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Paul Bernays
4 quotes
“Enlightened humanity has sought in rational definiteness its liberating refuge from the dominating influence of the merely authoritative. At the present time, however, this has for a large part been lost to consciousness, and to many people scientific validity that has to be acknowledged appears as an oppressing authority.”
Paul Bernays (1888–1977) said by 1977 at the latest wikiquote, CC BY-SA 4.0 source
“I shall now address you on the subject of the present situation in research in the foundations of mathematics. Since there remain open questions in this field, I am not in a position to paint a definitive picture of it for you. But it must be pointed out that the situation is not so critical as one could think from listening to those who speak of a foundational crisis. From certain points of view, this expression can be justified; but it could give rise to the opinion that mathematical science is shaken at its roots.”
Paul Bernays (1888–1977) first seen 1934 wikiquote, CC BY-SA 4.0 source
Recorded in: Paul Bernays, Platonism in mathematics (1935) Lecture delivered June 18, 1934, in the cycle of Conferences internationales des Sciences mathematiques organized by the University of Geneva, in the series on Mathematical …
“Enlightened humanity has sought in rational definiteness its liberating refuge from the dominating influence of the merely authoritative. At the present time, however, this has for a large part been lost to consciousness, and to many people scientific validity that has to be acknowledged appears as an oppressing authority.”
Paul Bernays (1888–1977) first seen 1959 wikiquote, CC BY-SA 4.0 source
Recorded in: Bernays, Paul. "Comments on Ludwig Wittgenstein's Remarks on the foundations of mathematics." Ratio 2.1 (1959): 1-22.
“The truth is that the mathematical sciences are growing in complete security and harmony. The ideas of Dedekind, Poincare, and Hilbert have been systematically developed with great success, without any conflict in the results. It is only from the philosophical point of view that objections have been raised. They bear on certain ways of reasoning peculiar to analysis and set theory. These modes of reasoning were first systematically applied in giving a rigorous form to the methods of the calculus. [According to them,] the objects of a theory are viewed as elements of a totality such that one can reason as follows: For each property expressible using the notions of the theory, it is [an] objectively determinate [fact] whether there is or there is not an element of the totality which possesses this property. Similarly, it follows from this point of view that either all the elements of a set possess a given property, or there is at least one element which does not possess it”
Paul Bernays (1888–1977) first seen 1935 wikiquote, CC BY-SA 4.0 source
Recorded in: Paul Bernays, Platonism in mathematics (1935)