Everything in the following is based on work that Carolyn and I are doing on the foundations of quantum mechanics, and although I happen to be writing down this version, her influence and thought are present in every line. The same is true of the last few days journal entries on metaphysics.
The axioms of objectivism are usually given as something like:
Consider the first two. They are timeless, literally. They make no mention of time in any way. They apply equally to things in local and nonlocal senses. They are not just tautologies, but are tautologies of such a general and non-specific kind as to be entirely useless.
Everything that exists, exists, the first axiom tells us. Everything that exists, exists in a particular way, the second axiom tells us. That way may or may not have anything to do with the categories of space and time that we create based on our experiences. There is no reason to believe that, based on the first two axioms, that the way anything exists will be such that it can be identified in terms of spatial and temporal categories such as "here" and "now".
There is nothing in the first two axioms to pick out any categorical division over any other. We have lots of useful categories that don't cleanly divide the world up. SEX for instance, is not a universal categorizer of living things, because some living things are asexual or hermaphroditic, and so cannot be classified as MALE or FEMALE. We have no reason to believe, on the basis of the first two axioms, that existence will be universally, unambiguously classifiable in terms of TIME and SPACE.
The third axiom is much richer in content: it is a "substantial tautology."
A substantial tautology is one that entails an existential commitment. An example of this is Newton's Second Law: force equals mass times acceleration. Neither force nor mass have definitions that are independent of the second law: masses are compared via the forces the exert under acceleration, and forces are compared via the amount the accelerate a mass. To say, "A exerts a force on B" is to just say that A causes B to accelerate in proportion to it's mass (or would, in the absence of an opposing force.) Likewise, to say, "A has a mass M" is just to say that under the application of a force, A accelerates at a rate proportional to M.
Neither mass nor force is independent of the other, and it seems therefore that Newton's Second Law, the foundation of physics, is a tautology and therefore, by the usual interpretation, vacuous. This turns out not to be the case because of the claim that force causes acceleration. For something to be a cause it must perform an action. For there to be an action there must be something that acts. The substance in Newtonian physics is the discovery of the actors, which in modern terms are fields. To be a Newtonian is to have a commitment that for every acceleration there is a field that causes the force the causes the acceleration.
Because Newton's second law is a substantial tautology, it is possible for it to fail, which it does in the case of electrons bound in atoms. At the end of the 19th century, the "plum pudding" model of the atom viewed electrons as stationary "raisins" and the "pudding" of positive charge that made up the bulk of the atom. Rutherford's scattering experiments made it clear that this was not the case: the positive charge of the atom was all concentrated in a nucleus that was a thousand times smaller than the cloud of electrons around it.
The problem then arose that there did not seem to be any way to keep the electrons stationary, which they had to be because otherwise, by the laws of electrodynamics, they would have radiated away all their energy and come to stop, falling into the atomic core under the force of attraction from the positively-charged nucleus. As they manifestly did not fall into the nucleus, something had to be holding them up: to a Newtonian, there had to be another force--which is to say another field--acting on the electrons to hold them in place.
No such field could be found. In particular, if there were such a field we would expect it to act on other particles passing by the atom, such as those in Rutherford's scattering experiments. No evidence of such a field appeared anywhere. It was as if the electrons in the atom were subject to a field that they alone felt. Thus, the Newtonian tautology required a belief in something that had no other manifestation, a field that only acted on bound electrons and not free electrons. Rather than describe the world in terms of such a chimeral entity, physicists found it simpler to understand the nature of the atom in terms of new dynamical laws: quantum mechanics.
The third axiom looks much more substantial than the first two. The first two are claims about everything that exists, even things that cannot be categorized in terms of space and time. The third is a claim about YOU, and it says that you exist and therefore exist in a particular way, and that the way you exist is to have the ability to be aware of existence.
There is no doubt that this is axiomatic in the sense that to deny it requires you to accept it. You can hardly in the absence of contradiction argue, "I do not exist."
But there's much more to it than that. For example, you can't argue, "I do not exist IN TIME." That is, you are a temporal being--you act and actions take place temporally, they are classifiable or categorizable unambiguously in temporal terms. Likewise, actions can be given unambiguous, though possibly distributed, spatial categorizations. That is, they have spatio-temporal identity.
Making an argument is an action, so you can't make an argument that you aren't the kind of being that acts, which means you can't make an argument that you don't exist in space and time. It is therefore axiomatic that your consciousness can be identified in spatio-temporal terms.
Ray's analysis of the concept PERSON [Ray99] is essentially an extended defense of this kind of claim about consciousness. We could as well replace the third axiom with "You are a person", which would make the axiomatic character of our existential commitments clear. To say, "I am not a person" is self-refuting because the very possibility of making the claim or engaging in argument entails accepting most of the features of personhood Ray defends:
So unlike the first two axioms, consciousness commits us to substantial existential claims that are much narrower than the first two axioms. In particular, it commits us to the claim that our consciousness exists in a way such that we can identify it unambiguously in time and space. This accords well with our experience: we experience ourselves HERE and NOW.
Consciousness is therefore more limited than existence and identity. It is clear that things may exist and have identity, in accordance with the first two axioms, but not exist and have identity in such a way as to admit of unambiguous classification by a consciousness in spatio-temporal terms. Our commitment to being conscious, which is undeniable, also commits us to being conscious in space and time.
Space and time, like all categories, are the product of the way we are as much as they are the product of what we categorize. We find them useful in part because they capture something important to us about mind-independent reality. We find them necessary because they are required for the kind of consciousness we have: a consciousness that is capable of acts of awareness. For consciousness to act, it must act in space and time. If we could be aware without action, we would not have this constraint. But that is not the kind of consciousness we are.
Consciousness, as described above, is in physicist's jargon "local". A thing is local if it admits of unambiguous identification in terms of space and time, if it has a HERE and a NOW.
Everything we know about the physics of the brain suggests that the "here" and "now" of consciousness are the "here" and "now" of special relativity. That is, when I say that consciousness is in time and space, I mean the time and space as understood in terms of special relativity.
The photon pair described in the experiment above can be seen as a non-local entity. We can think of it as two separate photons connected by some influence that results in the kind of correlation that is observed between polarization measurements on each member of the pair.
My purpose in the rest of this discussion is to give an account of this influence in conceptualist terms, without imputing reality to any particular category used for classification over and above the reality of the particulars that are subsumed under the category by a conscious subject. In particular, TIME and SPACE will be treated as names of mind-dependent abstractions, not as real abstract features of existence.
The Laws of Thought
The first two axioms don't get us very far when it comes to constraining our understanding of reality. In fact, they don't get us anywhere at all, because the nature of consciousness puts far tighter constraints on our understanding than the axioms do. To be interesting, constraints on our understanding must at least have a temporal aspect. A temporal aspect alone is sufficient because of the relationship between space and time given by special relativity. If something has a "here" it also has a "now" if it is local in the sense of special relativity.
What is required, then are local principles that our categorization of reality must conform to if reality is to be understood by consciousness. These principles are the laws of thought, and there are two:
The first of these should be familiar: its explicitly temporal statement dates back at least to Aristotle. The second is the temporally explicit form of the law of causality, and is new. Both these laws are local in the sense described above.
The what a thing is of the law of causality means "how a thing is categorized by a consciousness." When I say, "X is now Y" I am engaging in an act of identification, and declaring that X now falls into or is subsumed by the category named by Y. My identifications must obey the law of non-contradiction and the law of causality. If I identify X as Y, I cannot also assert that X is simultaneously not-Y. And if I identify X as Y, I cannot assert that it simultaneously acts as not-Y.
Identification by consciousness is, for the reasons given above, necessarily local identification.
Reality, as evidenced by the experiment described above, is nonlocal.
To the extent that it is nonlocal, it therefore does not admit of identification by a conscious subject. It is not possible to identify (categorize) the nonlocal aspects of reality in such a way as to make our identifications obey the laws of thought.
On this account, it is apparent that quantum mechanics is an attempt to capture the local consequences of nonlocal aspects of existence. It is an attempt to create a set of local categories we can use to identify aspects of existence that are not local. The well-known "weirdness" of quantum mechanics, its resistance to realist interpretation and ambiguous relationship to classical physics (which is local) is a result of this.
The aspects of existence underlying quantum phenomena are constrained by the axioms: they exist, and they exist in some way. But they do not conform to the conditions required by the laws of thought. They do not admit of unambiguous identification in spatio-temporal terms.
This is disturbing to realists, because to them universals have exactly the same kind of existence as particulars, and so it would be impossible for there to be universals (the categories of nonlocal reality) that are not graspable by consciousness. This would be like have particulars that have an influence on other particulars, but are not in any way perceptible. But conceptualists understand universals as made things, and in particular things made by conscious subjects for their own purposes. It is no surprise to a conceptualist that some aspects of reality are such that they are not susceptible to categorization. To a conceptualist it is not that there are categories that cannot be known, but rather aspects of reality that cannot be categorized. If things exist that don't conform to requirements of the laws of thought, then a conceptualist should be content to not try to categorize them.
The foregoing argument is not entirely different from Kant's transcendental idealism. But there are important distinctions.
The most important is that Kant eschewed any possibility of knowing anything about mind-independent reality, about "things as such." But the experiment described above tells us something very important about mind-independent reality: it is nonlocal. This single fact, the legacy of John Bell, is the death-knell of the Kantian program.
Given the existence of a single fact about mind-independent reality, we are justified in asking what else we might learn about it. Any future metaphysics to come forth as a science will not have a prolegomena written by Kant, because this is precisely the kind of program that he argued was impossible.
The nature of the conceptualist argument is also quite different from Kant's who was obviously not motivated by questions about two-photon correlation experiments.
Does It Have To Be This Way?
Mind-independent reality is nonlocal and therefore unknowable by consciousness because consciousness knows things by categorizing them in ways that obey the laws of thought, and nonlocal reality cannot be so categorized with regard to space and time.
Is this necessarily the case?
There are several sense in which this question can be taken. One is in terms of physics, where we might ask if there is anything in this argument that could lead us to predict the value of Planck's constant. How such an argument could be formulated is not entirely clear, but it would take as its starting point the condition that if something is unknowable to one observer, it must be unknowable to all observers. This is the condition that mind-independent reality must be independent of all minds. Future work will focus on this possibility, although it seems like a pretty tenuous possibility.
Another sense in which this question can be taken is to ask about the relationship between being and change that has dominated metaphysics since the pre-Socratics. Is there any sense in which the nonlocality of mind-independent reality necessary for the world of being and change that we experience?
In particular, the randomness that is such a prominent characteristic of quantum mechanical phenomena can be seen as a result of nonlocal reality. Although it is obscured by the usual statements of the theory, every particle emitted in a quantum-mechanical process can be viewed as a member of a correlated pair. When we say an atom emits a single photon, for instance, we should view the photon as being correlated with the source atom until something interacts with one or the other of them to destroy the correlation. It seems likely that the nonlocal connection between source and particle is related to the randomness of the emission process, though of course how the two are related is impossible to say, because to do so would require us to categorize nonlocal reality.
But it is curious that the stable, persistent world we experience seems to be built on such a random, wildly fluctuating foundation. Yet we might wonder if the stability we experience necessitates the randomness beneath it. A useful analogy in this regard is that of commodities markets. Prices experienced by consumers of bread, for example, are extremely stable. Yet the reason for this is the existence of wheat futures, which are traded at very volatile prices, and it is necessary for this volatility to exist for the stable prices consumers experience to exist. Without the volatility of commodities markets, stable consumer prices would not exist. We might ask if the randomness of quantum phenomena are equally necessary for the stable existence of the world of experience.
The early workers in quantum mechanics, notable Bohr and especially Heisenberg, recognized a great deal of what I've argued for here. But influenced by realism, they did not clearly distinguish between "obeys the laws of thought" and "exists". Conceptualism allows us to do this, and to come to an understanding that leaves the central mysteries of quantum mechanics no less mysterious, except to the extent that we now understand why they are mysterious.