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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...
Apr 19, 2016 · Mathematical objects exist, although they do so in a different manner than that in which physical objects exist. Their existence is reflected in the structure of the physical world, as well as their conceivability in the human mind. One discovery of set theory is that all of classical mathematics can be formulated within set theory.
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
Feb 23, 2007 · Mathematics as Human Invention: According to the middle Wittgenstein, we invent mathematics, from which it follows that mathematics and so-called mathematical objects do not exist independently of our inventions.
Jun 8, 2023 · In modern mathematics, entities no longer need to be constructed or computed in order to be named and manipulated; they simply need to exist. What was the transformative change that enabled this level of abstraction to be embraced and widely adopted, namely the distinction between mere existence and actual realization?
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Feb 25, 2016 · Most people use mind-independence as a criterion for existence of mathematical objects. The real question (appears to) come down to mind-independence vs. psychologism. If neo-logicism is successful, then it can be shown that mathematics has a mind-independent ontology.
