Topic: limitations of formalism
Topic: mathematical proof
Group: philosophy of mathematics
Topic: abstraction
 
Quotation
Verification differs from proof precisely because it is analytical, and because it leads to nothing. It leads to nothing because the conclusion is nothing but the premises translated into another language. A real proof, on the other hand, is fruitful, because the conclusion is in a sense more general than the premises. The equality 2+2=4 can be verified because it is particular. ... There is no science but the science of the general. It may even be said that the object of the exact science is to dispense with these direct verifications.
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Published before 1923
Additional Titles
Quote: a real proof is fruitful, its conclusion is in a sense more general than its premises
 Quote: there is no science but the science of the general

Related Topics
Topic: limitations of formalism (92 items)
Topic: mathematical proof (23 items)
Group: philosophy of mathematics (11 topics, 330 quotes)
Topic: abstraction (62 items)
