I conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.
Interpretation
Science is limited to factual knowledge and cannot determine moral values.
Bertrand Russell's quote emphasizes the limitations of science in addressing questions of value, arguing that such inquiries lie beyond the scope of empirical truth. He asserts that knowledge should be pursued through scientific methods, and that anything beyond what science can uncover remains unknowable to humanity.
In practice
In a debate about the role of science in society, this quote could highlight its limitations.
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.
I have called this principle, by which each slight variation, if useful, is preserved, by the term of Natural Selection.
I can easily conceive, most Holy Father, that as soon as some people learn that in this book which I have written concerning the revolutions of the heavenly bodies, I ascribe certain motions to the Earth, they will cry out at once that I and my theory should be rejected.
Companies are the first to see the costs of climate change.
Perhaps... some day the precision of the data will be brought so far that the mathematician will be able to calculate at his desk the outcome of any chemical combination, in the same way, so to speak, as he calculates the motions of celestial bodies.
The problem of neurology is to understand man himself.
I am a futurist, projecting trends in science into the next decades and century, but ironically my two daughters - one is a neuroscientist and the other is a pastry chef - tell me that my taste in music is positively prehistoric.
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