The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
Interpretation
Mathematics is fundamentally rooted in symbolic logic, highlighting its logical structure and principles.
In this quote, Bertrand Russell emphasizes the profound interconnection between mathematics and logic. He asserts that recognizing mathematics as an extension of symbolic logic is a pivotal achievement, suggesting that the essence of mathematical principles lies in their logical analysis and formulation, rather than in arbitrary rules or procedures.
In practice
This quote can be used in a mathematics lecture to inspire students to appreciate the underlying logic in math.
St. Paul introduced an entirely novel view of marriage, that it existed primarily to prevent the sin of fornication. It is just as if one were to maintain that the sole reason for baking bread is to prevent people from stealing cake.
Freedom comes only to those who no longer ask of life that it shall yield them any of those personal goods that are subject to the mutations of time.
Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.
At all times, except when a monarch could enforce his will, war has been facilitated by the fact that vigorous males, confident of victory, enjoyed it, while their females admired them for their prowess.
Moreover, the attitude that one ought to believe such and such a proposition, independently of the question whether there is evidence in its favor, is an attitude which produces hostility to evidence and causes us to close our minds to every fact that does not suit our prejudices.
Extreme hopes are born from extreme misery.
The distribution of species on islands and continents throughout the world is exactly what you'd expect if evolution was a fact. The distribution of fossils in space and in time are exactly what you would expect if evolution were a fact. There are millions of facts all pointing in the same direction and no facts pointing in the wrong direction.
While it is quite reasonable for scientists to be skeptical of new ideas that do not fit within the accepted realm of scientific knowledge, the best science often emerges from situations where results carefully obtained do not fit within the accepted paradigms.
If we look at the way the universe behaves, quantum mechanics gives us fundamental, unavoidable indeterminacy, so that alternative histories of the universe can be assigned probability.
A physicist is just an atom's way of looking at itself.
Evolution is one of the two or three most primally fascinating subjects in all the sciences.
In science, you really do need to have a purpose-driven life. You will succeed to the extent that you get the most out of your career so that you can give the most back. Try to be an addict, driven to achieve discoveries, learning new things, and then writing about them.
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