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Updated: May 29, 2025
And, those words being excepted which designate objects in their nature absolutely incapable of a more or less and of every qualitative difference, I should be disposed to consider other exceptions to this assertion exceedingly rare.
Indeed, to an observer who trains himself on the lines indicated in this book, even the quantitative secrets of nature will become objects of intuitive judgment, just as Goethe, by developing this organ of understanding, first found access to nature's qualitative secrets.
This is just the Hegelian standard of measurement according to which mere quantitative expansion or contraction causes a sudden qualitative change at a given point, as for example with heated or cooled water, there are points where the spring into a new set of conditions is fulfilled under normal circumstances, and where therefore quantity suddenly changes into quality.
Now it is upon the nature of the systems which we ultimately form in the mind of the child and upon the method which we pursue in our process of system or knowledge making that the resultant character of our education depends. A system of knowledge may be related as regards its parts by some qualitative or quantitative bond of identity.
Whenever the qualitative standard had been operative, it was necessary that the leaders in any form of creative action should be men of highly developed intellect, fine sensibility, wide and penetrating vision, nobility of instinct, passion for righteousness, and a consciousness of the eternal force of charity, honour, and service.
It may be asked whether there is any reason to think that there is now less regard for the higher, the qualitative values of life, than at other periods.
In his recently published tome "The Free-Market Innovation Machine Analysing the Growth Miracle of Capitalism", William Baumol of Princeton University, concurs. He daringly argues that productive innovation is at its most prolific and qualitative in oligopolistic markets. This is achieved by constant innovation and by incessant advertising.
That which goes from yellow to green is not like that which goes from green to blue: they are different qualitative movements. That which goes from flower to fruit is not like that which goes from larva to nymph and from nymph to perfect insect: they are different evolutionary movements. The action of eating or of drinking is not like the action of fighting: they are different extensive movements.
It must condense them into manageable form by means of descriptive formulæ, qualitative and quantitative. It must search for those connections between facts which form the ultimate conclusions of every science. II. The facts of humanity, with their complex and varied character, cannot be reduced like chemical facts to a few simple formulæ.
The more complete this transparency, the more it seems to me that in the same conditions there must be a repetition of the same fact. Our inductions are certain, to our eyes, in the exact degree in which we make the qualitative differences melt into the homogeneity of the space which subtends them, so that geometry is the ideal limit of our inductions as well as of our deductions.
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