timelets

...it is the mutability of mathematically precise structures (by morphisms) which is the essential content of category theory. If the structures are themselves categories, this mutability is expressed by functors, while if the structures are functors, the mutability is expressed by natural transformations.

--- F. William Lawvere, 2005.

Then in 1963 Lawvere embarked on the daring project of a purely categorical foundation for all mathematics.

For they pay honours to Poseidon on the eighth day of every month. The number eight, as the first cube of an even number and the double of the first square, fitly represents the steadfast and immovable power of this god, to whom we give the epithets of Securer and Earth-stayer.

Plutarch, The Life of Theseus.

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Theseus*.html

Why can one say `he believes that p, but it is not the case that p', whereas one cannot say `I believe that p, but it is not the case that p'?

--- Peter Hacker, quoted by Michael Starks, The logical structure... 2nd ed, p. 17

The eternal and exclusive Becoming, the total instability of all reality and actuality, which continually works and becomes and never is, as Heraclitus teaches—is an awful and appalling conception, and in its effects most nearly related to that sensation, by which during an earthquake one loses confidence in the firmly-grounded earth.

It required an astonishing strength to translate this effect into its opposite, into the sublime, into happy astonishment.

Heraclitus accomplished this through an observation of the proper course of all Becoming and Passing, which he conceived of under the form of polarity, as the divergence of a force into two qualitatively different, opposite actions, striving after reunion.

A quality is set continually at variance with itself and separates itself into its opposites: these opposites continually strive again one towards another.

The common people of course think to recognise something rigid, completed, consistent; but the fact of the matter is that at any instant, bright and dark, sour and sweet are side by side and attached to one another like two wrestlers of whom sometimes the one succeeds, sometimes the other. ”.

-- Friedrich Wilhelm Nietzsche. “Early Greek Philosophy & Other Essays / Collected Works, Volume Two.”