Fire, Water, and Numbers

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.

Infinity

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Revisiting Russell on Cause

We discussed Bertrand Russell’s criticism of the first cause argument here. As I said there, he actually suggests, although without specifically making the claim, that there is no such thing as a cause, when he says:

That argument, I suppose, does not carry very much weight nowadays, because, in the first place, cause is not quite what it used to be. The philosophers and the men of science have got going on cause, and it has not anything like the vitality it used to have.

This is absurd, and it is especially objectionable that he employs this method of insinuation instead of attempting to make an argument. Nonetheless, let me attempt to argue on Russell’s behalf for a moment. It is perhaps not necessary for him to say that there is no such thing as a cause. Suppose he accepts my account of cause as an explanatory origin. Note that this is not purely an objective relationship existing in the world. It includes a specific relationship with our mind: we call something a cause when it is not only an origin, but it also explains something to us. The relatively “objective” relationship is simply that of origin.

A series of causes, since it is also a series of explanations, absolutely must have a first, since otherwise all explanatory force will be removed. But suppose Russell responds: it does not matter. Sure, this is how explanations work. But there is nothing to prevent the world from working differently. It may be that origins, namely the relationship on the objective side, do consist of infinite series. This might make it impossible to explain the world, but that would just be too bad, wouldn’t it? We already know that people have all sorts of desires for knowledge that cannot be satisfied. A complete account of the world is impossible in principle, and even in practice we can only obtain relatively local knowledge, leaving us ignorant of remote things. So you might feel a need of a first cause to make the world intelligible, Russell might say, but that is no proof at all that there is any series of origins with a first. For example, consider material causes. Large bodies are made of atoms, and atoms of smaller particles, namely electrons, protons, and neutrons. These smaller particles are made of yet smaller particles called quarks. There is no proof that this process does not go on forever. Indeed, the series would cease to explain anything if it did, but so what? Reality does not have to explain itself to you.

In response, consider the two following theories of water:

First theory: water is made of hydrogen and oxygen.

Second theory: every body of water has two parts, which we can call the first part and the second part. Each of the parts themselves has two parts, which we can call the first part of the first part, the second part of the first part, the first part of the second part, and the second part of the second part. This goes on ad infinitum.

Are these theories true? I presume the reader accepts the first theory. What about the second? We are probably inclined to say something like, “What does this mean, exactly?” But the very fact that the second theory is extremely vague means that we can probably come up with some interpretation that will make it true, depending in its details on the details of reality. Nonetheless, it is a clearly useless theory. And it is useless precisely because it cannot explain anything. There is no “causality” in the second theory, not even material causality. There is an infinite series of origins, but no explanation, and so no causes.

The first theory, on the other hand, is thought to be explanatory, and to provide material causes, because we implicitly suppose that we cannot go on forever in a similar way. It may be that hydrogen and oxygen are made up of other things: but we assume that this will not go on forever, at least with similar sorts of division.

But what if it does? It is true, in fact, that if it turns out that one can continue to break down particles into additional particles in a relatively similar manner ad infinitum, then “water is made of hydrogen and oxygen” will lose all explanatory force, and will not truly be a causal account, even in terms of material causes, even if the statement itself remains true. It would not follow, however, that causal accounts are impossible. It would simply follow that we chose the wrong account, just as one would be choosing wrongly if one attempted to explain water with the second theory above. The truth of the second theory is irrelevant; it is wrong as an explanation even if it is true.

As I have argued in a number of places, nature is not in the business of counting things. But it necessarily follows from this that it also does not call things finite or infinite; we are the ones who do that. So if you break down the world in such a way that origins are infinite, you will not be able to understand the world. That is not the world’s problem, but your problem. You can fix that by breaking down the world in such a way that origins are finite.

Perhaps Russell will continue to object. How do you know that there is any possible breakdown of the world which makes origins finite? But this objection implies the fully skeptical claim that nothing can be understood, or at least that it may turn out that nothing can be understood. As I have said elsewhere, this particular kind of skeptical claim implies a contradiction, since it implies that the same thing is known and unknown. This is the case even if you say “it might be that way,” since you must understand what you are saying when you say it might be that way.

Form is Not Matter

I have touched on this at other times, as here, here, and here. In the present post I am simply emphasizing the point more directly potentially for future reference.

If you receive an IKEA table in the mail, you have the parts that go to make up a table, but they are not yet put together in the form of a table. But very obviously, the form is not an additional part that you need to make the table. One does not say, “We need six parts for the table: the four legs, the tabletop, and the form of the table.” The form is something additional, but it is not an additional part. It is the “being put together as a table” that the parts require in order to be a table.

To say that the parts exist “in the form of a table” is also an informative expression here. One speaks as though “the form of a table” were a place, somewhat like Newton’s absolute space, in which the parts of the table exist together. This idea is helpful because just as Newton’s absolute space does not actually exist, so there will be analogous errors about form, as for example the idea that form is an additional part. Likewise, understanding the actual truth about place will help us to understand the truth about form.

Idealized Idealization

On another occasion, I discussed the Aristotelian idea that the act of the mind does not use an organ. In an essay entitled Immaterial Aspects of Thought, James Ross claims that he can establish the truth of this position definitively. He summarizes the argument:

Some thinking (judgment) is determinate in a way no physical process can be. Consequently, such thinking cannot be (wholly) a physical process. If all thinking, all judgment, is determinate in that way, no physical process can be (the whole of) any judgment at all. Furthermore, “functions” among physical states cannot be determinate enough to be such judgments, either. Hence some judgments can be neither wholly physical processes nor wholly functions among physical processes.

Certain thinking, in a single case, is of a definite abstract form (e.g. N x N = N²), and not indeterminate among incompossible forms (see I below). No physical process can be that definite in its form in a single case. Adding cases even to infinity, unless they are all the possible cases, will not exclude incompossible forms. But supplying all possible cases of any pure function is impossible. So, no physical process can exclude incompossible functions from being equally well (or badly) satisfied (see II below). Thus, no physical process can be a case of such thinking. The same holds for functions among physical states (see IV below).

In essence, the argument is that squaring a number and similar things are infinitely precise processes, and no physical process is infinitely precise. Therefore squaring a number and similar things are not physical processes.

The problem is unfortunately with the major premise here. Squaring a number, and similar things, in the way that we in fact do them, are not infinitely precise processes.

Ross argues that they must be:

Can judgments really be of such definite “pure” forms? They have to be; otherwise, they will fail to have the features we attribute to them and upon which the truth of certain judgments about validity, inconsistency, and truth depend; for instance, they have to exclude incompossible forms or they would lack the very features we take to be definitive of their sorts: e.g., conjunction, disjunction, syllogistic, modus ponens, etc. The single case of thinking has to be of an abstract “form” (a “pure” function) that is not indeterminate among incompossible ones. For instance, if I square a number–not just happen in the course of adding to write down a sum that is a square, but if I actually square the number–I think in the form “N x N = N².”

The same point again. I can reason in the form, modus ponens (“If p then q“; “p“; “therefore, q”). Reasoning by modus ponens requires that no incompossible forms also be “realized” (in the same sense) by what I have done. Reasoning in that form is thinking in a way that is truth-preserving for all cases that realize the form. What is done cannot, therefore, be indeterminate among structures, some of which are not truth preserving. That is why valid reasoning cannot be only an approximation of the form, but must be of the form. Otherwise, it will as much fail to be truth-preserving for all relevant cases as it succeeds; and thus the whole point of validity will be lost. Thus, we already know that the evasion, “We do not really conjoin, add, or do modus ponens but only simulate them,” cannot be correct. Still, I shall consider it fully below.

“It will as much fail to be truth-preserving for all relevant cases as it succeeds” is an exaggeration here. If you perform an operation which approximates modus ponens, then that operation will be approximately truth preserving. It will not be equally truth preserving and not truth preserving.

I have noted many times in the past, as for example here, here, here, and especially here, that following the rules of syllogism does not in practice infallibly guarantee that your conclusions are true, even if your premises are in some way true, because of the vagueness of human thought and language. In essence, Ross is making a contrary argument: we know, he is claiming, that our arguments infallibly succeed; therefore our thoughts cannot be vague. But it is empirically false that our arguments infallibly succeed, so the argument is mistaken right from its starting point.

There is also a strawmanning of the opposing position here insofar as Ross describes those who disagree with him as saying that “we do not really conjoin, add, or do modus ponens but only simulate them.” This assumes that unless you are doing these things perfectly, rather than approximating them, then you are not doing them at all. But this does not follow. Consider a triangle drawn on a blackboard. Consider which of the following statements is true:

  1. There is a triangle drawn on the blackboard.
  2. There is no triangle drawn on the blackboard.

Obviously, the first statement is true, and the second false. But in Ross’s way of thinking, we would have to say, “What is on the blackboard is only approximately triangular, not exactly triangular. Therefore there is no triangle on the blackboard.” This of course is wrong, and his description of the opposing position is wrong in the same way.

Naturally, if we take “triangle” as shorthand for “exact rather than approximate triangle” then (2) will be true. And in a similar way, if take “really conjoin” and so on as shorthand for “really conjoin exactly and not approximately,” then those who disagree will indeed say that we do not do those things. But this is not a problem unless you are assuming from the beginning that our thoughts are infinitely precise, and Ross is attempting to establish that this must be the case, rather than claiming to take it as given. (That is, the summary takes it as given, but Ross attempts throughout the article to establish it.)

One could attempt to defend Ross’s position as follows: we must have infinitely precise thoughts, because we can understand the words “infinitely precise thoughts.” Or in the case of modus ponens, we must have an infinitely precise understanding of it, because we can distinguish between “modus ponens, precisely,” and “approximations of modus ponens“. But the error here is similar to the error of saying that one must have infinite certainty about some things, because otherwise one will not have infinite certainty about the fact that one does not have infinite certainty, as though this were a contradiction. It is no contradiction for all of your thoughts to be fallible, including this one, and it is no contradiction for all of your thoughts to be vague, including your thoughts about precision and approximation.

The title of this post in fact refers to this error, which is probably the fundamental problem in Ross’s argument. Triangles in the real world are not perfectly triangular, but we have an idealized concept of a triangle. In precisely the same way, the process of idealization in the real world is not an infinitely precise process, but we have an idealized concept of idealization. Concluding that our acts of idealization must actually be ideal in themselves, simply because we have an idealized concept of idealization, would be a case of confusing the way of knowing with the way of being. It is a particularly confusing case simply because the way of knowing in this case is also materially the being which is known. But this material identity does not make the mode of knowing into the mode of being.

We should consider also Ross’s minor premise, that a physical process cannot be determinate in the way required:

Whatever the discriminable features of a physical process may be, there will always be a pair of incompatible predicates, each as empirically adequate as the other, to name a function the exhibited data or process “satisfies.” That condition holds for any finite actual “outputs,” no matter how many. That is a feature of physical process itself, of change. There is nothing about a physical process, or any repetitions of it, to block it from being a case of incompossible forms (“functions”), if it could be a case of any pure form at all. That is because the differentiating point, the point where the behavioral outputs diverge to manifest different functions, can lie beyond the actual, even if the actual should be infinite; e.g., it could lie in what the thing would have done, had things been otherwise in certain ways. For instance, if the function is x(*)y = (x + y, if y < 10^40 years, = x + y +1, otherwise), the differentiating output would lie beyond the conjectured life of the universe.

Just as rectangular doors can approximate Euclidean rectangularity, so physical change can simulate pure functions but cannot realize them. For instance, there are no physical features by which an adding machine, whether it is an old mechanical “gear” machine or a hand calculator or a full computer, can exclude its satisfying a function incompatible with addition, say quaddition (cf. Kripke’s definition of the function to show the indeterminacy of the single case: quus, symbolized by the plus sign in a circle, “is defined by: x quus y = x + y, if x, y < 57, =5 otherwise”) modified so that the differentiating outputs (not what constitutes the difference, but what manifests it) lie beyond the lifetime of the machine. The consequence is that a physical process is really indeterminate among incompatible abstract functions.

Extending the list of outputs will not select among incompatible functions whose differentiating “point” lies beyond the lifetime (or performance time) of the machine. That, of course, is not the basis for the indeterminacy; it is just a grue-like illustration. Adding is not a sequence of outputs; it is summing; whereas if the process were quadding, all its outputs would be quadditions, whether or not they differed in quantity from additions (before a differentiating point shows up to make the outputs diverge from sums).

For any outputs to be sums, the machine has to add. But the indeterminacy among incompossible functions is to be found in each single case, and therefore in every case. Thus, the machine never adds.

There is some truth here, and some error here. If we think about a physical process in the particular way that Ross is considering it, it will be true that it will always be able to be interpreted in more than one way. This is why, for example, in my recent discussion with John Nerst, John needed to say that the fundamental cause of things had to be “rules” rather than e.g. fundamental particles. The movement of particles, in itself, could be interpreted in various ways. “Rules,” on the other hand, are presumed to be something which already has a particular interpretation, e.g. adding as opposed to quadding.

On the other hand, there is also an error here. The prima facie sign of this error is the statement that an adding machine “never adds.” Just as according to common sense we can draw triangles on blackboards, so according to common sense the calculator on my desk can certainly add. This is connected with the problem with the entire argument. Since “the calculator can add” is true in some way, there is no particular reason that “we can add” cannot be true in precisely the same way. Ross wishes to argue that we can add in a way that the calculator cannot because, in essence, we do it infallibly; but this is flatly false. We do not do it infallibly.

Considered metaphysically, the problem here is ignorance of the formal cause. If physical processes were entirely formless, they indeed would have no interpretation, just as a formless human (were that possible) would be a philosophical zombie. But in reality there are forms in both cases. In this sense, Ross’s argument comes close to saying “human thought is a form or formed, but physical processes are formless.” Since in fact neither is formless, there is no reason (at least established by this argument) why thought could not be the form of a physical process.

 

Zombies and Ignorance of the Formal Cause

Let’s look again at Robin Hanson’s account of the human mind, considered previously here.

Now what I’ve said so far is usually accepted as uncontroversial, at least when applied to the usual parts of our world, such as rivers, cars, mountains laptops, or ants. But as soon as one claims that all this applies to human minds, suddenly it gets more controversial. People often state things like this:

I am sure that I’m not just a collection of physical parts interacting, because I’m aware that I feel. I know that physical parts interacting just aren’t the kinds of things that can feel by themselves. So even though I have a physical body made of parts, and there are close correlations between my feelings and the states of my body parts, there must be something more than that to me (and others like me). So there’s a deep mystery: what is this extra stuff, where does it arise, how does it change, and so on. We humans care mainly about feelings, not physical parts interacting; we want to know what out there feels so we can know what to care about.

But consider a key question: Does this other feeling stuff interact with the familiar parts of our world strongly and reliably enough to usually be the actual cause of humans making statements of feeling like this?

What would someone mean by making the original statement that “I know that physical parts interacting just aren’t the kinds of things that can feel by themselves”? If we give this a charitable interpretation, the meaning is that “a collection of physical parts” is something many, and so is not a suitable subject for predicates like “sees” and “understands.” Something that sees is something one, and something that understands is something one.

This however is not Robin’s interpretation. Instead, he understands it to mean that besides the physical parts, there has to be one additional part, namely one which is a part in the same sense of “part”, but which is not physical. And indeed, some tend to think this way. But this of course is not helpful, because the reason a collection of parts is not a suitable subject for seeing or understanding is not because those parts are physical, but because the subject is not something one. And this would remain even if you add a non-physical part or parts. Instead, what is needed to be such a subject is that the subject be something one, namely a living being with the sense of sight, in order to see, or one with the power of reason, for understanding.

What do you need in order to get one such subject from “a collection of parts”? Any additional part, physical or otherwise, will just make the collection bigger; it will not make the subject something one. It is rather the formal cause of a whole that makes the parts one, and this formal cause is not a part in the same sense. It is not yet another part, even a non-physical one.

Reading Robin’s discussion in this light, it is clear that he never even considers formal causes. He does not even ask whether there is such a thing. Rather, he speaks only of material and efficient causes, and appears to be entirely oblivious even to the idea of a formal cause. Thus when asking whether there is anything in addition to the “collection of parts,” he is asking whether there is any additional material cause. And naturally, nothing will have material causes other than the things it is made out of, since “what a thing is made out of” is the very meaning of a material cause.

Likewise, when he says, “Does this other feeling stuff interact with the familiar parts of our world strongly and reliably enough to usually be the actual cause of humans making statements of feeling like this?”, he shows in two ways his ignorance of formal causes. First, by talking about “feeling stuff,” which implies a kind of material cause. Second, when he says, “actual cause of humans making statements” he is evidently speaking about the efficient cause of people producing sounds or written words.

In both cases, formal causality is the relevant causality. There is no “feeling stuff” at all; rather, certain things are things like seeing or understanding, which are unified actions, and these are unified by their forms. Likewise, we can consider the “humans making statements” in two ways; if we simply consider the efficient causes of the sounds, one by one, you might indeed explain them as “simple parts interacting simply.” But they are not actually mere sounds; they are meaningful and express the intention and meaning of a subject. And they have meaning by reason of the forms of the action and of the subject.

In other words, the idea of the philosophical zombie is that the zombie is indeed producing mere sounds. It is not only that the zombie is not conscious, but rather that it really is just interacting parts, and the sounds it produces are just a collection of sounds. We don’t need, then, some complicated method to determine that we are not such zombies. We are by definition not zombies if we say, think, or understanding at all.

The same ignorance of the formal cause is seen in the rest of Robin’s comments:

If yes, this is a remarkably strong interaction, making it quite surprising that physicists have missed it so far. So surprising in fact as to be frankly unbelievable. If this type of interaction were remotely as simple as all the interactions we know, then it should be quite measurable with existing equipment. Any interaction not so measurable would have be vastly more complex and context dependent than any we’ve ever seen or considered. Thus I’d bet heavily and confidently that no one will measure such an interaction.

Again, he is asking whether there is some additional part which has some additional efficient causality, and suggesting that this is unlikely. It is indeed unlikely, but irrelevant, because consciousness is not an additional part, but a formal way of being that a thing has. He continues:

But if no, if this interaction isn’t strong enough to explain human claims of feeling, then we have a remarkable coincidence to explain. Somehow this extra feeling stuff exists, and humans also have a tendency to say that it exists, but these happen for entirely independent reasons. The fact that feeling stuff exists isn’t causing people to claim it exists, nor vice versa. Instead humans have some sort of weird psychological quirk that causes them to make such statements, and they would make such claims even if feeling stuff didn’t exist. But if we have a good alternate explanation for why people tend to make such statements, what need do we have of the hypothesis that feeling stuff actually exists? Such a coincidence seems too remarkable to be believed.

First, there is no “extra feeling stuff.” There is only a way of being, namely in this case being alive and conscious. Second, there is no coincidence. Robin’s supposed coincidence is that “I am conscious” is thought to mean, “I have feeling stuff,” but the feeling stuff is not the efficient cause of my saying that I have it; instead, the efficient cause is said to be simple parts interacting simply.

Again, the mistake here is simply to completely overlook the formal cause. “I am conscious” does not mean that I have any feeling stuff; it says that I am something that perceives. Of course we can modify Robin’s question: what is the efficient cause of my saying that I am conscious? Is it the fact that I actually perceive things, or is it simple parts interacting simply? But if we think of this in relation to form, it is like asking whether the properties of a square follow from squareness, or from the properties of the parts of a square. And it is perfectly obvious that the properties of a square follow both from squareness, and from the properties of the parts of a square, without any coincidence, and without interfering with one another. In the same way, the fact that I perceive things is the efficient cause of my saying that I perceive things. But the only difference between this actual situation and a philosophical zombie is one of form, not of matter; in a corresponding zombie, “simple parts interacting simply” are the cause of its producing sounds, but it neither perceives anything nor asserts that it is conscious, since its words are meaningless.

The same basic issue, namely Robin’s lack of the concept of a formal cause, is responsible for his statements about philosophical zombies:

Carroll inspires me to try to make one point I think worth making, even if it is also ignored. My target is people who think philosophical zombies make sense. Zombies are supposedly just like real people in having the same physical brains, which arose the through the same causal history. The only difference is that while real people really “feel”, zombies do not. But since this state of “feeling” is presumed to have zero causal influence on behavior, zombies act exactly like real people, including being passionate and articulate about claiming they are not zombies. People who think they can conceive of such zombies see a “hard question” regarding which physical systems that claim to feel and otherwise act as if they feel actually do feel. (And which other systems feel as well.)

The one point I want to make is: if zombies are conceivable, then none of us will ever have any more relevant info than we do now about which systems actually feel. Which is pretty much zero info! You will never have any info about whether you ever really felt in the past, or will ever feel in the future. No one part of your brain ever gets any info from any other part of your brain about whether it really feels.

The state of “feeling” is not presumed to have zero causal influence on behavior. It is thought to have precisely a formal influence on behavior. That is, being conscious is why the activity of the conscious person is “saying that they feel” instead of “producing random meaningless sounds that others mistakenly interpret as meaning that they feel.”

Robin is right that philosophical zombies are impossible, however, although not for the reasons that he supposes. The actual reason for this is that it is impossible for a disposed matter to be lacking its corresponding form, and the idea of a zombie is precisely the idea of humanly disposed matter lacking human form.

Regarding his point about “info,” the possession of any information at all is already a proof that one is not a zombie. Since the zombie lacks form, any correlation between one part and another in it is essentially a random material correlation, not one that contains any information. If the correlation is noticed as having any info, then the thing noticing the information, and the information itself, are things which possess form. This argument, as far as it goes, is consistent with Robin’s claim that zombies do not make sense; they do not, but not for the reasons that he posits.

Parts and Parmenides

Much of the difficulty of the topic of the previous post simply results from the difficulty of understanding the idea of part and whole. In our original discussion of these concepts, I noted that in order to be a whole, a thing must be itself, but also in a certain way other things which it simply speaking is not.

There is a temptation to say that this is a contradiction: since we admit that the whole is not its part, it cannot be that part in any way, and therefore it cannot satisfy our definition of a whole. And thus it would be impossible to have a whole and parts.

Parmenides attempts to resolve this problem in a simplistic manner, namely by denying the reality of distinction. Since it is impossible for one thing to be distinct from another, it is impossible to for there to be many things which could be made into a whole. There is only one thing, and consequently no need to make anything out of parts.

A more sophisticated and more common solution is to admit the reality of distinction, but to continue to deny the possibility of forming wholes from parts. By confusing the idea of “fundamental” as the primary material cause with the idea of “fundamental” as most real, Sean Carroll accepts this solution.

Both proposed solutions are contrary to common sense, and both effectively deny the reality of all the things of our common experience. Parmenides makes this denial openly, Carroll by implication, although he at least wishes to avoid it.

There is an additional inconsistency in Carroll’s view insofar as we cannot avoid thinking of the universe as a kind of whole. In other words, just as Parmenides wished to say, “there is only one thing,” Carroll wishes to say, “there are only many things.” But this cannot be done: for there cannot be many things, unless those many are in some way one.

Alexander Pruss attempts to formulate a still more sophisticated solution, which to some extent we have already discussed:

Some people are attracted to nihilism about proper parthood: no entity has proper parts. I used to be rather attracted to that myself, but I am now finding that a different thesis fits better with my intuitions: no entity is (fully) grounded. Or to put it positively: only fundamental entities exist.

This has some of the same consequences that nihilism about proper parthood would. For instance, on nihilism about proper parthood, there are no artifacts, since if there were any, they’d have proper parts. But on nihilism about ontological grounding, we can also argue that there are no artifacts, since the existence of an artifact would be grounded in social and physical facts. Moreover, nihilism about ontological grounding implies nihilism about mereological sum: for the existence of a mereological sum would be grounded in the existence of its proper parts. However, nihilism about ontological grounding is compatible with some things having parts–but they have to be things that go beyond their parts, things whose existence is not grounded in the existence and relations of their parts.

Note that he states that he was formerly attracted to the view that “no entity has proper parts.” This would assert, like the views of Parmenides and Sean Carroll, that wholes and parts are impossible. Since this seems too opposed to common sense, he formulates a new view, where it is possible for a thing to have parts, but the thing must “go beyond” its parts in some way. The existence of the whole “is not grounded” in the existence and relations of its parts.

It is not clear to me precisely what he means by grounding here, and his position could be true, if this is understood in some ways, and not true, if it is understood in others. It could be taken in a fairly tautological sense: something with parts is real if it is really one thing, and not merely many things. But we could just as well say that many things cannot exist without being in some way one. And this does not seem to be Pruss’s intended meaning, since he denies the reality of artifacts, even in this text, which would not be necessary on this understanding.

In any case there does seem to be some remaining desire to deny in some way the possibility of whole and part, indicated for example in the statement that “only fundamental entities exist.” Of course if we understand “fundamental” to mean “real,” then the statement is that only real things exist, and this is obviously true. But like in the case of Carroll, it is evident that fundamental here is meant to refer in some way to what things are made from, namely to material causes. The difference is that rather than saying that the fundamental things are particles of some kind, Pruss would say that some fundamental things are particles, while others are human beings and so on.