(Most quotes verbatim Henri Louis Bergson, some paraphrased.)
(Relevant to Pirsig, William James Sidis, and Quantonics Thinking Modes.)
|"Let us begin with deduction. The same movement by which I trace a figure in space engenders its properties: they are visible and tangible in the movement itself; I feel, I see in space the relation of the definition to its consequences, of the premisses to the conclusion. All the other concepts of which experience suggests the idea to me are only in part constructible a priori; the definition of them is therefore imperfect, and the deductions into which these concepts enter, however closely the conclusion is linked to the premisses, participate in this imperfection. But when I trace roughly in the sand the base of a triangle, as I begin to form the two angles at the base, I know positively, and understand absolutely, that if these two angles are equal the sides will be equal also, the figure being then able to be turned over on itself without there being any change whatever. I know it before I have learnt geometry. Thus, prior to the science of geometry, there is a natural geometry whose clearness and evidence surpass the clearness and evidence of other deductions. Now, these other deductions bear on qualities, and not on magnitudes purely. They are, then, likely to have been formed on the model of the first, and to borrow their force from the fact that, behind quality, we see magnitude vaguely showing through. We may notice, as a fact, that questions of situation and of magnitude are the first that present themselves to our activity, those which intelligence externalized in action resolves even before reflective intelligence has appeared."||
Bergson restarts his footnote counts on each page. So to refer a footnote, one must state page number and footnote number.
Our bold and color highlights follow a code:
This example, given by a human of Bergson's repute appears somewhat too simple. In general it holds not, just via 3D perspectives of any spherical triangle where apparent line and angle 'equalities' vary except for one unique perspective where that which Bergson describes is seen. Extended to N dimensions and N perspectives Consider maximum total angles of a spherical equilateral triangle. Then consider its 4D brethren. Then imagine a 2D perspective.
"The savage understands better than the civilized man how to judge distances, to determine a direction, to retrace by memory the often complicated plan of the road he has traveled, and so to return in a straight line to his starting-point.(1) If the animal does not deduce explicitly, if he does not form explicit concepts, neither does he form the idea of a homogeneous space. You cannot present this space to yourself without introducing, in the same act, a virtual geometry which will, of itself, degrade itself into logic. All the repugnance that philosophers manifest towards this manner of regarding things comes from this, that the logical work of the intellect represents to their eyes a positive spiritual effort. But, if we understand by spirituality a progress to ever new creations, to conclusions incommensurable with the premisses and indeterminable by relation to them, we must say of an idea that moves among relations of necessary determination, through premisses which contain their conclusion in advance, that it follows the inverse direction, that of materiality. What appears, from the point of view of the intellect, as an effort, is in itself a letting go. And while, from the point of view of the intellect, there is a petitio principii in making geometry arise automatically from space, and logic from geometryon the contrary, if space is the ultimate goal of the mind's movement of detension, space cannot be given without positing also logic and geometry, which are along the course of the movement of which pure spatial intuition is the goal.
"It has not been enough noticed how feeble is the reach of deduction in the psychological and moral sciences. [Quantonics notices! See our QQAs.] From a proposition verified by facts, verifiable consequences can here be drawn only up to a certain point, only in a certain measure."
Note (1) - Bastian, The Brain as an Organ of the Mind, pp. 214-16.
(Our link, brackets, bold, and color.)
Rather, real space is closer to an included-middle both/and of space/actuality and nonspace/nonactuality
Pure spatial intuition is an oxymoron; pure intuition is not purely spatial; pure space is not intuitive; immutable stasis is not intuitive.
|213||"Very soon appeal has to be made to common sense, that is to say, to the continuous experience of the real, in order to inflect the consequences deduced and bend them along the sinuosities of life. Deduction succeeds in things moral only metaphorically, so to speak, and just in the measure in which the moral is transposable into the physical, I should say translatable into spatial symbols. The metaphor never goes very far, any more than a curve can long be confused with its tangent. Must we not be struck by this feebleness of deduction as something very strange and even paradoxical? Here is a pure operation of the mind, accomplished solely by the power of the mind. It seems that, if anywhere it should feel at home and evolve at ease, it would be among the things of the mind, in the domain of the mind. Not at all; it is there that it is immediately at the end of its tether. On the contrary, in geometry, in astronomy, in physics, where we have to do with things external to us, deduction is all-powerful! Observation and experience are undoubtedly necessary in these sciences to arrive at the principle, that is, to discover the aspect under which things must be regarded; but, strictly speaking, we might, by good luck, have hit upon it at once; and, as soon as we possess this principle, we may draw from it, at any length, consequences which experience will always verify. Must we not conclude, therefore, that deduction is an operation governed by the properties of matter, molded on the mobile articulations of matter, implicitly given, in fact, with the space that underlies matter? As long as it turns upon space or spatialized time, it has only to let itself go. It is duration that puts spokes in its wheels."||(Our bold.)|