The Quantum Synthesis of The World: A Kantian resolution of the mystery of quantum mechanics

Kant is clear that a representation, being primitive, cannot be defined; but we might get a provisional, rough understanding of it by thinking of what is before our minds when we see, hear, or think of something. (This is essentially what Descartes understood by the term “idea”, which explains Kant’s naming his logical space a kind of idealism. Kant himself, on the other hand, was going to use “idea” in a more limited and technical sense.) What is wrong with the provisional understanding is that it makes a representation into a relation between a mind and an object, or less controversially (the object might not exist!) a state of a mind, so it fits the concept of a representation into the Aristotelian framework and makes it dependent upon a substance or two. We need to resist this tendency: try our outmost to detach a representation from anything whose representation it is and anything to which it belongs—from anything at all, in fact—and contemplate it in its purity, in a vacuum of references to some other concepts that would ground it. As we make this effort, we will become aware of Kant’s most serious difficulty: the conceptual space we adopt shapes our language (or, as I would prefer to put it, the other way around; but that is a story for another day); so, since TR’s space has been dominant for a couple of millennia, our expressive means are conditioned by it and phrasing what another conceptual space might be like is virtually impossible. We can only hope that, as we counter the natural associations set by the hegemonic way of thinking and speaking every step of the way, hints of a new jargon and mindset surface in the long run.

Meanwhile, a crucial remark is in order. As was the case with the concept of a substance in TR, the concept of a representation in TI, though the foundational primitive, is not without an interesting, complex logical structure. Every representation is of something and from a specific point of view. I must insist that these are internal parameters of the representation, as in TR qualities and quantities were internal parameters of a substance, in order not to be in conflict with what I said a few lines above: that a representation must be detached from anything whose representation it is, or anything that has it. What I meant then is that, insofar as the concept of a representation is foundational in TI, it cannot be dependent (to address that element first) on the concept of some object represented, as might be the case in TR. Whereas the sense in which a representation now (in TI) is always of something is that what is represented is part of what the representation is, conceptually dependent on the representation. In phenomenological circles, it has been common to talk about intentional objects, and the term may be useful here, as long as it is properly understood: an intentional object is not (again!) a kind of object, as a red or a round object would be; indeed it is not an object at all, if by that we mean the objects of everyday life. It is only the objective, the target, at which a representation points, entirely determined by the representation and ontologically subordinate to it: no more representation, no more intentional object—just as: no more apple, no more red of it. Kant at times calls this a representation’s transcendental object, and it is a term we may well allow.

That every representation is from a point of view is an equally delicate matter. Kant says that it is always associated with an I-think, and speaks in this regard of a transcendental subject, which has given rise to all sorts of confusions. Most seriously, it has generated the fantasy that the I is—or, more mundanely, that I, myself, am—some kind of ultrasubject responsible for the very constitution of the world: what is famously (or infamously) known as Kant’s subjectivism, from which various characters have tried to save Kant himself, philosophy, or Western civilization. The conceit, and the worry, are misplaced: at this early stage of the game, no object and no subject have been identified yet; what Kant is saying is as harmless as saying that two different pictures of a cup show themselves (as the very pictures they are) to be taken from different angles—different points of view. The I-think, or transcendental subject, is as much an internal parameter of a representation, an element of its logical structure, as its intentional object is. Severing a subject, or an object, from the representation will take considerable work, which we have not yet started on. And, when a subject were to be so detached, it would be as an object like any other—an empirical object, to use a term I am about to introduce—and one that has no conceptual priority over any others. I will know my self, my (empirical) subject, in the same way in which I know tables and chairs; and, just as with tables and chairs, it will often be the case that others know my self, my subject, much better than I do.

Let us start on this work, then. What Kant does is put conditions on representations that will define them as cognitive, or objective, or amounting to knowledge, and correspondingly will define their intentional objects as real objects—objects, period, without the qualification “intentional” which brackets their objectivity. Thus ontology (the doctrine of what it is to be an object) comes to be TI’s characteristic project, as epistemology was for TR. Conditions will be put not on isolated representations but on sets or systems of them, and will be known as categories: conceptual conditions, or criteria, of objectivity. The word “category” recurs; but, as we should expect, whereas Aristotelian categories divide being and cluster around substance, Kantian categories apply to TI’s foundational primitive: representations.

I will discuss only a few examples of categories. First, a system of representations is objective, and amounts to knowledge, to the extent that it is consistent. If the system includes the representation of a person dying at a certain time, and another representation of the same person showing up for dinner a few hours later, something is amiss: the system is suspicious and, at a minimum, some emendation of it is required. Second, the representations belonging to a system must not come together haphazardly, with no rhyme or reason, but must be connected by necessary links that provide an explanation of how and why they occur—if need be, by expanding the system in some relevant way. If a person shows up in a representation, the expectation is that she must be coming from somewhere, and that, if they are not already part of the system, other representations might be added to it showing her original location and her itinerary to the place where she showed up. If this were not to happen, if representations followed one another randomly and there were no manner, in principle, of fixing that feature of the system they belong to, we would take the system to be unreal, to have no cognitive, objective status: to be part of a dream, say, or of a hallucination subsequent on too much drinking.

The third category I will mention is identifiability. The intentional objects of a system of representations must be such that we can tell whether they are the same or different: that we can count them. Kant believes that humans can only identify and distinguish things, hence count them, in spacetime (importantly: not in time alone; space is also needed): only in spacetime can they have representations of individuals, of which it can be known that they are what they are and not another thing. Those representations he calls intuitions. Therefore, the representations belonging to an objective system must be intuitions, or traceable to intuitions. I could entertain the thought of humans (a thought is a kind of representation), but that thought could only be objective if I cashed it out in terms of Socrates and Plato and Aristotle…—all in principle objects of intuitions. If I were to stick Odysseus in there, and there were in principle no way of having an intuition of Odysseus (because he is a mythical figure), I would not know how many Odysseus I am talking about, hence how many humans I am talking about, hence I would stop making any legitimate cognitive claim (which Kant expresses by saying that thoughts without intuitions are empty). Another way of saying all of this is: the only representations that amount to knowledge are empirical ones, part of what we can now officially call experience (I used the word informally so far; but for Kant experience, German Erfahrung, is necessarily abiding by the categories, and necessarily spatiotemporal), either themselves spatiotemporal or traceable to spatiotemporal ones; and the only objects are empirical objects, situated in spacetime.

The intentional objects of a system of representations are indeed objects, objects for real, and the representations in the system amount to knowledge, to the extent that those objects and representations fulfill the categories. To the extent that such is the case, representations coalesce in a single, unitary experience, and we can talk of the transcendental subject of that experience as being itself unified. This statement must be expounded carefully because it has been vastly misinterpreted: those who attribute subjectivism to Kant have often argued that, because the subject is one and the subject “makes” the world, the world must also be one. But that is another fantasy. Transcendental philosophy cannot decide that the subject is one, or that the world is: it is limited to discerning conceptual connections, and here the conceptual connection is that, the more unified representations are by the conceptual criteria of objectivity, the more we can think of the subject of those representations as also unified, and vice versa. Empirical (psychological) theories inspired by this philosophy might make the empirical assertion that, when an empirical subject suffers from an irreparable disintegration of its experience—as a consequence, say, of a serious trauma—and sees its world break down, it will no longer be able to piece itself together. I would be sympathetic to such theories; but here I need to state clearly that the empirical subject does not belong in transcendental philosophy (though its concept does)—what transcendental philosophy deals with is, again, the conceptual connection between the point of view from which a system of representations issues and the intentional objects of that system.

3. Antinomies

I have been talking of systems of representations, of these systems expanding, and of them being objective to the extent that they fulfill the categories. Now the question arises: how far should these systems expand, how large should they be, in order to drop the qualification and be objective, period. Ideally (a word that will turn out to have specific significance shortly), for this to happen a system would have to be a total one: the kind of system that would represent an entire world. But here we encounter a drastic limitation of the Kantian framework: the thought of a world is conceptually incoherent; categorial criteria, if totalized, generate antinomies.

Take an ordinary question we would need to answer if we were to check on the objectivity of something. For this table being represented now to be objective, it must be in space and time, so let us ask ourselves where it is. It is in this room, we might answer, and where is the room? In this building, which is in this city, which is in this country, which is on this planet, which is in the universe—that is, within the totality of all there is. So far, so good; but suppose we ask now where the universe is. That question makes no sense: I can tell where something is only as it relates to something else; but if I am talking about the totality of all there is then there is nothing else left that I can relate it to; hence it is not as if I did not know what the answer is—the question itself becomes incomprehensible.

Same thing if I asked when the now is in which the table is being represented. I could answer that it is a certain day of a certain month of a certain year, but all those specifications relate the present moment to other moments; and if, after running back and forth in history for a while, I were to ask when the whole time series is (or, perhaps, begins), again the question would make no sense. In theological contexts, this sort of question often arose as the challenge of what God was doing before creating the world, and it was very well for Augustine to answer it by saying that God created the world not in time but with time: whatever that means—and it does not mean much—, it applies to a transcendent being, with whose incomprehensibility the faithful had long reconciled themselves. (This issue will come up again, and when it does the answer will have some meaning—though not one that Augustine would have liked.)

Same thing if I asked why the table is here. For the table to be real there must be a cause that necessitates its presence at this location, and that cause must have a cause…, and all the elements of the causal chain must in principle be objects of intuitions. But what about the totality of the series? Is it infinite, which means that the presence of the table here and now would never have come to pass? Or is it finite, which means that I could ask the same question of its alleged first member—as Lucretius’ archer, having supposedly reached the end of the world, was still able to shoot an arrow beyond it?

Same thing if I asked what the table is made of. Molecules, I could answer: those are the objects, the subjects of predication, that compose it—“the table” is nominal shorthand for the highly complex verb that would summarize all of those molecules’ properties and relations as they come together to form the table. But of course the same could be said about the molecules: they too could be turned into a verb. So suppose we asked what the basic objects are: the ultimate subjects of predication. Once again, the question would make no sense: for something to be real, it must be in spacetime; but everything in spacetime can be divided indefinitely, hence everything that is the result of any stage of this division is not a basic object, and can be turned into a verb. It is turtles all the way down.

The representation of a whole world or, in general, the representation of a totality (of the totality of space, the totality of time, the totality of the causal chain, the totality of the process of composition) is an idea in the technical sense Kant assigns to this term: the representation of something that cannot be experienced, not because of empirical limitations that could in principle be overcome but because of logical limitations that belong to the very nature of TI’s conceptual space—overcoming them is unthinkable. And yet, (human) reason has, according to Kant, an irrevocable tendency to systematicity: to connecting everything together. So the critique of reason—the critique reason conducts of itself—seems to arrive at a desperate outcome: reason cannot be satisfied, and reason itself can prove it. But this is only despair from a viewpoint that is itself limited. At the beginning of the first Critique, Kant describes his task as having to deny reason to make room for faith. Which is a colorful but essentially correct way of describing the upshot of his probe, except for one final irony: the contribution faith must make is one that eventually reason will appropriate. In the final analysis, reason will not be denied.

4. Appearances

Let us take stock of the negative outcome first. If reason cannot satisfy its totalizing tendency to systematicity, it must resign itself to doing partial work, within contexts that have boundaries; it must project itself into such modest work, leaving aside what have revealed themselves as empty ambitions to contextless inquiries, problems, and solutions. The projection of reason into bounded contexts is called understanding; and understanding can address and resolve problems. A plumber can apply the reading that the understanding (notice I did not say: his understanding) provides of pipes to fix a leaking faucet, without bothering to think whether the kitchen where the faucet is has bright enough painting on its walls to make people happy; with the reading understanding provides of building areas and conditions, an architect can safely raise a skyscraper near an earthquake fault without bothering to think of why there are faults, or of whether they could be fixed. When addressing such problems, the understanding will select, choose a context, and only pursue questions and projects that can be configured within it; once the selection is made, everything in the context will be definite, defined by it—will have a definite spacetime location, definite causal factors, and will be made of definite elements (any reference to protons or neutrons, say, will be out of context for fixing a faucet). Based on the choice of a context, the categories will succeed in bringing about objectivity and knowledge.

But then, one might ask, why not simply supplement the categories with the notion of a context and reach objectivity after all? Why not say that, though it makes no sense to ask where or when a thing is, or what it is made of, or why it is here, in a general, absolute way, it makes sense to ask such questions, and to answer them, and to account for the thing’s objectivity, within its context? Because, to put it in terms familiar to philosophers of language, the definite description “its context” is improper: it is irredeemably ambiguous. There is no one context for any thing or any event that could be called its own; every thing and every event are simultaneously in indefinitely many contexts of maddeningly various sizes and shapes. What is my context right now? This day, this year, this millennium? This country, this continent, this galaxy? The bunch of people who speak a certain language, the different bunch of people who belong to a certain religion (or to no religion), the yet different bunch of people who, no matter what language they speak or what religion they belong to, have a certain professional occupation and expertise? That a context must be, as we said, selected or chosen was not a casual phrase: it means, we can see now, that an arbitrary act must be performed to set up a particular context, among the indefinitely many that could be set up—an act that is itself not determined by anything, that is the result of arbitrium, that is freely willed. Nor would things change if we tried (as my examples might suggest) to have the pragmatics of the situation determine this choice: “situation” is but another name for a context, and a situation’s pragmatics—the sorts of concerns that are relevant to it—issue from the same arbitrary choice I just described. It is a choice that makes a plumber ignore the painting on the kitchen walls, and makes a builder ignore what causes earthquake faults; both choices might be regretted later; in both cases wishes might be expressed later that the “situation,” or context, had been seen differently.

We would expect an object to have autonomous being, to stand on its own, for as long as it is: not to be parasitical on something else for its existence in the way a quality is parasitical on a substance in the Aristotelian framework or an intentional object is parasitical on a representation in TI. But now we have concluded that all objects to be found in spacetime—all empirical objects—depend for their being on an act of choice: that, unless a context is arbitrarily set, there are no objects to speak of. Therefore, Kant says, all empirical objects are less than full-fledged objects, less than what the idea (see below) of an object would demand: they are appearances. Not empirical appearances, as ghosts are: given an appropriate context, we can decide that ghosts only appear to be whereas trees do not. But transcendental appearances: lesser objects for conceptual, necessary reasons. And, of course, empirical objects are the only objects there are; so the only objects there are turn out to be appearances, and the representation of a full-fledged object is indeed an idea in Kant’s technical sense of the term: we can think of a full-fledged object, but we will never encounter one. This verdict can be profitably compared with Plato’s. For the latter, spatiotemporal objects were equally appearances, but ideal ones, ideas, were not: there we would find real objects—and there we should focus, letting spatiotemporal objects go. For Kant, on the other hand, the only real objects are those half-objects, those poor excuses for objects, we find in spacetime; ideal objects would certainly fit what we expect of objects, but they are not. So Kantian philosophy promises no rest but only a perpetual, unsolvable oscillation between what is perfect but unreal and what is real but imperfect. Which is not so strange after all: empirical friends, though real, are always somewhat unreliable, but the ideal friend that we use as a measuring stick to acknowledge their unreliability is nowhere to be seen.

Let me now bring up the positive side of the coin. The presence of objects depends on selecting a context, I said; and that selection is a free act. This statement invokes a philosophical theory of freedom: of what defines an act as opposed to something that just occurs, just happens. And the development of such a theory will keep Kant busy from the publication of his masterpiece until his death: the metaphysics of morals he painstakingly worked at during that time is nothing but a metaphysics of (free) action. But I can leave that development aside here (except for mentioning that, as was adumbrated above, an event will count as an action to the extent that it is rational—reason has the last word); what matters for us is that, however an action is defined, knowledge is for Kant something that is done, not received. The Aristotelian soul had no form of its own so that its form would not be in the way as it acquired the form of anything it knew—and then lost it, ready to acquire another one. The Aristotelian best kind of perception came from sight: the one sense that leaves the object of perception most unbothered, even appreciating it from a distance. And Aristotle had a principled aversion to experiments, for if you intervene in the object of observation then you modify it and, as a consequence, observe something other than what you meant—which is why, for the two thousand years in which Aristotle was, simply, the Philosopher, it would be artisans, not intellectuals, who changed the world, and intellectuals only turned to that enterprise after rejecting Aristotelian philosophy. Kant, of course, comes in the wake of this rejection and opens the first Critique with glowing references to paradigms (some genuine, some not) of the experimental method. Moving from those inspiring references to the body of his transcendental philosophy, it is not just that knowledge is (empirically) best acquired by poking into nature (or subjecting it to vexations, as Bacon suggested) but also that knowledge is to be defined as something that implies a making.

“[E]xperience cannot be given but must be made,” Kant says in the Opus postumum; the world is made in the process of being known; it must be put together so that there be something to know. This “putting together,” in Greek terminology, is called synthesis: the act of establishing a context—the things, tools, and pragmatic concerns that will frame a specific episode of knowledge, which can only arise within the context thus provided. In the absence of this act, and of the effort, the commitment it involves, no knowledge is possible. There is no disinterested knowledge. “Faith” is a highly charged translation of the German “Glaube” Kant uses in the passage from the second preface alluded to above: “belief” and “opinion” would be adequate too. But “faith” signals a vital feature of what is going on here: if by “opinion” we mean a purely passive state of mind, something nonchalantly entertained and easily shaken, that is the wrong picture, and “faith” is to warn us that an active stance is needed, a holding-onto that, as soon as it relaxes, will see the world dissipate into indeterminacy. So it is not as if we have lost the object along the way, and TI’s ontology is as hopeless as TR’s epistemology: it is, rather, that objectivity and knowledge are projects to be responsible for, projects that can only be pursued if we go beyond the Aristotelian goal of contemplation and reach into the dirtying of hands that makes implements come out of Hephaestus’s workshop, and objects come out of the synthetic workshop of reason.

Further unpacking of these claims is in order, to prepare the ground for what is to come. To begin with, I stress what kind of making, and of holding onto, is involved here. There is empirical making and holding onto (someone made the faucet; workers, following the architect’s instructions, make the skyscraper; both faucets and skyscrapers need to be maintained); but that is not the making or holding onto I am talking about. What is relevant here is the making and holding onto that are required for something to be perceived as a faucet, or as a skyscraper: conceptual making, gathering bits and pieces of experience and interpreting them as faucets or skyscrapers; and the continued allegiance to that interpretation. Without this work, there might still be something, but no faucets or skyscrapers. And it is not work that plumbers or architects do, as empirical individuals (it is not as if their understanding were involved in it): it is, in fact, as much needed for them to be empirical plumbers or architects as it is for there to be empirical faucets and skyscrapers. It is work that must be presupposed in order to understand what happens when a plumber enters a kitchen and proceeds to fix a faucet.

I have been careful to use passive constructions like “a context must be chosen,” “the world is made,” and to avoid active ones like “I (or anyone) must choose a context (or make the world).” If we did the latter, and took “I” to be more than just a pronoun, a form of speech, if we took it to designate the empirical object that is me, we would fall into what I earlier called subjectivism—which would be wrong, because that empirical object is as much in need to be synthesized in order to be known, and as much at risk of losing coherence and connectedness, hence objectivity, as any other. What Kant claims is not the empirical dependence of an object of knowledge on some act of a subject (however the latter is substantively, not grammatically, construed), but the logical (semantic, transcendental) dependence of the concept of objectivity on the concept of an act: unless an act is referred to, knowledge cannot be accounted for. (Unless words or images are referred to, a book cannot be accounted for—and never mind whose words or images they are.)

Moving now to something else that needs to be clarified, I pointed out the incoherence of thinking of the whole world, but I also said that an act of synthesis makes a world, precisely in the sense of making it possible to think of it in a definite way. In order to resolve this apparent inconsistency we must adapt to the situation the Aristotelian distinction between actual and potential. A potential infinity is one that is generated one step at a time, in a process that never comes to an end, as in the generation of prime numbers. An actual infinity is one that is given at once, as in Dedekind’s definition of an irrational number. According to that definition, √2 is an ordered pair each of whose members is an infinite set of rational numbers (intuitively, those smaller and those larger than √2); so, if those two infinite sets were not given to us, we would not know what √2 is. In a similar vein, we can think of the world potentially or actually (and independently of whether we take it to be infinite or not): we can conceive of it being generated one step at a time or being given all at once. It is the thought of an actual whole world that brings up antinomies, and it is this thought that would have to be used in order to provide a definitive judgment of objectivity for any given system of representations: such a judgment would have to be based, I said, on inserting the system into a total objective one—unless everything is (definitively) objective, nothing is. We have found that to be impossible; but, even in the wake of this impossibility, it remains feasible, indeed required, that synthesizing anything as an object means inserting it into a larger objective environment, and then into an even larger one… (Which, to reiterate a crucial distinction, does not imply that larger and larger environments are gradually built, as a skyscraper would be, but that they are gradually recognized as being set up by the act of synthesis.) At any step of this way we have not gotten to the end of it, and we may run into a failure of objectivity at the next step; but to keep going is not just an option—it belongs to the very ethos of knowledge. So, again, every act of synthesis of an object is, potentially, a synthesis of a world: it is a promise (which we will never know was kept) that a world will be found to harbor the object. And it is the germ of an overarching theory of that world, which describes its structure in the terms the act of synthesis has set up.

The contrast between empirical and conceptual must be emphasized again here. Understanding the world in terms of plumbing means, potentially, taking every part or aspect of the world as an element of plumbing, or as conducive or subservient to plumbing. This vision might start with a single faucet, in a kitchen, but it has an irrepressible tendency to extend to the next apartment, to the next building, … and to the significance of banks and schools and governments. An empirical individual plumber (unless he is deranged) never identifies with such a one-sided vision, and as a consequence will shift back and forth between putting matters of interest in different contexts—between synthesizing and understanding them differently. At the conceptual level, however, the synthesis cannot be other than one-sided.

Finally, as was pointed out before relative to similar concerns, there may be empirical (for example, psychological) theories inspired by Kant that detail how individual (empirical) subjects make their own worlds—how they synthesize them. But this kind of empirical construction has no currency in transcendental philosophy, nor is it necessary to adopt any such theory if one espouses Kant’s framework: within this framework, empirical theories that were to describe individual subjects as passively receptive of information about a world which is just given to them would be as dependent on acts of synthesis as any others.

QUANTUM

1. Theories

Imagine you have an anthropological theory T that explains the migration patterns of various ethnic groups. T is an empirical theory, and we can assume that it has outstanding empirical success: that its predictions are amply confirmed by tests and observations. Based on what I said, T can attain success—or, indeed, can make any definite empirical claims at all, to be confirmed (or not confirmed) through observations and tests—by relying on an act of synthesis that establishes its vocabulary and agenda, its context of concepts and concerns: that determines it is ethnic groups it deals with, not random individuals, and migration patterns, not occasional—maybe tourist—traveling. The act of synthesis is external to T, it is a presupposition of T’s very existence, and T can say nothing about it: among other things, T cannot say who makes it, or on what grounds. From within T’s point of view, it is entirely arbitrary, which means at least the following: (a) it is contingent (it could have been other than it is, giving rise to different vocabularies and different theories), and (b) it is free, in the negative sense of freedom already proffered—no rationale can be given for it having occurred.

But T is a theory about humans, who are highly inquisitive objects (and subjects). So sometime one of them is going to inquire about those grounds for the act of synthesis that made T possible. What is an ethnic group?, she will ask; how do we distinguish ethnic groups from one another? how do we decide that there is not a single ethnic group that pertains to all humans, so that the very notion of an ethnic group drops out as futile? And she will have answers too: she will say that the concept of an ethnic group issues from the nation state, which, from as far back as Plato’s ideal republic, finds it easy to build its unity and maintain its stability as that of an extended family, hence to push aside (or worse) all those regarded as not belonging to the same family (“nation” comes from “nasci,” Latin for “to be born”), all the barbarians—and, for that strategy to be viable, it needs to construct the fiction of other families competing for the same resources.

What has thus been provided is another theory T´, that explains what T could not possibly explain (or even ask): what selected the vocabulary and the agenda (the context of concepts and concerns) in which T operates (it was the nation state) and why it did so (to maintain its unity and stability). As T´ also deals with humans, we could also call it anthropological, and we could attribute great predictive success to it too. T´, of course, is an empirical theory for which the same condition holds as I stated above for T: it has a definite vocabulary and agenda (a definite context of concepts and concerns), and as a consequence can raise definite questions and obtain definite answers for them, by presupposing an act of synthesis that selects a context for it—that decides that nation states are its field of inquiry, not clouds or storms (or ethnic groups), and that a nation state is something that can survive over time and be worried about its prospects for survival over a long time. The act of synthesis that sets the context in which T´ operates is inscrutable from the point of view of T´: as contingent and (negatively) free as the one setting the context for T was for T, and as external to it. It is just as opaque as it was for T that this act be performed by some definite agent, for some definite reason.

And yet, nothing prevents some (other) human from addressing precisely those opaque matters, and coming up with another theory T´´ according to which theories like T´ are the product of redundant intellectuals with too much time on their hands, who find it pleasantly aggrandizing and impertinent to turn against the very institutions that feed them, as children turn against their parents, and who just as vainly see them lugubriously conspiring for evil. T´´ can account for the synthesis from which T´ originates: for what made it and why. And T´´ is another empirical theory (another anthropological one, we could say, as it continues to deal with humans), operating in a context of intellectuals and institutions, and perhaps of Oedipus and Electra complexes, which it requires to be set before T´´ can go to work scrutinizing the context in which T´ will (inscrutably, as far as it goes) operate.

This nesting of empirical theories could go on indefinitely, and we could entertain any number of variations on the relations involved. There could be an infinite regress, as my example suggests, or a symmetrical structure where each of two theories explains the synthesis that makes the other possible, or a loop where theories explain each the synthesis of the next in what is ultimately a circular way. The option I want to privilege is one attempting to short the process: where a theory, that is, attempts to provide for the synthesis that makes it possible with resources internal to itself.

How would that go? Return to our original T, and to its vocabulary of ethnic groups and migration patterns. Consider an individual A going from one place to another. She could be a single individual escaping from a threatening neighborhood, or a member of a family being pressured out of its village by rival clans, or part of an ethnic group being dislocated by an internecine conflict. Suppose we make A a carrier of all these alternative descriptions, and we say that, were the choice to be made in favor of the last one (of her being a part of an ethnic group being dislocated by an internecine conflict), the mechanism would be set for T to run its course and provide its explanation (in terms of ethnic groups), whereas, if the choice were made differently, a different mechanism would be activated and a different explanation would be forthcoming. What we would have done then is to move not from T to another theory placed at the same empirical level and subject to the same conditions as any empirical theory, but to a supertheory T* endeavoring to incorporate all the empirical theories that could be constructed to explain the same fact: that A goes from one place to another. I call a supertheory of this kind a quantum theory.

Before we go any further, let us reflect on this term I just introduced. “Quantum” points to discreteness, which is a suggestion of synthesis. Every world that will (potentially) issue from an act of synthesis is continuous, specifically in the way in which it is structured by continuous chains of causes and effects, but the choice among worlds made by this act is a discrete event: one that is not connected to anything previously occurring and providing a causal explanation for it; one that just instantaneously (and mysteriously, insofar as what is not explained is mysterious) takes place. Ordinarily, this act is external to a theory; the theory starts and goes on from there, but cannot look back at it, even less comprehend it or justify it. A quantum theory such as I described, however, does what is taken to be impossible for ordinary ones: reach out to the synthetic act and make it part of what it says. The act is still mysterious, as it is still the case that no explanation is provided for it, and that is the price to pay for the overreach. If a theory is supposed to make an area of inquiry transparent, based on how that area has been independently selected and characterized, a theory wanting to break the mold and talk about the very process of selection and characterization whence it issues will have to be, to that extent, constitutionally and irremediably opaque.

2. Details about the supertheory

Consider T* then. We can think of it as a two-stage theory. To begin with, T* stays undecided on which vocabulary and agenda is going to be adopted. It could be the ones relevant to T in the end, and then T* will be talking about ethnic groups and migration patterns; but at the first stage none of that is decided, so nothing definite can be said in T* about ethnic groups. What can be said is that, if the choice is going to go for T, then the individual A will belong to one of the ethnic groups that T recognizes, perhaps even that it will be more likely that it belong to one of those groups rather than another. Then the choice is made and we enter the second stage, in which (say) T* commits itself to T; as a consequence, A will definitely belong to an ethnic group, with the higher likelihood that it be one rather than the other that was already signaled in the first stage. Because the theory describing A in terms of her personal preferences and problems was not chosen, nor was the theory describing her as a member of her family, everything that could be said in terms of the vocabularies and agendas of those other theories will stay indefinite: relative to the choice that has been made, A will continue to have no definite personal or family preferences and problems—it will continue to be the case that she could have any of a number of them (those allowed by the corresponding theories), possibly some of them with a higher likelihood than others.

But none of this is set in stone: the choice of T can be revoked later on, and a different theory chosen, with a different vocabulary and agenda, and then A will be described in that new vocabulary, the very notion of an ethnic group will recede into the background, and what ethnic group A belongs to will return to be indefinite. What stays fixed through all these vicissitudes is T*; the various outgrowths of it based on the various choices that can be made within it of different vocabularies and agendas, on the other hand, come and go as those choices come and go.

The relation between T and T´ (or T´ and T´´) was a hierarchical one, in the following sense: T´ could explain the selection that constituted T (and T´´ could do the same for T´), but not vice versa. No such relation holds between T* and the various theories resulting from the various choices possible within it: T* has incorporated those theories, not placed itself above them, so the choices constituting them are (as I said earlier) just as opaque for T* as they are for them. Within T*, we can only say what we said already: that, if a particular choice is made (notice the passive form, and remember what it means), then a particular theory is constituted. Conceivably, one could have a theory external to T* which relates to T* as T´ does to T, and explains the various choices possible within T*; but that would recreate the same situation as we had before—an infinite regress or a loop, no incorporation.

Though it is uncommitted with respect to a range of vocabularies, T* is not totally uncommitted. For one thing, I called A an individual, to suggest that, for present purposes, it is to be thought of as an unanalyzed entity, with no structure of its own. But of course, if A is a human being, she has a structure, and that structure is going to enter into whatever theory is chosen. So T* is indefinite up to a point; it is undecided not among all conceivable vocabularies but among a specific, definite range of them, that can be thought of as itself the result of a selection process. Which makes us go back to Kant, and opens up an issue of supplementing or revising some of what he said.

Kant’s synthesis (potentially) puts together a world and makes it be. The question to be asked now is: puts it together out of what? And the answer, which has already surfaced briefly, is: out of an undifferentiated multiplicity, what William James was to call a “blooming, buzzing confusion.” In other words, before the synthesis there is no structure at all, and the synthesis creates structure, much like God created the world from nothing. (If we identify being with structure, the analogy becomes a perfect one.) But that move, from no structure to a definite structure, requires a kind of thinking of (and to) the limit—much like the thinking we do of pure matter in the Aristotelian framework. If we engage in more concrete thinking, we realize that the indefiniteness preceding a synthetic act (chaos, if you will) is not structureless confusion; it is, rather, a confusion of structures. A world is made out of worlds; being is always already articulated; what the understanding does is select one of several options as to what the world could be—options that preexist the selection. And the selection is made not among all the possibilities, but among a preselected set of them: preselected by a prior act of synthesis. If there were a beginning to synthetic acts, the ambitions of reason would finally be satisfied; but there isn’t and they are not. It is always only understanding at work: choosing a vocabulary in which to set up a world among a range of vocabularies that have already been set up by a choice of them, and so on forever. T*’s incorporation of theories is a partial incorporation of some theories—it could not be a total incorporation of all theories.

We may get this point better by changing the subject—somewhat. The Creation is considered Joseph Haydn’s masterpiece. Its first movement is an overture called “Representation of Chaos,” which starts with a resounding unison C, lacking a third and therefore giving no indication of tonality. From then on tonality is never established, as we shift around from C minor to A-flat major, nor is any clear melody pursued: several are intimated but they lack cadences and are not resolved (there are half-cadences, but they are deceptive); and the ascending and descending chromatic passages that might suggest the approach to a specific note are interrupted, or repeated, again leaving no clear sense of direction. It is innovative music, quite revolutionary for its time (1799—a time when Kant was still alive and actively working), but the point I want to emphasize is that the chaos that precedes creation is not depicted here as just a bleary mess: it is, rather, a clamor of conflicting voices that keep breaking into one another, of conflicting indications about where it will all go, of conflicting meanings the whole thing might acquire. Each recognizable for a moment, until it is superseded by the racket of its rivals.

Haydn was in England for eighteen months in 1791/92: his first time out of Austria. In June 1792 he visited the celebrated observatory at Slough, where William and Caroline Herschel were revolutionizing astronomy. They had a lot to talk about: William was an accomplished organist and composer; his sister had trained as an opera singer. But they could also talk about the universe, as the Herschels were theorizing the existence of galaxies beyond our own and the formation of our solar system (one of millions) from nebulous material. (This nebular hypothesis, later incorporated by Laplace in his Exposition of the System of the World of 1796, had been first proposed by Kant in the Universal Natural History and Theory of the Heavens of 1755.) What Caroline Herschel may have impressed upon Haydn (William seems not to have been present at the time) is the view of the universe as a laboratory, in which stars and planets and systems are constantly in the making, constantly being created. The constant nature of the process I will take up later; now let us focus on how this creation operates. It does not make something out of nothing: it empowers and develops some of the countless inchoate structures that are already there. It chooses among them, and it promotes what it has chosen. Whether or not he got his inspiration from the Herschels, this is the creation Haydn describes.

The first chapter of Genesis, on which Haydn’s libretto was based (in part, for it also relied on the Psalms and on Milton’s Paradise Lost), is quite ambiguous about what is going on. It says “In the beginning, God created the heavens and the earth,” but it does not say what that means. In fact, there is only one passage in the whole Bible, in II Maccabees (a book that, by the way, is not part of the Jewish Bible), in which we seem to be given what has become the standard, orthodox narrative of a creation ex nihilo: “I beseech you, my child, to look at the heaven and the earth and see everything that is in them, and recognize that God did not make them out of things that existed.” What we read in Genesis is compatible with creation being nothing other than the organization of existing material, much as in the ancient Greek myth of the gods bringing an orderly cosmos out of chaos—the myth Haydn seems to be alluding to in his overture. But, even if we take this course, it remains to be seen how the material and its organization should be construed.

Anaximander (quoted by Heisenberg in Physics and Philosophy) echoes the same myth by talking about an “indefinite” (ápeiron) from which things come. Here is what Simplicius (an Aristotelian commentator of the sixth century A. D.; Anaximander himself was active in the sixth century B. C.) says about him: “Anaximander … said that the indefinite was the first principle and element of things that are, and he was the first to introduce this name for the first principle. He says that the first principle is neither water nor any other of the things called elements, but some other nature which is indefinite.” And here is the only extant fragment from Anaximander (also considered the oldest fragment from Greek philosophy), embedded in another sentence of Simplicius (the Anaximander quote is in italics): “The things that are perish into the things out of which they come to be, according to necessity, for they pay penalty and retribution to each other for their injustice in accordance with the ordering of time, as he says in rather poetical language.” Which seems to align itself with a conception of chaos as totally undifferentiated and unstructured: the bleary mess we mentioned earlier. This is how Kant thinks of the “creation” accomplished by synthesis: independently of it, there is only an undifferentiated manifold, “a blind play of representations, less even than a dream.” He may be influenced here by his own nebular hypothesis; and, if he is, he is led astray by it. Because thinking of synthesis this way forces him into a blind alley: into opening a gap in his own account that he is incapable of filling.

Locke believed that general ideas are the result of abstraction: we see a variety of dogs, of all different shapes, sizes, and colors, and eventually we abstract what they all have in common into the general idea of a dog. But that does not seem to work, for how do we know who the dogs are in the first place, to abstract the idea of a dog from them? It is a huge problem, since the general idea (or, to speak Kantian language, the concept) of a dog provides a verbal definition of a dog, and how do we come to attach that element of language to the multifarious images of dogs we encounter in empirical life? How do we fit conceptual specifications to the spacetime manifold? Kant’s answer is provided by the doctrine of schematism: each concept is associated with a schema, which is a rule for the production of all the possible images that are consistent with the concept. We go about experiencing the world equipped with the schema of a dog and, when a portion of the manifold happens to agree with one of the images the schema produces, we label that portion a dog. Which sounds fine as long as you ask no questions, put no pressure on it; but otherwise crumbles miserably. How can a portion of something that is totally indefinite, that has no structure whatsoever, “agree” with a specific image? Why should it agree with that image instead of any other?

Haydn has the answer. The ápeiron, the spacetime manifold, chaos, is not a colorless fog, a murky nebula offering no hold to perception; what is chaotic about it is that it offers multiple holds, competing ones, and within this pandemonium (a Milton word: the place of all devils, for there is something devilish about chaos) none of the holds sustains attention long enough, until and unless an action is performed that selects a particular hold. This is what creation is, and what is synthesis. The image of a dog is there, together with images of cats and bushes; making experience is privileging one image over the competition—not over a misty haze.

Descartes believed that creation cannot be a once-and-for-all affair. Finite substances depend on God for their continued existence, not just their origin. God must sustain them constantly; if his support were to fail for an instant, in that instant they would be annihilated. So, even if the universe appears steady, the steadiness is the result of a continuous creation that continuously confirms the structure created earlier. (In a humanistic variant of this model, Sartre claimed that we choose to be what we are at every instant, even if many of our choices are confirmations of ones already made.) This is an important addition that must be made to Kantian, and quantum, synthesis. The world emerges from the underlying reality of chaos at every moment; the act that must be posited to understand how a world is possible cannot just be an initial one, but must be constantly repeated, and as a consequence the world is always open to changing its shape. The one thing Haydn got wrong, then, was calling “The Representation of Chaos” an overture.

3. Moving to the physical world

I called a theory quantum if it has a feature that depends on no specific science, and my example of a quantum theory was an anthropological one. But “quantum” is a term with a specific meaning and history, and is ordinarily applied to the physical theory associated with the names of Planck, Bohr, Heisenberg, von Neumann and other distinguished scientists. How does my use of the term conform with the standard one? I will now address this crucial question, with one crucial proviso: I am no physicist. I know enough about quantum mechanics to understand (I believe) the problems it poses and what attitude physicists (and others) should take with regard to them. But I can and will offer none of the experimental or mathematical work that is for them to perform: I will only, as someone who trafficks in philosophy, give them a clear and general account of what sense that work makes—and of why in part it does not appear to make much sense. I will summarize my moral at the end, in no uncertain terms; now let me proceed gradually.

Suppose you study a particle. You could describe it in a variety of theories. One of them will have a vocabulary limited to positions in spacetime, and will describe the evolution of the particle’s positions. Another one will have a vocabulary limited to velocities, and will describe the alterations in the particle’s velocity. There will be more, but not too many more: the vocabularies in play here will be part of a context that is preselected by a previous act of synthesis and will include none that describe the particle’s feelings, or its popularity in night clubs. A supertheory Q of the kind I discussed in 1 and 2 will incorporate the various theories that belong to this bunch. In its first stage, the particle will have no definite positions or velocities, but will carry the information that, if the theory describing its positions were to be selected, the particle would have (at a given time) one of the positions which that theory acknowledges, perhaps one such position with a higher probability than another—and analogously if the theory were selected that describes its velocities. In the second stage of Q, a theory is selected and the particle has, say, a definite position, though, if such is the case (if the theory describing its positions is chosen), it will continue to have no definite velocity because that other theory was not selected.

Q is a quantum theory in my sense and is also the quantum theory of the tradition (from now on: the traditional theory) understood from my perspective. I will now further elaborate on this perspective by showing how some key elements of the traditional theory look within it.

3.1. Collapse

The most popular interpretation of the traditional theory—the Copenhagen one—assigns two different dynamics to a particle. In the linear dynamics, the particle has no definite values for its various parameters, that for the sake of illustration we can limit to the two already mentioned: position and velocity. So the particle, in the linear dynamics, has no definite position and no definite velocity. What it has, rather, is a superposition of a number of positions and velocities, each with a coefficient; for example, the particle has ½ position a, ¼ position b, and ¼ position c. Then a measurement is taken, say, of the particle’s position and the particle collapses into a definite position; its behavior is then described by the collapse dynamics, according to which the particle’s current position was acquired with a probability that can be calculated from that position’s coefficient in the superposition. To continue with my example, when measured for its position the particle will turn out to have position a with a probability of ½, position b with a probability of ¼, and position c with a probability of ¼. Its velocity will stay indefinite.

Within my perspective, call T₁ the theory describing the particle in terms of positions and T₂ the theory describing it in terms of velocities. The “collapse” into a definite position is the act of synthesis which selects T₁ (the context appropriate to T₁) among its rivals and moves Q from its first to its second stage. The particle “acquires” a definite position because a vocabulary and an agenda have been chosen in which positions are relevant, and continues not to have a definite velocity because that other vocabulary and agenda which would make velocities relevant has not been chosen. As the choice of a vocabulary is not set in stone, a different choice can be made later, and then, if T₂ is chosen, the particle will “acquire” a definite velocity while its position recedes into indefiniteness.

Also, because in this (Kantian) perspective something exists only insofar as it is connected (entangled) with everything else, choosing a description of a particle in terms of positions means choosing the world described that way (one of several: a world is made out of worlds, not of undifferentiated multiplicity). A world that is never completed, never wholly given, always only potentially present and in the course of being made (which means, remember: recognized); but whose making—the surfacing of the connectedness (entanglement) of its components with one another, as being set up by the act of synthesis—will spread that same description all around. It is not, therefore, that information travels instantaneously (and, puzzingly, faster than light), for such would be an empirical occurrence and has no place here. What is instantaneous (we know) is the act of synthesis that makes the entanglement of bodies relative to (say) their positions suddenly show up and become relevant. And do not ask: “show up” from being hidden before (from being “hidden variables”)? There is no “before” or “after” in the transcendental locale where acts of synthesis occur—one such act is needed to establish any time line, and is instantaneous in the sense in which instants are out of time. This is how Augustine’s view of God creating the world with time could be resurrected, though at the price (which Augustine would not have paid) of turning God into a nonexistent presupposition of existence.

3.2. Measurement

We talked about measurement; but what is measurement? Notoriously, though measurement is a basic parameter for the traditional theory, this theory does not explain what a measurement is, and people (including Einstein) have worried if a measurement (or, as is also called, an observation) could be taken by a mouse, or a fly, or some other particle. All this uncertainty is for good reason, I claim, because words like “measurement” and “observation” are signposts for the act of synthesis that selects a vocabulary—an act which, I pointed out, neither Q nor any of the theories it incorporates can say anything definite about, for conceptual, not empirical, reasons. It is an act that, from within Q, is performed by no one and for no reason; more precisely, from within Q, it is not an empirical act but a conceptual condition that must be invoked for it to be understood how Q can move from its first to its second stage. We could say it is performed by the transcendental subject, as long as it is clear that the transcendental subject is nothing but an internal feature of the act itself, which cannot be detached from it: the transcendental subject is the whatever it is that performs the act, or, as Kant put it, “this I or He or It (the thing) which thinks.”

In empirical terms, when a measurement is taken then some empirical things are done. A screen, say, is put up, or some kind of device that detects the passage of a particle. But those empirical steps are only indications of what really matters: that a commitment is made to a particular vocabulary and agenda—not made by the person putting up the screen or the device, because the commitment is not empirical, hence not made by an empirical agent. The commitment is, to repeat, a conceptual condition for the existence of a definite world, or of any definite part (particle) of it; without referring to that commitment, it could not be understood how the world, or any part(icle) in it, could have any definite value for any of its parameters. “Measurement,” then, is code word for the act that inaugurates a second stage of Q, and should not be confused with the concrete dealings that take place in a laboratory. Nor should the theory’s failure to account for what a measurement is to be blamed as a defect of it: what we are dealing with here is an impassable conceptual barrier.

3.3. Multiple worlds

Several interpretations of the traditional theory, alternative to Copenhagen’s, introduce a multiplicity of worlds, though it is never quite clear whether that means that the physical world itself has disintegrated into several distinct realities or that these “worlds” must in some way coalesce in making sense of one and the same world—in which case they would indeed be worlds in scare-quotes: explanatory devices, not distinct realities at all.

Within my perspective, it makes sense both that there be multiple worlds referred to and that the relation between them and “the world” be an obscure one. For, in its first stage, Q does contain multiple options as to how the world can be made definite, and each act of synthesis will make one of them “the world” (once again: a world is made out of worlds); but the step turning an optional world in the first stage into the world in the second stage is constitutionally obscure, as it is a precondition for the establishing of clarity itself—and so is the relation between the world in the second stage and all those other worlds in the first stage that were not chosen. The word “beable” has been used in this connection; so we could say that what turns a beable into a being is not something that Q or any of the theories it has incorporated can say anything informative about. But we don’t need the neologism: we could get the same meaning across in old-fashioned Aristotelian jargon by saying that what turns a potential world into an actual one—or the potential entities belonging to it into actual ones—is not something on which Q or the incorporated theories provide any hint.

3.4. One or many minds

Other alternative interpretations introduce one or many (even infinitely many) minds in order to think the world into definiteness. I have no objection to such talk, as long as a mind is not understood as some kind of object, on a par with those that are made be by an act of synthesis. “Mind” is another name for the transcendental subject, which we know not to be an object at all, and that there be multiple (even infinitely many) nested minds may be seen as a reminder that there is no bottom to synthesis: that, as I said before, every act of synthesis applies to material which is the outcome of a previous act of synthesis.

What surfaces in this talk of minds, and must be decided, is the contrast between Descartes and Kant. For the former, my mind is not only an object but indeed the most fundamental object—the only one I can be absolutely certain of, and on the basis of which I can try to build (unsuccessfully, I would argue) the rest of the objective world. For the latter, all there is is empirical objects—appearances, that is—and the mind is not one of them, primarily because it is not one, or it cannot be established that it is (rather than being two, or several): what is not in space cannot be counted, so it cannot fulfill the category of identifiability, so it cannot be an object as my fingers and toes are. I side with Kant; therefore, talk of minds for me is going to stay just that—talk, never graduating into reality.

4. Backing up from the physical world

The quantum physical theory has been vastly regarded as mysterious and counterintuitive. If it did not work as extraordinarily well as it does, many might want to ditch it. In the reading I have been providing, the mystery is not an unnatural occurrence (there is no mystery that it be a mystery), nor is the fact that the theory runs counter to our intuitions. In a Kantian framework, intuitions are confined to what can be visualized, the conditions that make visualization possible cannot themselves be visualized, and yet the quantum physical theory speaks about those very conditions. As for the mystery, I rehash what I said already: what makes for clarity cannot itself be clarified (it takes a leap of faith). And, as promised, I summarize here the basic lessons to be learned from my reading:

• What is novel, and what is puzzling, about quantum mechanics with respect to any other physical theories is that it speaks about the very act of synthesis that makes the construction of a theory possible. It can do nothing other than posit it; it cannot explain it; but posit it it does, and that was never done before in the sciences (though it was done in literature).
• The act of synthesis potentially originates a world, which is never wholly given but constantly growing as various components of it get recognized as connected (entangled) with one another. As this happens, the vocabulary and agenda set by the act of synthesis extend progressively to all that comes to belong to the world, and the world progressively gains a more definite outlook (objects entangled with one another come to share definite parameters).
• The various interpretations that have been provided for quantum mechanics are all struggling with this set of issues and phrasing it in different words, using different metaphors. Whether it be multiple dynamics operating, or multiple worlds, or multiple minds, we are always faced by the same constraint: a theory that talks about the very synthetic act that makes it possible will have to, to that extent, lack definiteness, and to be open to various possible outcomes of the act.
• The theory cannot be “completed,” in the sense of providing a transparent elucidation of all it says. Some of it must stay fuzzy; the only alternative here is to get rid of it—not to adopt its attitude of overweening ambition. (But, in the history of science, there is no going back from an ambitious stance once it is taken.)
• The theory is not entirely an empirical one. Insofar as it speaks of its own synthetic acts, it has no empirical content: it is situated at a conceptual (unreal) level. And at that level there are no means of identifying and counting objects; so, for example, there is no way of saying who the “observer” is who “collapses” the superposition. If we take physics to be by definition an empirical science, then the dominating “physical” theory straddles that definition.

For physicists, this is all I have to offer. There is, however, a more general lesson that I want to draw from the above. In my reading, though the quantum physical theory has the undeniably great merit of bringing forth these conceptual points, and imposing them on the practitioners of the hardest of sciences, hence placing them, with the highest distinction, at the very center of contemporary culture, there is nothing specifically physical about them.

A quantum theory in my sense not only can but must belong in any area of inquiry, and in fact I introduced it by reference to a social science—a most typical soft science. For, in every area of inquiry, humans face the same conundrum. They are not able to understand how there could be definite experience, hence knowledge, of definite objects without appealing to an act that, within that experience, cannot itself be considered objective—though it could be if experience were to be redefined, but then the redefinition would encounter the same requirement, and the same mystery. To bring up another popular metaphor, there can be knowledge only within a horizon, and the horizon, too, could be made into an object of knowledge, but only within a new horizon.

In my reading, the quantum physical theory is telling us that a Kantian framework is very much in order, that within this framework the worlds studied by physics, much like the worlds studied by anthropology, or history, or politics, are to be conceived as made in the course of being known, hence the barrier between an autonomous, indifferent physical reality, that can only be coolly appreciated, and the reality that engages the many humanities, reflective of human efforts and struggles, must be broken. There are many worlds, but they all share the same conceptual dependency on commitment and freedom.