Whitehead continues into abstraction today, beginning with a description of mathematics as was developed through Pythagoras. He lays claim for the abstraction of mathematics as a strong basis for the ability of scientists to relate and empirically define relationships within the environment. Whitehead constrasts the a priori thought, or hypothesis/formulae construction versus the classification techniques of field science, and asserts that the reason why scientists are able (in both the epochs of Pythagoras-Plato and the Enlightment periods of 17th 18th Centuries) to make significant headway in the observation of nature is that “Mathematics supplied the background of imaginative thought. . . Galileo produced formulae, Descartes produced formulae, Huyghens produced formulae, Newton produced formulae”
He describes the most general aesthetic property arising from the mere fact of concurrent existence as the harmony of logical reason.
However, abstraction is not without its shortcomings. He lays 3 criticisms. Firstly, abstract functions cannot be justified a priori in the sense that there would always be difficulties in collating all the possible abstract conditionings in making connection, and often a result of human error in calculations, a mistake is made that makes all the difference. Secondly, even if there were a very dimished level of human error in these calculations the connections would sport a lack of simplicity. For the most part this is alright, since mathematics is by its very abstraction unknown and not easily accessible, but it diminishes the aesthetic pleasure in the mathematical reasoning by being too complex, and that would not help our verification of the abstract postulates in the face of any one particular event. Thirdly, and following on from the statement of all observation is selection, Whitehead asserts that all observation is essentially selection. and that induction is necessary to the process; albeit the remorse-less bane of philosophy. The real difficulty here is in estimating the evidence for the applicability of the mathematical principle.
He however, also relates (naturally) language, and also the function of the mind to this forms of abstraction, really separating the individual from the field that he is studying. While he considers periodicity in nature – light, sound, pendulums, violin strings, planetary orbits, does he also imagine himself as an oscillatory being, that we ourselves are in a state of oscillation and that perception arises from complementary or conductive periods of vibratory continuum. He does mention the research into quantum energy and the temporo-spatial characteristics of atoms, relating this abstract language of theoretical physics to an inconsequential particulate existence in time where because an entity is in constant flux, its properties are determined only within a average position at the centre of its period, and therefore must be represented by a series of detached positions in space – ‘sampling’ . But generally, he resolves the spatiality of the observer as being out of the system – possibly because of the use of an abstraction.
Main point is that the rise of scientific thought and empirical knowledge and equating relationships in the environment and mapping abstract functions to geometry, shapes, characters and spatial existence came about because of the progression of thought through pythagoras–plato epochs and carried on with several grecian thinkers. I guess we’ll see who they are in the next chapter.
“the paradox is now fully established that the utmost abstractions are the true weapons with which to control our thought of concrete fact”.(p32)
All this works towards is to awakened curiosity and a movement towards the reconstruction of traditional ways. – “Each generation criticises the unconscious assumptions made by its parent. It may assent to them, but it brings them out in the open”(p24)