On
On mathematics
Foundations
Hilary Putnam (1971, p. 327; quoted in @2020clarke-doaneMorality)
[Q]uantification over mathematical entities is indispensable for science … but this commits us to … the [independent] existence of the mathematical entities [that satisfy our theories]. This type of argument stems, of course, from Quine, who has for years stressed both the indispensability of quantification over mathematical entities and the intellectual dishonesty of denying the existence of what one daily presupposes.
Structuralism
Hermann Weyl (1939, p. 500; quoted in @2006mclartyEmmy)
In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.
On philosophy
Russell, 1918 (quoted in @2020clarke-doaneMorality, 55)
My desire and wish is that the things I start with should be so obvious that you wonder why I spend my time stating them. This is what I aim at because the point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.
On science
The general scientific enterprise
Jakob von Uexküll (1909, p. 227; quoted in @2023smaldinoModeling)
The truth lies directly before us in the reality surrounding us. However, we cannot use it as it is. An unbroken description of reality would be simultaneously the truest and most useless thing in the world, and it would certainly not be science. If we want to make reality and therefore truth useful to science, we must do violence to reality. We must introduce the distinction, which does not exist in nature, between essential and inessential. In nature, everything is equally essential. By seeking out the relationships that seem essential to us, we order the material in a surveyable way at the same time. Then we are doing science.
Biology
D’Arcy Thompson, On Growth and Form
Everything is what it is because it got that way.
Theodosius Dobzhansky (1973; quoted in @2022levinTechnological)
Nothing in biology makes sense except in light of evolution.
Physics
It is only slightly overstating the case to say that physics is the study of symmetry. The first demonstration of the power of this idea may have been by Newton, who may have asked himself the question: What if the matter here in my hand obeys the same laws as that up in the sky—that is, what if space and matter are homogeneous and isotropic?
Psychology
Tomasello (2022), The Evolution of Agency (quoted in @2024abelThree)
Every scientific discipline begins with a proper domain, a first principle. In biology, that proper domain or first principle is life: physical substances organized in particular ways to perform particular organismic functions. In psychology, depending on one’s theoretical predilections, that proper domain or first principle might be either behavior or mentality. But my preferred candidate would be agency, precisely because agency is the organizational framework within which both behavioral and mental processes operate.