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Questions related to Philosophy of Mathematics
Heard a math or related joke? Perhaps it has hidden instructive properties? Perhaps not? Here is one that is just arithmetic (rounding), but appears scientifically worded. I do not know its...
12 December 2014 9,897 8 View
There are the old schools of philosophy of mathematics: Logicism, formalism and intuitionism. These have been developed into e.g. Realism, Fictionalism, structuralism, etc. There was the...
12 December 2014 500 14 View
What is the simplest definition, if it exists, of Colombeau's new generalized functions?
12 December 2014 3,635 6 View
- Seeking the scientific philosophy of mathematics.
09 September 2014 9,425 1 View
As opposed to mathematics being an invention, what evidence would convince us that mathematics is there already in Nature?
09 September 2014 4,383 85 View
Based on applications? Based on possible impact on further researches? What really should be the criteria in ranking mathematical results?
07 July 2014 4,206 46 View
A.N. Whitehead contended that the science of pure mathematics is the most original creation of the human spirit (Science and the modern world. 1948). Number and Geometry appear to be earliest...
07 July 2014 1,543 87 View
It was true that mathematics was done in argumentation and discourse or rhetoric in ancient times. The 6 volumes of Euclid’s elements have no symbols in it to describe behaviors of properties at...
06 June 2014 6,678 90 View
Consider x^y, when x = 0, as y --> 0, z --> 0. But when y = 0, as x --> 0, z --> 1. Surely z can't be 0 and 1 all at the same time? What is the resolution to this apparent paradox?
05 May 2014 5,878 49 View
According to conventional wisdom, mathematicians tend to accept platonism but find logicism wildly implausible if not ridiculous, whereas philosophers tend to find platonism wildly implausible if...
24 March 2014 2,135 3 View
By Godel's incompleteness theorem it is impossible to prove consistency of the current widely accepted foundation of mathematics ZFC within ZFC. But this theorem says nothing about existence or...
03 March 2014 1,448 17 View
03 March 2014 3,299 3 View
The word "pattern" in everyday parlance often means something typical that can be repeated, something characteristically capable of repetition into similar copies (Ulf Grenander, Elements of...
28 February 2014 8,808 74 View
It was observed in an earlier thread that G.H. Hardy made the following observation in his 194o book A Mathematician's Apology: "The mathematician's patterns, like the painter's or the poet's,...
02 February 2014 2,692 96 View
02 February 2014 5,029 75 View
01 February 2014 6,812 96 View
• Goethe's observation to Eckermann that, properly speaking, “our intellectual work lies not so much in thinking new thoughts as in thinking the old ones again” (229-30). There is a saying by...
14 January 2014 4,574 20 View
Infinity in mathematics is a property of a set of objects that is not finite. The traditional view of infinity has its origin in the writings of Aristotle and the notion of potential infinity. "It...
08 January 2014 6,731 99 View
01 January 2014 7,134 100 View
01 January 2014 1,705 21 View
It is all too simple to say that we can "model" reality mathematically, but nothing in mathematics corresponds, say, to the experience of seeing blue. Mathematics can only express the formal...
01 January 2014 6,338 19 View
The principle of linear superposition holds for the integers, eg. 3 + 4 = 7. However, when we take the integers out to infinity we now obtain nonlinear behaviour. Infinity plus any amount is...
01 January 2014 1,008 42 View
It is not easy to define a new result in, say, mathematics. I cannot do this. I think that a new result must contain new ideas or techniques, ...? Can we speak of a new result in the following...
01 January 2014 1,876 2 View
Some physicists say”everything is quantum”? Why would they say so? And what is the meaning of this sentence? No one doubts that quantum theory is successful. But from this statement it does not...
12 December 2013 4,118 36 View