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Unshakeable foundations of all knowledge:

a priori intuitions

Reality and representation

Johann Wolfgang von

Goethe, 1749–1832

Ideas in the human brain are actively produced and are not mere reflections of the outside world. Visual images, for example, result from the processing of incident electromagnetic radiation. Just how synthetic the picture is can be illustrated by an operation in which the optic nerves of a chameleon are switched: afterwards, it directs its tongue in precisely the opposite direction from its prey. The illusion is perfect: the subject considers itself an impartial witness of the presence of objects and demonstrates, as a matter of course, total reliance on the constructed picture. Goethe, on the other hand, in observing nature, constantly asked himself the question, “Is it the object or is it myself that is being expressed here?”

A photograph requires photographic paper, the molecules of which react specifically to wavelengths of incident electromagnetic radiation, for example to 400 nanometres for the reflection of violet light. However, the Mona Lisa can also be represented by the appropriate planting of grass in a field, or the course of a road can be drawn in the sand using the big toe. A substrate is required for a picture, and it is irrelevant what this is in itself; but in the picture there has to be order among the pixels. In a photograph, for example, there are no spatial relationships, but only two-dimensional ones, which the eye reconstructs into objects in space based on the laws of perspective. A drawing in the sand (“here is Rome and here is Paris”) implies scale and a north-south axis; the sequence of images in a film requires the addition of a temporal order.

Thomas Aquinas,

1225–1274

This is true not only for visual images, but for all ideas—however the human brain constructs its pictures, they have to offer reliable help in our perception of the world. Thomas Aquinas sums it up perfectly: “An object in the mind is adopted according to the mind—and not according to the object.”

If it is understood that

–space can only be experienced through movement—and therefore in time; time similarly only through movement— and therefore in space;

–only bodies can have such “experiences”,

–bodies are characterised by the fact that they are permanent (in time) and impenetrable (in space),

this is no circular argument in which the hypothesis already contains that which is to be proved, but rather an expression of the nature of the process of representation which is only concerned with the correspondence of relations. Bodies, space and time are not reality, but the phylogenetically-provided means of producing an idea of reality.

The fundamental and literal impossibility of grasping time and space led Kant in 1781 to introduce the concept of “a priori intuitions” to philosophy: “Space is not experience, for all spatial experience assumes the idea of space.” And “Time is nothing other than the subjective condition under which all intuitions can take place within us.”

Kant had trouble with “matter”, or “substance” as he called it. He did put forward a “principle of the permanence of substance”: “All appearances are in time ... In [them] the substrate must be found ... [which] is permanence ... Therefore in all appearances, permanence is the object itself ...” He did not, however, establish the link between substance and space (impenetrability) that is analogous to this sub-stance-time relationship (permanence). He lacked the concept of atomism which sees all matter as made up of the smallest units, and was therefore unable to classify substance in its “multiplicity of appearance” as an a priori intuition, although he wrote about it as if it were possible.

It is not surprising that Kant had difficulty with the concept of substance, for physics is equally unable to define what substance in the sense of “mass” is. One knows how “heavy” a mass is, in the material sense, from the pull the Earth exerts on it—mass multiplied by gravity—and how “inert” it is by its resistance to acceleration—mass multiplied by acceleration. When equating the two, mass is removed so that acceleration is equal to gravity, which is the same for all objects of any mass, from goose feathers to lead bullets. This only establishes the gravitational field of the Earth, that is the interaction of masses—not what mass actually is.

Physics simply treats mass as a given and uses its behaviour to derive force fields, which are mathematically expressed in field theories. All field theories contain a continuum, in Einstein the “space-time continuum”. Thus, conventional physics proceeds from this inductively, namely by inferring a continuum from the phenomenon.

Deductive physics takes the opposite route, from the continuum to mass as the dynamic of it. The constituents of this continuum are pure bodies, defined as permanent, impenetrable volumes, the opposite of empty space and characterised by nothing else, which is why deductive physics adds “body” as a third a priori intuition in addition to those of “space” and “time”. Hence, all that is needed for the representation of the material world is the system of coordinates covering time and space, and the bodies within it, all material phenomena being derived from them.

The three a priori intuitions have a correspondence in the three fundamental physical constants, which would confirm philosophy as well as science in their claim to be the basis for all knowledge—if a century ago the theory of relativity had not come up with ideas that declared a priori intuitions invalid: with time being stretched, space being stretched and curved, and with mass increasing as its own speed increases, tending to infinity at the speed of light.

The triumphant proof by experimentation of Einstein’s predictions undermined philosophy, and in order to regain a firm footing it is necessary to get to grips with the theory of relativity. As children begin their development without consciousness of space and time as dimensions independent of their own existence, the first thing to be observed is how this emerges as a capacity for abstraction and objectification.

Deductive Physics

What are the benefits to a person of knowing how matter can be thought about? Firstly, the natural reflex of wanting to have everyhing explained is satisfied. It can be built on, and an explanation for “life” found in a few steps. It is now possible to understand “intellect”, the essence of which, although it may go beyond matter, is nevertheless a structure of matter. Finally there comes freedom from all speculation, freedom to construct one’s idea of the world on the solid foundation of recognised laws.

Acquiring space-time concepts

With freedom of movement comes the need to explore the space where it occurs. Here it is only a matter of distinguishing between “space” and “impenetrability”, not of what the impenetrable barrier is.

Infants’ first experiences of touch establish impenetrability: is there a body in the way of the hands or not? Playing with wooden bricks teaches them that two objects cannot occupy the same space at once, and conversely one cannot be in two places at the same time. By the age of eight months they have internalised the concept of permanence; if an object is covered they look for it, whereas previously they would simply have turned their attention to something else.

At first, space manifests itself only as the distance from the child to an object; later the perspective widens with the awareness of differences in length. Time is initially understood in terms of earlier and later, faster and slower, longer and shorter. If one of two trains running on parallel tracks in a model railway is faster than the other, a toddler will see it as going further, without the ability to express the idea that it will arrive at its destination sooner.

Children cannot conceive of objective time and objective space, both existing independently of the child’s own presence, until the age of seven or eight—and from then on they can never again imagine them not existing. They are inescapable, and yet philosophy was stalled in 1919, when an experiment during the solar eclipse in England confirmed Einstein’s mathematics, which he construed as a sequence of the stretching and bending of space and time, something which from the perspective of deductive physics is unnecessary.

Fundamental constants

Inductive physics represents the material world in space and time, but instead of the “body” dimension it relies on “mass”. It defines mass in terms of a specific volume of a specific substance: a litre of water is a kilogram, and all substances that are similarly inert and heavy are the same.

All statements made in physics are stated using the three dimensions of length (for space) in metres, m, time in seconds, s, and mass in kilograms, kg. Electricity is linked to mass by means of the dimensionless fine-structure constant α, and does not represent an additional dimension. Also, as physics uses three dimensions to express itself, there are three fundamental constants1:

Metres, seconds and kilograms are arbitrary measures: a 40,000,000th part of the equatorial circumference, an 86,400th part of a day, the inertia and weight of a litre of water—while in contrast the fundamental constants c, G, ħ are facts, and are what they are independently of the measurement units of physics. If they had different values, the world would look different: elementary masses would be larger or smaller, or there would be none at all. Gravitation would be so strong that all celestial objects would be drawn together into a single lump, or would be so weak that nothing would hold together. Quantum mechanical interferences would be so weak that electrons would fall into their atomic nuclei, so that no molecules and no life could arise, etc.

As in deductive physics the fundamental constants are the properties that determine the continuum in space and time, and as all materials are derived from the dynamics of this continuum, all phenomena are based on a priori intuitions and therefore assumed “according to the mind”.Thomas Aquinas

Space and time coordinates run to infinity, revealing their nature as concepts. On the other hand, the universe as portrayed within these coordinates is seen to be finite. In retrospect the two giants can be reconciled: Newton’s “absolute space” and “absolute time” relate to the coordinate system of all representation, while Einstein’s “absolute speed of light” relates to the continuum represented within it.

Irritation from the theory of relativity

Kant’s a priori intuitions are the most fundamental examinations of thought that philosophy has produced, but at the same time they are the most persistently refuted: thinkers are constantly putting forward new speculations, in particular about the nature of time.

In 1905, Einstein introduced the terms “expansion of time”, “time dilation” and “space-time continuum”, adding “curved space” ten years later, thus causing bewilderment and relief in equal measure: bewilderment for those who believed they understood the concept of a priori intuitions; relief for others as there was now something much more inconceivable, so it must be the truth.

The special theory of relativity goes beyond any intuition right from the start of the derivation: a “four-vector” is first introduced for spaces, then rotated around an imaginary angle, and later it is concluded formulaically that impulse is also a four-vector (with time in the fourth dimension)—and after a chain of abstract operations, E = mc2 is obtained. A professor* at the Swiss Federal Institute of Technology (ETH) once said to his students, “You go through it step by step, accept what emerges, and understand nothing. No-one understands it.”

In his lectures at Princeton in May 1921, Einstein made fun of the fact that physicists had been obliged to “bring down ... the concepts of time and space ... from the Olympus of the a priori ...” He was apparently confusing “a priori” with “absolute” and failed to appreciate that Kant’s a priori intuitions identified a more radical relativity than his theory of relativity, i.e. that between thought and reality—not merely that between two bodies moving relative to one another (special theory of relativity) or interacting with one another (general theory of relativity).2

Albert Michelson, 1852–1932 ; Edward Morley,

1838–1923

Knowledge grows from the resolution of contradictions, and the contradiction first resolved by Einstein was this: if a source of light moves towards an observer at speedv, and the light is moving away from the source at the speed of light c, the observer intuitively expects an arrival speed of c + v. But in the 1880s, it was determined by measurement that the velocity was c in all circumstances (Michelson and Morley). How did Einstein resolve this contradiction? His very first step contains all the irritation of the later results: he said to himself that if the speed of light is to remain constant at c regardless of the position of the observer, then distance and time simply have to be “relativised”. Instead of Newton’s space and time, he therefore proposed c as the absolute. He then tested out how a system of coordinates K’ with its origin in the light source would have to relate to the observer’s system of coordinates K, to enable light both to be emitted from there at c.

His conclusion was that space and time are contracted around the light source, but the consequences go much further: mass increases as v increases and thus also the momentum (momentum = mass multiplied by velocity). A momentum3 has an energy and a cross-multiplication supplies directly the result of the century—that this energy is not zero, even at rest, but the famous E_rest= mc2 .4

Einstein would have been severely taken aback had he realised that his result originated in Newton’s formulation of the momentum conservation law: if Newton had simply written “force equals mass multiplied by acceleration”, Einstein would not have made such a leap forward. He was merely lucky, since in 1905 there was as yet no experimental proof that Newton’s intuitive formulation applies.5 But even leaving this aside there was great cause for amazement as kinetic energy was now to be understood as a pure increase of something that no-one had bargained with: rest energy mc2. It is an indication that that mass is a dynamic, not a corpuscle.

The simple reason for this, that light from any source is radiated at c and received by any mass at c, regardless of whether they are moving relative to one another, depends from the point of view of deductive physics on the fact that

–the continuum directly on the surface of a mass is at rest (in the same way that air is at rest on the outer ear despite the strongest wind—it does not blow into or through the ear),

–the speed of propagation of all disturbances (such as waves) in a continuum at rest is c.

Hendrik Antoon Lorentz,

1853–1928

However the frequency of lightwaves hitting the observer should not merely be expected in terms of linear addition (the original quantity of signals per second plus the gain from the approach6), as the field of a mass, spherical when at rest, is contracted if it moves at v relative to the continuum—like a source in the countercurrent. This shortens the wavelength of the radiation by the factor known as the Lorentz contraction, and the frequency is increased in inverse proportion, which leads to the Doppler effect7, in which the frequency increases at more than a linear rate, and for v → c becomes infinite (approximately corresponding to a sonic boom). This enables all the results of the special theory of relativity to be understood and also some of those of the general theory of relativity, if kinetic potential is replaced by gravitational potential in the formulae. The assumption of a continuum and the representation of a mass dynamic within is therefore sufficient to avoid the concept, incompatible with thinking, that space and time can expand and bend.

The predictions of the theory of relativity are true, but Einstein’s interpretations of the correct mathematical results as the expansion of space and time should be replaced:

–It is not that the time of the mass in motion moves more slowly, but that its signals take longer to reach the observer,

–Space does not expand or contract, but the continuum in space, similar to the air that flows around a body,

–It is not the mass that increases with velocity, but its effect—similar to the pattering of rain at high speed against a windscreen,

–Mass should be thought of as a dynamic, as compelled by E= mc2, and the idea of literally inconceivable corpuscles should be abandoned.

Lorentz contraction

Ultimately, the theory of relativity only formalises the relativity of interactions: as a motorbike approaches a listener, the listener registers higher-frequency sounds, and as it goes away, lower. The theory of relativity does not offer anything else to philosophy, although it introduced a new era in physics.

Irritation from quantum mechanics

As an infant’s consciousness first begins to develop, there is an undirected movement of the limbs until an effect is achieved; after several repetitions this is then stored as an action-effect pattern. The action does not result from a physiological need, but a reflex that trains the brain. The pattern contains the idea prior to the triggering of the action, in the same way as a bird “imagines” the landing before settling onto a branch.

In this way, infants register their own intentions, and at nine months children recognise their intentions to such an extent that they can also recognise those of other people. Others are understood per se as intentional beings with intentions analogous to those of the child. This is manifested in the form of pointing to things and persons, in other words in attracting people’s attention, something that is not observed even among the most attentive of the other primates.Tomasello By analogy, children later attribute intention to all processes, saying things like, “The ball wants to come to me” and seeking intention everywhere: “Why does a cherry tree want to blossom?” Theories of cause are also stated: “The moon shines so we can find our way home.” The history of ideas began in similar fashion: mythologies invented beings with intentions in response to questions of cause and purpose; religions responded with creation stories.

A child of western civilisation gradually learns to transpose intentionality into causality and explain reality from reality. This was the giant step forward made by the pre-Socratic philosophers with the causality principle: “Everything has a cause” and the law of cause and effect: “Equal causes have equal effects”.

One of the first experiences of causality a child encounters is that a body which was there first must be removed if another is to take its place. Kant considered causality to be a priori; however, it is not to the extent that, in the final regression, it is attributable to the fact that space can only be occupied by one single body, and so is already contained in the three a priori intuitions of space, time and body. Causality describes sequences of conditions, of stationary images, the earlier of which are termed causes and the later, effects. The stationary images are subjective constructs—considered objectively, “everything is in a state of flux”, one thing flows from another, and in this sense everything that happens is from the outset “causal”.

At the start of the 20th century physical experiments were advancing into atomic dimensions, revealing an acausal, inexplicable world. In the 1920s a handful of brilliant physicists developed quantum mechanics, with which all the probabilities and inexplicable conditions could be calculated—but not explained, for which reason the uncertainties are stated to be objective and the probability calculations raised to the ranks of fundamental laws of nature. The expectation of causality at the root of all phenomena was challenged. Philosophy was dumbfounded, and conventional physics was expanded by a further colossal dimension in addition to the theory of relativity.

In deductive physics, all quantum-mechanical facts arise from interferences of the waves that are emitted by masses and transmitted by the continuum. The specific values are shown to be resonances—like the vibrations in musical instruments—and the uncertainties consequences of the fact that interactions occur in waves and it cannot be determined precisely where the masses from which they originated were located in the wave. Deductive physics thus explains all phenomena causally, yet the information on an atomic scale is never sufficient for more than the calculation of probabilities, for which quantum mechanics provides the perfect instruments.

Philosophers have used the quantum-mechanical facts to perform “bold works of genius”,Kant’s expression going as far as an explanation of free will, although quantum phenomena are no more significant than others that can only be determined statistically, such as the behaviour of gas molecules (thermodynamics) or traffic. In everyday life there is much that appears to be acausal, or “chance”—we meet a neighbour in a remote place, or lightning strikes. The chance element here is that we had not taken account of our neighbour’s trip round the world or of the electrical discharges from the sky. Both had causes, but neither had any kind of intention, concepts that are easily confused in everyday life. The thermal movements of the individual molecules of a gas also have causes, but they cannot be computed mathematically. But there are populations of them, which lead to the thermodynamic laws with the mean values of density and temperature.

Causes are frequently sought at too high a level, for example, there is no “cause of traffic”, only causes for the individual drivers or passengers. Similarly, there is no “cause of human beings”, merely a practically infinite number of evolutionary stages.

The categorisation as “chance” is therefore always based on a lack of knowledge 0r represents that which someone had not taken into account, the incalculable (Einstein: “The point where our calculations fail we call chance”), or that which has come about as a hyperstasis from a substrate underlying the phenomenon.

Causality is not equal to determination (“anonymous intention”). The latter would require a plan that “knows” the future outcome in advance and seeks to achieve it—from the smallest to the universal scale. But such plans are inconceivable, because they would contradict fundamental knowledge, in particular the development of thought from biological data processing and the mind from thought.

Could there not be a power in the universe, hidden from man, which acts, connects, steers, causes someone in London to cry out in the middle of the night only to discover subsequently that at that moment his brother in Alaska had died? There is much that is unexplained, but nothing is to be gained by explaining this away with the inexplicable (such as “there must be something out there”). It remains inexplicable until it is explained. The amount that is hidden is limited only by the imagination. But as long as it remains hidden, it cannot be used as an explanation. At any given time, the structure of knowledge only contains what has been discovered to date, and to talk of anything beyond that is in vain.

Long-distance effect, continuum

When children are asked what the sun is made of, they say something like: “From tiny shining pieces of cloud”; or where sugar dissolved in water has gone: “It’s in pieces so small that you can’t see them.” The arguments of the pre-Socratic philosophers were similar: they got as far as indivisible particles from which everything is made. Anaximander called this apeiron, while Heraclitus added that it was constantly in a state of flux and Democritus went further by saying that everything real was made up of compounds of it. With hindsight it can be seen that the continuum was no quirk of Anaximander, Plotinus, Descartes or Einstein, but an expression of the nature of thought.

Einstein clearly assumed that Descartes’ aether was immutably linked to Newton’s absolute space, which is not compatible with the “constancy of the speed of light”, and this is why he rejected the idea of an aether. If it is allowed that the aether (or whatever name is given to the continuum) can also flow, there is no longer any incompatibility with the a priori intuitions. At the latest when it comes to the expansion of the universe it is no longer possible to avoid an acceptance of flux.

Anaximander, around 611–545 BC; Heraclitus, around 545–475 BC; Democritus, 460/459–400/380/370 BC

It is logically essential to think of space as filled with a continuum when seeking to examine long-distance effects: if A is to have an effect on B, A must be in contact with B. Infants demonstrate that they understand this concept by pulling on a sheet in order to be able to reach an object that is resting on it. Descartes ascribed the transfer of effect to his aether; the constituents of the aether would collide, thus passing on momentum. All field theories state simply that: the field connects causes and effects through contact at extremely small (in mathematical terms: “infinitesimal”) intervals.

Albert Einstein, 1879–1955; Isaac Newton,

1643–1727

Since Anaximander the continuum has been an analogy for air, a gas consisting of molecules with potential—manifest in its continuous motion—and space. The continuum is and remains the “One”which cannot be further divided, like the sand in a sandbox from which children build castles.

Not only is it an essential prerequisite of empty space that there are permanent, impenetrable bodies—or the concept of space would be pointless—, but these can and must move, or the concept of time would be pointless. The continuum fills the framework provided by a priori intuitions.

If the continuum were a gas, the fundamental constants c, G and ħ would represent temperature, reciprocal density and free path length. To reiterate, the constituants as such do not have mass, but only volume, distance from one another and movement. Mass is only constituted through their dynamics.

What is the meaning of “existence”?

If all phenomena are traced back to bodies, their “existence” is determined by the existence attributed to the a priori intuition of “body”. Permanence and impenetrability say it all, and “existence” turns out to be anticipated by the a priori intuitions.

What is the existence of the mind? In terms of “matter”, the mind is information, the essence of which does not lie in the corporeal, but in structures. If it is understood that by the impenetrability of bodies it is not any fact that is meant, but rather an interaction, in other words the extent to which bodies block the way of other bodies, push them around or are pushed around by them—in the same way as small children discover bodies—, then by analogy it becomes clear that the “existence” of information also means the effect of information. Information is the structure that is communicated.

Physics talks of electrical charge, although it cannot say what constitutes charge, but rather measures interactions; for these it assumes charge to be the underlying cause. Charge is a property of elementary particles and has no isolatable existence, just as acid is its acidic effect, the wall perceived by a bat is something it cannot penetrate, and a “house” is an expression of its sheltering function. The existence of human beings is what they cause and tolerate—not their biomass.

In abstract terms, “existence” means “to be in a state of interaction”. “Existence” grows from linguistic usage: it is said of an objectivised object, thus one that is separate from oneself, that it “exists”. The object is part of the inventory of the speaker’s world—what is actually being expressed is that the speaker has noticed the object. Existence, or the verb “to be”, can thus be replaced in the following sentences: berries are/glow red; schoolchildren are/sit in the classroom; two and two are/make four. The fact that something is or exists as a projection of the speaker is, like all verbal expressions, only justified by its usefulness.

Limits of knowledge

Those who want to conceive of reality must also consider their capacity for knowledge as part of objectifiable reality, beginning with the understanding that continuum, space and time are not part of the picture, are not reality, but the material and framework for forming it—sand and sandbox with which a model of the world can be built up.

The a priori intuitions should be accepted and not interpreted further. So why all the fuss about them? Because the framework they mark out for all philosophising cannot be transcended, even if the intention is to consider “outside” aspects. Philosophy was clearly too uncertain of the a priori intuitions to call Einstein back to the drawing board when he postulated the bending and expansion of space and the expansion of time. “Nature has given us the chessboard beyond which we cannot operate …”Goethe

Copernican turning points

Nicolaus Copernicus,

1473–1543

Ask a three-year-old who has a brother whether the latter also has a brother and he will answer no, there are only two of them. Not until a year later will he come to consider his relationship with his brother from the outside, thereby objectivising it. Small children also relate the rest of the world to themselves, for example, when they say the moon shines so they can find their way home. The cognitive development of the human race, as well as individuals, is characterised by increasingly letting go of a viewpoint defined by how the outside world affects us.

Animism in hunter-gatherer cultures projects intentions onto everything that happens in the world—clouds as an expression of the moods of the gods, these in turn being a response to human behaviour. The first turning point in intellectual history was initiated by the pre-Socratic philosophers (600–400 BC): they considered world events as something apart from divine intentions, and justified reality with reality, although spatially as well as spiritually people were still at the heart of things. This world view, to which Ptolemy (100–170 AD) put the final touches, held its ground and was supported by scholars for some 2000 years.

Giordano Bruno,

1548–1600

It was Copernicus who introduced the second turning point: the universe did not revolve around the Earth, but the Earth around the sun. His grounds for believing this were because it made it easier to understand the movement of celestial objects: “Any visible movement of the firmament with its fixed stars is not due to movement of the firmament, but as it is seen from the Earth ...” The Earth and the human race were thus shifted from the centre of all cause and purpose—a colossal attack on the word of God, the authority of the church and the understanding at that time of the self and the world. To begin with, Copernicus was not taken seriously by very many (Luther considered him a fool), but then, sixty years after the publication of his work, Giordano Bruno was burnt at the stake for making the same statements.

In 1905, Einstein’s theory of relativity introduced a third turning point, although this upset the a priori intuitions. It does not show that physics is thought out within the limits of human cognitive capability; nor does it show that it is a collection of abstract concepts and principles to explain the aspects phenomena have in common.

It has always been apparent contradictions that have led to new findings, in particular to a higher plane of objectivisation:

–Copernicus asked: “Why do the planets not move in the same way as the other celestial objects?”,

–Einstein asked: “Why does light arrive at c, when it would be expected to have been emitted at c + v?” (where c is the speed of light, and v is the approach velocity of the emitting light source),

–In deductive physics the equivalent would be, “If the a priori intuitions are an immutable part of the thought process, how can the results of the theory of relativity be brought into harmony with one another?”