Posts Tagged ‘René Descartes’
Quote of the Day
There are no paths available to human beings to a certain knowledge of the truth apart from clear intuition and necessary deduction.
What is intuition?
One can have memory of the future as well as of the past. Memory of the future is usually called instinct in animals, intuition in human beings.
Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it…Logic, which alone can give certainty, is the instrument of demonstration; intuition is the instrument of invention.
Intuition is a mode of gathering.
Mathematical intuition need not be conceived of as a facility giving an immediate knowledge of the objects concerned. Rather it seems that, as in the case of physical experience, we form our ideas also of those objects on the basis of something else which is immediately given.
[Intuition] grasps a succession which is not juxtaposition, a growth from within, the uninterrupted prolongation of the past into a present which is already blending into the future. It is the direct vision of the mind by the mind.
Intuition is the ability not to construct solutions to problems in a rational manner, but rather to produce them spontaneously (holistically) according to situational demands…Intuition is, we could perhaps say, a fire that lights itself.
My intuition made me work…Intuition makes us look at unrelated facts and then think about them until they can all be brought under one law.
By intuition I do not mean the fluctuating testimony of the senses or the deceptive judgment of the imagination as it botches things together, but the conception of a clear and attentive mind, which is so easy and distinct that there can be no room for doubt about what we are understanding…Intuition is the indubitable conception of a clear and attentive mind which proceeds solely from the light of reason.
Intuition [in Nobel laureates] is closely associated with a sense of direction; it is more often about finding a path than arriving at an answer or reaching a goal. The ascent of intuition is rooted in extended, varied experience of the object of research: although it may feel as if it comes out of the blue, it does not come out of the blue.
Descartes’s four rules of logic
As a multitude of laws often only hampers justice, so that a state is best governed when, with few laws, these are rigidly administered; in like manner, instead of the great number of precepts of which logic is composed, I believed that the four following would prove perfectly sufficient for me, provided I took the firm and unwavering resolution never in a single instance to fail in observing them.
The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgment than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.
The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.
The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.
And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.
Alec Nevala-Lee 