The Alternative to Abstract Thinking : the Generic

Continuing from the previous post Is There an Alternative to Abstraction?

Having taken in Hegel’s little gem of wisdom we are now able to answer the question, “What does a radio shock jock and a theoretical physicist have in common?” The answer, of course is – abstraction.

However, this doesn’t answer the question as to the alternative to abstraction. Our Western universities have become abstraction factories. Is there an alternative product? The purpose of this book is to present the natural sibling to abstraction. I call it the generic. Instead of thinking abstractly, think generically. However, what is the generic?  Equally, what is abstraction for that matter?

Our aim is to move towards a formal knowledge of knowledge. There are two kinds of knowledge. On one side, there is what we call left side knowledge, which is dependent on a priori information. On the other hand, right side knowledge expounds on what can be known, without any a priori information. Each kind of knowledge answers a different question. Thus, two very precise questions characterise each of the two sciences. We can simplify much of philosophical and scientific tussling over different answers if we recognise that there are two different questions behind the scene. The questions are in a natural opposition and antonymic symmetry with each other.

The domain of discourse for each question is totally disjoint. The questions are so distinct that they can be imagined as being “orthogonal” to each other. The first question, suitably schematically simplified, was posed by Kant in the Critique of Pure Reason:

The answer would fall under the rubric of metaphysics. This question is familiar to all modern philosophers but is still waiting to be answered.

To some, like Karl Popper, the question is summarily dismissed. The problem posed by Kant is “not only insoluble but also misconceived.” (Popper, 1963) The problem was insoluble as we all know from Hume that there is no such thing as certain knowledge of universal truths. The only possibility was knowledge gleaned from observation of singular or particular instances. The inescapable truth is clearly “that all theoretical knowledge was uncertain.”

According to Popper, the problem was misconceived because Kant, even though he mentioned it, was not talking about metaphysics, but was really talking about what he didn’t mention; notably the pure natural science that had burst on the scene in his day, the science embodied in Newton’s gravitational theory. Newton’s theory has since been shown not to be the infallible exercise in pure reason that so impressed eighteenth century thinkers like Kant, but rather “no more than a marvellous conjecture, an astonishingly good approximation.” With the passage of time, Newton comes crashing down to earth and brings Kant’s question down with him. This demonstrates Kant’s misconception.

Popper concludes his demolition by replacing Kant’s bold question with his own languid alternative. “His question, we now know, or believe we know, should have been: ‘How are successful conjectures possible?’”

In this book, in order to arrive at a refutation, we actually go much further than Popper by bringing in some modern arguments to prove more convincingly that Q1 is insoluble. This is accomplished by showing that it is out of bounds of all formal mathematical reasoning.

To answer Q1 no axioms are allowed. Not only are operators of all sorts dispensed with – the commutative, the non-commutative, the associative, the non associative, even operator composition is declared a no go area. Traditional mathematics simply becomes non-operational in this zone. This is the domain where nothing can be said to proceed or succeed anything else.

In the business world, there is nothing more enticing to the entrepreneur than the accepted wisdom that something simply cannot be done. The proposition becomes even more enticing when learned abstract thinkers like Popper claim to have proven that it cannot be done.

Kant’s question Q1 viciously casts us into this apparently hopeless ultimate state of undetermined chaotic ignornace, However, by Popper arguing the futility of the enterprisse, the question becomes so well defined that surely there must be an answer. After all, it is only when the prisoner is actually placed in the confines of the four concrete walls of his cell can he really start plotting his way out. You cannot escape until you are locked up. Kant built the prison, Popper slams shut the door and rams home the bolt. It’s time to get out of this hell hole.

Once Q1 is clearly shown to be absolutely mathematically insoluble beyond any shadow of a doubt, we are then in possession of our first truth arrived at from pure reason alone. This is achieved without recourse to any experimental evidence whatsoever. We thus arrive at our first negative fact. We could call it a neg fact. The exercise then becomes one of building metaphysics out of neg facts in some way. This is obviously not an exercise in formal mathematics but an exercise in another genus of formalisation. We call it formal anti-mathematics. This and the remarkable results flowing from anti-mathematics eventually leads to code; a kind of “DNA of the Cosmos” so to speak. This is the principle theoretical contribution of this work and clearly the most enigmatic.

We now come to the second question, diametrically opposed to the first. It reads:

The question is very brief and needs to be expanded somewhat in order to convey the intent. What kind of knowledge can be achieved under the assumption that only what is measured is real and only what is real is that which is being measured? What knowledge can be obtained by totally excluding counter factual reasoning?  Stated this way the answer to the question is probably already apparent as will be seen below. The implication is that the moon only exists if you are looking at it. What kind of knowledge can imply that?

In the first question the only discernable real was that discerned by all embracing pure reason – the Parmenidean real, the big picture. Q1 addresses the uppermost confines of the top down reality bucket barrel. On the other hand. this second question, Q2 imposes the opposite sense of what is real. It demands the ferociously materialist atomism and absolutist one to one nominalism that only the Epicureans ever had the audacity to contemplate to the fullest degree. To each sensation there is something, to each something a sensation. There is nothing else. For the Epicureans, this was the way the world ticks. For modern science, it becomes a particular scientific methodological paradigm. It’s the way the world ticks from a particular viewpoint. It’s the view from the bottom up. What kind of knowledge can be achieved within the confines of such a dogmatic straight jacket?

In this case the answer historically came before the question was ever seriously posed. The ancient answer was the physics of the Epicureans complete with their deterministic atoms moving along Bertrand Russel like causal lines but armed with an occasional, unpredictable, and at that time, indiscernible “swerve.” The modern answer is in the form of quantum mechanics, Heisenburg’s uncertainty principle, and in particular the classical Copenhagen interpretation of quantum mechanics.

The Epicurean ontological straightjacket implicit in Q1 limits the knowledge quest downwards to the minute, indivisible “Epicurean atoms” of reality: the elementary subatomic particles of modern physics. The only difference is that the atoms of Epicurus we assumed ot have extent. Modern physics is more radical in this regard. The elementary particles have no extent whatsoever. They are assumed to be point like. Such particles have nothing in the their interior. They simply don’t even have an interior. If there is something in the interior, your particle is not elementary. You haven’t reached rock bottom of the reality bucket.

The brutal minimalism of QM is succinctly expressed in Dirac’s razor principle.

This is the declaration that QM is a philosophical desert. QM declares that it is fundamentally a philosophical, metaphysical, epistemological, ontological, theological, spiritual vacuum. This is not a weakness, it is strength. It is this that gives it its rigour and even its vigour.

A situation arises in QM that there can exist minute particle systems which are non-localised. Consider the case of a pair of entangled photons produced by a photon splitting in two. Pairs of such photons can be produced in experiments. The polarisation of one entangled photon will be the opposite to that of the other. According to QM the actual polarisation for each photon would be indeterminate until the polarisation of one of the photons was actually measured. The measurement performed on one particle would flip its polarisation to say horizontal or vertical. According to QM, the polarisation of the other photon will instantly become the opposite polarity irrespective of how far away it is.

Einstein didn’t like the indeterminacy aspects of QM – “God doesn’t throw dice” but it was this “spooky action at a distance” that really bothered him. In the famous EPR paper, written with Podolsky and Rosen, he argued his case. QM conflicted totally with the classical view of physical reality that Einstein adhered to. According to his view a theory must allow for the simultaneous existence of “elements of reality” which are independent of measurement. The EPR paper gave a very concise and lucid definition of elements of reality:

The EPR paper then put forward a thought experiment that revealed a paradox in the QM theory of entangled particles. The EPR paper argued that each of the “entangled” photons would possess their own element of reality and have their polarisations determined at the time of the pair’s  creation, not at the time when one of them was measured. The measurement of  the polarity of one wouldn’t affect that of the other as its polarisation had already been determined and couldn’t be altered by any “spooky action at a distance,” as predicted by QM.

Basically the EPR paper argued for what is sometimes called “local realism”. The two fundamental principles are that there exist elements of physical reality or “hidden variables” and that this realism be local. The locality principle demands that theory must adhere to the principles of relativity (causes cannot propagate faster than the speed of light). Thus the measurement on one member of an entangled pair of particles should not effect any measurement carried on the other member.

The simplified argument is that either the locality principle and with it the special theory of relativity was violated or the elementary particles harboured internal “hidden variables.” In the first case relativity theory is proved wrong. Alternatively in the second case there are aspects of reality not accounted for by QM. QM is not proved wrong but is proved “incomplete.”

With the passage of time thanks to the ingenious theorem of J. S. Bell and the experiments devised by A. Aspect et al and others, it has been demonstrated that the EPR paper’s proposed construct of local hidden variables could not possibly explain particle entanglement. This left the possibility that QM entanglement explanation would violate relativity theory. However, that is not a problem either as there is no determinate causal relationship between the particle pairs. The process cannot possibly be exploited for signalling and thus does not violate relativity theory.

We have used Karl Popper as a point of reference for the first of our reality barrel questions, the one stemming from Kant. He dismissed the question outright with scant regard to any possible answer. For symmetry we should consider the other side of the reality barrel where we found an already existing answer in want of a suitable question. We provide the question but what would Popper think of the answer? The answer was in the form of a twentieth century science called quantum mechanics. Would Popper in fact agree that quantum mechanics was a proper science? As is well known Popper had great difficulty accepting many of the tenants of QM. For a start, QM would have to abide by his falsifiable criterion in order to be acceptable as a science. This allows provisionally valid propositions to be deemed scientific provided that there existed the potentiality for the propositions to be proven false. To Popper, all that was admissibly scientific was uniquely constructed from such potentially falsifiable propositions.

If one takes the long view at what Popper is saying here, one can easily get the impression that Popper is more concerned in fighting political dogmatism on the campus, than engaging in real science. He was more intent on arguing that what was inherently anti dogmatic was inherently scientific. But was hard core science itself inherently hard core non dogmatic?

This question takes on great importance when we consider quantum mechanics, the most fundamental and deepest of the empirical physical sciences. The difference between quantum mechanics and all other empirical sciences is not expressed in the details of the subject matter addressed, but in the fact that it is the only pure empirical science. Being purely empirical, methodologically pushes its subject down to the very bottom reaches of reality. It means that quantum mechanics is the only empirical science which tolerates absolutely no “elements of reality” which exist independently of the actual act of measurement.  In order to achieve this goal it must dig down to the bare, nude essentials of reality.

It is the only such science. To put it another way, quantum mechanics is dogmatically empirical. To put it even more bluntly, quantum mechanics is empericism as an absolute dogma. This dogmatism is most clearly expressed with its Epicurean like dogma of the one to one relationship between the sensation and the real. Quantum mechanics theory of the real is that only what is measured is real. This science, located at the very bottom of the bucket of reality, where is nothing is deemed below, expresses itself in empirical tautologies. The measured and the real are two sides of the one thing. As such, this most reliable, accurate, and most dogmatic of the empirical sciences is inherently unfalsifiable at its core.

All the same, Popper stuck to his guns and had no alternative but to reject some of the essential tenants of quantum mechanics as being, in his terms, “unscientific”. In so doing, he ignored one of the two most fundamental questions one can ask concerning knowledge of reality. In the case of Q2, the knowledge is not only true, but measurably so. After all the Copenhagen dogma declares only that which is measured is real. What is real is only that which is measured.

This has lead to a tautology, an implicit “analytic judgment”. Kant would have found that fascinating. Moreover, this fundamental tautology appears not on the transcendental side of the equation but on the empirical. Even more fascinating is that this fundamental construct defines the pure empirical itself. The pure empirical is, well…, purely empirical. Such is the fundamental nature of quantum mechanics as declared in the Copenhagen interpretation.

There are two takes on reality. There are tow fundamental questions Q1 and Q2 that express the fundamental opposition between the two fundamental perspectives on reality. The fundmanetl opposition reveals itself in many ways. An important consideration concerns whether ther is a fundamantal level of reality.

Is there a fundamental level? Jonathan Schaffer asks the question and summarises the fundamentalist response. “The fundamentalist starts with (a) a hierarchical picture of nature as stratified into levels, adds (b) an assumption that there is a bottom level which is fundamental, and winds up, often enough, with (c) an ontological attitude according to which the entities of the fundamental level are primarily real, while any remaining contingent entities are at best derivative, if real at all.” He lists the physicalist, epiphenomenalist and atomist variants on the theme. Finding plausible the hierachial view of nature in (a) as being compatible with the discoveries of science, Schaffer homes in on (b) as the problem area, which he remarks has been almost entirely neglected. Concerning the primacy of what is real, the fate of (c) is linked to (b) as a reasonable but not inevitable conclusion.

And so is there a fundamental, bottom of the bucket, level in Reality?

In our preceding discussion of quantum mechanics we argued, with scarcely camouflaged glee, for a dogmatic interpretation of the science findings which would seem to place us firmly in Schaffer‘s camp of fundamentalists. We were advocating the bottom of the reality bucket theory. On the face of it we supported without reservation all three tenants of the fundamentalist argument. At the risk of seeming, or even blatantly being, excessively schematic we identified the ontological approach of quantum mechanics as smacking of pure Epicureanism, a natural logical set of conclusions resulting from a pure unadulterated atomistic,

uncompromisingly blunt materialism and one to one nominalism evolving down from Democritus, a thinker not particularly notable for his subtlety and dexterity of thought, At least Aristotle didn’t seem to be very impressed., advocating at one time that Democritus’s books should all be burnt. These Epicurians, and by implication the author, certainly seem to resemble Schaffer’s bottom feeding fundamentalists.

But the Epicurians should not be treated too harshly. They were, after all, primarily engaged in a peaceful quest for happiness in this life. They had identified perhaps the greatest obstacle to leading a happy life, notably fear of the gods and the accompanying troublesome predisposition towards deep, contemplative ways of thinking. An anti-metaphysical, anti-philosophizing, theologically bland, and some would say, anti-thinking creed called Epicureanism was the result. Few would have predicted that this creed would one day serve as the ontological stalwart of the successful and accurate modern sciences of today. Modern physics can even mathematically describe, at least probabalistically, the dynamics of Epicure’s mysterious micro-physicalist “swerve”. Strong on empirical scientific prediction and mathematical accuracy on one side, a self declared philosophical, ontological desert on the other. It aims to describe it all but can explain nothing. It’s as they say in the classics, you can’t have everything. At least not at the same time.

We return to the question. Is there a bottom fundamental level? We have answered in the affirmative. In so doing we have sided with a kind of metaphysic which, as Schaffer points out, is not particularly palatable for the more reasonable and civilised of people. Painfully it appears that we have excluded ourselves from such a community. Self declared metaphysical pariahs, we must face the dire consequences of our apparently foolhardy prise de position.

However, as we have argued throughout this work, there are two takes on reality, not just one. Hence we have assented to the proposition that there is a fundamental layer. This corresponds to the left side science take on the world, the simple, rather simplistic, abstract, naïvely realistic view of the world.

The right side science take on reality has a different vocation to its uncivilised and rather uncouth partner in crime. Right side science must not merely be content with describing the qualities that a thing has, it must explain what a thing is.

From a historical perspective, we argue that the ancient exponents of the left side take on reality were the Epicureans. In our sometimes desperate attempt to gain some traction for a right side science, we have singled out the Epicurean’s nemesis, the Stoics.

Of immediate concerns to our current discussion is the Stoic view on whether or not there is a fundamental level. The general view amongst the Stoics was that there was no bottom fundamental level. In some way reality was infinitely divisible, at no matter what level. This was also a position held by Leibnitz who made pains to add the nuance of being infinitely divided rather than infinitely divisible.

As for the Stoics, Chrysippus is credited with saying: