Plato was not a mathematical Platonist /
Landry, Elaine M.,
Plato was not a mathematical Platonist / Elaine Landry. - 1 online resource (48 pages) : digital, PDF file(s). - Cambridge elements. Elements in the philosophy of mathematics . - Cambridge elements. Elements in the philosophy of mathematics. .
Also issued in print: 2023. "An online version of this work is published at doi.org/10.1017/9781009313797 under a Creative Commons Open Access license CC-BY-NC-ND 4.0 which permits re-use, distribution and reproduction in any medium for non-commercial purposes providing appropriate credit to the original work is given"--Title page verso.
Includes bibliographical references.
Open Access.
This text shows that Plato keeps a clear distinction between mathematical and metaphysical realism and the knife he uses to slice the difference is method. The philosopher's dialectical method requires that we tether the truth of hypotheses to existing metaphysical objects. The mathematician's hypothetical method, by contrast, takes hypotheses as if they were first principles, so no metaphysical account of their truth is needed. Thus, we come to Plato's methodological as - if realism: in mathematics, we treat our hypotheses as if they were first principles, and, consequently, our objects as if they existed, and we do this for the purpose of solving problems. Taking the road suggested by Plato's 'Republic', this book shows that methodological commitments to mathematical objects are made in light of mathematical practice; foundational considerations; and, mathematical applicability.
Specialized.
9781009313797 No price No price
10.1017/9781009313797 doi
Plato.
Mathematics--Philosophy.
B395 / .L3 2023
184
Plato was not a mathematical Platonist / Elaine Landry. - 1 online resource (48 pages) : digital, PDF file(s). - Cambridge elements. Elements in the philosophy of mathematics . - Cambridge elements. Elements in the philosophy of mathematics. .
Also issued in print: 2023. "An online version of this work is published at doi.org/10.1017/9781009313797 under a Creative Commons Open Access license CC-BY-NC-ND 4.0 which permits re-use, distribution and reproduction in any medium for non-commercial purposes providing appropriate credit to the original work is given"--Title page verso.
Includes bibliographical references.
Open Access.
This text shows that Plato keeps a clear distinction between mathematical and metaphysical realism and the knife he uses to slice the difference is method. The philosopher's dialectical method requires that we tether the truth of hypotheses to existing metaphysical objects. The mathematician's hypothetical method, by contrast, takes hypotheses as if they were first principles, so no metaphysical account of their truth is needed. Thus, we come to Plato's methodological as - if realism: in mathematics, we treat our hypotheses as if they were first principles, and, consequently, our objects as if they existed, and we do this for the purpose of solving problems. Taking the road suggested by Plato's 'Republic', this book shows that methodological commitments to mathematical objects are made in light of mathematical practice; foundational considerations; and, mathematical applicability.
Specialized.
9781009313797 No price No price
10.1017/9781009313797 doi
Plato.
Mathematics--Philosophy.
B395 / .L3 2023
184