...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.
Terrorists are not following Islam. Killing people and blowing up people and dropping bombs in places and all this is not the way to spread the word of Islam. So people realize now that all Muslims are not terrorists.
To be a human being is to be in a state of tension between your appetites and your dreams, and the social realities around you and your obligations to your fellow man.
Out of the experience of extraordinary human disaster that lasted too long, must be born a society of which all humanity will be proud.
Our dreams prove that to imagine - to dream about things that have not happened - is among mankind's deepest needs.
I've wondered why it took us so long to catch on. We saw it, and yet we didn't see it. Or rather we were trained not to see it. Conned perhaps into thinking that the real action was metropolitan and all this was just boring hinterland. It was a puzzling thing. The truth knocks on the door and you say, "Go away. I'm looking for the truth." And so it goes away. Puzzling.
Annihilation has no terrors for me, because I have already tried it before I was born --a hundred million years --and I have suffered more in an hour, in this life, than I remember to have suffered in the whole hundred million years put together.
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