- 23 Mar 2013 19:04
#14199953
I honestly have no idea where to post this thread, but it is sciencey and I harbor an innate hatred for philosophical masturbation.
The question is based on/explained by/introduced by the following video:
I'd have a discussion on the video thread, but YouTube comments are fucking horrible for that.
Anyway, I'm not a mathematician. I'm generally pretty bad at math, though I love the theories. This video discusses three interpretations of "do numbers exist" that are almost more philosophy than math... the platonism, nominalism, and the fictionalism approaches. There may be more, but these are experts and they narrow it down to these three concepts. They are defined in the video better than I can summarize.
My reply somewhere in the comments section is:
I state "would it be correct" because I do not have a good understanding of university level math or mathematical philosophy; my question is genuine, not reflective. If my understanding is true, then I would definitely lean towards the nominalist approach.
From the platonism view, as I understand it, "a blue banana shaped like a starfish" is an equally valid "abstract idea" as 1,748.392 (random number for example).
One comment on the video is
Well, I'm not a child, but I am "uneducated" at a university level (I met my requirement with statistics because fuck calculus). But I don't have a problem adopting zero or negative numbers. I can certainly say that there are zero bananas on my desk, and I can understand a negative number in a more abstract way... I can't say there are -1 bananas on my desk (don't ask me why I'm fixated on bananas), but I can comprehend there being one less banana on my desk than could potentially be there. I usually just think of such things on a graph.
I also don't have a problem with sqrt(-1) or other imaginary numbers, since I take the operative word "imaginary" literally. Maybe fictionalism makes more sense there, since it literally doesn't fucking exist ever anywhere, and that may work for more abstract concepts. Dividing by zero I can imagine since I picture it on a graph:
I'm not sure if that is technically nominalism or platonism or fictionalism though.
But I don't think that "1" exists. "1" is specifically 1 of something. You don't have to necessarily mention or define that something, but 1 unit divided by 2 units is half of 1 unit.
Thoughts?
The question is based on/explained by/introduced by the following video:
I'd have a discussion on the video thread, but YouTube comments are fucking horrible for that.
Anyway, I'm not a mathematician. I'm generally pretty bad at math, though I love the theories. This video discusses three interpretations of "do numbers exist" that are almost more philosophy than math... the platonism, nominalism, and the fictionalism approaches. There may be more, but these are experts and they narrow it down to these three concepts. They are defined in the video better than I can summarize.
My reply somewhere in the comments section is:
Would it be correct to say that a nominalist viewpoint would be that a number is "of something"... saying 1,748,392 means nothing, but saying 1,748,392 kg means something. Similarly, pi (or tau if you prefer) is only a thing when it is applied to a circle. Without the circle, it isn't anything.
So, like, "1" has no meaning in itself (unless it is "1 of something"), but if you give it even an arbitrary meaning like "1 AU", then it exists.
I state "would it be correct" because I do not have a good understanding of university level math or mathematical philosophy; my question is genuine, not reflective. If my understanding is true, then I would definitely lean towards the nominalist approach.
From the platonism view, as I understand it, "a blue banana shaped like a starfish" is an equally valid "abstract idea" as 1,748.392 (random number for example).
One comment on the video is
Nominalism is how children and the uneducated think about math, which is why humans had so much trouble adopting "zero" and negative numbers (not to mention the imaginary number sqrt(-1)) for so long. If you are a mathematician like me, you have seen lots of things much stranger than sqrt(-1), and are left with no other conclusion than that math is a logical tool. Fictionalism wins.
Well, I'm not a child, but I am "uneducated" at a university level (I met my requirement with statistics because fuck calculus). But I don't have a problem adopting zero or negative numbers. I can certainly say that there are zero bananas on my desk, and I can understand a negative number in a more abstract way... I can't say there are -1 bananas on my desk (don't ask me why I'm fixated on bananas), but I can comprehend there being one less banana on my desk than could potentially be there. I usually just think of such things on a graph.
I also don't have a problem with sqrt(-1) or other imaginary numbers, since I take the operative word "imaginary" literally. Maybe fictionalism makes more sense there, since it literally doesn't fucking exist ever anywhere, and that may work for more abstract concepts. Dividing by zero I can imagine since I picture it on a graph:
I'm not sure if that is technically nominalism or platonism or fictionalism though.
But I don't think that "1" exists. "1" is specifically 1 of something. You don't have to necessarily mention or define that something, but 1 unit divided by 2 units is half of 1 unit.
Thoughts?
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