4 ms·

Are you saying that some but not all cycles are kosher with ZFC?

by ganzuul 11y ago

ska 11y ago
I believe they are pointing out that the constraints on the construction of ZFC are not meaningfully/practically constraining the objects build atop the system that you would want to study and manipulate in CS. I can't see how your implication works either, can you make it explicit?
- ganzuul 11y ago
  Those tricky relationships arise from the most fundamental circuits that define CS, yes. What I am trying to say is that you do not need mathematical formulas to explain mathematical concepts, but certain vocal academics have managed to push a view that math is nothing but formulas AND that there is no controversy here. There is, in fact, a lot of controversy and this does lead back to Grothendieck since his work does not support the formulas-only view.
  - ska 11y ago
    > but certain vocal academics have managed to push a view that math is nothing but formulas AND that there is no controversy here. This isn't really a thing, which may explain why I'm having trouble understanding what you are trying to say. To be more concrete: from what I can understand of your somewhat incoherent characterization it does not match any mathematical community I know of - it may exist, but if so it is not mainstream.
omaranto 11y ago
The axiom of foundation forbids cycles in the membership relation, you are of course allowed to talk about other relations that do have cycles. For example, R={(1,2),(2,3),(3,1)} is a relation defined in ZFC that relates 1 to 2, 2 to 3 and 3 to 1. If you want to study cycles in directed graphs it never matters that you can't have membership cycles and I'm confused about why anyone would think it does.
- ganzuul 11y ago
  Thanks for the clarification. This is what set me off: https://en.wikipedia.org/wiki/Finite-state_machine https://en.wikipedia.org/wiki/Finite-state_machine Along with discussing the topic in ##math on Freenode.

Are you saying that some but not all cycles are kosher with ZFC?

by ganzuul 11y ago

Are you saying that some but not all cycles are kosher with ZFC?

ska 11y ago

I believe they are pointing out that the constraints on the construction of ZFC are not meaningfully/practically constraining the objects build atop the system that you would want to study and manipulate in CS. I can't see how your implication works either, can you make it explicit?

ganzuul 11y ago
Those tricky relationships arise from the most fundamental circuits that define CS, yes. What I am trying to say is that you do not need mathematical formulas to explain mathematical concepts, but certain vocal academics have managed to push a view that math is nothing but formulas AND that there is no controversy here. There is, in fact, a lot of controversy and this does lead back to Grothendieck since his work does not support the formulas-only view.
- ska 11y ago
  > but certain vocal academics have managed to push a view that math is nothing but formulas AND that there is no controversy here. This isn't really a thing, which may explain why I'm having trouble understanding what you are trying to say. To be more concrete: from what I can understand of your somewhat incoherent characterization it does not match any mathematical community I know of - it may exist, but if so it is not mainstream.

omaranto 11y ago

The axiom of foundation forbids cycles in the membership relation, you are of course allowed to talk about other relations that do have cycles. For example, R={(1,2),(2,3),(3,1)} is a relation defined in ZFC that relates 1 to 2, 2 to 3 and 3 to 1. If you want to study cycles in directed graphs it never matters that you can't have membership cycles and I'm confused about why anyone would think it does.

ganzuul 11y ago
Thanks for the clarification. This is what set me off: https://en.wikipedia.org/wiki/Finite-state_machine https://en.wikipedia.org/wiki/Finite-state_machine Along with discussing the topic in ##math on Freenode.