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 art of doing mathematics consists in finding that special case which contains all the germs of generality.
We must alter theory to adapt it to nature, but not nature to adapt it to theory.β
There is no physical law precluding particles from being organised in ways that perform even more advanced computations than the arrangements of particles in human brains.
If it were only a few degrees, that would be serious, but we could adapt to it. But the danger is the warming process might be unstable and run away. We could end up like Venus, covered in clouds and with the surface temperature of 400 degrees. It could be too late if we wait until the bad effects of warming become obvious. We need action now to reduce emission of carbon dioxide.
A scientist who is also a human being cannot rest while knowledge which might be used to reduce suffering rests on the shelf.
All you are is a bag of particles acting out the laws of physics. That to me is pretty clear.
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