Challenges to Structuralism and the Multiverse

For years now, a friend of mine and I have been debating how to interpret science metaphysically. Rather than issue comments piecemeal, it occurred to me that a detailed summary of my views would do the job better. As you can imagine, much has changed since 2018 when this essay first took shape, but there is enough here that remains worth consideration if nothing else, to share. A polemic against his and related ideas fashionable then, written in a cordial spirit, may it inspire others to think more deeply on these matters and respond with equal if not greater wit and kindness.

P.S. I hated the introductory paragraph so much, I cut it out entirely and never got back to writing another, so please excuse the strangely abrupt beginning.

2. Of course, formal systems are more general and less prone to revision than the diverse operations of human artifice, but they are also consequently too generous. The worst is for the Probability Theory behind much of Quantum Mechanics, which allows dramatic state changes in microscopic entities that are impossible for things of greater size. Roger Penrose recognizes this issue when he says “But randomness only comes in when you go from the quantum to the classical level. If you stay down at the quantum level, there’s no randomness. It’s only when you magnify something up, and you do what people call “make a measurement.” This consists of taking a small-scale quantum effect and magnifying it out to a level where you can see it. It’s only in that process of magnification that probabilities come in” and as Schlipp says, Einstein was “firmly convinced that the essentially statistical character of contemporary quantum theory is solely to be ascribed to the fact that this [theory] operates with an incomplete description of physical systems.” Physics then goes wrong if and when it assumes what is true of all the parts is true of the whole. Objects large enough to be seen have a stability which is an emergent property of the system, but this can only happen if the elements at bottom take on unambiguous values. “A natural view is that all properties in the world are fully determinate: a physical object is determinate in all respects, it has a perfectly precise colour, temperature, size, etc. It makes no sense to say that a physical object is light blue in colour, but is no definite shade of light blue (Armstrong 1961, 59). The author of the book i’m quoting from, “Quantum Ontology”, by Peter J. Lewis, proceeds to give an example to illustrate the converse of the aforementioned exert:

“…the spin of an electron along some particular direction — say the x-axis — can take two values, and hence is modeled by two mutually perpendicular vectors. One vector represents the electron as z-spin-up, the other… z-spin-down, and those are the only two z-spin properties the electron can have. The problem that has much concerned us over the course of the previous chapter is that there is a continuum of states between the eigenstates; if the electron has exactly two possible z-spin properties, then what do all the vectors that lie between the two mutually perpendicular ones represent? …the system as lacking a determinate value of the determinate properties represented by the operator… the fuzzy link coutances the possibility — albeit with a small probability — that a state in which a system has one determinate property can behave as if it has a different property… For example, according the the GRW theory, there is a nonzero chance that sometime during the next day my coffee mug will behave as if it is inside my desk drawer, even though… it is determinately on top of my desk. But this nonzero chance is less than one part in ten raised to the power ten to the power thirty four (Bassi & Ghirardi, 1999, 728); we would have to wait much, much longer than the age of the universe to stand a nonneglibile chance of seeing such behavior! What about in-between systems, like specks of dust? Such systems are [my emphasis] affected to an intermediate degree; their states are generally somewhat close to the relevant eigenstates, although they remain far from eigenstates for appreciable periods of time. But given the right lighting conditions, we can see [his emphasis] specks of dust, so presumably they should have determinate locations… Consider an object like a marble and a location like being inside a certain box.

The author goes on to detail the pertinent mathematics which for reasons of brevity, I am skipping past directly to the conclusion:

“That is, for a large-enough collection of marbles, each marble individually is determinately located in the box… but the collection of all N marbles does not have a determinate location (Lewis, 1997). This problem has become known as the counting anomaly (Clifton & Monton, 1999)… The attitude of most commentators seems to be that if the counting anomaly were in fact manifested by sets of objects, it would be a serious problem for quantum mechanics… In addition to the quantum state, they [Ghirardi, Grassi and Benatti, 1995] postulate a continuous distribution of mass over space; the quantum states act on this distribution, pushing it around so that it is dense in some places and rarefied in others. Roughly speaking, the mass density mirrors the probability density given by the square of the wave function amplitude. The mass density is higher where the probability density is high. It is mass distribution that directly describes the physical objects we interact with; marbles and coffee mugs are regions of relatively high mass density… Massy GRW has no need for a fuzzy link, since it eschews any direct link between the quantum state and physical properties.

This last view represents my own because it is I. continuous; quantifiable but not probabilistic II. dualist/pluralist between an underlying substrate and higher-order phenomena and III. determinate. Whatever the basic units of existence are, I believe they obey the following constraints which I term the “categorical disjunctive”; For every discrete, binary property, 1. A thing is never between states, 2. nor is it both at the same time, and 3. it cannot be neither. By contrast, an information theoretic alternative would have to be premised on inexplicable “brute facts” that are the tenets of a faith not rationally necessitated by scientific or metaphysical dictums. Add to that it’s monistic abstract ontology which leaves no room for anything else in a eliminativist, not just reductive manner, and it’s fundamentally indeterminate, random and “generous” character. I call any ontology “generous” which permits the absurd. Boltzmann’s Brain illustrates just how preposterous the statistically real, not just measured uncertainty of finite beings is. Pushing these absurdities out into other universes does nothing to alleviate the problem either: if the multiverse permits so much as one random event (an uncaused occurrence that does not follow from its antecedent conditions, like a mug finding it’s way into a drawer from the top of a desk without moving through a progression of gradual, orderly steps) then ALL universes are the stuff of chaos soup. If the laws of physics in conjunction with each other, as described by science, fail to predict a given real-world outcome or worse, foresee with near-certainty the spontaneous autogenesis of cognizing organic bodies that suddenly formed on their own via the haphazard energy spikes of a vacuum, in numbers vastly greater than naturally occurring ones, then at best, the science is incomplete or at worst, it is patently false. As my old professor was fond of saying “you should never try and explain the unknown by the more unknown.” and “fluctuations” of the sort alluded to in the previous sentences are, by every account, a mystery with no explanatory power whatsoever. Finally, by what means are quantum states multiply realized across distinct cosmic regions? The process is a mystery to not only myself:

In order that such a many-worlds picture be consistent with, for instance, the perceived absence of multiple Coulomb forces (imagine an electrically charged cat), the space-time itself must presumably split into branches which are topologically disconnected after the measurement is made. The miracle of Process 1 on the orthodox interpretation is replaced by the new miracle of the splitting of space-time. Not only is there no hint as to what causal mechanism would produce such a splitting, there is not even a characterization of where and when it takes place. If the establishment of a correlation between the object system and measuring apparatus were sufficient for measurement then systems would be continuously undergoing Process 1 collapse (on the orthodox interpretation) or splitting (on the many-worlds interpretation). The fact that they are not and what more is needed for Process 1 or splitting to come into play are left unexplained by both interpretations.

All we are told on such a theory is that if A happens in our universe, B takes place in another, or the reverse, but that is the problem. To be explanatory, we must be told how one is brought about within this spacetime region by the model. Were you to just stipulate that “If X, then A or B” your causal story is at best incomplete. You may have narrowed down the range of alternatives, but you are obviously missing some tertiary acting factor which makes it the case that A transpires here, and B, elsewhere or the other way around. For any X of the indifferent kind I have spoken of, there must be some Y, such that A or B is determinately selected. For example, how would you like to receive ten dollars in change? If you prefer to have the fewest bills possible, a ten dollar bill will do. If you are going to a strip club then ten one dollar bills is preferable, and if you have promised to split the amount evenly between you and a friend, then two fives are best. In each case, there is a sufficient reason for the choice, each of which corresponds to a different, intelligible world. Of course, the cause need not be teleological, but it ought at minimum to be determinable, appealing to the structure of the object(s).

3. Furthermore, I do not see how a one-to-one mapping of “alphabetic” particles with symbolic counterparts in an unbroken chain of logical relations, gives us any better idea of what it is that renders applied mathematics so “unreasonably” effective. Is it the formal system? The unextended, timeless, acausal principles of organization? That hardly seems possible for the reasons argued in the previous objection and given the serious discrepancies not only between the facts of experience and science, but among the sciences themselves, namely general relativity and quantum mechanics and further still deep within the latter’s mutual exclusive interpretations, ranging from the deterministic to stochastic, branching and collapsing, mental or naturalistic, etc. The shear volume of opinion on the matter is to my way of thinking, a blight on physics, one for which your proposed logical edifice is no cure, since even if we assume your rational optimism (which I share), the problem will just recur at the formal level as either, to take the first set of possibilities, a Newtonian/Einsteinian calculus and geometry (of finite dimension) or a Born/Heisenberg statistics, theories totally at odds with each other. But perhaps there is a way to reconcile these hypothetical machine languages through a breakdown and synthesis of their principles according to which are responsible for “charting” the features of the universe the other does not. If so, then we may conceivably derive a single formal system that includes axioms of both whose metaphysical scope ranges over all the entities in the domain of science. Nevertheless, whatever formal system you end up with, the extent to which it accurately reflects the structural and dynamic characteristics of the universe will remain contingent upon our perceptible surroundings, not the inert, intangible abstract blueprints. The only way to know how well your theoretic apparatus matches the things it is believed to mirror in every detail is by testing it via observation and experiment. If this formal system cannot predict the future with absolute certainty, it’ll require the constant readjustment of your original parameters to keep up with changes in the environment until hopefully one day, it reaches a uniform, stable fit.

Considering just how ambiguous and inclusive simulation/multiverse theories are, verifying or falsifying them is practically out of the question. As one critic put it “In any multiverse-promoting book, one should look for the part where the author explains what their scenario implies about physics. At Level II, Susskind’s book The Cosmic Landscape could come up with only one bit of information in terms of predictions (the sign of the spatial curvature), and Steve Hsu soon argued that even that one bit isn’t there.” Just about any state of affairs you can imagine is compatible with what little they claim. To quote Paul Davies: “Appealing to everything in general to explain something in particular is really no explanation at all.” In other words, a theory which doesn’t rule out anything, doesn’t establish anything either. But assuming they were to get more specific, I do not see how that would demonstrate a link between formalisms and the universe, so long as it remains possible for one to vary independently of the other. What if you conceived of a brand new formal system or several totally distinct from the first, that describes the same phenomena just as well? Then the choice of axioms is at least somewhat arbitrary, rendering your formalist strategies inconclusive at best. The paper I cited earlier raises a point in much the same vein.

“But is it true that OSR (Ontological Structural Realism) provides a general and substantial framework that any detailed reasonable interpretation of QM has to respect, that framework consisting in the claim that there are certain structures in the domain of quantum physics by contrast to objects with an intrinsic identity? Infinitely many branches of the universe with correlated values of properties in each branch (“relative states”), density of stuff or mass in four-dimensional space-time (smeared-out values), pointlike flashes sparsely distributed in space-time and particles with definite trajectories in space-time are radically different proposals for an ontology of QM, although all these ontologies can be regarded as being committed to certain structures, namely structures of entanglement. However, these ontologies are radically different not because they pose different sorts of objects in addition to agreeing on being committed to structures of entanglement, but because they spell out what entanglement means in radically different ways: superpositions of correlations in the form of objects being many times copied across different branches of the universe whose properties are correlated within each branch; superpositions of correlations in the form of overlapping smeared-out values in physical space making up a continuous distribution of stuff (mass density) in space; correlated OSR and the interpretation of quantum mechanics 11 flashes occurring at space-time points; position values of particles that develop in time in a correlated manner.”

This brings me to my doubts about OSR in general, the doctrine that only extrinsic properties or relations exist, not objects and their qualities. I subscribe to the more modest Epistemic Structural Realism which I will get to at the end but first I must make the case against the former, beginning with a quote …it is impossible that the ordinals should be, as Dedekind suggests, nothing but the terms of such relations as constitute a progression. If they are to be anything at all, they must be intrinsically something; they must differ from other entities as points from instants, or colours from sounds. What Dedekind intended to indicate was probably a definition by means of the principle of abstraction…But a definition so made always indicates some class of entities having… a genuine nature of their own. This alone should caste doubt on the thesis in question. The idea is akin to saying there can be lines without points which is absurd, when of course, you can have a single point that connects to nothing without raising any issue or as another man put it “To say that information exists in and of itself is akin to speaking of spin without the top, of ripples without water, of a dance without the dancer, or of the Cheshire Cat’s grin without the cat.”. For any effect, there is always a cause grounded in some being, and the former always takes after the latter. Data however, stripped of all connection to the stuff of the world, does not resemble or have a likeness to what it describes.

My contention is reiterated in the following quote: “It has often been said that units are units in respect of being perfectly similar to each other but though they may be perfectly similar in some respects, they must be different in at least one point… If three coins were so similar that they occupied the same place at the same time, they would not be three coins but one.” Here again, what should be obvious is made clear to those who have forgotten the Law of Identity trafficking in theories that do away with reason altogether in favor of some contrived notion that mystifies rather than explains. Consider for instance one plus one equal two. If indeed these numbers were the same, they could not be added, the first being equivalent to the second. Of course we can speak of them as two just as we can Clark Kent and Superman, but that does not make them distinct. Yet numbers in general, are strongly individuated as evidenced by the following passage in Michael Heller’s book Ultimate Explanations of the Universe “… the set of real numbers compromise an uncountable number of elements. But in spite of this, every real number occurs just once in that endless set. No number comes a second time. What’s more, we are able to attribute a name to every real number (to any degree of accuracy), e.g. 0.123345…, and we can do this because each has its own individuality. What gives it an individuality is that every real number has properties that are proper only to itself (e.g. every number has its own prime factorization) and properties resulting from that order on the real number axis.” Indeed, things cannot differ quantitatively but not qualitatively.

Also, if Pythagoreanism were true, then it would make sense to ask where and when is a number or shape. It would have to manifest itself within space and time, such that Euler’s Identity or a Mobius Strip could be found somewhere in the cosmos, presumably made up of subatomic particles or vast celestial bodies, since there is no difference on that account between the material and Platonic Heaven, which is absurd.

4. Back to the question of worlds and their number, I defer to Don Page, theoretical physicist from the University of Alberta, who explicates his objection to their multitudinous below.

“My argument against Level 4 is that different mathematical structures can be contradictory, and contradictory ones cannot co-exist. For example, one structure could assert that spacetime exists somewhere and another that it does not exist at all. However, these two structures cannot both describe reality. Now one could say that different mathematical structures describe different existing universes, so that they each apply to separate parts of reality and cannot be contradictory. But this set of existing universes, and the different mathematical structures with their indexed statements about each of them, then forms a bigger mathematical structure. At the ultimate level, there can be only one world and, if mathematical structures are broad enough to include all possible worlds or at least our own, there must be one unique mathematical structure that describes ultimate reality. So I think it is logical nonsense to talk of Level 4 in the sense of the co-existence of all mathematical structures.”

In other words, there is a unity in multiplicity within which there is everything and beyond which there is nothing. One cannot divide reality into separate “pockets”, tucked away in regions cut-off from one another, any more than you can isolate numbers from their predecessors and successors. They all together form a whole that is naturally interwoven and unbreakable. There are no walls between them, no distant shores left unconquered by the axioms, no hidden depths to seek refuge in from the might of imperial logic which is all-pervasive. Which is to say, there are no other worlds any more than there are alternative mathematics. The universe is a maximal set of compatible beings, as explained by Leibniz when he writes

“Everything possible demands existence, and hence will exist unless something else prevents it, which also demands existence and is incompatible with the former. It follows from this that that combination of things always exists by which the greatest possible number of things exists, so that if we assume A, B, C, D to be equal with regard to essence, i.e. equally perfect, or equally demanding existence, and if we assume that D is incompatible with A and with B, while A is compatible with any except D, and similarly with regard to B and C, it follows that this combination, A, B, C, excluding D, will exist; for if we wish D to exist, it will not be able to coexist with anything except C, therefore the combination C, D will exist, which is certainly more imperfect than the combination A, B, C. And so it is obvious that things exist in the most perfect way.”.

So for instance, I cannot both move forward and back at the same time, but there is always in every situation, a reason for preferring one set of behaviors to another. Imagine for example, you are walking through a maze in search of the destination. The rational choice is the shortest path between you and the exit. If such circumstances were realized many times over across space and time in fragmented pockets of material subsistence, the right outcome would occur once by brute force so to speak, when all options have been exhausted, just as the odds of rolling a five on a twelve sided die are one given an infinite number of tosses. Yet this could only happen if there is a desire to escape and a means of propulsion. Yet something acting randomly, that is, without due cause, will not have these properties, because a meaningless universe is simplest in form and as Leibniz indicates, the easier a thing is to produce, the likelier it is, and what could be more effortlessly done than nothing? To this you will undoubtedly retort that universal privation or an empty world is impossible and there is at least one necessary thing, too which I would add there can be at most one necessary being, for one is enough for all other derivative things if it is sufficient unto itself. Furthermore, according to Leibniz’s definition “Nothing is necessary whose opposite is possible” and matter is inversely related to antimatter and perhaps even dark matter, so there is no reason to prefer either and therefore neither will exist besides through something essential whose nature it is to create them in this or that way. Yet if all possibilities were realized at once, each thing and its antithesis would negate one another. For instance, someone who moves left and right, responds to a yes or no question in both the affirmative and negative, or is cold and hot, has not moved, fails to give an answer one way or another and is neither frozen nor gaseous and lacks in all things. So too shall the sum of every physical configuration. The collision of an electron and positron supplies a further, literal illustration, while of course obeying the conservation of energy, but a universe so populated, that is, by every natural property and it’s complement, including the opposite of energy, will cancel each other out. Finally, everything and nothing are more alike than they are different, if you filled in a six by eight region with white squares, it would be indistinguishable from an empty grid. Likewise, my believing this and not this is the same as my having no opinion, as has been shown. Let us assume however, for the purposes of discussion, that there exists the basic positive qualities and their opposite, n/u, m/w. Then you could have the possible composite objects nm, nw, um, uw where order doesn’t matter. You could then have the possible combinations, the world of singletons (4), the world of duos (nm, nw), (nm, um), (nm, uw), (nw, um), (nw, uw), (uw, um), the world of trios (nm, nw, um), (nm, nw, uw), (nm, um, uw), (nw, um, uw), and the world of all four. Now either all these worlds exist, some of them exist, or one of them exists. If I am right, and there are no structural properties then only the totality of objects will exist for any subset of this set belongs to that set. The axiom responsible for this conclusion is “if objects are possibly combinable they are actually combined.” So if you ask, where is (nm, uw)? There can be no doubt that it is in the World-Set. But then you will say order matters because of time and there is an objective sequence of events that is irreversible. But if time intervals are necessarily connected, then there is only one world-set. Take for example a series of diminishing magnitude like Russian Nesting Dolls. Open the largest, you find one smaller, etc. The first one entails the next and you cannot rearrange this series. Entropy is a perfect analogue to this situation. The less organized always comes from the more organized. A state of greatest “compactness” results in an even distribution or as Peirce says “the greatest disorder is the simplest order.” or, to put it another way, complexity terminates in uniformity. Therefore, if you knew everything of revelerance, you could deduce the succeeding occurrence with absolute certainty until you reach the end. So even if the world-series is linearly ordered, it will have one acceptable sorting.

But what kind of law shall the elements follow? Consider the words of Gregory Chaitin and the numbers listed below as a definition of randomness.

“01010101010101010101

01101100110111100010

The first is obviously constructed according to a simple rule; it consists of the number 01 repeated ten times. If one were asked to speculate on how the series might continue, one could predict with considerable confidence that the next two digits would be 0 and 1. Inspection of the second series of digits yields no such comprehensive pattern. There is no obvious rule governing the formation of the number, and there is no rational way to guess the succeeding digits. The arrangement seems haphazard; in other words, the sequence appears to be a random assortment of 0’s and 1's”

Let us consider the series AB which is basically the same as the first one in his example. It is a pattern just in case it repeats at least once and call the part that repeats the unit. Let us say the next part in the series is B not A, such that it now reads ABB. The unit has changed from the alternating pair AB, to include another B as the next element. We could easily make sport of this topic by adding to the series without repeating. So for example, if ABB is to never repeat, B must be next in the series, but then we have a new pattern of the form “All B’s after A” so we must use A after B, to make ABBA and from that, ABBABA, increasing the unit once more and so on. You will notice however that this game is quite predictable, and is therefore not random. For example ABBABA could become ABBABAA or ABBABAB but if you are perceptive enough, you will notice a pattern emerging in the latter of these, that reads “AB repeating after ABB.” and so the former is maximally random, and If you take ABBABAA and add B, so as to avoid yet another pattern of repeating A’s, you get ABBABAAB and so on. In the end, our most random series is anything but uncertain and the idea that anything could be or behave indeterministically dies with it.

As we’ve reviewed, a series may be incompressible or the length of the procedure equals the output, in which case, he calls it random, which is wrong for the following reason. To be unpredictable, something must vacillate between one of a number of outcomes. For example, my next word might consist of one of twenty-four letters, followed by one of twenty four letters and so on until I halt. This is difficult to predict, unless you were to know my intentions. Why is this so? Because the options are many. If the possibilities could be narrowed down according to a standard, the following letter would eventually be necessitated and invariant and this is fixed and easy to deduce. Take for instance the description “the smallest perfect number which is also a factorial” uniquely designates six. This is true of every number, provided you supply the appropriate criteria, and would be true of speech and writing as well for much the same reason. Once you formulate a definition specifically enough, it will eventually single out one and only a thing and the random is no different and even for those numbers that cannot be expressed algorithmically like the primes which one is unable to write in scientific notation, they too are not random, because, as we’ve discussed, for that each would have to be possibly other than they are, which is quite impossible.

What then, is the opposite of this (false) notion of random? As Leibniz states, our world is “…the one which is […] simplest in hypotheses and the richest in phenomena” so by my argument, the universe should be the smallest program with the largest output. As Max Planck says

“In this connection mention may certainly be made of Leibniz’s theorem, which sets forth fundamentally that of all the worlds that may be created, the actual world is that which contains, besides the unavoidable evil, the maximum good. This theorem is none other than a variations principle, and is, indeed, of the same form as the later principle of least action. The unavoidable combination of good and evil corresponds to the given conditions, and it is clear that all the characteristics of the actual world may be derived from the theorem, even to the details, provided that, on the one hand the standard for the quantity of good, and on the other hand the given conditions, be rigidly defined along mathematical lines — the second is just as important as the first.”

Seen in this way, in light of the Principle of Sufficient Reason, no world lesser than ours is owed existence, and indeed, on account of their deficiency, each is categorically denied being and no world greater is possible, since if there were one surpassing this realm in excellence, it would exist instead of what there is, and thus we would either be there or fail to be at all.

With that taken care of, we return to the topic of identity with yet another important quotation: While the existence of an irreflexive relation certainly entails the diversity of the entities to which it applies, it is far from clear that this relation is prior to their diversity. Indeed, it presupposes this diversity. An irreflexive relation is identity-involving if its analysis involves the identity-relation; it is object-involving if its analysis involves appeal to particular objects. The standard examples of weakly discernible entities discussed in the literature certainly appear to use object-involving irreflexive relations: for instance, each of Black’s spheres is a mile away from the other but not a mile from itself.” Black’s sphere refers to a thought experiment involving a universe populated by two identical spheres. These however, while hypothetically possible as intellections, are defied by the unending complexity of nature ruled by four principles: ontic completeness whereby for each predicate, the subject has it or the negation and ontic consistency, the idea that all predicates are compatible. This further entails that objects never have all the same properties and that properties are infinite. If they were finite, a reason could be found for another property and so on. For example a polygon can always have n+1 sides. One can only categorize what has been named and the set of known traits is a priori less than all of them, but the details which escape the senses, are everything and without bounds. The endless division of matter also suggests a omnifarious continuum, one which isn’t possibly reducible to punctiform fundaments. Philosopher David Odenburg writes “[T]he very idea of a material metaphysical simple makes no sense. If a material object were simple it would be unextended — but then in what sense would it be material? An extensionless point is not a something but a nothing, and so cannot be a locus for concepts, which are something. Further, extensionless points cannot have any constitutive relations to the extended.” Physics professor Chris Baird writes in his article on the shape of an electron “If you find the concept of a fixed amount of mass being contained in the infinitely small volume of a single point illogical, then you should…” and philosopher Jonathan Schaffer astutely observes ”Indeed, the history of science is a history of finding ever-deeper structure. We have gone from ‘‘the elements’’ to ‘‘the atoms’’ (etymology is revealing), to the subatomic electrons, protons, and neutrons, to the zoo of ‘‘elementary particles,’’ to thinking that hadrons are built out of quarks, and now we are sometimes promised that these entities are really strings, while some hypothesize that the quarks are built out of preons (in order to explain why quarks come in families). Should one not expect the future to be like the past?” and the Stanford Encyclopedia of Philosophy notes “For instance, an object’s change of speed, or even its simple change of spatial location may be transformations of one Turing-uncomputable real-valued quantity into another. Turing-uncomputable value is certainly a Turing-uncomputable operation. Hence, it would seem that given many of our physical theories, the physical world is chock-full of operations that outstrip the power of Turing machines. If this is correct, it falsifies Bold Physical CTT.[Church-Turing Thesis]” From both a rational and empirical perspective then, one ought not to expect and find a smallest denomination of matter. In fact, I would go so far as to say that what sharply distinguishes concepts from objects is that the former are simple and delimited, having just those properties that are necessary to define them, while the latter are complex and infinite, having all those properties which they are capable of supporting. I think we agree that simples are conceptual but while yours come from physics and resemble or are Wheeler’s bits mine are Leibniz’s monads, which Godel describes as “…not another kind of material particles; they are not in fixed parts of space, they are nowhere and therefore not material objects… they also have something inside” namely perceptions and drives. A problem for the “It from Bit” view is that it defines its terms in opposition to one another. X is nonY and Y is nonX, however this way of understanding both is empty. We shall for the purposes of argument ignore this objection and move on. Let zero, one and rocks exist. Assume rocks are just bits. Then let a liquid, which is also bits, exist within the same group as rocks. The question is, are the zero and one members of this set? It may be swiftly assumed that they must, since that is all bits are. This will not do, however, since each bit is modified by every other bit, except zero and one themselves. For example, if you added a single electron to the universe, its gravitational force would distort the field, but zero and one would go unaffected. If this notion is unconvincing, it is always possible to imagine another set of zeroes and ones which is not a part of the world-set and it exists; otherwise, we could not perceive it. More importantly, the bits are many, but there are The Zero and One itself, the universal dichotomy out of which all the others have sprung, and they are unique. They are logically and metaphysically prior to any number of bits that may come after, which can only be crude approximations of the original model. This I call the transcendental axiom of Platonism. We ought then to conclude that the “yes/no” binary is an insufficient source of existence, for that presupposes a query, which requires a deeper foundation. Additionally, On theoretical grounds, it is always best to keep the number of primitive terms to a minimum. With that so, my view, that no physical simples exist, is a superior one because it leaves nothing unexplained. Analysis is never-ending but furthers our understanding of nature with increasing precision. If a finite description were supposedly complete, there would be steps missing in the process linking one thing to another. If movement occured by a leap, it would be teleportation which suggests the instantaneous annihilation and sudden autogenesis of an entity from nothing. This is not to say there is no absolute distinctness between things. On the contrary, they must be, or things would be partly themselves, and somewhat another thing when in reality, a true indivisible unit is unlike anything else.

Allow me to sketch in brief my own view on the topic of nature’s most general constitution.

Suppose there is a basic positive quality, V and its complement Λ which are simple, discrete and pure. According to plentitude, the world shall then realize every degreed value in between the two in the form of composite objects. For example, whatever is 3/10th V is 7/10th Λ such that said thing is complete but limited in each of its defining properties. For example if V is acceleration and Λ is endurance, where the more you have of the former, the less you have of the latter (the faster you run, the more tired you are, the less tired you are, the slower you run) you can never have both fully, you can only have a good balance of each on Aristotelian grounds. If the path is short (a sprint), a person blessed with enough V will be rewarded, if the path is long (a marathon) he may succumb to fatigue before crossing the finish line. A perfect being on the other hand, would not so much as break a sweat to reach his destination. If there could be a flawless mover, he would change places instantaneously from one point to another without loss of strength or in other words, a runner so fast, the intermediate steps between start and end would be traversed without going through them — an impossibility according to physics, where the faster you go the heavier you get and the more energy you need to maintain the same speed, therefore no such entity can be material. In view of this illustration, we have a few axioms to consider. (a) Objects consist of two or more properties (b) that are inversely-related © where the proportion of each is always equal to one.

This analysis merely explicates the structure of basic positive qualities and objects, it does nothing to suggest the quantity or nature of types. There are quite a few things which might fall into this category; black/white, curved/straight, good/bad, etc. Yet not all of these are compatible, as Descartes famously argued when he noted how mindless matter cannot be a thinking thing, which is known as the problem of intentionality stating roughly that bodies cannot so much as represent their own states or identity (nevermind anything else) by means of the physical without transcending that condition which makes them solely brute bulk. It is still a mystery how the intellect and the somatic parts it commands interact, but if I am right, they cannot do so directly through any mutual exchange. Instead, they must conform to one another through a system of preestablished harmony, as Leibniz theorized, for no sense can be made of the “influx” hypothesis, according to which, an entity gives up something of itself for the benefit of another and either fades away completely when its resources are depleted, or is compensated for its loss by something else in the exchange process. This notion is easy prey for the Ship of Theseus objection, given the fact that if X is made of the parts AB, and X is deprived of B only to receive C, and then A is likewise replaced by D, the new compound, CD will and will not be X, if we assume X to be defined just in terms of its parts. Either X is something over and above its parts, or it dies with their loss. If there is nothing fixed or essential to a whole, the same is true of the parts, but if objects are infinitely redefineable by means of substitution, then each will lack an identity proper to it and their essence would be unintelligible. Consider for example a word like “hair” remove the h and you have another word entirely, add “less” to the end, and you have its negation and so on, yet the concept itself does not change with the manipulation of symbols because ideas expressed in language are not contingent upon the techniques invented for the purposes of communication. This is the foundation of intensional logic. The postmodernist and other sophists confuse the need we have to articulate our thoughts in sounds and shapes chosen and changeable arbitrarily, with the very essences they are used to represent which are naturally prior to and independent of human thinking.

In what follows, I will briefly explicate my theory of causation and time. Consider some entity using a primitive notion of expressed and suppressed properties. Suppose that X is the properties Ab, where capital letters are expressed properties and lowercase ones are suppressed by an expressed property of something else connected to X. Let Y, the composite of Bc represent another object. The causal rules governing these objects are as follows. 1. All objects express at least one property. 2. Whatever they express is suppressed in all other objects. Consequently, 3. No two objects have the same condition and 4. no dependent object expresses all its properties. Now, suppose b in X becomes B. B in Y will become b resulting from 2. Since by 1, Y must express itself some how, c will become C and A will become a in X due to 4, in which case, X will represent to itself aB and Y will represent bC. This is a toy example that roughly outlines an idea of internal modifications necessitated by logical axioms that range over all entities in its domain, and would be a great deal harder to imagine in a system consisting of even one more property and/or object but I hope it gives you a intuitively plausible notion of change.

Back to the question of types, I propose three mutually exclusive ontological domains, though by no means are these the only kinds of things there are. Like the animal kingdom, one can break them down into further subclasses, but those which are the focus of our discussion are the following: subjects, objects and concepts. Now all objects as we’ve seen are conceptual “bundles” yet they are more than this insofar as they can be experienced. The form of infinity or parallelism or justice cannot be tasted, heard, felt, smelled or viewed, nor can they be located in time and space but they can be intuited. Here is a clear divide between the sensible and intelligible. The mind itself however, is something besides even these; a self-referential system that is neither fully abstract or concrete, and is home to emotional states like joy, anger, and sadness, the five primary colors and feelings like pleasure and pain. All three of these kinds are not representable nor do they exist independently of consciousness and therefore fail to meet Plato’s requirements of what an idea must be. This is what defines the finite, that it has some attributes which preclude others. The question remains however, can anything be all three? For any two or more contrasting properties, there is something they have in common which they are about. Hot and cold are both forms of temperature for instance. So too are the thinkable, thought and thinker together united in one being which is not another species of being but The Being of beings, pure, unqualified and limitless, something that lies beyond distinctions and above opposites. Particulars, the individual elements that reality is divided into, are negations of the Absolute, which is necessary, eternal and perfect whereas the former are contingent, transitory and deficient in some respect.

At the top of the metaphysical hierarchy, there exists The One, which like the number itself is both divisible and indivisible. If we treated each half of one as parts, one would be two, which is absurd. Therefore, mereology has to be distinct from mathematics in some important way. As Godel says of sets “Sets are multitudes which are also unities. A multitude is the opposite of a unity. How can anything be both a multitude and a unity? But a set is just that. It is a seemingly contradictory fact that sets exist.” Perhaps we can resolve this dilemma by stipulating the independence of types from their tokens. Consider for instance the essence of gold, it’s very possibility, or the conditions that must be satisfied for that metal to instantiate. The more or less actual gold there is in the universe, in no way changes its very nature. All the gold could fall apart tomorrow, or it might have never formed at all, and there would remain Gold as it is in itself. But what about the set of triangles of different angles equaling 180? They are necessary members that could not fail to exist, and indeed, they are mutually-entailing implications of each other. It does not make sense to speak of one, and omit another, just as we could not speak of three and five without understanding the number between them. Yet we are not here concerned with the relation of abstract entities to other abstract entities but rather with the instantiation of universals and the difficulties with self predication. Is the form of horse itself a horse? It can’t run, has no size or color, doesn’t grow or have parents and isn’t alive. If we take these to be essential features of any real horse, then surely, as Aristotle insisted, no idealized notion of one, however scientifically descriptive, could pass for the genuine article. Yet given what is now known about genetics, it seems more evident that information fundamentally captures the very essence of biological traits, distilling the crux which makes an organism this or that species. Therefore, whatever sets a horse apart from all other animals, will have a place among eternal truths. Allow me to supply another illustration: picture yourself trying to sample every kind of music. What ought you look for? A deliberately organized arrangement of sounds. The question becomes, are these very criteria themselves a song? The obvious answer is of course not. I have stated only what all compositions must be, yet I have not, for that reason, composed something. Therefore, what makes a set of particular tunes rhythmic is not listed among them as itself some audible noise, which demonstrates how Third Man Arguments fail. Indeed, there is a sense in which no universal is really instantiated.

With that in mind, one can see how your position and mine are not all that far apart. We both analyze metaphysics in terms of dichotomous properties, the main difference being that I posit more of these.

On a different note, suppose the previous arguments concerning the infinitesimal makeup of nature are wrong and matter actually is discrete. Then where do we get our idea of continuity from? Not from the world obviously and therefore, I submit, that the only explanation for this is an ideal object are an uncountable set of them like the real numbers, that does exist, which yet again makes the case for Platonism undeniable.

Let us bring our attention back to OSR in particular and imagine for a moment a boundless sea of red. No structure would occur within without some nonred stuff present. You could not find the midpoint, the volume or shape without distinct comparative substances at work. But were red alone, it would still be that color, which is to say, you must first identify a nonrelational property before mapping out the links between things. A similar worry is brought up in an example from physics: Now imagine flipping positive and negative charge… in the new state of affairs, here is a particle with charge -3 Coulombs, there is another with charge +2 Coulombs. I agree that this new state of affairs will behave, e.g. change over time, in a manner that mirrors the behaviour of the original state of affairs… But I do not need to go into details about the mirroring of the original state of affairs’ behaviour. For the relevant point — -the point I want to emphasize — -is a different, and a simpler, one. It is just that the new state of affairs is different from the original. And just that point is enough to imply that there are facts — -‘content’ or ‘nature’ — -about, say, negative charge, or having an exact value of negative charge (e.g. -2 Coulombs) that outstrip its web of relations to other quantities: that cannot be ‘analysed away’ in terms of the quantity’s position as a node in the web. For the ‘flip’ being a symmetry of the laws implies that this web of relations is shared with positive charge (or the corresponding exact value: in my example, +2 Coulombs): but the states of affairs are different!

Here the point is a deceptively simple one. The relation remains the same but the things related are different, indeed, the opposite! This can only make sense if they exist in their own right. The problem is magnified further when considering inextricably-linked properties. Without positing knowledge of individual objects we cannot explain why certain properties and relations tend to cohere.This objection is due to Chakravartty (2003) who points out that certain properties tend to be found together, for example, negative charge and a certain rest mass, and then asks ‘coincidence or object?’. Steven French, a major proponent of OSR, accepts the former. This simply won’t do as a response however, for what could be more insightful than discovering properties that tend to come together as one thing, only to deny their conjunction any metaphysical significance?

Extrinsic relations presuppose intrinsic qualities. Two bodies at a distance of a mile takes for granted that both are stuff that occupies a locale which must be characterized if one is to detect their presence. Then again, you could interchangeably substitute one for the other or for things of a different kind and preserve the relation, but then you have told us nothing about the entities, which is the point I think. So if two wooden chairs are switched or replaced by plastic ones, they remain apart from each other but this fact reveals little. “Wooden” may also be structural relationships, yet this too has its difficulties, for if little masses of the same type were to take the position of their counterparts, maintaining the original configuration, once again, we are told nothing about the elements, and to have a full description of nature we must understand them just as well as we do the composites they form. If an extended thing were made up of points that are themselves extended, you are left with empty, hollow, insubstantial objects and if the most fundamental bits are unextended than said things can have no material properties as those require a body to fill a volume and resist penetration. Setting aside the previous issue, how do we explain forces unless things are endowed with an inherent capacity for acting and being acted upon? If you say that a being can acquire this property however, then it must already have the means sufficient for receiving the input. If an infant can grow up to learn speech, they must already have a predisposition for language. Words do not come to them from thin air but through the mind’s natural endowment. This can only be so if there is an innermost core to beings that they have essentially and that they are void without, since having a role in the world is to actively influence through efficacious processes.

Relations are logically impossible. For subjects “I” and “II” to be related, both must share in a predicate common to them, such that they are made up of terms AX and AY where the first is universal and the second, particular. But A is not possibly combinable with X without a term that joins them. Let A be CD and X be CE but then C must have something D and E have which merges it with the pair, call it F. C will therefore be FG, D, FH and E, FJ. When X=CE A=CD, C=FG, then I=(((F)C)A))) or (((F)G)H))) the sum of its unique qualities, but these are held together by yet more general categories, as F will itself be reducible or F will have nothing which links it to G, H and I.

If you say that two or more terms are different from one another you can never be wrong — there is nothing but variety, if however you say two things are the same, you can never be right, because there are no repeated terms. Each thing merely “imitates”, “mirrors” or approaches a value without ever reaching it, in a dim and faint way.

Ascribing a universal to a particular does not tell you about their individuality which is always somewhat at odds with it’s kind. Let us assume that names are short for intersecting extensions such as “the only three-legged brown horse” that is the class of 1. tripods, 2. orange mixed with black things, and 3. equestrian creatures where for example, the first has twelve members nine of which are primary colored, and within that subset of three, one is a mustang. Taxonomically useful though it may be, the description given does not tell us anything concerning the subject, for all it’s properties are ones we already knew about and we could have imagined their union without an observed instance of said thing apriori. That is because generalization only works if you remove from the individual the specific properties that make it one. Finally, there is the problem of universals. These forms, if they exist, cannot be in multiple places at once, for what is, cannot be found outside itself. If it were, any given paradigmatic type would be A and nonA simultaneously which is a contradiction in terms. It also means they have properties inconsistent with one another. Numbers for example are unchanging and eternal, yet abstract relations, as science attests to, describe the world of space and time which is always in flux and pliable. So while there may be a formalistic tie between these realms, they cannot be ontologically dependent upon one another. If anything, the physical is a derived from mathematics though we experience the reverse. It is as if things were created with these logical regularities in mind without actually being the same as their instructional content and indeed it can be proven that entities are not bound to follow the rules governing them because the parameters set from the beginning, the constants and the laws, could have been otherwise and this would not necessarily result in a change of the intrinsic properties of objects. For instance if I lost all my senses, my faculty of reasoning would preserve me, and if I lost that too, a certain disposition or attitude would remain and this “bias” (something that informs my decisions) would adapt to the circumstances.

But what about the logic of relations itself? Does it make sense to speak of connections in a vacuum? Leibniz considers a scenario that would later be known as Bradley’s Regress:

Suppose, for example, that there is a relation between a and b, and call it c; then, consider a new relation between a and c: call it d, and so forth to the infinite. It seems that we do not have to say that all these relations are a kind of true and real ideas. Perhaps they are only mere intelligible things, which may be produced, i.e., that are or will be produced.

The issue if not already clear is made acute with the help of some formality.

1. Suppose that there is a relation R uniting qualities A and B.
2. If R is nothing to A and B, they are not related.
3. If R is something to A and B, then R itself is something.
4. If R is something itself then it cannot relate and needs further relations, such as R′ to relate it to A and B.
5. The same process is then repeated with R′ and further relations, ad infinitum

Suppose that R just is AB, as I do on my view. Then it can be substituted, A for C and B for D, but if R=AB it cannot also be CD, CD would have to form a completely new R, so this fails, because R’s properties cannot be accidental and yet if it is a mere conjunction with no essential unity, nothing will prevent each of the two pieces from being replaced due to the fact that it is structure-preserving, the only thing that matters in OSR. If they were one however, the whole is greater than the sum of its parts, and will be more than AB. Now let us assume R is in fact something in itself. Then it is apart from A and B, but an independent entity cannot unite separate things, so another object must be invoked that itself is either synonymous with ABR in which case it is nothing over and above the group and is therefore no relation either, or it is in a right of it’s own, but then it does not relate. One can think of R as in between two things AB, A-R-B, but then to use Leibniz’s reasoning, there is another relation between A and R and R and B, and so on. The problem that he does not explicitly state, is that none of these “get close to” or explains how A and B are together, anymore than Zeno’s hair would reach its destination in a finite number of steps, because you are constantly having to appeal to ever more relations. Bradley puts it like this “Contradiction everywhere is the attempt to take what is plural and diverse as being one and the same,..” which is another way of saying that you cannot recognize a multitude’s numerosity whilst also reducing it to some property that all the elements have in common, because each will have, as Jevons rightly insists, a quiddity or “thisness” which sets it apart from the group. Expressing a slightly different but even more important idea, Bradley continues elsewhere: if you predicate what is different, you ascribe to the subject what it is not; and if you predicate what is not different, you say nothing at all. This key passage is one that should be illustrated to understand. Think for example of a white bench. A chair is not a color (nor is the paint for that matter) and white does not have a weight or dimensions. The two properties happen to coincide on the Bundle Theory, but they may even be necessarily connected such as being a whale and swimming, Happy and alive, or numerous and different as we’ve seen, but this does not reveal to us their very essence, for in defining any particular object, we cannot refer to anything outside the subject. Consequently there is no telling what a thing is in terms other than itself, therefore, true properties whilst real are ineffable.

Suppose for example you reduce whale to aquatic mammal and swimming to hydraulic motion and aquatic to fluid submerged and mammal to warm-blooded vertebrate. Now, a whale swims essentially or it would not be a whale but warm-blooded and vertebrate are not necessarily connected. The linkage of these two is metaphysical not logical. A unicorn can be defined by a conical section, cranial protrusion and as a white horse in every other respect. Now the set of these individually exists but not in conjunction. There is nothing that has all these properties at once. Unity is a special trait of existence. consider again warm-blooded and vertebrate. Let the first be A and the second B. A will have a relation to B, C a whale and B will have a relation to C, skeletal R1, and A will have a relation to C, cardiovascular R2 to make AR2BR1C. R1 will have a relation to B, straight R3, C, embodied R4, and A, veined R5 and so on. Rather than bring together disparate things, our process has accomplished just the opposite. We may understand the whale better for it, but not in simplest terms.

This does not hinder our knowledge of things altogether. Relations still give us a hint as to what lies beyond appearances, but never the full idea. So while one must deal with extrinsic connexions to describe the world, the lesson is that no picture of it is complete that does not admit the existence of qualities, particulars and their identities.

5. The Mathematical Universe Hypothesis is false for the following reasons: not every function is computable. “Any device or organ whose internal processes can be described completely by means of (what Church called) effectively calculable functions can be simulated exactly by a Turing machine (providing that the input into the device or organ is itself computable by Turing machine). But any device or organ whose mathematical description involves functions that are not effectively calculable cannot be so simulated. As Turing showed, there are uncountably many such functions. It is an open question whether a completed neuroscience will need to employ functions that are not effectively calculable.”

Even if a computer had a list of all the reals between zero and one, there would be a number different from any other on it by Cantor’s diagonal argument.

This is worsened if we consider examples from physics of what is uncomputable.

In 2012, Eisert et al.19 showed “[T]he very natural physical problem of determining whether certain outcome sequences cannot occur in repeated quantum measurements is undecidable, even though the same problem for classical measurements is readily decidable.” and “Cubitt et al.14 described another such undecidability result in a 2015 Nature article, outlining their proof that “[T]he spectral gap problem is algorithmically undecidable: There cannot exist any algorithm that, given a description of the local interactions, determines whether the resultant model is gapped or gapless.” While this by no means definitively rules MUH out, the next does, for Godel’s incompleteness theorems preclude it. To quote physicist Mark Afford in a debate between Piet Hut and Max Tegmark where he was the neutral party; “The methods allowed by formalists cannot prove all the theorems in a sufficiently powerful system… The idea that math is ‘out there’ is incompatible with the idea that it consists of formal systems.” Tegmark responds by conceding that perhaps only the Godel-complete (fully decidable) mathematical structures exist. But this desperate ploy of last resort does little to save Tegmark’s weak argument from the critiques he is trying to avoid. For one, it comes at the expense of ignoring the larger body of rigorously defined mathematical propositions outside it for no other reason than maintain what would otherwise be an indefensible position. A far sounder conclusion in view of the massive literature in evidence against his modified Computable Universe Hypothesis would be to embrace metaphysical Platonism and accept that formal systems have certain definite limits. Secondly, but no less damning than the previous charge, even if one were willing to limit themselves to what little mathematical knowledge remains after accepting CUH, by no means does this guarantee that it will be Godel-complete and therefore computable, it merely casts doubt on disproving the possibility but does nothing to prove it. Last but not least, our best scientific theories contradict the CUH, so unless you are prepared to trash that too, without so much as a remotely viable alternative in the works that stands a chance in hell of replacing the physics of the last three hundred some years, the more exuberant claims of pancomputationalism must be rejected. The mind however, has no such limitations. As Godel himself remarks “the results mentioned in this postscript [incompleteness theorems] do not establish any bounds for the powers of human reason, but rather for the potentialities of pure formalism in mathematics”

There are also issues concerning just what counts as a mathematical structure. In a review of Tegmark’s book, computer scientist Scott Aaronson addresses this question using the thought of a universe populated by a single cube; “we could make a list of all self-delimiting computer programs, then count the total weight of programs that generate a single cube and then halt, where each n-bit program gets assigned 1/2n weight. Sure, the resulting fraction would be uncomputable, but at least we’d have defined it. Except wait … which programming language should we use? (The constant factors could actually matter here!) Worse yet, what exactly counts as a “cube”? Does it have to have faces, or are vertices and edges enough? How should we interpret the string of 1’s and 0’s output by the program, in order to know whether it describes a cube or not? (Also, how do we decide whether two programs describe the “same” cube? And if they do, does that mean they’re describing the same universe, or two different universes that happen to be identical?) then there’s the question of which mathematical structures are compatible with one another, or what makes typical ones more likely than the very complex?

6. Probing a simulation for cosmic knowledge, has less chances of leading to greater understanding than a mastery of your favorite video games, since those at least are based upon something and not themselves. By explicitly conflating syntax with semantics and soundness with validity implicitly, you make every informal fallacy true by virtue of their form alone which is absurd. The reasons one can have for thinking the universe could be simulated, must come from a nonsimulated universe. If it is already in the process of being simulated, then the natural laws that make a world objective are subject to arbitrary modification just as computer programs are, in which case the evidence for claiming the universe is simulated undermines itself. Like Decartes’s Demon, or the brain-in-vat thought experiment, if we did in live The Matrix, where anything can happen no matter how preposterous, and whatever does is totally without reason or for purposes contrary to appearances, then we can be certain only of our own deception.

And what if there are essences? If there are such things, no amount of manipulation will change one into another. Yet we are told that mass is the same as energy. If that were true without qualification, and the physical makeup of the world is really an undifferentiated amorphous blob, then our multifaceted experience of it would be an illusion and so would charge and a numbing of antithetical properties, since a featureless reality void of all qualities is equivalent to nothing. So there must be something distinctive already latent in nature that is intransmutable, like for example the fundamental particles or some attribute(s) of them. You could probably mimic the behaviors of some entities, but it is impossible to rearrange them in an order that elicits a given quality. At best, a simulation could do the former but not that latter.

Take the proposition “He saw a bird flying past him in the sky above.” If this event and the entities therein are reducible to lines of code, and I do not see how they could be anything more on your account, how can we say with any credibility that the proposition expresses the fact of some matter? Even if it had yet to happen or never happened, the thought alone would make no sense. Bits, qubits or abstract objects of a still unspecified variety is not a organism that lays eggs, chirps, and is never suspended off the ground or located anywhere else. What is this seeing? A calculated function of a subroutine registering new inputs which it processes by transcribing data into a richer machine language that organizes lines of code into “bits” according to the command scheme of a larger computer program? Uninterpreted computer variables stand for nothing because they refer to nothing and are therefore meaningless. If there were no persons to interface with a computer in search of certain definite patterns that match the expectations of the user, the information could not “inform” or be about forms of things. Philosopher John Searle makes this same very point with the following illustration: “The window in front of me is a very simple computer. Window open = 1, window closed = 0. That is, if we accept Turing’s definition according to which anything to which you can assign a 0 and a 1 is a computer, then the window is a simple and trivial computer.” It is therefore arbitrary how you assign these values to phenomena. If one description is enough to characterize two things, then the description is incomplete.

The contrast between the semantic content of my propositional expression and the syntactic order of any formal system could not be sharper or more dissimilar. “Meaning” is a correspondence between apparent and actual things viewed in the abstract, but the abstract, intentional object is a partial indication of what we know, which can always be elaborated upon further, with more detail and precise wording. As Walter Chatton put it in his Anti-Razor; “If three things are not enough to verify an affirmative proposition about things, a fourth must be added, and so on.” Thus formal analysis of transconceptual subject matter is inexhaustive. Furthermore, all human conventions are never strictly representative, while Platonic forms are. The Rutherford-Bohr Model of the atom is one such illustration. You can learn a great deal about the properties of chemical elements by studying a diagram labelled with all the relevant features. Yet no educated person would confuse this with the real thing, which corresponds to no image. To quote the mathematician Luitzen Brouwer “The languageless constructions which arise from the self unfolding of the basic intuition are, on the sole basis of their presence in memory, exact and correct, but the human faculty, of memory which must survey these constructions is, even when it seeks the support of linguistic signs, by it’s nature limited and fallible. “ It is interesting that Brouwer should use the word “unfolding” as Leibniz was known to use it from time to time. He describes bodies in a metaphor using folds: “[ . . . ] the division of the continuum must not be considered to be like the division of sand into grains, but like that of a sheet of paper or tunic into folds. And so although there occur some folds smaller than others infinite in number, a body is never thereby dissolved into points or minima. [ . . . ] It is just as if we suppose a tunic to be scored with folds multiplied to infinity in such a way that there is no fold so small that it is not subdivided by a new fold [ . . . ] And the tunic cannot be said to be resolved all the way down into points; instead, although some folds are smaller than others to infinity, bodies are always extended and points never become parts, but always remain mere extrema.” The physicist Bohm makes generous use of this concept himself to contrast the explicate and implicate order. “Generally speaking, it is only possible to perceive one of the two possible cubes at a time — while one is enfolded in perception (an implicate order), the other is unfolded in perception (an explicate order). This phenomenon is significantly amplified when one views the hypercube — many possible geometric orders remain enfolded in perception (a complex implicate order), while only one is unfolded at any given moment (an explicate order)”

Thus, on my view, it is not that hidden variables are unknowable. For that they would have to be secret variables. Instead, it is simply a (complex) matter of specifying in detail, the properties of objects further removed from ordinary experience. I think I have written more than enough for now on that, though I have much more to say which is not critical, but constructive along these lines should you be interested.