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- Could the objects of mathematics be somehow both partly invented and partly discovered. In this connection, the late distinguished English philosopher, Michael Dummett, has suggested that the objects of mathematics might somehow be ‘prodded’ into existence.
www.cambridge.org/core/journals/think/article/mathematics-discovery-or-invention/D95CA7FFC636B147C9BD17F1409BAD36MATHEMATICS: DISCOVERY OR INVENTION? | Think | Cambridge Core
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Could the objects of mathematics be somehow both partly invented and partly discovered. In this connection, the late distinguished English philosopher, Michael Dummett, has suggested that the objects of mathematics might somehow be ‘prodded’ into existence.
Sep 1, 2019 · Mathematicians judge foundational objects (such as negative numbers) and their properties (such as the result of multiplying them together) within the context of a larger, consistent mathematical...
In this connection, the late distinguished English philosopher, Michael Dummett, has suggested that the objects of mathematics might somehow be prodded into existence (he actually talks of probing but ‘prodding’, I think, is the more suggestive term).
- Kit Fine
Jul 18, 2009 · Some views in the philosophy of mathematics are object realist without being platonist. One example are traditional intuitionist views, which affirm the existence of mathematical objects but maintain that these objects depend on or are constituted by mathematicians and their activities.
We expected the constructability of all Platonic objects we can predict the existence of, and we cannot have it. But I think those results really shoot down the Classical expectation. So we need to adapt, and the right direction to move is toward Intuitionism or farther into Construcivism.
mathematics, see [1997], pp. 22-35.) Those sympathetic to the idea that mathmematical ob-jects like numbers and functions have an existence (or not!) quite independent of their set the-oretic surrogates should regard this paper as a discussion of truth and existence in set theory.
May 12, 2020 · As to the existence condition, “in mathematics as practised, set theory” is “taken to be the ultimate court of appeal for existence questions,” so “a certain type of mathematical objects” can be said to exist if “objects of this type can be found or modelled in the set-theoretic hierarchy” (ibid., 288).
