What does “logically coherent” mean?
Good question!
I’m thinking sometime like, why do we trust PA?
It is because it is:
Logically consistent
Never lies (i. e. its outputs are the same as its conclusions)
And I’m thinking something like that, only in a person.Well, it does’t have to be a person, but my intuition prefers to think in terms of personhood.
“It is provable in PA that X is true” translates to “I am a logically coherent entity and I am telling you that X is true”
What do you mean by “its outputs are the same as its conclusions”? If I had to guess I would translate it as “PA proves the same things as are true in every model of PA”. Is that right?
No I just literally mean it cannot lie.
A human can hold one model of the world in his mind, but say something that fits with a different model of the world. A lie.
PA does not do that.
So I’m making it clear that I’m talking about entities like PA which do not (or cannot) lie.
What does “logically coherent” mean?
Good question!
I’m thinking sometime like, why do we trust PA?
It is because it is:
Logically consistent
Never lies (i. e. its outputs are the same as its conclusions)
And I’m thinking something like that, only in a person.
Well, it does’t have to be a person, but my intuition prefers to think in terms of personhood.
“It is provable in PA that X is true” translates to “I am a logically coherent entity and I am telling you that X is true”
What do you mean by “its outputs are the same as its conclusions”? If I had to guess I would translate it as “PA proves the same things as are true in every model of PA”. Is that right?
No I just literally mean it cannot lie.
A human can hold one model of the world in his mind, but say something that fits with a different model of the world. A lie.
PA does not do that.
So I’m making it clear that I’m talking about entities like PA which do not (or cannot) lie.