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Views of the Essence of Numbers over the Course of History
Pages 5 (1255 words)
Mathematics, despite being part of some of the most fundamental ways we understand our universe such as physics and chemistry, still remains something of a philosophical mystery. This mystery centres on numbers and their place in the world, what they are and why they function the way they do.
The second is the idea that mathematics and numbers are simply a way of interpreting and interacting with arbitrarily defined symbols, and that holds their only usefulness (36). The final is the idea of the logicians led by Russel, who claim that mathematics are useful because the universe is structured in a logically coherent way, and mathematics are thus simply an expression of that logic (36). The latter two theories have enough holes in them that they have been considered disproven, so many mathematical philosophers rely on the first, Platonic theory to describe the role of numbers in our universe. This, however, is completely un-provable, and sidesteps around the problem of describing what numbers are without actually explaining anything; if numbers are simply things that exist in another realm, that is not philosophically useful and thus not a very compelling theory. I believe that numbers and mathematics actually need to be explained by a new theory, and that while we currently do not have a completely formulated theory to explain what numbers are and how mathematics work, each of the aforementioned theories has some of the components that a complete theory of mathematics must have. The single biggest problem with the Platonic theory is its lack of utility. ...
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