Universality and the Philosophy of Mathematics
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This paper reviews the major schools of thought in phlosophy of math, in relation to their ability to speak to maths' universality and applicability. The views of Plato and Aristotle are considered, as well as Kant's synthesis. The paper examines the logicism of Frege and Russell, as well as the works of more recent thinkers who rely on math as structuralism to address the topic.
From the Paper:"For much of human history, it has been considered orthodox and irrefutable (at least among lay people) that mathematics presents a type of universal knowledge. The truth indicated by the sentence "2+2=4" is true everywhere, according to this view, and -- once the meanings behind symbols and the content of rules are correctly understood and applied -- one can take confidence that, whatever else is discovered in the world of ideas, anytime one adds a couple of some quantity designated as "two" one will always get a quantity designated as "four." But is this actually true? And if so, what about it makes it "true"? These are some of the questions that..."
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Universality and the Philosophy of Mathematics (2006, December 01) Retrieved September 19, 2021, from https://www.academon.com/analytical-essay/universality-and-the-philosophy-of-mathematics-130070/
"Universality and the Philosophy of Mathematics" 01 December 2006. Web. 19 September. 2021. <https://www.academon.com/analytical-essay/universality-and-the-philosophy-of-mathematics-130070/>