Conceptual Truth can be understood as math

What is the basis for reason? And mathematics?

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Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » 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.

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

Re: Truth can be understood as math

Post by PeteOlcott » 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)

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » 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
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

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

Re: Truth can be understood as math

Post by PeteOlcott » Wed Aug 28, 2019 9:41 pm

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.

Skepdick
Posts: 1846
Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » Wed Aug 28, 2019 10:59 pm

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.

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