Every work of science great enough to be well remembered for a few generations affords some exemplification of the defective state of the art of reasoning of the time when it was written; and each chief step in science has been a lesson in logic.
Interpretation
Scientific advancements often reflect the reasoning limitations of their time, teaching us important lessons in logic.
In this quote, Charles Sanders Peirce highlights how significant scientific works not only contribute to knowledge but also reveal the shortcomings in logic and reasoning prevalent during their creation. Each breakthrough in science serves as an opportunity for reflection and learning, showcasing the evolution of thought and the advancement of rational understanding over generations.
In practice
During a lecture on the history of science, this quote can be used to emphasize the importance of critical thinking.
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.
Do not become archivists of facts. Try to penetrate to the secret of their occurrence, persistently search for the laws which govern them.
The slow rejection of the foreign skin grafts fascinated me. How could the host distinguish another person's skin from his own?
The physicist is like someone who's watching people playing chess and, after watching a few games, he may have worked out what the moves in the game are. But understanding the rules is just a trivial preliminary on the long route from being a novice to being a grand master. So even if we understand all the laws of physics, then exploring their consequences in the everyday world where complex structures can exist is a far more daunting task, and that's an inexhaustible one I'm sure.
Science does not know its debt to imagination.
Extra dimensional theories are sometimes considered science fiction with equations. I think that's a wrong attitude. I think extra dimensions are with us, they are with us to stay, and they entered physics a long time ago. They are not going to go away.
All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
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