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.
There are as many species as the infinite being created diverse forms in the beginning, which, following the laws of generation, produced many others, but always similar to them: therefore there are as many species as we have different structures before us today.
Science is a collaborative enterprise, spanning the generations. When it permits us to see the far side of some new horizon, we remember those who prepared the way - seeing for them also.
Nature allows only experimental situations to occur which can be described within the framework of the formalism of quantum mechanics
nd now that man's history has been for the first time systematically considered as a whole, and has been found to be, like all other phenomena, subject to invariable laws, the preparatory labours of modern Science are ended.
In the good old days physicists repeated each other's experiments, just to be sure. Today they stick to FORTRAN, so that they can share each other's programs, bugs included.
There was a time when 'universe' meant 'all there is.' Everything. The whole shebang. The notion of more than one universe, more than one everything, would seemingly be a contradiction in terms.
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