But the situation for mathematics is not all good:
As the proof for the uniqueness of the prime factorization is no more valid,
there might be different factorizations in different layers. — Trestone
And what is with liars that speak about all layers?
„LA:= This proposition is not true in all layers“
In layer logic meta propositions about layers and truth values have to be nearly classic:
They can only be true or wrong and have to have the same truth value in all layers >=1.
So if LA is true in layer 1 it has to be true in all layers, so LA is false – in all layers, that would be a contradiction.
If LA is not true in layer 1 it has to be not true in all layers, so LA is true – in all layers, that would be a contradiction.
Therefore LA is not an allowed meta proposition in layer logic. — Trestone
Let's start with a logical paradox:
> "I always lie"
Here is the problem with this statement:
- If that statement is a lie: then I lied about "always lying", which means I must have told the truth at some point.
- If that statement is the true: then I don't always lie, because I just told the truth.
Thus one can never say "I always lie"
Now let's add a bit of truth to the first statement.
> "I mostly lie"
Hopefully you don't know people in your life who mostly lie. But it's still possible for someone to do so. — maytham naei
Thus one can never say "I always lie" — maytham naei
> "I mostly lie"
Hopefully you don't know people in your life who mostly lie. But it's still possible for someone to do so. — maytham naei
Hopefully you don't know people in your life who mostly lie. — maytham naei
Analysis of most classical indirect proofs show — Trestone
by constructing the contradictions we have to use different layers,
and different truth values in different layer are not a contradiction in layer logic. — Trestone
all the proofs you named are valid no more — Trestone
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.