Posted by: Sk | February 17, 2009

5 What is none of your concern

Science is a relatively contemporary phenomenon, although its roots are quite old. Most of scientific branches as known in our modern world, are based on observations and conclusions of ancient Greece, were it mathematics, biology, physics, chemistry and medicine. At those time, these sciences were branches of philosophy. As philosophy, as appearing at those times, was either associated to atheistic ot polytheistic currents, it was heavily fought against after Constantine instauring christianism as religion of state in Byzance. It will though put the basis of most of theology of those times.

Aristotle reaches back Europe around the 10th century through Saint Thomas of Aquinos, having though some problems to be accepted. He thus pushes back the only to christian philosophy sympathetic philosopher, Plato.

Around the 17th century, while the Church is controling knowledge inside of frames that are restricting the ability of understanding natural phenomena, different metaphysics appear that do aim at the justification of knowledge outside of a theistic frame. In fact, already Newton and Galilee or Giordano Bruno, are trying to prove that things are not as it is figured out at those times, basing their observations on instruments, mainly glasses and lenses, that do allow affirming without too much of a doubt, that the earth is turning around the sun and not the other way round. This evidence is the one that pushes philosophers to try understanding the world outside of the given interpretation of scriptures.

As much Descartes as Hume, Leibniz or Spinoza, Kant or Schopenhauer, are trying to establish that knowledge is depending on proper structures that have nothing to do with God. Having to hide themselves away from the constant attacks arriving from the church, a somewhat shivering and trembling science as product of the human mind is born during the french ‘illustration’ (end of 18th) which will steadily develop itself in England and Germany mainly during the 19th.

Finally, the separation of the realms of science and religion is obtained around 1880, it being said that science’s field is what is of empirical evidence and of the church, what is of the realm of souls. Science is though suspended from metaphysics and thus from a branch of philosophy, as it is said that ‘metaphysics is the mother of all science’.

Why? Science is the sum of knowledge in its possible application resulting of a frame of validation that may only be given by metaphysics. To say, that ‘truth’ is not empirical and has thus little to do with empiricism. ‘To know’ is a field of knowledge whose restricted area concerns philosophy in its establishment of proper theories of knowledge. Which theory or what is to be considered ‘true’ concerns in its validation philosophy, and only.

Philosophy has thus the responsibility of establishing under which theory of knowledge which definitions are acceptable and which logical frame and thus, can establish which theory may have some validity or not. The limits of given theories of knowledge may oblige to redefine those which may lead to the acceptation of rejected theories or the rejection of accepted theories.

To give an example of what happens when scientifics do try to go beyond their reasonable field of action, it’s nothing but to consider the definition of real numbers by mathematicians. They say ( I remember from when I was at school, but you can still verify in wikipedia) that numbers correspond to points on a line. If this is so, then you obtain through a  certain number of operations, numbers that can’t correspond to a point, and which necessarily are ‘irrational numbers’. Those to which can be attributed a point, are rational numbers. (??!!)

Why though should numbers correspond to points on a line? Through essential identity? There is none. Nothing in the concept of ‘number’ says that it is a point, nor that a point can be derived of it. There is no association possible between a series and a line, either. Through accidental identity? (Image) Were it that you can build up an image as ressembling structures given between a series and a line, in no case it justifies a derived categorization inside of the group of numbers that is the result of observations on the behaviour of figures in their relationship to geometrical figures (lines).

Why does this mistake appear? The number is fused with the geometrical appearance because given metaphysics are not sufficient. If there are only empirical evidences, then necessarily the unit as foundation of the number is either belonging to the formal patterns of sensibility in space (geometry) or in time (Saint Augustin) = (this in a kantian definition frame, which is though the most advanced).

Derive the unit as formal concept from the act of identification. The principle of identity in this that it seizes ‘natures’ (in essence) necessarily produces a ‘unit’ as derived formal entity. A unit is not necessarily a number and even less a quantity, a series or an amount. Formal patterns in the structuring of understanding show though the ability of seizing the ’summing’ = and or &. The use of this function with a formal entity as the ‘unit’ is, allows the progressive development of entities as ‘numbers’. Further functions that can be put in relationship with the formal entity ‘unit’ are ‘-’ or ‘x’ or ‘/’.

At the beguinning it seems that these functions were mostly used for the ‘having’ or ‘exchanging’ and not in order to frame time and/or space.

The continuous effort of abstraction leads progressively to the abstraction of what can be called spatial units (cubes, triangles, circles, etc.) as much as the abstraction of time units (hours, months, seconds). Numbers are used in order to divide these determined entities in equal or unequal units, to put them in relationship one to the other, etc.

To say: it is different to talk about numbers as referring themselves to ‘things’ or to formal units, and if it is the latter, to formal spatial or temporal units. Which means, that the number has no nature in itself, but as derived entity, is depending for its exact determination on the realm it is used for. One and one drop, will never be more than one drop, in their sum. While one fish and one fish, are always going to be two fish.

The abstract formal ordering of numbers makes appear a series in sum and a volume in division. The result of a division, which is to say, some types of fractions, can not belong to the series (if I’m not wrong, the irrational numbers), because through the very operation they do not form series anymore, but volume. Why this is so, is a little bit complicated, but explainable.

In fact, the operation of division is a volume holding operation, which is not the case for the operation of summing. And this because ’division’ (in one of its meanings: if you make the difference between deviding something in itself, which can never have irrational numbers as effect, and distributing among) is the formal abstract function of ’sharing’, which through the fact that it implies another with another in accidental relationship, is of volume (abstraction of relation). To say: the original formal pattern of ‘division’ in this understanding implies a certain number of referential units to which are attributed secondary units (formal pattern in structures of understanding: either general to particular and/or essential to accidental = always of volume as implying more than a ‘one’ in its proper nature). This original pattern is the one affecting the ‘misbehaviour’ of numbers in fraction.

Contrary to what mathematics maintains, numbers are neither ‘per se’, nor absolutely perfect units in the field of abstraction. They are not but if not ordered inside of a determined field, as if they aren’t, they are just units in their formal determination. Numbers are already the relationship of the unit to a given environment, were it formal, it is still of the realms of sensitivity (time or space). There is no perfection in numbers. The perfection that belongs to some formal entities, as the very unit, is derived of the principle identity and perfect in its relationship to this one and not in its application to other sensitive entities.

Pretending to much more than it actually is, the application of functions or operations with numbers is not anymore related to a certain field, that makes the results ‘relative to’ assuming some ‘absolute validity’ that is factually, none. Actually, due mainly to problems of abstraction of the form of time, mathematics does not only fuse the absolute formal (unit) with the spatial sensitive formal but also with the temporal sensitive formal. Result? Mistakes in symbolic logic and … the big bang (!)

You have to prove that science is wrong, Hannah said. Well, I answered, perhaps not wrong, just mistaken … And even more so if invading other people’s territory.

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