Really and Truly True

There are two persons in a room with a table between them. One says, “There is a table on the right.” The other says, “There is a table on the left.”

Which person is right? The obvious answer is that both are right. But suppose they attempt to make this into a metaphysical disagreement.

“Yes, in a relative sense, the table is on the right of one of us and on the left of the other. But really and truly, at a fundamental level, the table is on the right, and not on the left.”

“I agree that there must be a fundamental truth to where the table is. But I think it is really and truly on the left, and not on the right.”

Now both are wrong, because it is impossible for the relationships of “on the right” and “on the left” to exist without correlatives, and the assertion that the table is “really and truly” on the right or on the left means nothing here except that these things do not depend on a relationship to an observer.

Thus both people are right, if they intend their assertions in a common sense way, and both are wrong, if they intend their assertions in the supposed metaphysical way. Could it happen that one is right and the other wrong? Yes, if one intends to speak in the common sense way, and the other in the metaphysical way, but not if they are speaking in the same way.

In the Mathematical Principles of Natural Philosophy, Newton explains his ideas of space and time:

I. Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

II. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is vulgarly taken for immovable space; such is the dimension of a subterraneous, an æreal, or celestial space, determined by its position in respect of the earth. Absolute and relative space, are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be perpetually mutable.

III. Place is a part of space which a body takes up, and is according to the space, either absolute or relative. I say, a part of space; not the situation, nor the external surface of the body. For the places of equal solids are always equal; but their superfices, by reason of their dissimilar figures, are often unequal. Positions properly have no quantity, nor are they so much the places themselves, as the properties of places. The motion of the whole is the same thing with the sum of the motions of the parts; that is, the translation of the whole, out of its place, is the same thing with the sum of the translations of the parts out of their places; and therefore the place of the whole is the same thing with the sum of the places of the parts, and for that reason, it is internal, and in the whole body.

IV. Absolute motion is the translation of a body from one absolute place into another; and relative motion, the translation from one relative place into another. Thus in a ship under sail, the relative place of a body is that part of the ship which the body possesses; or that part of its cavity which the body fills, and which therefore moves together with the ship: and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which the ship itself, its cavity, and all that it contains, is moved. Wherefore, if the earth is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on the earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth, in immovable space; partly from the relative motion of the ship on the earth; and if the body moves also relatively in the ship; its true motion will arise, partly from the true motion of the earth, in immovable space, and partly from the relative motions as well of the ship on the earth, as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth. As if that part of the earth, where the ship is, was truly moved toward the east, with a velocity of 10010 parts; while the ship itself, with a fresh gale, and full sails, is carried towards the west, with a velocity expressed by 10 of those parts; but a sailor walks in the ship towards the east, with 1 part of the said velocity; then the sailor will be moved truly in immovable space towards the east, with a velocity of 10001 parts, and relatively on the earth towards the west, with a velocity of 9 of those parts.

While the details of Einstein’s theory of relativity may have been contingent, it is not difficult to see that Newton’s theory here is mistaken, and that anyone could have known it at the time. It is mistaken in precisely the way the people described above are mistaken in saying that the table is “really and truly” on the left or on the right.

For example, suppose the world had a beginning in time. Does it make sense to ask whether it could have started at a later time, or at an earlier one? It does not, because “later” and “earlier” are just as relative as “on the left” and “on the right,” and there is nothing besides the world in relation to which the world could have these relations. Could all bodies have been shifted a bit in one direction or another? No. This has no meaning, just as it has no meaning to be on the right without being on the right of something or other.

In an amusing exchange some years ago between Vladimir Nesov and Eliezer Yudkowsky, Nesov says:

Existence is relative: there is a fact of the matter (or rather: procedure to find out) about which things exist where relative to me, for example in the same room, or in the same world, but this concept breaks down when you ask about “absolute” existence. Absolute existence is inconsistent, as everything goes. Relative existence of yourself is a trivial question with a trivial answer.

Yudkowsky responds:

Absolute existence is inconsistent

Wha?

Yudkowsky is taken aback by the seemingly nonchalant affirmation of an apparently abstruse metaphysical claim, which if not nonsensical would appear to be the absurd claim that existence is impossible.

But Nesov is quite right: to exist is to exist in relation to other things. Thus to exist “absolutely” would be like “being absolutely on the right,” which is impossible.

Suppose we confront our original disputants with the fact that right and left are relative terms, and there is no “really true truth” about the relative position of the table. It is both on the right and on the left, relative to the disputants, and apart from these relationships, it is neither.

“Ok,” one responds, “but there is still a deep truth about where the table is: it is here in this room.”

“Actually,” the other answers, “The real truth is that it is in the house.”

Once again, both are right, if these are taken as common sense claims, and both are wrong, if this is intended to be a metaphysical dispute where one would be true, the real truth about where the table is, and the other would be false.

Newton’s idea of absolute space is an extension of this argument: “Ok, then, but there is still a really true truth about where the table is: it is here in absolute space.” But obviously this is just as wrong as all the other attempts to find out where the table “really” is. The basic problem is that “where is this” demands a relative response. It is a question about relationships in the first place. We can see this in fact even in Newton’s account: it is here in absolute space, that is, it is close to certain areas of absolute space and distant from certain other areas of absolute space.

Something similar will be true about existence to the degree that existence is also implicitly relative. “Where is this thing in the nature of things?” also requires a relative response: what relationship does this have to the rest of the order of reality? And in a similar way, questions about what is “really and truly true,” if taken to imply an abstraction from this relative order, will not have any answer. In a previous post, I said something like this in relation to the question, “how many things are here?” Reductionists and anti-reductionists disputing about whether a large object is “really and truly a cloud of particles” or “really and truly a single object,” are in exactly the same position as the disputants about the position of the table: both claims are true, in a common sense way, and both claims are false, if taken in a mutually exclusive metaphysical sense, since speaking of one or many is already to involve the perspective of the knower, in particular as knowing division and its negation.

Of course, an anti-reductionist has some advantage here because they can respond, “Actually, no one in a normal context would ever call a large object a cloud of particles. So it is not common sense at all.” This is true as far as it goes, but it is not really to the point, since no one denies in a common sense context that large objects also consist of many things, as a person has a head, legs, and arms, and a chair has legs and a back. It is not that the “cloud of particles” account is so much incorrect as it is adopting a very unusual perspective. Thus someone on the moon might say that the table is 240,000 miles away, which is a very unusual thing to say of a table, compared to saying that it is on the left or on the right.

None of this is unique to the question of “how many.” Since there is an irreducible element of relativity in being itself, we will be able to find some application to every question about the being of things.

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