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3 ideas
23186 | Numbers enable us to manage the world - to the limits of counting [Nietzsche] |
Full Idea: Numbers are our major means of making the world manageable. We comprehend as far as we can count, i.e. as far as a constancy can be perceived. | |
From: Friedrich Nietzsche (Unpublished Notebooks 1885-86 [1886], 34[058]) | |
A reaction: I don't agree with 'major', but it is a nice thought. The intermediate concept is a 'unit', which means identifying something as a 'thing', which is how we seem to grasp the world. So to what extent do we comprehend the infinite. Enter Cantor… |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
Full Idea: If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics. | |
From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) | |
A reaction: Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application. |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
Full Idea: Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers. | |
From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2) | |
A reaction: Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated. |