Thales

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.

Semi-Parmenidean Heresy

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In his book The Big Picture, Sean Carroll describes the view which he calls “poetic naturalism”:

As knowledge generally, and science in particular, have progressed over the centuries, our corresponding ontologies have evolved from quite rich to relatively sparse. To the ancients, it was reasonable to believe that there were all kinds of fundamentally different things in the world; in modern thought, we try to do more with less.

We would now say that Theseus’s ship is made of atoms, all of which are made of protons, neutrons, and electrons-exactly the same kinds of particles that make up every other ship, or for that matter make up you and me. There isn’t some primordial “shipness” of which Theseus’s is one particular example; there are simply arrangements of atoms, gradually changing over time.

That doesn’t mean we can’t talk about ships just because we understand that they are collections of atoms. It would be horrendously inconvenient if, anytime someone asked us a question about something happening in the world, we limited our allowable responses to a listing of a huge set of atoms and how they were arranged. If you listed about one atom per second, it would take more than a trillion times the current age of the universe to describe a ship like Theseus’s. Not really practical.

It just means that the notion of a ship is a derived category in our ontology, not a fundamental one. It is a useful way of talking about certain subsets of the basic stuff of the universe. We invent the concept of a ship because it is useful to us, not because it’s already there at the deepest level of reality. Is it the same ship after we’ve gradually replaced every plank? I don’t know. It’s up to us to decide. The very notion of “ship” is something we created for our own convenience.

That’s okay. The deepest level of reality is very important; but all the different ways we have of talking about that level are important too.

There is something essentially pre-Socratic about this thinking. When Carroll talks about “fundamentally different things,” he means things that differ according to their basic elements. But at the same kind the implication is that only things that differ in this way are “fundamentally” different in the sense of being truly or really different. But this is a quite different sense of “fundamental.”

I suggested in the linked post that even Thales might not really have believed that material causes alone sufficiently explained reality. Nonetheless, there was a focus on the material cause as being the truest explanation. We see the same focus here in Sean Carroll. When he says, “There isn’t some primordial shipness,” he is thinking of shipness as something that would have to be a material cause, if it existed.

Carroll proceeds to contrast his position with eliminativism:

One benefit of a rich ontology is that it’s easy to say what is “real”- every category describes something real. In a sparse ontology, that’s not so clear. Should we count only the underlying stuff of the world as real, and all the different ways we have of dividing it up and talking about it as merely illusions? That’s the most hard-core attitude we could take to reality, sometimes called eliminativism, since its adherents like nothing better than to go around eliminating this or that concept from our list of what is real. For an eliminativist, the question “Which Captian Kirk is the real one?” gets answered by, “Who cares? People are illusions. They’re just fictitious stories we tell about the one true world.”

I’m going to argue for a different view: our fundamental ontology, the best way we have of talking about the world at the deepest level, is extremely sparse. But many concepts that are part of non-fundamental ways we have of talking about the world- useful ideas describing higher-level, macroscopic reality- deserve to be called “real.”

The key word there is “useful.” There are certainly non-useful ways of talking about the world. In scientific contexts, we refer to such non-useful ways as “wrong” or “false.” A way of talking isn’t just a list of concepts; it will generally include a set of rules for using them, and relationships among them. Every scientific theory is a way of talking about the world, according to which we can say things like “There are things called planets, and something called the sun, all of which move through something called space, and planets do something called orbiting the sun, and those orbits describe a particular shape in space called an ellipse.” That’s basically Johannes Kepler’s theory of planetary motion, developed after Copernicus argued for the sun being at the center of the solar system but before Isaac Newton explained it all in terms of the force of gravity. Today, we would say that Kepler’s theory is fairly useful in certain circumstances, but it’s not as useful as Newton’s, which in turn isn’t as broadly useful as Einstein’s general theory of relativity.

…

A poetic naturalist will agree that both Captain Kirk and the Ship of Theseus are simply ways of talking about certain collections of atoms stretching through space and time. The difference is that an eliminativist will say “and therefore they are just illusions,” while the poetic naturalist says “but they are no less real for all of that.”

There are some good things about what Carroll is doing here. He is right of course to insist that the things of common experience are “real.” He is also right to see some relationship between saying that something is real and saying that talking about it is useful, but this is certainly worth additional consideration, and he does not really do it justice.

The problematic part is that, on account of his pre-Socratic tendencies, he is falling somewhat into the error of Parmenides. The error of Parmenides was to suppose that being can be, and can be thought and said, in only one way. Carroll, on account of confusing the various meanings of “fundamental,” supposes that being can be in only one way, namely as something elemental, but that it can be thought and said in many ways.

The problem with this, apart from the falsity of asserting that being can be in only one way, is that no metaphysical account is given whereby it would be reasonable to say that being can be thought and said in many ways, given that it can be in only one way. Carroll is trying to point in that direction by saying that our common speech is useful, so it must be about real things; but the eliminativist would respond, “Useful to whom? The things that you are saying this is useful for are illusions and do not exist. So even your supposed usefulness does not exist.” And Carroll will have no valid response, because he has already admitted to agreeing with the eliminativist on a metaphysical level.

The correct answer to this is the one given by Aristotle. Material causes do not sufficiently explain reality, but other causes are necessary as well. But this means that the eliminativist is mistaken on a metaphysical level, not merely in his way of speaking.

Science and Certain Theories of Sean Collins

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Sean Collins discusses faith and science:

Since at least the time of Descartes, there has come to be a very widespread tendency to see faith as properly the activity of an individual who stands in opposition to a larger, potentially deceptive, world. Faith so conceived is of a piece with individualist notions about the true and the good. At its extreme, the problematic character of faith thus conceived leads some to suppose it can only be an exercise in irrationality. And that is one very common reason why faith, and religion along with it, comes to be  despised.

What needs to be recovered, far away from that extreme, is consciousness of participation as lying at the foundation of all ontology, but in particular at the foundation of what faith is. Faith is knowledge by participation. But what we still tend to have, instead, is an individualist conception even of knowledge itself.

These misconceptions are receding more and more, though, in one very surprising place, namely contemporary science! (It is characteristic of our psychological hypochondria that they recede for us as long as we don’t pay attention to the fact, and thus worry about it.) Everyone uses the expression, “we now know.” “We now know” that our galaxy is but one among many. “We now know” that the blood circulates, and uses hemoglobin to carry oxygen to cells; we now know that there are more than four elements…. One might expect this expression to be disturbing to many people, on account of the contempt for faith I alluded to above; for what the expression refers to is, in fact, a kind of faith within the realm of science. Yet this faith is too manifestly natural for anyone to find it disturbing.  To find it disturbing, one would have to return to the radical neurotic Cartesian individualism, where you sit in a room by yourself and try to deduce all of reality. Most people aren’t devoid of sense enough to do that.

What is especially interesting is that the project of modern science (scientia, knowledge) has itself become obviously too big to continue under the earlier enlightenment paradigm, where we think we must know everything by doing our own experiments and making our own observations. And nobody worries about that fact (at least not as long as “politics,” in the pejorative sense, hasn’t yet entered the picture). Real people understand that there is no reason to worry. They are perfectly content to have faith: that is, to participate in somebody else’s knowledge. An implicit consciousness of a common good in this case makes the individualist conception of faith vanish, and a far truer conception takes its place. This is what real faith — including religious faith — looks like, and it isn’t as different from knowledge or from “reason” as many tend to think.

This is related to our discussion in this previous post, where we pointed out that scientific knowledge has an essential dependence on the work of others, and is not simply a syllogism from first principles that an individual can work out on his own. In this sense, Collins notes, science necessarily involves a kind of faith in the scientific community, past and present, and scientists themselves are not exempt from the need for this faith.

The implication of this is that religious faith should be looked at in much the same way. Religious faith requires faith in a religious community and in revelation from God, and even those in authority in the community are not exempt from the need for this faith. There is no more reason to view this as problematic or irrational than in the case of science.

James Chastek makes a similar argument:

The science of the scientist is, of itself, just as hidden as the God of the priests and consecrated persons. The great majority of persons have no more direct or distinct experience of God than they have a justified insight into scientific claims, and the way in which they could learn the science for themselves if they only had the time and talent is the same way in which they could become preternaturally holy and achieve the unitive way if they only had the time and talent.  If I, lacking the science, trust your testimony about dark matter or global warming (probably after it’s backed up by anecdotes, a gesture at some data, the social pressure to believe, and my sense that you just sound like a smart guy) then I’m in a cognitive state called faith. Taking a pragmatist approach, we come to know the value of science by its fruits in technology just as we know the value of religion though the holiness of the saints. In good logic, Pinker sees the value that many give to holiness as disordered and mistaken,  but there are all sorts of persons who say the same thing about technology.

The similarity between the title of this post and that of the last is not accidental. Dawkins claims that religious beliefs are similar to beliefs in fairies and werewolves, and his claim is empirically false. Likewise Sean Collins and James Chastek claim that religious beliefs are similar to scientific beliefs, and their claim is empirically false.

As in the case of Dawkins, Collins notes from the beginning this empirical discrepancy. Religious faith is seen as “the activity of an individual who stands in opposition to a larger, potentially deceptive, world,” and consequently it appears irrational to many. “And that is one very common reason why faith, and religion along with it, comes to be  despised.” But note that this does not commonly happen with science, even if in principle one could think in the same way about science, as Chastek points to some critics of technology.

While the empirical differences themselves will have their own causes, we can point to one empirical difference in particular that sufficiently explains the different way that people relate to scientific and religious beliefs.

The principle difference is that people speak of “many religions” in the world in a way in which they definitely do not speak of “many sciences.” If we talk of several sciences, we refer to branches of science, and the corresponding speech about religion would be branches of theology. But “many religions” refers to Catholicism, Islam, Judaism, and so on, which contain entirely distinct bodies of theology which are strongly opposed to one another. There is no analog in the case of science. We might be able to find scientific disagreements and even “heresies” like the denial of global warming, but we do not find whole bodies of scientific doctrine about the world which explain the world as a whole and are strongly opposed to one another.

There are many other empirical differences that result from this one difference. People leave their religion and join another, or they give up religion entirely, but you never see people leave their science and join another, or give up science entirely, in the sense of abandoning all scientific beliefs about the world.

This one difference sufficiently explains the suspicion Collins notes regarding religious belief. The size of the discrepancies between religious beliefs implies that many of them are wildly far from reality. And even the religious beliefs that a person might accept are frequently “rather implausible from a relatively neutral point of view,” as Rod Dreher notes. In the case of scientific beliefs, we do find some that are somewhat implausible from a relatively neutral point of view, but we do not find the kind of discrepancy which would force us to say that any of them are wildly far from reality.

A prediction that would follow from my account here would be this: if there were only one religion, in the way that there is only one science, people would not view religion with suspicion, and religious faith would actually be seen as very like scientific faith, basically in the way asserted by Sean Collins.

While we cannot test this prediction directly, consider the following text from St. Augustine:

1. I must express my satisfaction, and congratulations, and admiration, my son Boniface, in that, amid all the cares of wars and arms, you are eagerly anxious to know concerning the things that are of God. From hence it is clear that in you it is actually a part of your military valor to serve in truth the faith which is in Christ. To place, therefore, briefly before your Grace the difference between the errors of the Arians and the Donatists, the Arians say that the Father, the Son, and the Holy Ghost are different in substance; whereas the Donatists do not say this, but acknowledge the unity of substance in the Trinity. And if some even of them have said that the Son was inferior to the Father, yet they have not denied that He is of the same substance; while the greater part of them declare that they hold entirely the same belief regarding the Father and the Son and the Holy Ghost as is held by the Catholic Church. Nor is this the actual question in dispute with them; but they carry on their unhappy strife solely on the question of communion, and in the perversity of their error maintain rebellious hostility against the unity of Christ. But sometimes, as we have heard, some of them, wishing to conciliate the Goths, since they see that they are not without a certain amount of power, profess to entertain the same belief as they. But they are refuted by the authority of their own leaders; for Donatus himself, of whose party they boast themselves to be, is never said to have held this belief.

2. Let not, however, things like these disturb you, my beloved son. For it is foretold to us that there must needs be heresies and stumbling-blocks, that we may be instructed among our enemies; and that so both our faith and our love may be the more approved—our faith, namely, that we should not be deceived by them; and our love, that we should take the utmost pains we can to correct the erring ones themselves; not only watching that they should do no injury to the weak, and that they should be delivered from their wicked error, but also praying for them, that God would open their understanding, and that they might comprehend the Scriptures. For in the sacred books, where the Lord Christ is made manifest, there is also His Church declared; but they, with wondrous blindness, while they would know nothing of Christ Himself save what is revealed in the Scriptures, yet form their notion of His Church from the vanity of human falsehood, instead of learning what it is on the authority of the sacred books.

3. They recognize Christ together with us in that which is written, “They pierced my hands and my feet. They can tell all my bones: they look and stare upon me. They part my garments among them, and cast lots upon my vesture;” and yet they refuse to recognize the Church in that which follows shortly after: “All the ends of the world shall remember, and turn unto the Lord; and all the kindreds of the nations shall worship before You. For the kingdom is the Lord’s; and He is the Governor among the nations.” They recognize Christ together with us in that which is written, “The Lord has said unto me, You are my Son, this day have I begotten You;” and they will not recognize the Church in that which follows: “Ask of me, and I shall give You the heathen for Your inheritance, and the uttermost parts of the earth for Your possession.” They recognize Christ together with us in that which the Lord Himself says in the gospel, “Thus it behooved Christ to suffer, and to rise from the dead the third day;” and they will not recognize the Church in that which follows: “And that repentance and remission of sins should be preached in His name among all nations, beginning at Jerusalem.” Luke 24:46-47 And the testimonies in the sacred books are without number, all of which it has not been necessary for me to crowd together into this book. And in all of them, as the Lord Christ is made manifest, whether in accordance with His Godhead, in which He is equal to the Father, so that, “In the beginning was the Word, and; the Word was with God, and the Word was God;” or according to the humility of the flesh which He took upon Him, whereby “the Word was made flesh and dwelt among us;” so is His Church made manifest, not in Africa alone, as they most impudently venture in the madness of their vanity to assert, but spread abroad throughout the world.

4. For they prefer to the testimonies of Holy Writ their own contentions, because, in the case of Cæcilianus, formerly a bishop of the Church of Carthage, against whom they brought charges which they were and are unable to substantiate, they separated themselves from the Catholic Church—that is, from the unity of all nations. Although, even if the charges had been true which were brought by them against Cæcilianus, and could at length be proved to us, yet, though we might pronounce an anathema upon him even in the grave, we are still bound not for the sake of any man to leave the Church, which rests for its foundation on divine witness, and is not the figment of litigious opinions, seeing that it is better to trust in the Lord than to put confidence in man. For we cannot allow that if Cæcilianus had erred,— a supposition which I make without prejudice to his integrity—Christ should therefore have forfeited His inheritance. It is easy for a man to believe of his fellow-men either what is true or what is false; but it marks abandoned impudence to desire to condemn the communion of the whole world on account of charges alleged against a man, of which you cannot establish the truth in the face of the world.

5. Whether Cæcilianus was ordained by men who had delivered up the sacred books, I do not know. I did not see it, I heard it only from his enemies. It is not declared to me in the law of God, or in the utterances of the prophets, or in the holy poetry of the Psalms, or in the writings of any one of Christ’s apostles, or in the eloquence of Christ Himself. But the evidence of all the several scriptures with one accord proclaims the Church spread abroad throughout the world, with which the faction of Donatus does not hold communion. The law of God declared, “In your seed shall all the nations of the earth be blessed.” Genesis 26:4 The Lord said by the mouth of His prophet, “From the rising of the sun, even unto the going down of the same, a pure sacrifice shall be offered unto my name: for my name shall be great among the heathen.” Malachi 1:11 The Lord said through the Psalmist, “He shall have dominion also from sea to sea, and from the river unto the ends of the earth.” The Lord said by His apostle, “The gospel has come unto you, as it is in all the world, and brings forth fruit.” Colossians 1:6 The Son of God said with His own mouth, “You shall be witnesses unto me, both in Jerusalem, and in all Judea, and in Samaria, and even unto the uttermost part of the earth.” Acts 1:8 Cæcilianus, the bishop of the Church of Carthage, is accused with the contentiousness of men; the Church of Christ, established among all nations, is recommended by the voice of God. Mere piety, truth, and love forbid us to receive against Cæcilianus the testimony of men whom we do not find in the Church, which has the testimony of God; for those who do not follow the testimony of God have forfeited the weight which otherwise would attach to their testimony as men.

Note the source of St. Augustine’s confidence. It is the “unity of the whole world.” It is “abandoned impudence to desire to condemn the communion of the whole world.” The Catholic Church is “established among all nations,” and this is reason to accept it instead of the doctrines of the heretics.

The comparison between religious beliefs and scientific beliefs applies much better to the time of St. Augustine. Even St. Augustine would know that alternate religions exist, but in a similar sense there might have appeared to be potentially many sciences, insofar as science is not at the time a unified body of ideas attempting to explain the world. Thales held that all things are derived from water, while others came out in favor of air or fire.

Nonetheless, even at the time of St. Augustine, there are seeds of the difference. Unknown to St. Augustine, native Americans of the time were certainly practicing entirely different religions. And while I made the comparison between religious heresy and dissent on certain scientific questions above, these in practice have their own differences. Religious heresy of itself contains a seed of schism, and thus the possibility of establishing a new religion. Scientific disagreement even of the kind that might be compared with “heresy,” never leads to the development of a new set of scientific doctrines about the world that can be considered an alternative science.

In contrast, if even religious heresy had not existed, St. Augustine would be entirely right simply to point to the consent of the world. Aristotle frequently points to the agreement of all men as one of the best signs of truth, for example here:

And about all these matters the endeavor must be made to seek to convince by means of rational arguments, using observed facts as evidences and examples. For the best thing would be if all mankind were seen to be in agreement with the views that will be stated, but failing that, at any rate that all should agree in some way. And this they will do if led to change their ground, for everyone has something relative to contribute to the truth, and we must start from this to give a sort of proof about our views; for from statements that are true but not clearly expressed, as we advance, clearness will also be attained, if at every stage we adopt more scientific positions in exchange for the customary confused statements.

And indeed, if there were in this way one religion with which all were in agreement, it is not merely that they would agree in fact, since this is posited, but the agreement of each would have an extremely reasonable foundation. In this situation, it would be quite reasonable to speak of religious faith and scientific faith as roughly equivalent.

In the real world, however, religious beliefs are neither like beliefs in fairies and unicorns, nor like scientific beliefs.

But as Aristotle says, “everyone has something relative to contribute to the truth,” and just as we saw some true elements in Dawkins’s point in the previous post, so there is some truth to the comparisons made by Collins and Chastek. This is in fact part of the reason why Dawkins’s basic point is mistaken. He fails to consider religious belief as a way of participating in a community, and thus does not see a difference from beliefs in werewolves and the like.

Not All Things are Water

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The basic point of the post on Thales was that material things are composed of one or more material elements. The ancient materialists were accustomed not only to maintain this position, but also to assert that it also followed that there was nothing but those elements. Thus Democritus is said to have said,

By convention, sweet; by convention, bitter; by convention, hot; by convention,
cold; by convention, color; but in reality, atoms and void.

One could say that this is an example of the attitude of “this or nothing.” If everything is made of atoms, then either a thing is atoms, or it is nothing.

The correct answer here is not to say “this or that,” but “this and that,” that is, that things made of atoms are in some way atoms, but they are also things made of them, and the things made of them are not merely atoms.

 

All Things are Water

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In book I of his Metaphysics, Aristotle comments on earlier opinions about the first causes:

Evidently we have to acquire knowledge of the original causes (for we say we know each thing only when we think we recognize its first cause), and causes are spoken of in four senses. In one of these we mean the substance, i.e. the essence (for the ‘why’ is reducible finally to the definition, and the ultimate ‘why’ is a cause and principle); in another the matter or substratum, in a third the source of the change, and in a fourth the cause opposed to this, the purpose and the good (for this is the end of all generation and change). We have studied these causes sufficiently in our work on nature, but yet let us call to our aid those who have attacked the investigation of being and philosophized about reality before us. For obviously they too speak of certain principles and causes; to go over their views, then, will be of profit to the present inquiry, for we shall either find another kind of cause, or be more convinced of the correctness of those which we now maintain.

Of the first philosophers, then, most thought the principles which were of the nature of matter were the only principles of all things. That of which all things that are consist, the first from which they come to be, the last into which they are resolved (the substance remaining, but changing in its modifications), this they say is the element and this the principle of things, and therefore they think nothing is either generated or destroyed, since this sort of entity is always conserved, as we say Socrates neither comes to be absolutely when he comes to be beautiful or musical, nor ceases to be when loses these characteristics, because the substratum, Socrates himself remains. just so they say nothing else comes to be or ceases to be; for there must be some entity-either one or more than one-from which all other things come to be, it being conserved.

Yet they do not all agree as to the number and the nature of these principles. Thales, the founder of this type of philosophy, says the principle is water (for which reason he declared that the earth rests on water), getting the notion perhaps from seeing that the nutriment of all things is moist, and that heat itself is generated from the moist and kept alive by it (and that from which they come to be is a principle of all things). He got his notion from this fact, and from the fact that the seeds of all things have a moist nature, and that water is the origin of the nature of moist things.

Some think that even the ancients who lived long before the present generation, and first framed accounts of the gods, had a similar view of nature; for they made Ocean and Tethys the parents of creation, and described the oath of the gods as being by water, to which they give the name of Styx; for what is oldest is most honourable, and the most honourable thing is that by which one swears. It may perhaps be uncertain whether this opinion about nature is primitive and ancient, but Thales at any rate is said to have declared himself thus about the first cause.

It is possibly for polemical motives that Aristotle portrays Thales as asserting that water alone is the principle of all things, to the exclusion of other kinds of cause besides the material cause. That is, most materialists, ancient and modern, do not believe that matter is the sole principle of reality. They may think it is the most important principle, but they recognize that other principles are involved, much as Lucretius recognizes that his atoms alone are insufficient to explain the world, but he must add something:

We wish thee also well aware of this:
The atoms, as their own weight bears them down
Plumb through the void, at scarce determined times,
In scarce determined places, from their course
Decline a little- call it, so to speak,
Mere changed trend. For were it not their wont
Thuswise to swerve, down would they fall, each one,
Like drops of rain, through the unbottomed void;
And then collisions ne’er could be nor blows
Among the primal elements; and thus
Nature would never have created aught.

We can understand however that even if Aristotle’s account may not be a completely accurate account of Thales’s opinions, Aristotle likely has a charitable motive for his presentation, namely the education of the reader, as by beginning by discussing the position that matter alone is the first cause, it becomes easier to see the necessity of other principles. And it is also possible that Thales did not mention any other principles simply because his interest was in the material principle, rather than from the wish to deny other principles.

There is some probability to the opinion, mentioned by Aristotle, that Thales’s idea about water had ancient predecessors. For example, there may be something like this in Genesis 1:

In the beginning when God created the heavens and the earth, the earth was a formless void and darkness covered the face of the deep, while a wind from God swept over the face of the waters. Then God said, “Let there be light”; and there was light. And God saw that the light was good; and God separated the light from the darkness. God called the light Day, and the darkness he called Night. And there was evening and there was morning, the first day.

And God said, “Let there be a dome in the midst of the waters, and let it separate the waters from the waters.” So God made the dome and separated the waters that were under the dome from the waters that were above the dome. And it was so. God called the dome Sky. And there was evening and there was morning, the second day.

And God said, “Let the waters under the sky be gathered together into one place, and let the dry land appear.” And it was so. God called the dry land Earth, and the waters that were gathered together he called Seas. And God saw that it was good.

The text speaks of a number of principles, including God, and formless matter. But the formless matter is virtually identified with water; even when the earth is a “formless void,” there is still a “deep”, and there is still a “face of the waters.” And God makes the world by divisions in the waters, creating first sky and world, and then creating dry land by limiting the lower waters.

We can ask whether Thales was right in several different ways:

First, was he right if he is understood as Aristotle understands him? In this way, his position would involve denying all principles other than material principles. And in this way Thales was wrong, since there are other principles.

Second, was he right if he is understood in contrast with other materialist philosophers such as Anaximenes, who said that all things are made of air? We can see that there is a certain difficulty in such a supposition from the beginning. For if there is only one material principle of all things, why call it “water” or “air” in particular? If water contains nothing but the first material principle, and air contains nothing but the first material principle, why is one of them identified with the principle rather than the other?

Nonetheless, we can understand the claim to be something like, “Water is the most basic and natural form of the first material principle.” In this case, what it means to be the most basic and natural would be a matter of investigation, but there is nothing impossible about it in principle. But if we understand it in this way, Thales’s position (along with that of Anaximenes and others) is refuted by modern science, since water is known to be made of other more basic things, namely oxygen and hydrogen.

But we can ask whether Thales and Anaximenes were both right in a third way, a more generic way. If we break composite material things down into their parts, and their parts into their parts, and so on, will we always arrive at one basic material “stuff” which all other things are made out of?

This would necessarily be different from the prime matter of Aristotle, because this matter is understood to be completely formless. So while it may be part of a substance along with substantial form, it is not a part in the way that an arm is a part of a human being, or in the way that oxygen is part of water. A part in the latter sense already has some actuality; an arm has a certain shape even apart from being a part of a human being, and oxygen has qualities that it has even apart from water, while prime matter has no actuality whatsoever.

Since every order of causes comes to a first cause, the same will be true if we follow the order of material causality found by asking, “What parts is this made out of?” This cannot be refuted even if it turns out that material things are infinitely divisible, because it will not actually be true that anything is made out of an infinite number of parts. If we say, “this is made out of two halves, and the halves out of more halves, and so on,” this is not an explanation at all, as was pointed out in the post linked above, and so it cannot be a true account of why the thing is as it is. It may be that the thing is potentially divisible in those ways; but it is not actually made out of those parts. Instead, we are asking what we will arrive at if we look at the material composition of things, looking only for things with some actuality, and stopping when we find something which is not made up of other things in this way.

We made a strong argument that there only one first efficient cause. But we cannot duplicate that argument to show that there must be only one first material part of things, since the first efficient cause could be an adequate explanation of two or more first material causes. The theory of the four (or five) elements is an explanation like this. The first material parts are thought be four or five, according to this account, and in this way Thales would have been mistaken.

We can see some motivation for holding such a position. If there is fundamentally only one kind of “stuff,” why do we see various things in the world, such as plants and animals, rocks, chairs, and people? An account with a number elements can say that they form various things by being combined in various proportions and ways, while it is not evident how this question can be answered, if there is only one element.

Nonetheless, this does not really refute the position that there is fundamentally a single material element. If that element can exist in various ways, then it would be possible to explain how it could be used to form more complex substances. It is true that this would still leave something to be explained, namely the nature of those various ways that the element can exist, and how and why they come to be.

The position is neither refuted nor established by modern science. The Standard Model of particle physics contains many elementary particles, but in any case it is not thought to be a complete theory of physics.

Considerations of simplicity would favor the position of Thales. Other things being equal, it should be thought that a theory with a single element is more likely than one with ten elements; one with ten more likely than one with a hundred, and so on. Nonetheless, there does not seem to be any proof of Thales’s general position, nor any refutation of it. But one way or another, there will be one or more simplest material parts that everything else is made out of.