Mathematics
In the foundations of mathematics, formalism is associated with a certain rigorous mathematical method: see formal system. In common usage, a formalism means the out-turn of the effort towards formalisation of a given limited area. In other words, matters can be formally discussed once captured in a formal system, or commonly enough within something formalisable with claims to be one. Complete formalisation is in the domain of computer science.
Formalism also more precisely refers to a certain school in the philosophy of mathematics, stressing axiomatic proofs through theorems, specifically associated with David Hilbert. In the philosophy of mathematics, therefore, a formalist is a person who belongs to the school of formalism, which is a certain mathematical-philosophical doctrine descending from Hilbert.
Read more about this topic: Formalism (philosophy)
Famous quotes containing the word mathematics:
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)