. As I stated above, he takes it to be a somewhat surprising discovery that we consistently find it possible to give mathematical accounts of the world, and this only makes sense if we assume it would in theory have been possible to discover something else. But that could not have happened, not because the world couldn’t have been a certain way, but because of the nature of explanation.

Anticipations of Darwin

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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.

Structure of Explanation

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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

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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.

 

And Fire by Fire

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Superstitious Nonsense asks about the last post:

So the answer here is that -some- of the form is present in the mind, but always an insufficient amount or accuracy that the knowledge will not be “physical”? You seem to be implying the part of the form that involves us in the self-reference paradox is precisely the part of the form that gives objects their separate, “physical” character. Is this fair? Certainly, knowing progressively more about an object does not imply the mental copy is becoming closer and closer to having a discrete physicality.

I’m not sure this is the best way to think about it. The self-reference paradox arises because we are trying to copy ourselves into ourselves, and thus we are adding something into ourselves, making the copy incomplete. The problem is not that there is some particular “part of the form” that we cannot copy, but that it is in principle impossible to copy it perfectly. This is different from saying that there is some specific “part” that cannot be copied.

Consider what happens when we make “non-physical” copies of something without involving a mind. Consider the image of a gold coin. There are certain relationships common to the image and to a gold coin in the physical world. So you could say we have a physical gold coin, and a non-physical one.

But wait. If the image of the coin is on paper, isn’t that a physical object? Or if the image is on your computer screen, isn’t your screen a physical object? And the image is just the colors on the screen, which are apparently just as “physical” (or non-physical) as the color of the actual coin. So why we would say that “this is not a physical coin?”

Again, as in the last post, the obvious answer is that the image is not made out of gold, while the physical coin is. But why not? Is it that the image is not accurate enough? If we made it more accurate, would it be made out of gold, or become closer to being made out of gold? Obviously not. This is like noting that a mental copy does not become closer and closer to being a physical one.

In a sense it is true that the reason the image of the coin is not physical is that it is not accurate enough. But that is because it cannot be accurate enough: the fact that it is an image positively excludes the copying of certain relationships. Some aspects can be copied, but others cannot be copied at all, as long as it is an image. On the other hand, you can look at this from the opposite direction: if you did copy those aspects, the image would no longer be an image, but a physical coin.

As a similar example, consider the copying of a colored scene into black and white. We can copy some aspects of the scene by using various shades of gray, but we cannot copy every aspect of the scene. There are simply not enough differences in a black and white image to reflect every aspect of a colored scene. The black and white image, as you make it more accurate, does not become closer to being colored, but this is simply because there are aspects of the colored scene that you never copy. If you do insist on copying those aspects, you will indeed make the black and white image into a colored image, and thus it will no longer be black and white.

The situation becomes significantly more complicated when we talk about a mind. In one way, there is an important similarity. When we say that the copy in the mind is “not physical,” that simply means that it is a copy in the mind, just as when we say that the image of the coin is not physical, it means that it is an image, made out of the stuff that images are made of. But just as the image is physical anyway, in another sense, so it is perfectly possible that the mind is physical in a similar sense. However, this is where things begin to become confusing.

Elsewhere, I discussed Aristotle’s argument that the mind is immaterial. Considering the cases above, we could put his argument in this way: the human brain is a limited physical object. So as long as the brain remains a brain, there are simply not enough potential differences in it to model all possible differences in the world, just as you cannot completely model a colored scene using black and white. But anything at all can be understood. Therefore we cannot be understanding by using the brain.

I have claimed myself that anything that can be, can be understood. But this needs to be understood generically, rather than as claiming that it is possible to understand reality in every detail simultaneously. The self-reference paradox shows that it is impossible in principle for a knower that copies forms into itself to understand itself in every aspect at once. But even apart from this, it is very obvious that we as human beings cannot understand every aspect of reality at once. This does not even need to be argued: you cannot even keep everything in mind at once, let alone understand every detail of everything. This directly suggests a problem with Aristotle’s argument: if being able to know all things suggests that the mind is immaterial, the obvious fact that we cannot know all things suggests that it is not.

Nonetheless, let us see what happens if we advance the argument on Aristotle’s behalf. Admittedly, we cannot understand everything at once. But in the case of the colored scene, there are aspects that cannot be copied at all into the black and white copy. And in the case of the physical coin, there are aspects that cannot be copied at all into the image. So if we are copying things into the brain, doesn’t that mean that there should be aspects of reality that cannot be copied at all into the mind? But this is false, since it would not only mean that we can’t understand everything, but it would also mean that there would be things that we cannot think about at all, and if it is so, then it is not so, because in that case we are right now talking about things that we supposedly cannot talk about.

Copying into the mind is certainly different from copying into a black and white scene or copying into a picture, and this does get at one of the differences. But the difference here is that the method of copying in the case of the mind is flexible, while the method of copying in the case of the pictures is rigid. In other words, we have a pre-defined method of copying in the case of the pictures that, from the beginning, only allows certain aspects to be copied. In the case of the mind, we determine the method differently from case to case, depending on our particular situation and the thing being copied. The result is that there is no particular aspect of things that cannot be copied, but you cannot copy every aspect at once.

In answer to the original question, then, the reason that the “mental copy” always remains mental is that you never violate the constraints of the mind, just as a black and white copy never violates the constraints of being black and white. But if you did violate the constraints of the black and white copy by copying every aspect of the scene, the image would become colored. And similarly, if you did violate the constraints of the mind in order to copy every aspect of reality, your mind would cease to be, and it would instead become the thing itself. But there is no particular aspect of “physicality” that you fail to copy: rather, you just ensure that one way or another you do not violate the constraints of the mind that you have.

Unfortunately, the explanation here for why the mind can copy any particular aspect of reality, although not every aspect at once, is rather vague. Perhaps a clearer explanation is possible? In fact, someone could use the vagueness to argue for Aristotle’s position and against mine. Perhaps my account is vague because it is wrong, and there is actually no way for a physical object to receive copied forms in this way.

Employer and Employee Model: Happiness

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We discussed Aristotle’s definition of happiness as activity according to virtue here, followed by a response to an objection.

There is another objection, however, which Aristotle raises himself in Book I, chapter 8 of the Nicomachean Ethics:

Yet evidently, as we said, it needs the external goods as well; for it is impossible, or not easy, to do noble acts without the proper equipment. In many actions we use friends and riches and political power as instruments; and there are some things the lack of which takes the lustre from happiness, as good birth, goodly children, beauty; for the man who is very ugly in appearance or ill-born or solitary and childless is not very likely to be happy, and perhaps a man would be still less likely if he had thoroughly bad children or friends or had lost good children or friends by death. As we said, then, happiness seems to need this sort of prosperity in addition; for which reason some identify happiness with good fortune, though others identify it with virtue.

Aristotle is responding to the implicit objection by saying that it is “impossible, or not easy” to act according to virtue when one is doing badly in other ways. Yet probably most of us know some people who are virtuous while suffering various misfortunes, and it seems pretty unreasonable, as well as uncharitable, to assert that the reason that they are somewhat unhappy with their circumstances is that the lack of “proper equipment” leads to a lack of virtuous activity. Or at any rate, even if this contributes to the matter, it does not seem to be a full explanation. The book of Job, for example, is based almost entirely on the possibility of being both virtuous and miserable, and Job would very likely respond to Aristotle, “How then will you comfort me with empty nothings? There is nothing left of your answers but falsehood.”

Aristotle brings up a similar issue at the beginning of Book VIII:

After what we have said, a discussion of friendship would naturally follow, since it is a virtue or implies virtue, and is besides most necessary with a view to living. For without friends no one would choose to live, though he had all other goods; even rich men and those in possession of office and of dominating power are thought to need friends most of all; for what is the use of such prosperity without the opportunity of beneficence, which is exercised chiefly and in its most laudable form towards friends? Or how can prosperity be guarded and preserved without friends? The greater it is, the more exposed is it to risk. And in poverty and in other misfortunes men think friends are the only refuge. It helps the young, too, to keep from error; it aids older people by ministering to their needs and supplementing the activities that are failing from weakness; those in the prime of life it stimulates to noble actions-‘two going together’-for with friends men are more able both to think and to act. Again, parent seems by nature to feel it for offspring and offspring for parent, not only among men but among birds and among most animals; it is felt mutually by members of the same race, and especially by men, whence we praise lovers of their fellowmen. We may even in our travels how near and dear every man is to every other. Friendship seems too to hold states together, and lawgivers to care more for it than for justice; for unanimity seems to be something like friendship, and this they aim at most of all, and expel faction as their worst enemy; and when men are friends they have no need of justice, while when they are just they need friendship as well, and the truest form of justice is thought to be a friendly quality.

But it is not only necessary but also noble; for we praise those who love their friends, and it is thought to be a fine thing to have many friends; and again we think it is the same people that are good men and are friends.

There is a similar issue here: lack of friends may make someone unhappy, but lack of friends is not lack of virtue. Again Aristotle is in part responding by pointing out that the activity of some virtues depends on the presence of friends, just as he said that temporal goods were necessary as instruments. Once again, however, even if there is some truth in it, the answer does not seem adequate, especially since Aristotle believes that the highest form of happiness is found in contemplation, which seems to depend much less on friends than other types of activity.

Consider again Aristotle’s argument for happiness as virtue, presented in the earlier post. It depends on the idea of a “function”:

Presumably, however, to say that happiness is the chief good seems a platitude, and a clearer account of what it is still desired. This might perhaps be given, if we could first ascertain the function of man. For just as for a flute-player, a sculptor, or an artist, and, in general, for all things that have a function or activity, the good and the ‘well’ is thought to reside in the function, so would it seem to be for man, if he has a function. Have the carpenter, then, and the tanner certain functions or activities, and has man none? Is he born without a function? Or as eye, hand, foot, and in general each of the parts evidently has a function, may one lay it down that man similarly has a function apart from all these? What then can this be? Life seems to be common even to plants, but we are seeking what is peculiar to man. Let us exclude, therefore, the life of nutrition and growth. Next there would be a life of perception, but it also seems to be common even to the horse, the ox, and every animal. There remains, then, an active life of the element that has a rational principle; of this, one part has such a principle in the sense of being obedient to one, the other in the sense of possessing one and exercising thought. And, as ‘life of the rational element’ also has two meanings, we must state that life in the sense of activity is what we mean; for this seems to be the more proper sense of the term. Now if the function of man is an activity of soul which follows or implies a rational principle, and if we say ‘so-and-so-and ‘a good so-and-so’ have a function which is the same in kind, e.g. a lyre, and a good lyre-player, and so without qualification in all cases, eminence in respect of goodness being added to the name of the function (for the function of a lyre-player is to play the lyre, and that of a good lyre-player is to do so well): if this is the case, and we state the function of man to be a certain kind of life, and this to be an activity or actions of the soul implying a rational principle, and the function of a good man to be the good and noble performance of these, and if any action is well performed when it is performed in accordance with the appropriate excellence: if this is the case, human good turns out to be activity of soul in accordance with virtue, and if there are more than one virtue, in accordance with the best and most complete.

Aristotle took what was most specifically human and identified happiness with performing well in that most specifically human way. This is reasonable, but it leads to the above issues, because a human being is not only what is most specifically human, but also possesses the aspects that Aristotle dismissed here as common to other things. Consequently, activity according to virtue would be the most important aspect of functioning well as a human being, and in this sense Aristotle’s account is reasonable, but there are other aspects as well.

Using our model, we can present a more unified account of happiness which includes these other aspects without the seemingly arbitrary way in which Aristotle noted the need for temporal goods and friendship for happiness. The specifically rational character belongs mainly to the Employee, and thus when Aristotle identifies happiness with virtuous action, he is mainly identifying happiness with the activity of the Employee. And this is surely its most important aspect. But since the actual human being is the whole company, it is more complete to identify happiness with the good functioning of the whole company. And the whole company is functioning well overall when the CEO’s goal of accurate prediction is regularly being achieved.

Consider two ways in which someone might respond to the question, “How are you doing?” If someone isn’t doing very well, they might say, “Well, I’ve been having a pretty rough time,” while if they are better off, they might say, “Things are going pretty smoothly.” Of course people might use other words, but notice the contrast in my examples: a life that is going well is often said to be going “smoothly”, while the opposite is described as “rough.” And the difference here between smooth and rough is precisely the difference between predictive accuracy and inaccuracy. We might see this more easily by considering some restricted examples:

First, suppose two people are jogging. One is keeping an even pace, keeping their balance, rounding corners smoothly, and keeping to the middle of the path. The other is becoming tired, slowing down a bit and speeding up a bit. They are constantly off balance and suffering disturbing jolts when they hit unexpected bumps in the path, perhaps narrowly avoiding tripping. If we compare what is happening here with the general idea of predictive processing, it seems that the difference between the two is that first person is predicting accurately, while the second is predicting inaccurately. The second person is not rationing their energy and breath correctly, they suffer jolts or near trips when they did not correctly expect the lay of the land, and so on.

Suppose someone is playing a video game. The one who plays it well is the one who is very prepared for every eventuality. They correctly predict what is going to happen in the game both with regard to what happens “by itself,” and what will happen as a result of their in-game actions. They play the game “smoothly.”

Suppose I am writing this blog post and feel myself in a state of “flow,” and I consequently am enjoying the activity. This can only happen as long as the process is fairly “smooth.” If I stop for long periods in complete uncertainty of what to write next, the state will go away. In other words, the condition depends on having at each moment a fairly good idea of what is coming next; it depends on accurate prediction.

The reader might understand the point in relation to these limited examples, but how does this apply to life in general, and especially to virtue and vice, which are according to Aristotle the main elements of happiness and unhappiness?

In a basic way virtuous activity is reasonable activity, and vicious activity is unreasonable activity. The problem with vice, in this account, is that it immediately sets up a serious interior conflict. The Employee is a rational being and is constantly being affected by reasons to do things. Vice, in one way or another, persuades them to do unreasonable things, and the reasons for not doing those things will be constantly pulling in the opposite direction. When St. Paul complains that he wills something different from what he does, he is speaking of this kind of conflict. But conflicting tendencies leads to uncertain results, and so our CEO is unhappy with this situation.

Now you might object: if a vicious man is unhappy because of conflicting tendencies, what if they are so wicked that they have no conflict, but simply and contentedly do what is evil?

The response to this would be somewhat along the lines of the answer we gave to the objection that moral obligation should not depend on desiring some particular end. First, it is probably impossible for a human being to become so corrupted that they cannot see, at least to some degree, that bad things are bad. Second, consider the wicked men according to Job’s description:

Why do the wicked live on,
reach old age, and grow mighty in power?
Their children are established in their presence,
and their offspring before their eyes.
Their houses are safe from fear,
and no rod of God is upon them.
Their bull breeds without fail;
their cow calves and never miscarries.
They send out their little ones like a flock,
and their children dance around.
They sing to the tambourine and the lyre,
and rejoice to the sound of the pipe.
They spend their days in prosperity,
and in peace they go down to Sheol.

Just as we said that if you assume that someone is entirely corrupt, the idea of “obligation” may well become irrelevant to them, without that implying anything wrong with the general idea of moral obligation, in a similar way, it would be metaphorical to speak of such a person as “unhappy”; you could say this with the intention of saying that they exist in an objectively bad situation, but not in the ordinary sense of the term, in which it includes subjective discontent.

We could explain a great deal more with this account of happiness: not only the virtuous life in general, but also a great deal of the spiritual, psychological, and other practical advice which is typically given. But this is all perhaps for another time.

Violations of Bell’s Inequality: Drawing Conclusions

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In the post on violations of Bell’s inequality, represented there by Mark Alford’s twin analogy, I pointed out that things did not seem to go very well for Einstein’s hope for physics, I did not draw any specific conclusions. Here I will consider the likely consequences, first by looking at the relationship of the experiments to Einstein’s position on causality and determinism, and second on their relationship to Einstein’s position on locality and action at a distance.

Einstein on Determinism

Einstein hoped for “facts” instead of probabilities. Everything should be utterly fixed by the laws, much like the position recently argued by Marvin Edwards in the comments here.

On the face of it, violations of Bell’s inequality rule this out, represented by the argument that if the twins had pre-existing determinate plans, it would be impossible for them to give the same answer less than 1/3 of the time when they are asked different questions. Bell however pointed out that it is possible to formulate a deterministic theory which would give similar probabilities at the cost of positing action at a distance (quoted here):

Moreover, a hidden variable interpretation of elementary quantum theory has been explicitly constructed. That particular interpretation has indeed a grossly non-local structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions.

Nonetheless, I have set aside action at a distance to be discussed separately, and I would argue that we should accept the above surface appearance: the outcomes of quantum mechanical experiments are actually indeterministic. These probabilities represent something in the world, not merely something in our knowledge.

Why? In the first place, note that “reproduces exactly the quantum mechanical predictions” can be understood in two ways. A deterministic theory of that kind would say that because the details are unknown to us, we cannot know what is going to happen. But the details are there, and they in fact determine what is going to happen. There is still a difference on the object level between a world where the present fixes the future to a single possibility, and one in which the future is left open, as Aristotle supposed.

Of course there is no definitive proof here that we are actually in the situation with the open future, although the need for action at a distance in the alternative theory suggests that we are. Even apart from this, however, the general phenomena of quantum mechanics directly suggest that this is the situation. Even apart from violations of Bell’s inequality, quantum mechanics in general already looked exactly as we should have expected a world with an indeterminate future to look.

If this is the case, then Einstein was mistaken on this point, at least to this extent. But what about the deterministic aspect, which I mentioned at the end of this post, and which Schrödinger describes:

At all events it is an imagined entity that images the blurring of all variables at every moment just as clearly and faithfully as does the classical model its sharp numerical values. Its equation of motion too, the law of its time variation, so long as the system is left undisturbed, lags not one iota, in clarity and determinacy, behind the equations of motion of the classical model.

The answer is that this is deterministic not because the future, as we know it, is deterministic, but because it describes all of the possibilities at once. Thus in the case of the cat it includes both the cat living and the cat dying, which are two possible outcomes. It is “deterministic” only because once you have stated all of the alternatives, there is nothing left to say.

Why did Einstein want a deterministic theory? He openly admits that he does not have a convincing argument for it. It seems likely, however, that the fundamental motivation is the conviction that reality is intelligible. And an indeterministic world seems significantly less intelligible than a deterministic one. But this desire can in fact be satisfied by this second kind of “determinism”; thus Schrödinger calls it “one perfectly clear concept.”

In this respect, Einstein’s intuition was not mistaken. It is possible to give an intelligible account of the world, even a “deterministic” one, in this sense.

Einstein on Locality

Einstein also wanted to avoid “spooky action at a distance.” Admitting that the future is indeterminate, however, is not enough to avoid this conclusion. In Mark Alford’s twin analogy, it is not only pre-determined plans that fail, but also plans that involve randomness. Thus it first appears that the violations of Bell’s inequality absolutely require action at a distance.

If we follow my suggestion here, however, and consequently adopt Hugh Everett’s interpretation of quantum mechanics, then saying that there are multiple future possibilities implies the existence of multiple timelines. And if there are multiple timelines, violations of Bell’s inequality no longer necessarily imply action at a distance.

Why not? Consider the twin experiment with the assumption of indeterminacy and multiple timelines. Suppose that from the very beginning, there are two copies of each twin. The first copy of the first twin has the plan of responding to the three questions with “yes/yes/yes.” Likewise, the first copy of the second twin has the plan of responding to the three questions with, “yes/yes/yes.” In contrast, the second copy of each twin has the plan of responding with “no/no/no.”

Now we have four twins but the experimenter only sees two. So which ones does he see? There is nothing impossible about the following “rule”: if the twins are asked different questions, the experimenter sees the first copy of one of the twins, and the second copy of the other twin. Meanwhile, if the twins are asked the same question, the experimenter sees either the first copy of each twin, or the second copy of each twin. It is easy to see that if this is the case, the experimenter will see the twins agree, when they are asked the same question, and will see them disagree when they are asked different questions (thus agreeing less than 1/3 of the time in that situation.)

“Wait,” you will say. “If multiple timelines is just a way of describing a situation with indeterminism, and indeterminism is not enough to avoid action at a distance, how is it possible for multiple timelines to give a way out?”

From the beginning, the apparent “impossibility” of the outcome was a statistical impossibility, not a logical impossibility. Naturally this had to be the case, since if it were a logical impossibility, we could not have coherently described the actual outcomes. Thus we might imagine that David Hume would give this answer:

The twins are responding randomly to each question. By pure chance, they happened to agree the times they were asked the same question, and by pure chance they violated Bell’s inequality when they were asked different questions.

Since this was all a matter of pure chance, of course, if you do the experiment again tomorrow, it will turn out that all of the answers are random and they will agree and disagree 50% of the time on all questions.

And this answer is logically possible, but false. This account does not explain the correlation, but simply ignores it. In a similar way, the reason why indeterministic theories without action at a distance, but described as having a single timeline, cannot explain the results is that in order to explain the correlation, the outcomes of both sides need to be selected together, so to speak. But “without action at a distance” in this context simply means that they are not selected together. This makes the outcome statistically impossible.

In our multiple timelines version, in contrast, our “rule” above in effect selected the outcomes together. In other words, the guideline we gave regarding which pairs of twins the experimenter would meet, had the same effect as action at a distance.

How is all this an explanation? The point is that the particular way that timelines spread out when they come into contact with other things, in the version with multiple timelines, exactly corresponds to action at a distance, in the version without them. An indeterministic theory represented as having a single timeline and no action at a distance could be directly translated into a version with multiple timelines; but if we did that, this particular multiple timeline version would not have the rule that produces the correct outcomes. And on the other hand, if we start with the multiple timeline version that does have the rule, and translate it into a single timeline account, it will have action at a distance.

What does all this say about Einstein’s opinion about locality? Was he right, or was he wrong?

We might simply say that he was wrong, insofar as the actual situation can in fact be described as including action at a distance, even if it is not necessary to describe it in this way, since we can describe it with multiple timelines and without action at a distance. But to the degree that this suggests that Einstein made two mistakes, one about determinism and one about action at a distance, I think this is wrong. There was only one mistake, and it was the one about determinism. The fact is that as soon you speak of indeterminism at all, it becomes possible to speak of the world as having multiple timelines. So the question at that point is whether this is the “natural” description of the situation, where the natural description more or less means the best way to understand things, in which case the possibility of “action at a distance” is not an additional mistake on Einstein’s part, but rather it is an artifact of describing the situation as though there were only a single timeline.

You might say that there cannot be a better or worse way to understand things if two accounts are objectively equivalent. But this is wrong. Thus for example in general relativity it is probably possible to give an account where the earth has no daily rotation, and the universe is spinning around it every 24 hours. And this account is objectively equivalent to the usual account where the earth is spinning; exactly the same situation is being described, and nothing different is being asserted. And yet this account is weird in many ways, and makes it very hard to understand the universe. The far better and “natural” description is that the earth is spinning. Note, however, that this is an overall result; just looking out the window, you might have thought that saying that the universe is spinning is more natural. (Notice, however, that an even more natural account would be that neither the earth nor the universe is moving; it is only later in the day that you begin to figure out that one of them is moving.)

In a similar way, a single timeline account is originally more natural in the way a Ptolemaic account is more natural when you look out the window. But I would argue that in a similar way, the multiple timeline account, without action at a distance, is ultimately the more natural one. The basic reason for this is that there is no Newtonian Absolute Time. The consequence is that if we speak of “future possibilities,” they cannot be future possibilities for the entire universe at once. They will be fairly localized future possibilities: e.g. there might be more than one possible text for the ending to this blog post, which has not yet been written, and those possibilities are originally possibilities for what happens here in this room, not for the rest of the universe. These future alternatives will naturally result in future possibilities for other parts of the world, but this will happen “slowly,” so to speak (namely if one wishes to speak of the speed of light as slow!) This fits well with the idea of multiple timelines, since there will have to be some process where these multiple timelines come into contact with the rest of the world, much as with our “rule” in the twin experiment. On the other hand, it does not fit so well with a single timeline account of future possibilities, since one is forced (by the terms of the account) to imagine that when a choice among possibilities is made, it is made for the entire universe at once, which appears to require Newton’s Absolute Time.

This suggests that Einstein was basically right about action at a distance, and wrong about determinism. But the intuition that motivated him to embrace both positions, namely that the universe should be intelligible, was sound.

Open Past

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Suppose that Aristotle was right, and the future is open. What would things be like in detail?

There are many ways things could go, so for concreteness let’s assume that (in some local area) there are approximately 100 possibilities for the next second, and approximately 100 x 100, or 10,000 possibilities for the next two seconds.

Then the question arises: do some of the two-second outcomes have overlapping paths? In other words, suppose we take the first option in the first second. Are all of the outcomes we can reach different from all of the outcomes we could reach if we took the second option in the first second?

It is at least plausible that some overlapping paths can exist. For example, something might swerve to the left in the first second, and then to the right in the second second, ending up just where it would have been if it had swerved to the right in the first second and to the left in the second. Let’s suppose it turns out this way. Thus we have situation A and time A, and situation B and time B, with a first and second path, both of which lead from situation A at time A, to situation B at time B.

When we get to situation B, what does the world look like? In particular, if someone is in situation B and says, “let’s look at the world and figure out what just happened,” what does it look like? Consider three different accounts:

  1. It looks like situation B except also that it looks like we took the first path
  2. It looks like situation B except also that it looks like we took the second path
  3. It looks like situation B, and we can’t tell which path was taken

The problem is evident. These are three different situations. If things currently look different, the situation is different. So these cannot possibly all be descriptions of situation B. And in particular, only the third is a reasonable description of the situation we should expect. We have set up the situation so that there is no difference in our current situation, whether the first or second path was taken. So of course in situation B it will be impossible to know which path was taken.

But what does that look like, exactly? “We don’t know” is not a description of a situation, but a description of our state of knowledge. What is it about situation B that makes it impossible to tell which path was taken? What happens if you describe the situation as exactly as possible, and then explain why that “exact” description still does not determine which path was taken?

Consider again Schrödinger’s confusion about his cat. The reason why the notion of “bluriness” came up at all was not merely that the wave equation seems to describe something blurred, but also because the actual results of experiments suggest that something blurred took place. Thus for example in double-slit experiments, interference patterns suggest that something is going through both slits at once, while if detectors are added to determine what, if anything, is going through the slits, one seems to find that only one slit is used at a time, and the interference pattern goes away.

This fits the above description of situation A and situation B  almost perfectly. In the double slit experiment, there are two paths that could be taken to arrive at the same outcome. But that “same outcome” is not one in which it looks like the first path was taken, nor one in which it looks like the second path was taken, but one in which the outcome’s relationship to the path appears to be confused. And on the other hand, if we can tell which path was taken, as we can when we add detectors, there is no such confusion, because the outcomes no longer overlap; the outcome where the first detector registers is not the same as an outcome where the second detector registers.

In this sense, quantum theory is simply the situation where Aristotle was right about the indeterminacy of the future, with the minor addition that it turned out to be possible to get to the same future by more than route.

Note, however, that this implies the worrisome outcome that I suggested in that post. Just as the future is indeterminate, so is the past. Just as the present has many possible future outcomes, there are many past paths that could have resulted in the present.

Open Future

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Let’s return for a moment to the question at the end of this post. I asked, “What happens if the future is indeterminate? Would not the eternalist position necessarily differ from the presentist one, in that case?”

Why necessarily different? The argument in that post was that eternalism and presentism are different descriptions of the same thing, and that we see the sameness by noting the sameness of relations between the elements of the description. But if the future is open, as Aristotle supposed, it is hard to see how we can maintain this. Aristotle says that the present is open to either having the sea battle tomorrow or not having it. With an eternalist view, the sea battle is “already there” or it is not. So in Aristotle’s view, the present has an open relationship to both possibilities. But the eternalist view seems to be truly open only to the possibility that will actually happen. We no longer have the same set of relationships.

Notice the problem. When I attempted to equate eternalism and presentism, I implicitly assumed that determinism is true. There were only three states of the universe, beginning, middle, and end. If determinism is false, things are different. There might be beginning, middle, and two potential ends. Perhaps there is a sea battle in one of the potential ends, and no sea battle in the other.

This suggests a solution to our conundrum, however. Even the presentist description in that post was inconsistent with an open future. If there is only one possible end, the future is not open, even if we insist that the unique possible end “currently doesn’t exist.” The problem then was not eternalism as such, but the fact that we started out with a determinist description of the universe. This strongly suggests that if my argument about eternalism and presentism was correct, we should be able to formulate eternalist and presentist descriptions of an open future which will be equivalent. But both will need to be different from the fixed “beginning-middle-end” described in that post.

We can simply take Aristotle’s account as the account of presentism with an open future. How can we give an eternalist account of the same thing? The basic requirement will be that the relationship between the present and the future needs to be the same in both accounts. Now in Aristotle’s account, the present has the same relationship to two different possibilities: both of them are equally possible. So to get a corresponding eternalist account, we need the present to be equally related to two futures that correspond to the two possiblities in the presentist account. I do not say “two possible futures,” but “two futures,” precisely because the account is eternalist.

The careful reader will already understand the account from the above, but let us be more explicit. The eternalist account that corresponds to the presentist account with an open future has multiple timelines, all of which “exist”, in the eternalist sense. The reader will no doubt be familiar with the idea of multiple timelines, at least from time travel fiction. In a similar way, the eternalist reworking of Aristotle’s position is that there is a timeline where the sea battle takes place, and another timeline where the sea battle does not take place. In this view, both of them “actually” happen. But even in this view, an observer in the middle location will have to say, “I do not, and cannot, know whether the sea battle will take place or not,” just as in Aristotle’s view. For the observer cannot traverse both timelines at once. From his point of view, he will take only one, but since his relationship to the two possibilities (or actualities) is the same, it is indeterminate which one it will be.

Even if one cannot prove my account of equivalence to be wrong, the reader may worry. Time travel fiction frequently seems incoherent, and this suggests that any view with multiple timelines may also be incoherent. But this potential incoherence supports the equivalence, rather than subtracting from it. For as we noted in the post on Aristotle, there is a definite appearance of incoherence in his position. It is not even clear how his view is logically possible. So it would not be surprising, but quite natural, if views which are intended to be equivalent to his position are also not clearly coherent. Nonetheless, the multiple timelines description does have some logical advantage over Aristotle’s position, in the sense that “the sea battle will take place in timeline A” does not even appear to contradict “the sea battle will not take place in timeline B.”

Aristotle on Future Contingents

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In Chapter 9 of On Interpretation, Aristotle argues that at least some statements about the future need to be exempted from the principle of Excluded Middle:

In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,’ one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. We have discussed this type also in a previous chapter.

When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. For the predicate cannot both belong and not belong to the subject at one and the same time with regard to the future.

Thus, if it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be either true or false.

Now if this be so, nothing is or takes place fortuitously, either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed. For either he that affirms that it will take place or he that denies this is in correspondence with fact, whereas if things did not take place of necessity, an event might just as easily not happen as happen; for the meaning of the word ‘fortuitous’ with regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions. Again, if a thing is white now, it was true before to say that it would be white, so that of anything that has taken place it was always true to say ‘it is’ or ‘it will be’. But if it was always true to say that a thing is or will be, it is not possible that it should not be or not be about to be, and when a thing cannot not come to be, it is impossible that it should not come to be, and when it is impossible that it should not come to be, it must come to be. All, then, that is about to be must of necessity take place. It results from this that nothing is uncertain or fortuitous, for if it were fortuitous it would not be necessary.

The argument here is that if it is already true, for example, that I will eat breakfast tomorrow, then I will necessarily eat breakfast tomorrow, and there is no option about this and no ability of anything to prevent it. Aristotle is here taking it for granted that some things about the future are uncertain, and is using this as a reductio against the position that such claims can be already true. He goes on to give additional reasons for the same thing:

Again, to say that neither the affirmation nor the denial is true, maintaining, let us say, that an event neither will take place nor will not take place, is to take up a position impossible to defend. In the first place, though facts should prove the one proposition false, the opposite would still be untrue. Secondly, if it was true to say that a thing was both white and large, both these qualities must necessarily belong to it; and if they will belong to it the next day, they must necessarily belong to it the next day. But if an event is neither to take place nor not to take place the next day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.

These awkward results and others of the same kind follow, if it is an irrefragable law that of every pair of contradictory propositions, whether they have regard to universals and are stated as universally applicable, or whether they have regard to individuals, one must be true and the other false, and that there are no real alternatives, but that all that is or takes place is the outcome of necessity. There would be no need to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow. For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time.

Further, it makes no difference whether people have or have not actually made the contradictory statements. For it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone. For events will not take place or fail to take place because it was stated that they would or would not take place, nor is this any more the case if the prediction dates back ten thousand years or any other space of time. Wherefore, if through all time the nature of things was so constituted that a prediction about an event was true, then through all time it was necessary that that should find fulfillment; and with regard to all events, circumstances have always been such that their occurrence is a matter of necessity. For that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be.

Yet this view leads to an impossible conclusion; for we see that both deliberation and action are causative with regard to the future, and that, to speak more generally, in those things which are not continuously actual there is potentiality in either direction. Such things may either be or not be; events also therefore may either take place or not take place. There are many obvious instances of this. It is possible that this coat may be cut in half, and yet it may not be cut in half, but wear out first. In the same way, it is possible that it should not be cut in half; unless this were so, it would not be possible that it should wear out first. So it is therefore with all other events which possess this kind of potentiality. It is therefore plain that it is not of necessity that everything is or takes place; but in some instances there are real alternatives, in which case the affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general tendency in one direction or the other, and yet can issue in the opposite direction by exception.

Now that which is must needs be when it is, and that which is not must needs not be when it is not. Yet it cannot be said without qualification that all existence and non-existence is the outcome of necessity. For there is a difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be, and similarly in the case of that which is not. In the case, also, of two contradictory propositions this holds good. Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about.

Let me illustrate. A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions, the corresponding affirmation and denial have the same character.

This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. The case is rather as we have indicated.

Basically, then, there are two arguments. First there is the argument that if statements about the future are already true, the future is necessary. If a sea battle will take place tomorrow, it will necessarily take place. Second, there is the argument that this excludes deliberation. If a sea battle will take place tomorrow, then it will necessarily take place, and no place remains for deliberation and decision about whether to fight the sea battle. Whether you decide to fight or not, it will necessarily take place.

Unfortunately for Aristotle, both arguments fail. Consider the first argument about necessity. Aristotle’s example is that “if it is true to say that a thing is white, it must necessarily be white.” But this is hypothetical necessity, not absolute necessity. A thing must be white if it is true that is white, but that does not mean that “it must be white, period.” Thus for example I have a handkerchief, and it happens to be white. If it is true that it is white, then it must be white. But it would be false to simply say, “My handkerchief is necessarily white.” Since I can dye it other colors, obviously it is not simply necessary for it to be white.

In a similar way, of course it is true that if a sea battle will take place, it will take place. It does not follow at all that “it will necessarily take place, period.”

Again, consider the second argument, that deliberation would be unnecessary. Aristotle makes the point that deliberation is causative with respect to the future. But gravity is also causative with respect to the future, as for example when gravity causes a cup to fall from a desk. It does not follow either that the cup must be able not to fall, nor that gravity is unnecessary. In a similar way, a sea battle takes place because certain people deliberated and decided to fight. If it was already true that it was going to take place, then it also already true that they were going to decide to fight. It does not follow that their decision was unnecessary.

Consider the application to gravity. It is already true that if the cup is knocked from the desk, it will fall. It does not follow that gravity will not cause the fall: in fact, it is true precisely because gravity will cause the fall. In a similar way, if it true that the battle will take place, it is true because the decision will be made.

This earlier discussion about determinism is relevant to this point. Asserting that there is a definite outcome that our deliberations will arrive at, in each case, goes against our experience in no way. The feeling of “free will,” in any case, has a different explanation, whether or not determinism is true.

On the other hand, there is also no proof that there is such a determinate outcome, even if in some cases there are things that would suggest it. What happens if in fact there is nothing ensuring one outcome rather than another?

Here we could make a third argument on Aristotle’s behalf, although he did not make it himself. If the present is truly open to alternative outcomes, then it seems that nothing exists that could make it be true that “a sea battle will take place,” and false that “a sea battle will not take place.” Presumably if a statement is true, there must be something in reality which is the cause of the statement’s truth. Now there does not seem to be anything in reality, in this scenario, which could be a cause of truth. Therefore it does not seem that either alternative could be true, and Aristotle would seem to be right.

I will not attempt to refute this argument at this point, but I will raise two difficulties. First of all, it is not clear that his claim is even coherent. Aristotle says that “either there will be a sea battle or there will not be,” is true, but that “there will be a sea battle” is not true, and “there will not be a sea battle” is not true. This does not seem to be logically consistent, and it is not clear that we can even understand what is being said. I will not push this objection too hard, however, lest I be accused of throwing stones from a glass house.

Second, the argument that there is nothing in reality that could cause the truth of a statement might apply to the past as well as to the future. There is a tree outside my window right now. What was in that place exactly 100 million years ago to this moment? It is not obvious that there is anything in the present world which could be the cause of the truth of any statement about this. One might object that the past is far more determinate than the future. There are plenty of things in the present world that might be the cause of the truth of the statement, “World War II actually happened.” It is hard to see how you could possibly have arrived at the present world without it, and this “necessity” of World War II in order to arrive at the present world could be the cause of truth. The problem is that there is still no proof that this is universal. Once things are far enough in past, like 100 million years, perhaps minor details become indeterminate. Will Aristotle really want to conclude that some statements about the past are neither true nor false?

I will more or less leave things here without resolving them in this post, although I will give a hint (without proof at this time) regarding the truth of the matter. It turns out that quantum mechanics can be interpreted in two ways. In one way, it is a deterministic theory, and in this way it is basically time reversible. The present fully determines the past, but it equally fully determines the future. Interpreted in another way, it is an indeterministic theory which leaves the future uncertain. But understood in this way, it also leaves the past uncertain.