Every philosophical problem, when it is subjected to the necessary analysis and justification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical.
Interpretation
Philosophical problems often dissolve under scrutiny or reveal themselves as logical issues.
In this quote, Bertrand Russell asserts that many problems we deem philosophical are either not genuinely philosophical upon deeper analysis or they boil down to logical matters. This highlights the importance of critical thinking and the analytical approach in philosophy, suggesting that philosophical inquiries should be rigorously examined to clarify their true nature.
In practice
During a university lecture on philosophy, you could use the quote to illustrate the importance of critical analysis in philosophical discussions.
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 am an invisible man. I am a man of substance, of flesh and bone, fiber and liquids - and I might even be said to possess a mind. I am invisible, understand, simply because people refuse to see me.
We object not to the narration of the deeds of our unregenerate condition, but to the mode in which it is too often done. Let sin have its monument, but let it be a heap of stones cast by the hands of execration - not a mausoleum erected by the hands of affection.
Society is the picnic certain individuals leave early, the party they fail to enjoy, the musical comedy they find not worth the price of admission.
Reason is the cause of our falsification of the evidence of the senses. In so far as the senses show becoming, passing away, change, they do not lie.
[L]iberty must at all hazards be supported. We have a right to it, derived from our Maker. But if we had not, our fathers have earned and bought it for us, at the expense of their ease, their estates, their pleasure, and their blood.
Weapons are ominous tools. They are abhorred by all creatures. Anyone who follows the Way shuns them.
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