...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
Interpretation
Mathematics is unique among sciences as it does not require ethical considerations to maintain its integrity.
In this quote, Charles Sanders Peirce emphasizes the profound nature of pure mathematics, suggesting that it remains grounded and rigorous in its principles without the complications introduced by ethical dilemmas that affect other sciences. Unlike disciplines such as logic or the natural sciences, which can become ambiguous or subjective, pure mathematics retains its clarity and robustness, embodying an ideal of scientific inquiry that is unaffected by ethical concerns.
In practice
In a lecture discussing the philosophy of science, one might use this quote to highlight the unique status of mathematics.
The final upshot of thinking is the exercise of volition, and of this thought no longer forms a part; but belief is only a stadium of mental action, an effect upon our nature due to thought, which will influence future thinking.
Notwithstanding all that has been discovered since Newton's time, his saying that we are little children picking up pretty pebbles on the beach while the whole ocean lies before us unexplored remains substantially as true as ever, and will do so though we shovel up the pebbles by steam shovels and carry them off in carloads.
My language is the sum total of myself.
All the evolution we know of proceeds from the vague to the definite.
The third class consists of men to whom nothing seems great but reason. If force interests them, it is not in its exertion, but in that it has a reason and a law. For men of the first class, nature is a picture; for men of the second class, it is an opportunity; for men of the third class, it is a cosmos, so admirable, that to penetrate to its ways seems to them the only thing that makes life worth living. These are the men whom we see possessed by a passion to learn.
A quality is something capable of being completely embodied. A law never can be embodied in its character as a law except by determining a habit. A quality is how something may or might have been. A law is how an endless future must continue to be.
Things looked at patiently from one side after another generally end by showing a side that is beautiful.
I was raised a black child in the South, where you're indoctrinated into a religion that an oppressor gave you.
Nothing causes us to so nearly resemble God as the forgiveness of injuries.
I got interested in the American culture war back in 2004, and it's one of the only growth stocks I've ever invested in.
The Word is living, being, spirit, all verdant greening, all creativity. This Word manifests itself in every creature.
Anti-social behavior is a trait of intelligence in a world full of conformists.
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