Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.
Interpretation
The quote emphasizes the importance of language clarity in philosophical and mathematical discussions.
Giuseppe Peano highlights that the ambiguity inherent in language poses significant challenges in philosophy, particularly regarding the foundations of mathematics. He suggests that without careful examination of the words we use, we may struggle to find clear and satisfactory solutions to complex issues, indicating a deep connection between language and understanding.
In practice
Referencing this quote in a philosophy class to discuss the importance of language in logical reasoning.
To work for libertarianism - to oppose the growth of government and aid the liberation of the individual - used to be an idealistic choice taken for purely idealistic reasons. Now it is an act of intelligent and almost desperate self-defense.
Every idea, extended into infinity, becomes its own opposite.
Death, so called, is a thing which makes men weep, And yet a third of life is passed in sleep.
The petty man is eager to make boasts, yet desires that others should believe in him. He enthusiastically engages in deception, yet wants others to have affection for him. He conducts himself like an animal, yet wants others to think well of him.
This [a state militia system] appears to me the only substitute that can be devised for a standing army, and the best possible security against it, if it should exist.
Fine words and an insinuating appearance are seldom associated with true virtue.
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