# Structure of Explanation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

# Place, Time, and Universals

Consider the following three statements:

1. The chair and keyboard that I am currently using are both here in this room.

2. The chair and keyboard that I am currently using both exist in January 2019.

3. The chair and keyboard that I am currently using both came in the color black.

All three claims, considered as everyday statements, happen to be true. They also have a common subject, and something common about the predicate, namely the “in.” We have “in this room,” “in January,” and “in the color black.” Now someone might object that this is a mere artifact of my awkward phrasing: obviously, I deliberately chose these formulations with this idea in mind. So this seems to be a mere verbal similarity, and a meaningless one at that.

The objection seems pretty reasonable, but I will argue that it is mistaken. The verbal similarity is not accidental, despite the fact that I did indeed choose the formulations deliberately with this idea in mind. As I intend to argue, there is indeed something common to the three cases, namely that they represent various ways of existing together.

The three statements are true in their ordinary everyday sense. But consider the following three questions:

1. Are the chair and keyboard really in the same room, or is this commonality a mere appearance?

2. Do the chair and keyboard really exist in the same month, or is this commonality a mere appearance?

3. Did the chair and keyboard really come in the same color, or is this commonality a mere appearance?

These questions are like other questions which ask whether something is “really” the case. There is no such thing as being “really” on the right apart from the ordinary understanding of being on the right, and there is no such thing as being really in the same room apart from the ordinary everyday understanding of being in the same room. The same thing applies to the third question about color.

The dispute between realism and nominalism about universals starts in the following way, roughly speaking:

Nominalist: We say that two things are black. But obviously, there are two things here, and no third thing, and the two are not the same thing. So the two do not really have anything in common. Therefore “two things are black” is nothing but a way of speaking.

Platonic Realist: Obviously, the two things really are black. But what is really the case is not just a way of speaking. So the two really do have something in common. Therefore there are three things here: the two ordinary things, and the color black.

Since the Platonic Realist here goes more against common speech in asserting the existence of “three things” where normally one would say there are “two things,” the nominalist has the apparent advantage at this point, and this leads to more qualified forms of realism. In reality, however, one should have stopped the whole argument at this point. The two positions above form a Kantian dichotomy, and as in all such cases, both positions affirm something true, and both positions affirm something false. In this particular case, the nominalist acts as the Kantian, noting that universality is a mode of knowing, and therefore concludes that it is a mere appearance. The Platonic Realist acts as the anti-Kantian, noting that we can know that several things are in fact black, and concluding that universality is a mode of being as such.

But while universality is a way of knowing, existing together is a way of being, and is responsible for the way of knowing. In a similar way, seeing both my chair and keyboard at the same time is a way of seeing things, but this way of seeing is possible because they are here together in the room. Likewise, I can know that both are black, but this knowledge is only possible because they exist together “in” the color black. What does this mean, exactly? Since we are discussing sensible qualities, things are both in the room and black by having certain relationships with my senses. They exist together in those relationships with my senses.

There is no big difference when I ask about ideas. If we ask what two dogs have in common in virtue of both being dogs, what they have in common is a similar relationship to my understanding. They exist together in that relationship with my understanding.

It might be objected that this is circular. Even if what is in common is a relationship, there is still something in common, and that seems to remain unexplained. Two red objects have a certain relationship of “appearing red” to my eyes, but then do we have two things, or three? The two red things, or the two red things and the relationship of “appearing red”? Or is it four things: two red things, and their two relationships of appearing red? So which is it?

Again, there is no difference between these questions and asking whether a table is really on the left or really on the right. It is both, relative to different things, and likewise all three of these methods of counting are valid, depending on what you want to count. As I have said elsewhere, there are no hidden essences, no “true” count, no “how many things are really there?

“Existing together,” however, is a reality, and is not merely a mode of knowing. This provides another way to analyze the problem with the nominalist / Platonic realist opposition. Both arguments falsely assume that existing together is either logically derivative or non-existent. As I said in the post on existential relativity,  it is impossible to deduce the conclusion that many things exist from a list of premises each affirming that a single thing exists, if only because “many things” does not occur as a term in that list. The nominalist position cannot explain the evident fact that both things are black. Likewise, even if there are three things, the two objects and “black,” this would not explain why the two objects are black. The two objects are not the third, since there are three. So there must be yet another object, perhaps called “participation”, which connects the two objects and blackness. And since they both have participation, there must be yet another object, participation in general, in which both objects are also participating. Obviously none of this is helping: the problem was the assumption from the start that togetherness (whether in place, time, or color) could be something logically derivative.

(Postscript: the reader might notice that in the linked post on “in,” I said that a thing is considered to be in something as form in matter. This seems odd in the context of this post, since we are talking about being “in a color,” and a color would not normally be thought of as material, but as formal. But this simply corresponds with the fact that it would be more usual to say that the color black is in the chair, rather than the chair in the black. This is because it is actually more correct: the color black is formal with respect to the chair, not material. But when we ask, “what things can come in the color black,” we do think of black as though it were a kind of formless matter that could take various determinate forms.)

# Schrödinger’s Cat

Erwin Schrödinger describes the context for his thought experiment with a cat:

The other alternative consists of granting reality only to the momentarily sharp determining parts – or in more general terms to each variable a sort of realization just corresponding to the quantum mechanical statistics of this variable at the relevant moment.

That it is in fact not impossible to express the degree and kind of blurring of all variables in one perfectly clear concept follows at once from the fact that Q.M. as a matter of fact has and uses such an instrument, the so-called wave function or psi-function, also called system vector. Much more is to be said about it further on. That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message. At all events it is an imagined entity that images the blurring of all variables at every moment just as clearly and faithfully as does the classical model its sharp numerical values. Its equation of motion too, the law of its time variation, so long as the system is left undisturbed, lags not one iota, in clarity and determinacy, behind the equations of motion of the classical model. So the latter could be straight-forwardly replaced by the psi-function, so long as the blurring is confined to atomic scale, not open to direct control. In fact the function has provided quite intuitive and convenient ideas, for instance the “cloud of negative electricity” around the nucleus, etc. But serious misgivings arise if one notices that the uncertainty affects macroscopically tangible and visible things, for which the term “blurring” seems simply wrong. The state of a radioactive nucleus is presumably blurred in such a degree and fashion that neither the instant of decay nor the direction, in which the emitted alpha-particle leaves the nucleus, is well-established. Inside the nucleus, blurring doesn’t bother us. The emerging particle is described, if one wants to explain intuitively, as a spherical wave that continuously emanates in all directions and that impinges continuously on a surrounding luminescent screen over its full expanse. The screen however does not show a more or less constant uniform glow, but rather lights up at one instant at one spot – or, to honor the truth, it lights up now here, now there, for it is impossible to do the experiment with only a single radioactive atom. If in place of the luminescent screen one uses a spatially extended detector, perhaps a gas that is ionised by the alpha-particles, one finds the ion pairs arranged along rectilinear columns, that project backwards on to the bit of radioactive matter from which the alpha-radiation comes (C.T.R. Wilson’s cloud chamber tracks, made visible by drops of moisture condensed on the ions).

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

We see here the two elements described at the end of this earlier post. The psi-function is deterministic, but there seems to be an element of randomness when someone comes to check on the cat.

Hugh Everett amusingly describes a similar experiment performed on human beings (but without killing anyone):

Isolated somewhere out in space is a room containing an observer, A, who is about to perform a measurement upon a system S. After performing his measurement he will record the result in his notebook. We assume that he knows the state function of S (perhaps as a result of previous measurement), and that it is not an eigenstate of the measurement he is about to perform. A, being an orthodox quantum theorist, then believes that the outcome of his measurement is undetermined and that the process is correctly described by Process 1 [namely a random determination caused by measurement].

In the meantime, however, there is another observer, B, outside the room, who is in possession of the state function of the entire room, including S, the measuring apparatus, and A, just prior to the measurement. B is only interested in what will be found in the notebook one week hence, so he computes the state function of the room for one week in the future according to Process 2 [namely the deterministic  wave function]. One week passes, and we find B still in possession of the state function of the room, which this equally orthodox quantum theorist believes to be a complete description of the room and its contents. If B’s state function calculation tells beforehand exactly what is going to be in the notebook, then A is incorrect in his belief about the indeterminacy of the outcome of his measurement. We therefore assume that B’s state function contains non-zero amplitudes over several of the notebook entries.

At this point, B opens the door to the room and looks at the notebook (performs his observation.) Having observed the notebook entry, he turns to A and informs him in a patronizing manner that since his (B’s) wave function just prior to his entry into the room, which he knows to have been a complete description of the room and its contents, had non-zero amplitude over other than the present result of the measurement, the result must have been decided only when B entered the room, so that A, his notebook entry, and his memory about what occurred one week ago had no independent objective existence until the intervention by B. In short, B implies that A owes his present objective existence to B’s generous nature which compelled him to intervene on his behalf. However, to B’s consternation, A does not react with anything like the respect and gratitude he should exhibit towards B, and at the end of a somewhat heated reply, in which A conveys in a colorful manner his opinion of B and his beliefs, he rudely punctures B’s ego by observing that if B’s view is correct, then he has no reason to feel complacent, since the whole present situation may have no objective existence, but may depend upon the future actions of yet another observer.

Schrödinger’s problem was that the wave equation seems to describe something “blurred,” but if we assume that is because something blurred exists, it seems to contradict our experience which is of something quite distinct: a live cat or a dead cat, but not something in between.

Everett proposes that his interpretation of quantum mechanics is able to resolve this difficulty. After presenting other interpretations, he proposes his own (“Alternative 5”):

Alternative 5: To assume the universal validity of the quantum description, by the complete abandonment of Process 1 [again, this was the apparently random measurement process]. The general validity of pure wave mechanics, without any statistical assertions, is assumed for all physical systems, including observers and measuring apparata. Observation processes are to be described completely by the state function of the composite system which includes the observer and his object-system, and which at all times obeys the wave equation (Process 2).

It is evident that Alternative 5 is a theory of many advantages. It has the virtue of logical simplicity and it is complete in the sense that it is applicable to the entire universe. All processes are considered equally (there are no “measurement processes” which play any preferred role), and the principle of psycho-physical parallelism is fully maintained. Since the universal validity of the state function is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the whole universe. In this sense this theory can be called the theory of the “universal wave function,” since all of physics is presumed to follow from this function alone. There remains, however, the question whether or not such a theory can be put into correspondence with our experience.

This present thesis is devoted to showing that this concept of a universal wave mechanics, together with the necessary correlation machinery for its interpretation, forms a logically self consistent description of a universe in which several observers are at work.

Ultimately, Everett’s response to Schrödinger is that the cat is indeed “blurred,” and that this never goes away. When someone checks on the cat, the person checking is also “blurred,” becoming a composite of someone seeing a dead cat and someone seeing a live cat. However, these are in effect two entirely separate worlds, one in which someone sees a live cat, and one in which someone sees a dead cat.

Everett mentions “the necessary correlation machinery for its interpretation,” because a mathematical theory of physics as such does not necessarily say that anyone should see anything in particular. So for example when Newton when says that there is a gravitational attraction between masses inversely proportional to the square of their distance, what exactly should we expect to see, given that? Obviously there is no way to answer this without adding something, and ultimately we need to add something non-mathematical, namely something about the way our experiences work.

I will not pretend to judge whether or not Everett does a good job defending his position. There is an interesting point here, whether or not his defense is ultimately a good one. “Orthodox” quantum mechanics, as Everett calls it, only gives statistical predictions about the future, and as long as nothing is added to the theory, it implies that deterministic predictions are impossible. It follows that if the position in our last post, on an open future, was correct, it must be possible to explain the results of quantum mechanics in terms of many worlds or multiple timelines. And I do not merely mean that we can give the same predictions with a one-world account or with a many world account. I mean that there must be a many-world account such that its contents are metaphysically identical to the contents of a one-world account with an open future.

This would nonetheless leave undetermined the question of what sort of account would be most useful to us in practice.

# Generalized Kantian Dichotomy

At the end of the last post I suggested that the confusion between the mode of knowledge and the mode of being might be a primary, or rather the primary, cause of philosophical error, with the exception of motivated error.

If we consider the “Kantian” and “anti-Kantian” errors in the last post, we can give a somewhat general account of how this happens. The two errors might appear to be mutually exclusive and exhaustive, but in fact they constitute a false dichotomy. Consider the structure of the disagreement:

A. Common sense takes note of something: in this case, that it is possible to know things. Knowledge is real.

B. The Kantian points out that the mode of knowing and the mode of being are not the same, and concludes that common sense is wrong. Knowledge is apparent, but not real.

C. The anti-Kantian, determined to uphold common sense, applies modus tollens. We know that knowledge is real: so the mode of knowing and the mode of being must be the same.

Each party to the dispute says something true (that knowledge is real, that the mode of being and the mode of knowing are not the same), and something false (that knowledge is not real, that the mode of being and the mode of knowing are the same.)

A vast number of philosophical disputes can be analyzed in a very similar manner. Thus we have the general structure:

A. Common sense points out that some item X is real.

B. The Kantian points out that the mode of knowing and the mode of being are not the same, and concludes that common sense is wrong. X is apparent, but not real.

C. The anti-Kantian, determined to uphold common sense, applies modus tollens. We know that X is real: so the mode of knowing and the mode of being must be the same.

Once again, in this general structure, each party to the dispute would say something true (that X is real, that the mode of knowing and being are not the same), and something false (the denial of one of these two.) As an example, we can apply this structure to our discussion of reductionism and anti-reductionism. The reductionist, in this case, is the Kantian (in our present structure), and the anti-reductionist the anti-Kantian. The very same person might well argue both sides about different things: thus Sean Carroll might be anti-reductionist about fundamental particles and reductionist about humans, while Alexander Pruss is anti-reductionist about humans and reductionist about artifacts. But whether we are discussing fundamental particles, humans, or artifacts, both sides are wrong. Both say something true, but also something false.

Several cautionary notes are needed in this regard.

First, both sides will frequently realize that they are saying something strongly counter-intuitive, and attempt to remedy this by saying something along the lines of “I don’t mean to say the thing that is false.” But that is not the point. I do not say that you intend to say the thing that is false. I say that you give an account which logically implies the thing that is false, and that the only way you can avoid this implication is by rejecting the false dichotomy completely, namely by accepting both the reality of X, and the distinction of the modes of knowing and being. Thus for example Sean Carroll’s does not distinguish his poetic naturalism from eliminativism in terms of what it says to be true, but only in terms of what it says to be useful. But eliminativism says that it is false that there are ships: therefore Carroll’s poetic naturalism also says that it is false that there are ships, whether he intends to say this or not, and whether or not he finds it useful to say that there are.

Second, this outline uses the terminology of “Kantian” and “anti-Kantian,” but in fact the two tend to blur into one another, because the mistakes are very similar: both imply that the unknown and the known, as such, are the same. Thus for example in my post on reductionism I said that there was a Kantian error in the anti-reductionist position: but in the present schema, the error is anti-Kantian. In part, this happened because I did not make these distinctions clearly enough myself in the earlier post. But is it also because the errors themselves uphold very similar contradictions. Thus the anti-reductionist thinks somewhat along these lines:

We know that a human being is one thing. We know it as a unity, and therefore it has a mode of being as a unity. But whenever anyone tries to explain the idea of a human being, they end up saying many things about it. So our explanation of a human being cannot be the true explanation. Since the mode of knowing and the mode of being must be the same, a true explanation of a human being would have to be absolutely one. We have no explanation like that, so it must be that a human being has an essence which is currently hidden from us.

Note that this reasons in an anti-Kantian manner (the mode of being and the mode of knowing must be the same), but the conclusion is effectively Kantian: possible or not, we actually have no knowledge of human beings as they are.

As I said in the post on reductionism, the parties to the dispute will in general say that an account like mine is anti-realist: realism, according to both sides, requires that one accept one side of the dichotomy and reject the other. But I respond that the very dispute between realism and anti-realism can be itself an example of the false dichotomy, as the dispute is often understood. Thus:

A. Common sense notes that the things we normally think and talk about are real, and that the things we normally say about them are true.

B. The Kantian (the anti-realist) points out that the mode of knowing and the mode of being are not the same, and concludes that common sense is wrong. The things we normally talk about appear to be real, but they are not.

C. The anti-Kantian (the realist) applies modus tollens. We know these things are real: so the mode of knowledge and the mode of being must be the same after all.

As usual, both say something true, and both say something false. Consider Scott Sumner, who tends to take an anti-realist position, as for example here:

Even worse, I propose doing so for “postmodern” reasons. I will start by denying the reality of inflation, and then argue for some substitute concepts that are far more useful. First a bit of philosophy. There is a lively debate about whether there is a meaningful distinction between our perception of reality, and actual reality. I had a long debate with a philosopher about whether Newton’s laws of motion were a part of reality, or merely a human construct. I took the latter view, arguing that if humans had never existed then Newton’s laws would have never existed. He argued they are objectively true. I responded that Einstein showed that were false. He responded that they were objectively true in the limiting case. I argued that even that might be changed by future developments in our understanding of reality at the quantum level. He argued that they’d still be objectively approximately true, etc, etc.

On the one hand, a lot of what Scott says here is right. On the other hand, he mistakenly believes that it follows that common sense is mistaken in matters in which it is not, in fact, mistaken. The reasoning is basically the reasoning of the Kantian: one notices that we have a specific mode of knowing which is not the mode of being of things, and concludes that knowledge is impossible, or in Scott’s terminology, “objective truth” does not exist, at least as distinct from personal opinion. He has a more extensive discussion of this here:

I don’t see it as relativism at all. I don’t see it as the world of fuzzy post-modern philosophers attacking the virtuous hard sciences. It’s important not to get confused by semantics, and focus on what’s really at stake. In my view, Rorty’s views are most easily seen by considering his denial of the distinction between objective truth and subjective belief. In order to see why he did this, consider Rorty’s claim that, “That which has no practical implications, has no theoretical implications.” Suppose Rorty’s right, and it’s all just belief that we hold with more or less confidence. What then? In contrast, suppose the distinction between subjective belief and objective fact is true. What then? What are the practical implications of each philosophical view? I believe the most useful way of thinking about this is to view all beliefs as subjective, albeit held with more or less confidence.

Let’s suppose it were true that we could divide up statements about the world into two categories, subjective beliefs and objective facts. Now let’s write down all our statements about the world onto slips of paper. Every single one of them, there must be trillions (even if we ignore the field of math, where an infinite number of statements could be constructed.) Now let’s divide these statements up into two big piles, one set is subjective beliefs, and the other pile contains statements that are objective facts. We build a vast Borgesian library, and put all the subjective beliefs (i.e. Trump is an idiot) into one wing, and all the objective facts (Paris is the capital of France) into the other wing.

Now here’s the question for pragmatists like Rorty and me. Is this a useful distinction to make? If it is useful, how is it useful? Here’s the only useful thing I can imagine resulting from this distinction. If we have a category of objective facts, then we can save time by not questioning these facts as new information arises. They are “off limits”. Since they are objective facts, they can never be refuted. If they could be refuted, then they’d be subjective beliefs, not objective facts.

But I don’t want to do that. I don’t want to consider any beliefs to be completely off limits—not at all open to refutation. That reminds me too much of fundamentalist religion. On the other hand, I do want to distinguish between different kinds of beliefs, in a way that I think is more pragmatic than the subjective/objective distinction. Rather I’d like to assign probability values to each belief, which represent my confidence as to whether or not the belief is true. Then I’d like to devote more of my time to entertaining critiques of highly questionable hypotheses, than I do to less plausible hypotheses.

Again, this makes a great deal of sense. The problem is that Scott thinks that either there is no distinction between the subjective and objective, or we need to be able to make that distinction subjectively. Since the latter seems an evident contradiction, he concludes that there is no distinction between subjective and objective. Later in the post, he puts this in terms of “map and territory”:

The other point of confusion I see is people conflating “the map and the territory”. Then they want to view “objective facts” as aspects of the territory, the underlying reality, not (just) beliefs about the territory. I don’t think that’s very useful, as it seems to me that statements about the world are always models of the world, not the world itself. Again, if it were not true, then theories could never be revised over time. After all, Einstein didn’t revise reality in 1905; he revised our understanding of reality–our model of reality.

“Statements about the world are always models of the world, not the world itself.” Indeed. That is because they are statements, not the things the statements are about. This is correctly to notice that the mode of knowledge is not the mode of being. But it does not follow that there are no objective facts, nor that objective facts are not distinct from opinions. Consider the statement that “dogs are animals.” We can call that statement a “model of the world.” But is not about a model of the world: it is about dogs, which are not our model or even parts of our model, but things moving around outside in the real world. Obviously, we cannot concretely distinguish between “things we think are true” and “things that are actually true,” because it will always be us talking about things that are actually true, but we can make and understand that distinction in the abstract. Scott is right, however, to reject the idea that some ideas are subjective “because they are about the map,” with other statements being objective “because they are about the territory.” In the map / territory terminology, all statements are maps, and all of them are about the territory (including statements about maps, which refer to maps as things that exist, and thus as part of the territory.)

We can see here how Scott Sumner is falling into the Kantian error. But what about the realist position? It does not follow from any of the above that the realist must make any corresponding error. And indeed, in all such dichotomies, there will be a side which is more right than the other: namely, the side that says that common sense is right. And so it is possible, and correct, to say that common sense is right without also accepting the corresponding falsehood (namely that the mode of knowing and the mode of being are the same.) But if we do accept the realist position together with the corresponding falsehood, this can manifest itself in various ways. For example, one might say that one should indeed put some things in the category of “off limits” for discussion: since they are objective facts, they can never be revised. Thus for example James Larson, as in an earlier discussion, tends to identify the rejection of his positions with the rejection of realism. In effect, “My beliefs are objectively true. So people who disagree with my beliefs reject objective truth. And I cannot admit that my beliefs might be false, because that would mean an objective truth could be false at the same time, which is a contradiction.” The problem will not always be manifested in the same way, however, because as we said in the last post, each end of the false dichotomy implies a similar contradiction and cannot be reasoned about coherently.

# Reductionist vs Anti-Reductionist Dichotomy

I started this post with a promise to return to issues raised by this earlier one. I haven’t really done so, or at least not as I intended, basically because it simply turned out that there was still too much to discuss, some but not all of which I discussed in the last two posts. I am still not ready to return to those original issues. However, the purpose of this post is to keep the promise to explain the relevance of my rejection of both reductionism and anti-reductionism to my account of form. To some extent this has already been done, but a clearer account is possible.

Before going through this kind of consideration, I expect almost everyone to accept implicitly or explicitly an account which maintains one or the other side of this false dichotomy. And consequently, I expect almost everyone to find my account of form objectionable.

Reductionists in general will simply deny the existence of form: there is nothing that makes a thing one, because nothing is actually one. We might respond that if you are reducing things to something else, say to quarks, there still must be something that makes a quark one. The reductionist is likely to respond that a quark is one of itself, and does not need anything else to make it one. And indeed, you might satisfy the general definition of form in such a way, but at that point you are probably discussing words rather than the world: the question of form comes up in the first place because we wonder about the unity of things composed of parts. Thus, at any rate, the most a reductionist will concede is, “Sure, in theory you can use that definition.” But they will add, “But it is a badly formed concept that will mostly lead people away from the truth.” The error here is analogous to that of Parmenides.

Anti-reductionists will admit the existence of form, but they will reject this account, or any other account which one actually explains in detail, because their position implicitly or explicitly requires the existence of hidden essences. The basic idea is that form should make a thing so absolutely one that you cannot break it down into several things even when you are explaining it. It is very obvious that this makes explanation impossible, since any account contains many words referring to many aspects of a thing. I mentioned Bertrand Russell’s remark that science does not explain the “intrinsic character” of matter. Note that this is precisely because every account, insofar as it is an account, is formal, and form is a network of relationships. It simply is not an “intrinsic character” at all, insofar as this is something distinct from such a network. Anti-reductionism posits form as such an intrinsic character, and as such, it requires the existence of a hidden essence that cannot be known in principle. The error here is basically that of Kant.

There is something in common to the two errors, which one might put like this: Nature is in the business of counting things. There must be one final, true answer to the question, “How many things are here?” which is not only true, but excludes all other answers as false. This cannot be the case, however, for the reasons explained in the post just linked. To number things at all, whether as many or as one, is to apply a particular mode of understanding, not to present their mode of being as such.

I expect both reductionists and anti-reductionists to criticize my account at first as one which belongs to the opposite side of this dichotomy. And if they are made aware that it does not, I expect them to criticize it as anti-realist. It is not, or at any rate not in a standard sense: I reject this kind of anti-realism. If it is anti-realist, it is anti-realist in a much more reasonable way, namely about “not being something,” or about distinction. If one thing is not another, that “not another” may be a true attribution, but it is not something “out there” in the world. While the position of Parmenides overall is mistaken, he was not mistaken about the particular point that non-being is not being.

# Replies to Objections on Form

This post replies to the objections raised in the last post.

Reply 1. I do not define form as “many relations”, in part for this very reason. Rather, I say that it is a network, and thus is one thing tied together, so to speak.

Nonetheless, the objection seems to wish to find something absolutely one which is in no way many and which causes unity in other things which are in some way lacking in unity. This does not fit with the idea of giving an account, which necessarily involves many words and thus reference to many aspects of a thing. And thus it also does not fit with the idea of form as that which makes a thing what it is, because it is evident that when we ask what a thing is, we are typically asking about things that have many aspects, as a human being has many senses and many body parts and so on.

In other words, form makes a thing one, but it also makes it what it is, which means that it also makes a thing many in various ways. And so form is one in some way, and thus called a “network,” but it also contains various relations that account for the many aspects of the thing.

Someone might extend this objection by saying that if a form contains many relations, there will need to be a form of form, uniting these relations. But there is a difference between many material parts, which might need a form in order to be one, and relations, which bind things together of themselves. To be related to something, in this sense, is somewhat like being attached to it in some way, while a number of physical bodies are not attached to each other simply in virtue of being a number of bodies. It is true that this implies a certain amount of complexity in form, but this is simply the result of the fact that there is a certain amount of complexity in what things actually are.

Reply 2. “Apt to make something one” is included in the definition in order to point to the relationships and networks of relationships that we are concerned with. For example, one could discuss the idea of a mereological sum, for example the tree outside my window together with my cell phone, and talk about a certain network of relationships intrinsic to that “sum.” This network would have little share in the idea of form, precisely because it is not apt to make anything one thing in any ordinary sense. However, I say “little share” here rather than “no share”, because this is probably a question of degree and kind. As I said here, “one thing” is said in many ways and with many degrees, and thus also form exists in many ways and with many degrees. In particular, there is no reason to suppose that “one” has one true sense compared to which the other senses would be more false than true.

Reply 3. A network of relationships could be an accidental form. Thus the form that makes a blue thing blue would normally be an accidental form. But there will be a similar network of relationships that make a thing a substance. If something is related to other things as “that in which other things are present,” and is not related to other things as “that which is present in something else,” then it will exist as substance, and precisely because it is related to things in these ways. So the definition is in fact general in comparison to both substance and accident.

Reply 4. This objection could be understood as asserting that everything relative depends on something prior which is absolute. Taken in this sense, the objection is simply mistaken. The existence of more than one thing proves conclusively that relationship as such does not need to depend on anything absolute.

Another way to understand the objection would be as asserting that whatever we may say about the thing in relation to other things, all of this must result from what the thing is in itself, apart from all of this. Therefore the essence of the thing is prior to anything at all that we say about it. And in this way, there is a truth here and an error here, namely the Kantian truth and the Kantian error. Certainly the thing is the cause of our knowledge, and not simply identical with our knowledge. Nonetheless, we possess knowledge, not ignorance, of the thing, and we have this knowledge by participation in the network of relationships that defines the thing.

Reply 5. The objection gratuitously asserts that our definition is reductionist, and this can equally well be gratuitously denied. In fact, this account includes the rejection of both reductionist and anti-reductionist positions. Insofar as people suppose that these positions are the only possible positions, if they see that my account implies the rejection of their particular side of the argument, they will naturally suppose that my account implies the acceptance of the other side. This is why the 10th objection claims the opposite: namely that my account is mistaken because it seems to be anti-reductionist.

Reply 6. I agree, in fact, that we are mostly ignorant of the nature of “blue,” and likewise of the natures of most other things. But we are equally ignorant of the network of relationships that these things share in. Thus in an earlier post about Mary’s Room, I noted that we do not even come close to knowing everything that can be known about color. Something similar would be true about pretty much everything that we can commonly name. We have some knowledge of what blue is, but it is a very imperfect knowledge, and similarly we have some knowledge of what a human being is, but it is a very imperfect knowledge. This is one reason why I qualified the claim that the essences of things are not hidden: in another way, virtually all essences are hidden from us, because they are typically too complex for us to understand exhaustively.

An additional problem, also mentioned in the case of “blue,” is that the experience of blue is not the understanding of blue, and these would remain distinct even if the understanding of blue were perfect. But again, it would be an instance of the Kantian error to suppose that it follows that one would not understand the nature of blue even if one understood it (thus we make the absurdity evident.)

Reply 7. God is not an exception to the claim about hidden essences, nor to this account of form, and these claims are not necessarily inconsistent with Christian theology.

The simplicity of God should not be understood as necessarily being opposed to being a network of relationships. In particular, the Trinity is thought to be the same as the essence of God, and what is the Trinity except a network of relations?

Nor does the impossibility of knowing the essence of God imply that God’s essence is hidden in the relevant sense. Rather, it is enough to say that it is inaccessible for “practical” reasons, so to speak. For example, consider St. Thomas’s argument that no one knows all that God can do:

The created intellect, in seeing the divine essence, does not see in it all that God does or can do. For it is manifest that things are seen in God as they are in Him. But all other things are in God as effects are in the power of their cause. Therefore all things are seen in God as an effect is seen in its cause. Now it is clear that the more perfectly a cause is seen, the more of its effects can be seen in it. For whoever has a lofty understanding, as soon as one demonstrative principle is put before him can gather the knowledge of many conclusions; but this is beyond one of a weaker intellect, for he needs things to be explained to him separately. And so an intellect can know all the effects of a cause and the reasons for those effects in the cause itself, if it comprehends the cause wholly. Now no created intellect can comprehend God wholly, as shown above (Article 7). Therefore no created intellect in seeing God can know all that God does or can do, for this would be to comprehend His power; but of what God does or can do any intellect can know the more, the more perfectly it sees God.

St. Thomas argues that if anyone knew all that God can do, i.e. everything that can be God’s effect, he would not only know the essence of God, but know it perfectly. This actually supports our position precisely: if you have an exhaustive account of the network of relationships between God and the world, actual and potential, according to St. Thomas, this is to know the essence of God exhaustively.

Reply 8. I concede the objection, but simply note that the error is on the part of Christian theology, not on the part of this account.

In this case, someone might ask why I included this objection, along with the previous, where even if I consider the theology defensible, I do not consider it authoritative. The reason is that I included objections that I expected various readers to hold in one form or another, and these are two of them. But what is the use of addressing them if I simply reject the premise of the objection?

There is at least one benefit to this. There is an important lesson here. Religious doctrines are typically defined in such a way that they have few or no undue sensible implications, as I said for example about the Real Presence. But philosophy is more difficult, and shares in much of the same distance from the senses that such religious claims have. Consequently, even if you manage to avoid adopting religious doctrines that have false scientific implications (and many don’t manage to avoid even this), if you accept any religious doctrines at all, it will be much harder to avoid false philosophical implications.

In fact, the idea of an immortal soul probably has false scientific consequences as well as false philosophical consequences, at least taken as it is usually understood. Thus for example Sean Carroll argues that the mortality of the soul is a settled issue:

Adam claims that “simply is no controlled, experimental[ly] verifiable information” regarding life after death. By these standards, there is no controlled, experimentally verifiable information regarding whether the Moon is made of green cheese. Sure, we can take spectra of light reflecting from the Moon, and even send astronauts up there and bring samples back for analysis. But that’s only scratching the surface, as it were. What if the Moon is almost all green cheese, but is covered with a layer of dust a few meters thick? Can you really say that you know this isn’t true? Until you have actually examined every single cubic centimeter of the Moon’s interior, you don’t really have experimentally verifiable information, do you? So maybe agnosticism on the green-cheese issue is warranted. (Come up with all the information we actually do have about the Moon; I promise you I can fit it into the green-cheese hypothesis.)

Obviously this is completely crazy. Our conviction that green cheese makes up a negligible fraction of the Moon’s interior comes not from direct observation, but from the gross incompatibility of that idea with other things we think we know. Given what we do understand about rocks and planets and dairy products and the Solar System, it’s absurd to imagine that the Moon is made of green cheese. We know better.

We also know better for life after death, although people are much more reluctant to admit it. Admittedly, “direct” evidence one way or the other is hard to come by — all we have are a few legends and sketchy claims from unreliable witnesses with near-death experiences, plus a bucketload of wishful thinking. But surely it’s okay to take account of indirect evidence — namely, compatibility of the idea that some form of our individual soul survives death with other things we know about how the world works.

Claims that some form of consciousness persists after our bodies die and decay into their constituent atoms face one huge, insuperable obstacle: the laws of physics underlying everyday life are completely understood, and there’s no way within those laws to allow for the information stored in our brains to persist after we die. If you claim that some form of soul persists beyond death, what particles is that soul made of? What forces are holding it together? How does it interact with ordinary matter?

Everything we know about quantum field theory (QFT) says that there aren’t any sensible answers to these questions. Of course, everything we know about quantum field theory could be wrong. Also, the Moon could be made of green cheese.

Among advocates for life after death, nobody even tries to sit down and do the hard work of explaining how the basic physics of atoms and electrons would have to be altered in order for this to be true. If we tried, the fundamental absurdity of the task would quickly become evident.

Even if you don’t believe that human beings are “simply” collections of atoms evolving and interacting according to rules laid down in the Standard Model of particle physics, most people would grudgingly admit that atoms are part of who we are. If it’s really nothing but atoms and the known forces, there is clearly no way for the soul to survive death. Believing in life after death, to put it mildly, requires physics beyond the Standard Model. Most importantly, we need some way for that “new physics” to interact with the atoms that we do have.

Very roughly speaking, when most people think about an immaterial soul that persists after death, they have in mind some sort of blob of spirit energy that takes up residence near our brain, and drives around our body like a soccer mom driving an SUV. The questions are these: what form does that spirit energy take, and how does it interact with our ordinary atoms? Not only is new physics required, but dramatically new physics. Within QFT, there can’t be a new collection of “spirit particles” and “spirit forces” that interact with our regular atoms, because we would have detected them in existing experiments. Ockham’s razor is not on your side here, since you have to posit a completely new realm of reality obeying very different rules than the ones we know.

There are certainly different ways to think about this, but this is in fact a common way of thinking about the soul in relation to the body. For example, consider this discussion by James Chastek:

Objection: Conservation laws require that outcomes be already determined. By your own admission, life has to be able to “alter what would happen by physical causes alone” and therefore violates conservation laws.

Response: Again, laws and initial conditions do not suffice to explain the actual world. Life only “alters” physical causes under the counterfactual supposition that physical causes could act alone, i.e. in a way that could suffice to explain outcomes in the actual world.

Objection: It is meaningless to describe life acting on physical laws and conditions when we can’t detect this. Life-actions are vacuous entities about which we can say nothing at all. What’s their Hamiltonian?

Response: Physical laws and conditions as physical are instrumental or partial accounts of the actual world. The interactive mechanisms and measurement devices appropriate to establishing the existence of physical causes are not appropriate tools for describing all causes of the actual world.

Chastek is deliberately ignoring the question that he poses himself. But we know his opinion of the matter from previous discussions. What physics would calculate would be one thing; what the human being will do, according to Chastek, is something different.

This almost certainly does imply a violation of the laws of physics in the sense of the discussion in Chastek’s post, as well as in the sense that concerns Sean Carroll. In fact, it probably would imply a violation of conservation of energy, very possibly to such a degree that it would be possible in principle to exploit the violation to create a perpetual motion machine, somewhat along the lines of this short story by Scott Alexander. And these violations would detectable in principle, and very likely in practice as well, at least at some point.

Nonetheless, one might think about it differently, without suggesting these things, but still suppose that people have immortal souls. And one might be forgiven for being skeptical of Sean Carroll’s arguments, given that his metaphysics is wrong. Perhaps there is some implicit dependence of his argument on this mistaken metaphysics. The problem with this response is that even the correct metaphysics has the same implications, even without considering Carroll’s arguments from physics.

It is easy to see that there still loopholes for someone who wishes to maintain the immortality of the soul. But such loopholes also indicate an additional problem with the idea. In particular, the idea that the soul is subsistent implies that it is a substantial part of a human being: that a human is a whole made of soul and body much as the body is a whole made of various parts such as legs and arms. If this were the case, the soul might not be material in a quantitative sense, but it would be “matter” in the sense that we have argued that form is not matter. In this case, it would be reasonable to suppose that an additional substantial form would be necessary to unify soul and body, themselves two substantial parts.

Reply 9. There in fact is an implicit reference to matter in the definition. “Apt to make something one” refers to what is made, but it also refers to what it is made out of, if there is anything out of which it is made. The form of a chair makes the chair one chair, but it also makes the stuff of the chair into one chair.

There is more to say about matter, but my intention for now was to clarify the concept of form.

Reply 10. The network of relationships is most certainly not a construct of the mind, if one places this in opposition to “real thing.” You cannot trace back relationships to causes that do not include any relationships, if only because “cause” is in itself relative.

I have argued against reductionism in many places, and do not need to repeat those arguments here, but in particular I would note that the objection implies that “mind” is a construct of the mind, and this implies circular causality, which is impossible.

Reply 11. The objection is not really argued, and this is mainly because there cannot be a real argument for it. There is however a rough intuition supporting it, which is that applying this idea of form to immaterial things seems unfair to reality, as though we were trying to say that the limits of reality are set by the limits of the human mind. Once again, however, this is simply a case of the usual Kantian error, mixed together with choosing something that would be especially unknown to us. An immaterial thing could not exist without having some relationship with everything else. As we have suggested elsewhere, “there is an immaterial thing,” cannot even be assigned a meaning without the implied claim that I stand in some relation with it, and that it stands in some relation to me. But evidently I know very little about it. This does not mean that we need some new definition of what it is to be something; it simply means I do not know much of what that thing is, just as I do not know much of anything about it at all.

# Form and Reality II

This is a followup to this earlier post, but will use a number of other threads to get a fuller understanding of the matter. Rather than presenting this in the form of a single essay, I will present it as a number of distinct theses, many of which have already been argued or suggested in various forms elsewhere on the blog.

(1) Everything that exists or can exist has or could have some relationship with the mind: relationship is in fact intrinsic to the nature of existence.

This was argued here, with related remarks in several recent posts. In a sense the claim is not only true but obviously so. You are the one who says or can say “this exists,” and you could not say or understand it unless the thing had or could have some relationship with your mind.

Perhaps this seems a bit unfair to reality, as though the limits of reality were being set by the limits of the thinker. What if there were a limited being that could only think of some things, but other things could exist that it could not think about? It is easy to see that in this situation the limited being does not have the concept of “everything,” and so can neither affirm nor deny (1). It is not that it would affirm it but be mistaken. It would simply never think of it.

Someone could insist: I myself am limited. It might be that there are better thinkers in the world that can think about things I could never conceive of. But again, if you have concept of “everything,” then you just thought of those things: they are the things that those thinkers would think about. So you just thought about them too, and brought them into relationship with yourself.

Thus, anyone who actually has the idea of “everything,” and thinks about the matter clearly, will agree with (1).

(2) Nothing can be true which could not in principle (in some sense of “in principle”) in some way be said to be true.

Thesis (1) can be taken as saying that anything that can be, can also be understood, at least in some way; and thesis (2) can be taken as saying that anything that can be understood, can also be said, at least in some way.

Since language is conventional, this does not need much of an argument. If I think that something exists, and I don’t have a name for it, I can make up a name. If I think that one thing is another thing, but don’t have words for these things, I can make up words for them. Even if I am not quite sure what I am thinking, I can say, “I have a thought in my mind but don’t quite have the words for it,” and in some way I have already put it into words.

One particular objection to the thesis might be made from self-reference paradoxes. The player in the Liar Game cannot correctly say whether the third statement is true or false, even though it is in fact true or false. But note two things: first, he cannot do this while he is playing, but once the game is over, he can explicitly and correctly say whether it was true or false. Second, even while playing, he can say, “the third statement has a truth value,” and in this way he speaks of its truth in a generic way. This is in part why I added the hedges to (2), “at least in some way”, and “in principle.”

(3) Things do not have hidden essences. That is, they may have essences, but those essences can be explained in words.

This follows in a straightforward way from (1) and (2). The essence of a thing is just “what it is,” or perhaps, “what it most truly is.” The question “what is this thing?” is formed with words, and it is evident that anyone who answers the question, will answer the question by using words.

Now someone might object that the essence of a thing might be hidden because perhaps in some cases the question does not have an answer. But then it would not be true that it has an essence but is hidden: rather, it would be false that it has an essence. Similarly, if the question “where is this thing,” does not have any answer, it does not mean the thing is in a hidden place, but that the thing is not in a place at all.

Another objection might be that an essence might be hidden because the answer to the question exists, but cannot be known. A discussion of this would depend on what is meant by “can be known” and “cannot be known” in this context. That is, if the objector is merely saying that we do not know such things infallibly, including the answer to the question, “what is this?”, then I agree, but would add that (3) does not speak to this point one way or another. But if it is meant that “cannot be known” means that there is something there, the “thing in itself,” which in no way can be known or expressed in words, this would be the Kantian error. This is indeed contrary to (3), and implicitly to (1) or (2) or both, but it is also false.

People might also think that the essence cannot be known because they notice that the question “what is this?” can have many legitimate answers, and suppose that one of these, and only one, must be really and truly true, but think that we have no way to find out which one it is. While there are certainly cases where an apparent answer to the question is not a true answer, the main response here is that if both answers are true, both answers are true: there does not need to be a deeper but hidden level where one is true and the other false. There may however be a deeper level which speaks to other matters and possibly explains both answers. Thus I said in the post linked above that the discussion was not limited to “how many,” but would apply in some way to every question about the being of things.

(4) Reductionism, as it is commonly understood, is false.

I have argued this in various places, but more recently and in particular here and here. It is not just one-sided to say for example that the universe and everything in it is just a multitude of particles. It is false, because it takes one of several truths, and says that one is “really” true and that the other is “really” false.

(5) Anti-reductionism, as it is commonly understood, is false.

This follows from the same arguments. Anti-reductionism, as for example the sort advocated by Alexander Pruss, takes the opposite side of the above argument, saying that certain things are “really” one and in no way many. And this is also false.

(6) Form makes a thing to be what it is, and makes it to be one thing.

This is largely a question of definition. It is what is meant by form in this context.

Someone might object that perhaps there is nothing that makes a thing what it is, or there is nothing that makes it one thing. But if it is what it is of itself, or if it is one of itself, then by this definition it is its own form, and we do not necessarily have an issue with that.

Again, someone might say that the definition conflates two potentially distinct things. Perhaps one thing makes a thing what it is, and another thing makes it one thing. But this is not possible because of the convertibility of being and unity: to be a thing at all, is to be one thing.

(7) Form is what is in common between the mind and the thing it understands, and is the reason the mind understands at all.

This is very distinctly not a question of definition. This needs to be proved from (6), along with what we know about understanding.

It is not so strange to think that you would need to have something in common with a thing in order to understand it. Thus Aristotle presents the words of Empedocles:

For ’tis by Earth we see Earth, by Water Water,

By Ether Ether divine, by Fire destructive Fire,

By Love Love, and Hate by cruel Hate.

On the other hand, there is also obviously something wrong with this. I don’t need to be a tree in order to see or think about a tree, and it is not terribly obvious that there is even anything in common between us. In fact, one of Hilary Lawson’s arguments for his anti-realist position is that there frequently seems to be nothing in common between causes and effects, and that therefore there may be (or certainly will be) nothing in common between our minds and reality, and thus we cannot ultimately know anything. Thus he says in Chapter 2 of his book on closure:

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

A useful way to think about Lawson is that he is in some way a disciple of Heraclitus. Thus closure is “holding that which is different as the same,” but in reality nothing is ever the same because everything is in flux. In the context of this passage, the mousetrap is either set or sprung, and so it divides the world into two states, the “set” state and the “sprung” state. But the universes with the set mousetrap have nothing in common with one another besides the set mousetrap, and the universes with the sprung mousetrap have nothing in common with one another besides the sprung mousetrap.

We can see how this could lead to the conclusion that knowledge is impossible. Sight divides parts of the world up with various colors. Leaves are green, the sky is blue, the keyboard I am using is black. But if I look at two different green things, or two different blue things, they may have nothing in common besides the fact that they affected my sight in a similar way. The sky and a blue couch are blue for very different reasons. We discussed this particular point elsewhere, but the general concern would be that we have no reason to think there is anything in common between our mind and the world, and some reason to think there must be something in common in order for us to understand anything.

Fortunately, the solution can be found right in the examples which supposedly suggest that there is nothing in common between the mind and the world. Consider the mousetrap. Do the universes with the set mousetrap have something in common? Yes, they have the set mousetrap in common. But Lawson does not deny this. His concern is that they have nothing else in common. But they do have something else in common: they have the same relationship to the mousetrap, different from the relationship that the universes with the sprung mousetrap have to their mousetrap. What about the mousetrap itself? Do those universes have something in common with the mousetrap? If we consider the relationship between the mousetrap and the universe as a kind of single thing with two ends, then they do, although they share in it from different ends, just as a father and son have a relationship in common (in this particular sense.) The same things will be true in the case of sensible qualities. “Blue” may divide up surface reflectance properties in a somewhat arbitrary way, but it does divide them into things that have something in common, namely their relationship with the sense of sight.

Or consider the same thing with a picture. Does the picture have anything in common with the thing it represents? Since a picture is meant to actually look similar to the eye to the object pictured, it may have certain shapes in common, the straightness of certain lines, and so on. It may have some colors in common. This kind of literal commonness might have suggested to Empedocles that we should know “earth by earth,” but one difference is that a picture and the object look alike to the eye, but an idea is not something that the mind looks at, and which happens to look like a thing: rather the idea is what the mind uses in order to look at a thing at all.

Thus a better comparison would be between the the thing seen and the image in the eye or the activity of the visual cortex. It is easy enough to see by looking that the image in a person’s eye bears some resemblance to the thing seen, even the sort of resemblance that a picture has. In a vaguer way, something similar turns out to be true even in the visual cortex:

V1 has a very well-defined map of the spatial information in vision. For example, in humans, the upper bank of the calcarine sulcus responds strongly to the lower half of visual field (below the center), and the lower bank of the calcarine to the upper half of visual field. In concept, this retinotopic mapping is a transformation of the visual image from retina to V1. The correspondence between a given location in V1 and in the subjective visual field is very precise: even the blind spots are mapped into V1. In terms of evolution, this correspondence is very basic and found in most animals that possess a V1. In humans and animals with a fovea in the retina, a large portion of V1 is mapped to the small, central portion of visual field, a phenomenon known as cortical magnification. Perhaps for the purpose of accurate spatial encoding, neurons in V1 have the smallest receptive field size of any visual cortex microscopic regions.

However, as I said, this is in a much vaguer way. In particular, it is not so much an image which is in common, but certain spatial relationships. If we go back to the idea of the mousetrap, this is entirely unsurprising. Causes and effects will always have something in common, and always in this particular way, namely with a commonality of relationship, because causes and effects, as such, are defined by their relationship to each other.

How does all this bear on our thesis (7)? Consider the color blue, and the question, “what is it to be blue?” What is the essence of blue? We could answer this in at least two different ways:

1. To be blue is to have certain reflectance properties.
2. To be blue is to be the sort of thing that looks blue.

But in the way intended, these are one and the same thing. A thing looks blue if it has those properties, and it has those properties if it looks blue. Now someone might say that this is a direct refutation of our thesis, since the visual cortex presumably does not look blue or have those properties when you look at something blue. But this is like Lawson’s claim that the universe has nothing in common with the sprung mousetrap. It does have something in common, if you look at the relationship from the other end. The same thing happens when we consider the meaning of “certain reflectance properties,” and “the sort of thing that looks blue.” We are actually talking about the properties that make a thing look blue, so both definitions are relative to the sense of sight. And this means that sight has something relative in common with them, and the relation it has in common is the very one that defines the nature of blue. As this is what we mean by form (thesis 6), the form of blue must be present in the sense of sight in order to see something blue.

In fact, it followed directly from thesis (1) that the nature of blue would need to include something relative. And it followed from (2) and (3) that the very same nature would turn out to be present in our senses, thoughts, and words.

The same argument applies to the mind as to the senses. I will draw additional conclusions in a later post, and in particular, show the relevance of theses (4) and (5) to the rest.

# Consistency and Reality

Consistency and inconsistency, in their logical sense, are relationships between statements or between the parts of a statement. They are not properties of reality as such.

“Wait,” you will say. “If consistency is not a property of reality, then you are implying that reality is not consistent. So reality is inconsistent?”

Not at all. Consistency and inconsistency are contraries, not contradictories, and they are properties of statements. So reality as such is neither consistent nor inconsistent, in the same way that sounds are neither white nor black.

We can however speak of consistency with respect to reality in an extended sense, just as we can speak of truth with respect to reality in an extended sense, even though truth refers first to things that are said or thought. In this way we can say that a thing is true insofar as it is capable of being known, and similarly we might say that reality is consistent, insofar as it is capable of being known by consistent claims, and incapable of being known by inconsistent claims. And reality indeed seems consistent in this way: I might know the weather if I say “it is raining,” or if I say, “it is not raining,” depending on conditions, but to say “it is both raining and not raining in the same way” is not a way of knowing the weather.

Consider the last point more precisely. Why can’t we use such statements to understand the world? The statement about the weather is rather different from statements like, “The normal color of the sky is not blue but rather green.” We know what it would be like for this to be the case. For example, we know what we would expect if it were the case. It cannot be used to understand the world in fact, because these expectations fail. But if they did not, we could use it to understand the world. Now consider instead the statement, “The sky is both blue and not blue in exactly the same way.” There is now no way to describe the expectations we would have if this were the case. It is not that we understand the situation and know that it does not apply, as with the claim about the color of the sky: rather, the situation described cannot be understood. It is literally unintelligible.

This also explains why we should not think of consistency as a property of reality in a primary sense. If it were, it would be like the color blue as a property of the sky. The sky is in fact blue, but we know what it would be like for it to be otherwise. We cannot equally say, “reality is in fact consistent, but we know what it would be like for it to be inconsistent.” Instead, the supposedly inconsistent situation is a situation that cannot be understood in the first place. Reality is thus consistent not in the primary sense but in a secondary sense, namely that it is rightly understood by consistent things.

But this also implies that we cannot push the secondary consistency of reality too far, in several ways and for several reasons.

First, while inconsistency as such does not contribute to our understanding of the world, a concrete inconsistent set of claims can help us understand the world, and in many situations better than any particular consistent set of claims that we might currently come up with. This was discussed in a previous post on consistency.

Second, we might respond to the above by pointing out that it is always possible in principle to formulate a consistent explanation of things which would be better than the inconsistent one. We might not currently be able to arrive at the consistent explanation, but it must exist.

But even this needs to be understood in a somewhat limited way. Any consistent explanation of things will necessarily be incomplete, which means that more complete explanations, whether consistent or inconsistent, will be possible. Consider for example these recent remarks of James Chastek on Gödel’s theorem:

1.) Given any formal system, let proposition (P) be this formula is unprovable in the system

2.) If P is provable, a contradiction occurs.

3.) Therefore, P is known to be unprovable.

4.) If P is known to be unprovable it is known to be true.

5.) Therefore, P is (a) unprovable in a system and (b) known to be true.

In the article linked by Chastek, John Lucas argues that this is a proof that the human mind is not a “mechanism,” since we can know to be true something that the mechanism will not able to prove.

But consider what happens if we simply take the “formal system” to be you, and “this formula is unprovable in the system” to mean “you cannot prove this statement to be true.” Is it true, or not? And can you prove it?

If you say that it is true but that you cannot prove it, the question is how you know that it is true. If you know by the above reasoning, then you have a syllogistic proof that it is true, and so it is false that you cannot prove it, and so it is false.

If you say that it is false, then you cannot prove it, because false things cannot be proven, and so it is true.

It is evident here that you can give no consistent response that you can know to be true; “it is true but I cannot know it to be true,” may be consistent, but obviously if it is true, you cannot know it to be true, and if it is false, you cannot know it to be true. What is really proven by Gödel’s theorem is not that the mind is not a “mechanism,” whatever that might be, but that any consistent account of arithmetic must be incomplete. And if any consistent account of arithmetic alone is incomplete, much  more must any consistent explanation of reality as a whole be incomplete. And among more complete explanations, there will be some inconsistent ones as well as consistent ones. Thus you might well improve any particular inconsistent position by adopting a consistent one, but you might again improve any particular consistent position by adopting an inconsistent one which is more complete.

The above has some relation to our discussion of the Liar Paradox. Someone might be tempted to give the same response to “tonk” and to “true”:

The problem with “tonk” is that it is defined in such a way as to have inconsistent implications. So the right answer is to abolish it. Just do not use that word. In the same way, “true” is defined in such a way that it has inconsistent implications. So the right answer is to abolish it. Just do not use that word.

We can in fact avoid drawing inconsistent conclusions using this method. The problem with the method is obvious, however. The word “tonk” does not actually exist, so there is no problem with abolishing it. It never contributed to our understanding of the world in the first place. But the word “true” does exist, and it contributes to our understanding of the world. To abolish it, then, would remove some inconsistency, but it would also remove part of our understanding of the world. We would be adopting a less complete but more consistent understanding of things.

Hilary Lawson discusses this response in Closure: A Story of Everything:

Russell and Tarski’s solution to self-referential paradox succeeds only by arbitrarily outlawing the paradox and thus provides no solution at all.

Some have claimed to have a formal, logical, solution to the paradoxes of self-reference. Since if these were successful the problems associated with the contemporary predicament and the Great Project could be solved forthwith, it is important to briefly examine them before proceeding further. The argument I shall put forward aims to demonstrate that these theories offer no satisfactory solution to the problem, and that they only appear to do so by obscuring the fact that they have defined their terms in such a way that the paradox is not so much avoided as outlawed.

The problems of self-reference that we have identified are analogous to the ancient liar paradox. The ancient liar paradox stated that ‘All Cretans are liars’ but was itself uttered by a Cretan thus making its meaning undecidable. A modern equivalent of this ancient paradox would be ‘This sentence is not true’, and the more general claim that we have already encountered: ‘there is no truth’. In each case the application of the claim to itself results in paradox.

The supposed solutions, Lawson says, are like the one suggested above: “Just do not use that word.” Thus he remarks on Tarski’s proposal:

Adopting Tarski’s hierarchy of languages one can formulate sentences that have the appearance of being self-referential. For example, a Tarskian version of ‘This sentence is not true’ would be:

(I) The sentence (I) is not true-in-L.

So Tarski’s argument runs, this sentence is both a true sentence of the language meta-L, and false in the language L, because it refers to itself and is therefore, according to the rules of Tarski’s logic and the hierarchy of languages, not properly formed. The hierarchy of languages apparently therefore enables self-referential sentences but avoids paradox.

More careful inspection however shows the manoeuvre to be engaged in a sleight of hand for the sentence as constructed only appears to be self-referential. It is a true sentence of the meta-language that makes an assertion of a sentence in L, but these are two different sentences – although they have superficially the same form. What makes them different is that the meaning of the predicate ‘is not true’ is different in each case. In the meta-language it applies the meta-language predicate ‘true’ to the object language, while in the object language it is not a predicate at all. As a consequence the sentence is not self-referential. Another way of expressing this point would be to consider the sentence in the meta-language. The sentence purports to be a true sentence in the meta-language, and applies the predicate ‘is not true’ to a sentence in L, not to a sentence in meta-L. Yet what is this sentence in L? It cannot be the same sentence for this is expressed in meta-L. The evasion becomes more apparent if we revise the example so that the sentence is more explicitly self-referential:

(I) The sentence (I) is not true-in-this-language.

Tarski’s proposal that no language is allowed to contain its own truth-predicate is precisely designed to make this example impossible. The hierarchy of languages succeeds therefore only by providing an account of truth which makes genuine self-reference impossible. It can hardly be regarded therefore as a solution to the paradox of self-reference, since if all that was required to solve the paradox was to ban it, this could have been done at the outset.

Someone might be tempted to conclude that we should say that reality is inconsistent after all. Since any consistent account of reality is incomplete, it must be that the complete account of reality is inconsistent: and so someone who understood reality completely, would do so by means of an inconsistent theory. And just as we said that reality is consistent, in a secondary sense, insofar as it is understood by consistent things, so in that situation, one would say that reality is inconsistent, in a secondary sense, because it is understood by inconsistent things.

The problem with this is that it falsely assumes that a complete and intelligible account of reality is possible. This is not possible largely for the same reasons that there cannot be a list of all true statements. And although we might understand things through an account which is in fact inconsistent, the inconsistency itself contributes nothing to our understanding, because the inconsistency is in itself unintelligible, just as we said about the statement that the sky is both blue and not blue in the same way.

We might ask whether we can at least give a consistent account superior to an account which includes the inconsistencies resulting from the use of “truth.” This might very well be possible, but it appears to me that no one has actually done so. This is actually one of Lawson’s intentions with his book, but I would assert that his project fails overall, despite potentially making some real contributions. The reader is nonetheless welcome to investigate for themselves.