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Quote by Giuseppe Peano

“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.”

Quote by Giuseppe Peano

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Giuseppe Peano
Giuseppe Peano

Giuseppe Peano was an Italian mathematician known for his contributions to the foundations of mathematics and logic. Born on August 27, 1858, and died on April 20, 1932, Peano is best known for creating a rigorous system of mathematical symbols and axioms, widely used in modern mathematics and logic. more

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“The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.”

“The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little inquiry into its nature and purpose as a deliberate human activity. Doubtless this is due to the inevitable drawback that mathematical study is saturated with technicalities from beginning to end.”

“The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.”

“There have been many authorities who have asserted that the basis of science lies in counting or measuring, i.e. in the use of mathematics. Neither counting nor measuring can however be the most fundamental processes in our study of the material universe-before you can do either to any purpose you must first select what you propose to count or measure, which presupposes a classification.”