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I think there are definitely interesting things to talk about in foundations, and also that many are now well motivated by computer science. It's not like these

by tel 11y ago

I think there are definitely interesting things to talk about in foundations, and also that many are now well motivated by computer science. It's not like these are either unknown or special, though. For most "practical", pure math arguing about foundations can't move your field forward as it is not holding your field back. Further, differences in communication rarely stem from foundational issues as much as merely the social construct that practitioners in separate fields have less to say to one another than those in the same field. This leads to semantic drift and development of independent metaphor technologies. Translation necessarily becomes more expensive and so higher ROI is required in order to motivate it.

deleted 11y ago
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ganzuul 11y ago
I think I can express my opinion simply now. Thank you. - "Practical" pure math appears to be based on formalism rather than intuitionism. Because foundations and therefore intuition does not hold formalism back, these practitioners drift further away from being able to communicate their metaphors to whose who rely on intuition; such as biologists. - And this is my opinion.
- tel 11y ago
  Are you uniting "intuitionism" and common "intuition"? I'm not personally sure I disagree here at all, but I'm certain many would!
  - ganzuul 11y ago
    Strictly no... Then We would have to debate what common intuition is and that is untenable. What I am trying to say is that math is a discipline of philosophy, that the integers are divine, and that the straightedge and compass ought to be enough for anybody. ;) I often rely on my intuition for abstract thought, and repeatedly find that others have reached the same conclusions that I do. Therefore (my own) intuition is repeatable, and therefore intuition is scientific. Juxtapose formalism, which seems to say that math is solely the practice of inventing rules and following them to the end. - I understand why this idea has its own beauty, haughty as it might seem, but at the same time it is a very strange and in my opinion frightening kind of beauty because it intends to remain unknowable. Turing, who I have apparently proclaimed a saint, seems to observe that both of these paradigms are needed for some kind of universal, and altogether anthropomorphic, program. I would be hard pressed to dismiss any idea which appears beautiful...

by tel 11y ago

deleted 11y ago

[deleted]

ganzuul 11y ago

I think I can express my opinion simply now. Thank you. - "Practical" pure math appears to be based on formalism rather than intuitionism. Because foundations and therefore intuition does not hold formalism back, these practitioners drift further away from being able to communicate their metaphors to whose who rely on intuition; such as biologists. - And this is my opinion.

tel 11y ago
Are you uniting "intuitionism" and common "intuition"? I'm not personally sure I disagree here at all, but I'm certain many would!
- ganzuul 11y ago
  Strictly no... Then We would have to debate what common intuition is and that is untenable. What I am trying to say is that math is a discipline of philosophy, that the integers are divine, and that the straightedge and compass ought to be enough for anybody. ;) I often rely on my intuition for abstract thought, and repeatedly find that others have reached the same conclusions that I do. Therefore (my own) intuition is repeatable, and therefore intuition is scientific. Juxtapose formalism, which seems to say that math is solely the practice of inventing rules and following them to the end. - I understand why this idea has its own beauty, haughty as it might seem, but at the same time it is a very strange and in my opinion frightening kind of beauty because it intends to remain unknowable. Turing, who I have apparently proclaimed a saint, seems to observe that both of these paradigms are needed for some kind of universal, and altogether anthropomorphic, program. I would be hard pressed to dismiss any idea which appears beautiful...