There’s evidence in the form of observations of events outside the cartesian boundary. There’s evidence in internal process of reasoning, whose nature depends on the mind.
My previous comment said:
both empirical and tautological evidence
With “empirical evidence” I meant “evidence in the form of observations of events outside the cartesian boundary” and with “tautological argument” I meant “evidence in internal process of reasoning, whose nature depends on the mind”.
When doing math, evidence comes up more as a guide to intuition than anything explicitly considered. There are also metamathematical notions of evidence, rendering something evidence-like clear.
Yes, but they are both “information that indicates whether a belief is more or less valid”. Mathematical proof is also evidence, so they have the same structure. Do you have a way to ground them? Or if you somehow have a way to ground one form of proof but not the other, could you share just the one? (Since the structure is the same I suspect that the grounding of one could also be applied to the other)
We have two examples of what “evidence” could mean here: mathematical proofs and physical events (things happening in a certain place at a certain time). You can study proofs. And you can study physics. There are hardly any arguments where these two different things are predictably interchangeable, so using the same word for them is a problem. Consider the statement “evidence exists”. Making it specific for our two examples, we get “proofs exist” and “physical events exist”. I’m not aware of a good use for these statements (it’s not at all clear what they could possibly mean).
My previous comment said:
With “empirical evidence” I meant “evidence in the form of observations of events outside the cartesian boundary” and with “tautological argument” I meant “evidence in internal process of reasoning, whose nature depends on the mind”.
Yes, but they are both “information that indicates whether a belief is more or less valid”. Mathematical proof is also evidence, so they have the same structure. Do you have a way to ground them? Or if you somehow have a way to ground one form of proof but not the other, could you share just the one? (Since the structure is the same I suspect that the grounding of one could also be applied to the other)
We have two examples of what “evidence” could mean here: mathematical proofs and physical events (things happening in a certain place at a certain time). You can study proofs. And you can study physics. There are hardly any arguments where these two different things are predictably interchangeable, so using the same word for them is a problem. Consider the statement “evidence exists”. Making it specific for our two examples, we get “proofs exist” and “physical events exist”. I’m not aware of a good use for these statements (it’s not at all clear what they could possibly mean).