Completeness Quotes
Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.
David Hilbert
It is truly a lordly spectacle how this great soul takes in all kinds of men and objects, a Falstaff, an Othello, a Juliet, a Coriolanus; sets them all forth to us in their round completeness; loving, just, the equal brother of all. Novum Organum, and all the intellect you will find in Bacon, is of a quite secondary order; earthy, material, poor in comparison with this. Among modern men, one finds, in strictness, almost nothing of the same rank. Goethe alone, since the days of Shakspeare, reminds me of it. Of him too you say that he saw the object; you may say what he himself says of Shakspeare: 'His characters are like watches with dial-plates of transparent crystal; they show you the hour like others, and the inward mechanism also is all visible.
Thomas Carlyle
Neophil: ...Leibniz, Wolff, and their various successors, to what a level of perfection and completeness they have brought philosophy! How proud Germany can be of them! Yet what does it help to claim more for oneself than is right? Let us always acknowledge that someone other than a German, I add further, someone other than a Christian, namely, Spinoza, has participated immensely in the work of bettering philosophy. Before the transition from the Cartesian to the Leibnizian philosophy could occur, it was necessary for someone to take the plunge into the monstrous abyss lying between them. This unhappy lot fell to Spinoza. How his fate is to be pitied! He was a sacrifice for the human intellect, but one that deserves to be decorated with flowers. Without him, philosophy would never have been able to extend its borders so far.
Baruch Spinoza