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Are numbers real? - Philosophy Stack Exchange
Oct 29, 2013 · We accept counting numbers as kind of real and question only more artificial ones like real numbers because we are accustomed to counting numbers. Still, the notions of counting numbers, fractions and amount are highly useful for our purposes today as explained by @Niel …
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See results only from philosophy.stackexchange.comHow do mathematical object…
The question seems to presuppose that (1) the real world is a determinate thing, …
metaphysics - Mathematical …
According to that definition, some numbers are real (integers, rational numbers, and …
Do numbers exist? What are the arguments? : …
According to Plato, numbers exist independently of everything - they are real as real can get. Aristotle on the other hand held that numbers existed in the world - we see three of something, so three must exist, etc.
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Philosophy of Mathematics - Stanford Encyclopedia of Philosophy
Sep 25, 2007 · If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the …
What Are Numbers? - Philosophy Talk
Mar 14, 2006 · Yet another view is that numbers are just abstractions from physical magnitudes. John points out that different units lead to assignment of different numbers to the same …
philosophy of mathematics - Do numbers exist independently from ...
The Pythagorean or Platonic reality of numbers has a long history in philosophy and mathematics. Physicists Max Tegmark and Roger Penrose, for example, argue for number as a fundamental …
Platonism in the Philosophy of Mathematics - Stanford …
Jul 18, 2009 · Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our …
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Metaphysics, Number Theory, Philosophy - Britannica
According to Aristotle, number speculation is the most characteristic feature of Pythagoreanism. Things “are” number, or “resemble” number.
metaphysics - Mathematical Platonism. Are numbers real?
Jan 15, 2023 · According to that definition, some numbers are real (integers, rational numbers, and even irrational like pi), and some are not like the imaginary i defined by i * i = -1. In the …
Philosophy of mathematics - Nominalism, Realism, Platonism
Nominalism is the view that mathematical objects such as numbers and sets and circles do not really exist. Nominalists do admit that there are such things as piles of three eggs and ideas of …
Are Numbers Real? - Google Books
In Are Numbers Real?, Brian Clegg explores the way that math has become more and more detached from reality, and yet despite this is driving the development of modern physics.
Do Numbers Exist? | A Plea for Natural Philosophy: And Other …
This essay addresses the further questions of ontology: do numbers exist?, is arithmetic the study of abstract objects, or is it an extremely useful, idealized theory that’s not literally true? Both …
Semantics and the Ontology of Number - Cambridge University …
After highlighting their motivations and challenges, I develop a comprehensive polymorphic semantics for number expressions.
Do numbers EXIST? - Numberphile
Jun 3, 2012 · An expert on the philosophy of mathematics, Dr Jonathan Tallant, outlines some of the key arguments about whether or not numbers ACTUALLY EXIST? Exploring platonism, …
Are Real Numbers Real? - PLATO AND THE NERD
Jun 20, 2017 · He points out mathematical, philosophical, and computational difficulties with real numbers and concludes that these difficulties undermine the common assumption that real …
Kant on ‘Number’ (Chapter 12) - Kant's Philosophy of Mathematics
Tait argues that Kant did not restrict the notion of number or the operations of arithmetic to the natural numbers, but rather, applies the notions of number and arithmetic to geometric …
How Inevitable Is the Concept of Numbers? - Stephen Wolfram
May 25, 2021 · We can aspire to generalize from numbers, and, for example, sample other representations of computational reducibility. But for now, numbers seem to be inextricably …
Platonism, Mathematical | Internet Encyclopedia of Philosophy
In particular, mathematical platonism takes at face-value such well known truths as that “there exist” an infinite number of prime numbers, and it provides straightforward explanations of …
Wittgenstein and the Real Numbers: History and Philosophy of …
Jul 21, 2010 · A real number, as an ‘extension’, is a homeless fiction; ‘homeless’ in that it neither is supported by anything nor supports anything. The picture of a real number as an ‘extension’ is …
Infinity - Stanford Encyclopedia of Philosophy
Apr 29, 2021 · The rigorous study of infinity began in mathematics and philosophy, but the engagement with infinity traverses the history of cosmology, astronomy, physics, and theology.
2. Generating the World of Numbers: Pythagorean and Platonist …
The position departs from classical Pythagorean number theory: the Pythagoreans claimed that numbers were corporeal, and that sense-perceptible things are, or are made of, numbers. But …
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