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.
A good science fiction story is a story with a human problem, and a human solution, which would not have happened at all without its science content.
The scientific method of examining facts is not peculiar to one class of phenomena and to one class of workers; it is applicable to social as well as to physical problems, and we must carefully guard ourselves against supposing that the scientific frame of mind is a peculiarity of the professional scientist.
When an economist says the evidence is "mixed," he or she means that theory says one thing and data says the opposite.
Many of the problems facing the nation and the world today may only be solved if their technical elements are understood - climate change, energy supply, health care, and infrastructure, to name just a few.
[T]here are depths of thousands of miles which are hidden from our inquiry. The only tidings we have from those unfathomable regions are by means of volcanoes, those burning mountains that seem to discharge their materials from the lowest abysses of the earth.
Today, all physicists know from studying Einstein and Bohr that sometimes an idea which looks completely paradoxical at first, if analyzed to completion in all detail and in experimental situations, may, in fact, not be paradoxical.
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