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Re: Truth can be understood as math
Posted: Wed Aug 28, 2019 8:13 am
by Skepdick
PeteOlcott wrote: ↑Tue Aug 27, 2019 7:58 pm
You can't see that is self-contradictory ?
To evaluate it as "self-contradictory" first I have to evaluate a truth-value.
Re: Truth can be understood as math
Posted: Wed Aug 28, 2019 3:10 pm
by PeteOlcott
Skepdick wrote: ↑Wed Aug 28, 2019 8:13 am
PeteOlcott wrote: ↑Tue Aug 27, 2019 7:58 pm
You can't see that is self-contradictory ?
To evaluate it as "self-contradictory" first I have to evaluate a truth-value.
∃x (x ↔ ¬x)
Re: Truth can be understood as math
Posted: Wed Aug 28, 2019 4:12 pm
by Skepdick
PeteOlcott wrote: ↑Wed Aug 28, 2019 3:10 pm
Skepdick wrote: ↑Wed Aug 28, 2019 8:13 am
PeteOlcott wrote: ↑Tue Aug 27, 2019 7:58 pm
You can't see that is self-contradictory ?
To evaluate it as "self-contradictory" first I have to evaluate a truth-value.
∃x (x ↔ ¬x)
Firstly, that's syntactically incomplete in a Type-theoretic universe.
What's x's Type?
Does it support negation?
What does it mean to negate things of type x ?
Secondly. Here is a Universe I've constructed in which ∃ Type:x (x ↔ ¬x)
https://repl.it/repls/SympatheticLovelyCondition
Re: Truth can be understood as math
Posted: Wed Aug 28, 2019 9:41 pm
by PeteOlcott
Skepdick wrote: ↑Wed Aug 28, 2019 4:12 pm
PeteOlcott wrote: ↑Wed Aug 28, 2019 3:10 pm
Skepdick wrote: ↑Wed Aug 28, 2019 8:13 am
To evaluate it as "self-contradictory" first I have to evaluate a truth-value.
∃x (x ↔ ¬x)
Firstly, that's syntactically incomplete in a Type-theoretic universe.
What's x's Type?
Does it support negation?
What does it mean to negate things of type x ?
Secondly. Here is a Universe I've constructed in which ∃ Type:x (x ↔ ¬x)
https://repl.it/repls/SympatheticLovelyCondition
If you want to be really nutty we can say that: ∃ Type:x (x ↔ ¬x)
means I am going to go buy some fresh fruit from Aldi's, thus it is true.
If we tone back the nuttiness so that this: ∃x (x ↔ ¬x)
has its conventional meaning, then we can know it is false.
Re: Truth can be understood as math
Posted: Wed Aug 28, 2019 10:59 pm
by Skepdick
PeteOlcott wrote: ↑Wed Aug 28, 2019 9:41 pm
If we tone back the nuttiness so that this: ∃x (x ↔ ¬x)
has its
conventional meaning, then we can know it is false.
Again. What is this "convention" thing you speak of?
Clearly you are interpreting the formalism the way it suits you to interpret it.
All swans are white, but
this one is black.