• It is sometimes said that mathematical reasoning is a process of logical deduction. If this is true, and if the conclusion of a proof must always be implied by (contained in) its premises, how can there
ever be new mathematical knowledge? • We can use mathematics successfully to model real-world processes. Is this because we create mathematics to mirror the world or because the world is intrinsically mathematical? • In the light of the questions above, is mathematics invented or discovered? • Are all mathematical statements either true or false? • It has been argued that we come to know the number 3 through examples such as three oranges or three cups. Does this support the independent existence of the number 3 and, by extension, numbers in general? If so, what of numbers such as 0, -1, i (the square root of -1) and a trillion? If not, in what sense do numbers exist? • Can mathematics be characterized as a universal language?
6 Comments
Mari Teixeira
5/2/2013 11:25:54 pm
Can mathematics be characterized as a universal language?
Reply
Gabriella Freeman
5/20/2013 02:55:05 am
Can mathematics be characterized as a universal language?
Reply
Sarah Godoy
6/16/2013 04:24:04 am
Reply
Sarah Godoy
6/16/2013 04:31:35 am
(continued)
Reply
Anna Pearson
6/18/2013 03:48:26 am
In the light of the questions above, is mathematics invented or discovered?
Reply
Athavan Balendran
6/18/2013 04:38:23 pm
Are all mathematical statements either true or false?
Reply
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