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a Subset cannot have greater cardinality than the set it derives from. Subjective existence cannot be reduced to Math because it is our explorations in subject

a Subset cannot have greater cardinality than the set it derives from. Subjective existence cannot be reduced to Math because it is our explorations in subjectivity that led to math’s invention and refinement

kybernetikos 9y ago
By refering to 'math's invention' you are already prejudicing the matter. It is precisely whether Maths is a subset of subjective experience that we invented or whether it has always been a superset of the universe our subjective experience is embedded in that we merely discovered is precisely what is at issue here. It's easy to get confused by the language used to frame things. I could say that language only has countably infinite possible statements, so it must therefore be impossible to use set theory which is learnt through and derives from language to analyse uncountably infinite sets, but it would be a bad argument.
drdeca 9y ago
A subset can have equal cardinality as the set it is a subset of, if the set is infinite. I don't think that subjectivity can be reduced to math, but reducing math to subjectivity doesn't obviously imply that subjectivity cannot be reduced to math, as far as I can see right now.
wolfgke 9y ago
> a Subset cannot have greater cardinality than the set it derives from. I am not completely certain in the subtleties of non-standard set theory, but at least if we replace the axiom of Choice (AC) by the axiom of Determinacy (AD) - which is perfectly fine, though it is less common to do mathematics in this system - we can partition the real line R by an equivalence relation that has more equivalence classes than elements of R. So at least we can partition R into more disjoint subsets than R has elements. Source: https://math.stackexchange.com/questions/1104028/what-are-disasters-with-axiom-of-determinacy/1148609#1148609 https://math.stackexchange.com/questions/1104028/what-are-di...
- xelxebar 9y ago
  Oh cool. Thanks for sharing this!
- titzer 9y ago
  > we can partition the real line R by an equivalence relation that has more equivalence classes than elements of R That's not surprising, since an equivalence relation is a function of two elements of the set, i.e. O(N^2), and a subset is a function of a single element, i.e. O(N) . The OP mentioned subsets, and an equivalence relation is not a subset of the original set--it doesn't even typecheck.
  - wolfgke 9y ago
    > That's not surprising, since an equivalence relation is a function of two elements of the set, i.e. O(N^2), and a subset is a function of a single element, i.e. O(N) . The OP mentioned subsets, and an equivalence relation is not a subset of the original set--it doesn't even typecheck. I don't understand your reasoning. Every equivalence relation partitions the set S on which it is defined on into subsets - these are called equivalence classes. Every equivalence class contains at least one element of S. So I find it quite surprising that there are more equivalence classes than elements of S (in this case S are the real numbers) if we assume AD.

kybernetikos 9y ago

By refering to 'math's invention' you are already prejudicing the matter. It is precisely whether Maths is a subset of subjective experience that we invented or whether it has always been a superset of the universe our subjective experience is embedded in that we merely discovered is precisely what is at issue here. It's easy to get confused by the language used to frame things. I could say that language only has countably infinite possible statements, so it must therefore be impossible to use set theory which is learnt through and derives from language to analyse uncountably infinite sets, but it would be a bad argument.

drdeca 9y ago

A subset can have equal cardinality as the set it is a subset of, if the set is infinite. I don't think that subjectivity can be reduced to math, but reducing math to subjectivity doesn't obviously imply that subjectivity cannot be reduced to math, as far as I can see right now.

wolfgke 9y ago

> a Subset cannot have greater cardinality than the set it derives from. I am not completely certain in the subtleties of non-standard set theory, but at least if we replace the axiom of Choice (AC) by the axiom of Determinacy (AD) - which is perfectly fine, though it is less common to do mathematics in this system - we can partition the real line R by an equivalence relation that has more equivalence classes than elements of R. So at least we can partition R into more disjoint subsets than R has elements. Source: https://math.stackexchange.com/questions/1104028/what-are-disasters-with-axiom-of-determinacy/1148609#1148609 https://math.stackexchange.com/questions/1104028/what-are-di...

xelxebar 9y ago
Oh cool. Thanks for sharing this!
titzer 9y ago
> we can partition the real line R by an equivalence relation that has more equivalence classes than elements of R That's not surprising, since an equivalence relation is a function of two elements of the set, i.e. O(N^2), and a subset is a function of a single element, i.e. O(N) . The OP mentioned subsets, and an equivalence relation is not a subset of the original set--it doesn't even typecheck.
- wolfgke 9y ago
  > That's not surprising, since an equivalence relation is a function of two elements of the set, i.e. O(N^2), and a subset is a function of a single element, i.e. O(N) . The OP mentioned subsets, and an equivalence relation is not a subset of the original set--it doesn't even typecheck. I don't understand your reasoning. Every equivalence relation partitions the set S on which it is defined on into subsets - these are called equivalence classes. Every equivalence class contains at least one element of S. So I find it quite surprising that there are more equivalence classes than elements of S (in this case S are the real numbers) if we assume AD.