There is no difference in principle between “absence of evidence” and “evidence to the contrary”.
There seems to be a fundamental misunderstanding here. By “absence of evidence” I mean our lack of knowledge. I don’t mean that “we checked and there’s no evidence”, as you seem to be suggesting—I mean “we haven’t checked because we don’t know how yet”. We have no evidence either way, that’s a complete absence of any kind of evidence.
You can’t use “faith” “in absence of evidence”
I wouldn’t normally use the word “faith” like this, but it’s the meaning given in the OP: faith is what you have whenever your evidence is less than P=1 (P=1 is possible with math proofs).
P!=NP is also a bad example, we have lots of explicit evidence.
We have evidence, yes, but not as much as we would like (no formal proof). The remaining uncertainty, small as it may be, requires the exercise of “faith” if we’re going to assume P!=NP in practice.
We have no evidence either way, that’s a complete absence of any kind of evidence.
That’s what I meant too. Not having observed evidence is not a privileged state. You can be right or wrong in your beliefs, overconfident or not confident enough, and it may be correct to hold a belief with certainty, all when you haven’t “observed any evidence”, just as well as after you’ve seen a ton of evidence.
Faith is what you have whenever your evidence is less than P=1
Strictly speaking, P=1 never attains, even with math, although with math (or algorithms) you can hoard as much certainty as you want. A class of beliefs with the level of certainty less than, say, 200 bits, is just a bad category to consider, suffering from fallacies of gray and compression.
The remaining uncertainty, small as it may be, requires the exercise of “faith” if we’re going to assume P!=NP in practice.
No it doesn’t. You don’t have to believe in the hypotheses to act on them, it’s everyday decision-making under uncertainty. The opposite side of the coin should too be taken into account, except when the limited resource of attention rules to not think of lesser detail.
That’s what I meant too. Not having observed evidence is not a privileged state. You can be right or wrong in your beliefs, overconfident or not confident enough, and it may be correct to hold a belief with certainty, all when you haven’t “observed any evidence”, just as well as after you’ve seen a ton of evidence.
I agree with all that.
You disagreed when I said:
Rationalists can use faith in the absence of evidence, as in “taking P<>NP on faith because we haven’t proved it yet”. Religious people, however, use faith to believe things despite evidence that contradicts their belief.
How about this reformulation: rationalists act despite having incomplete information and P<1 on their best theories (and sometimes P<<1). The quantity 1-P was called by the OP “faith” (and as I noted it’s not precisely the standard usage). In this sense, rationalists act “on faith”: it means nothing more than that they act as if some theories were true although they can’t be sure from the evidence.
Non-rational people, however, use “faith” (this time the ordinary sense of the word) to discount evidence. IOW, they refuse to update on new evidence that contradicts their faith-supported theory. That’s why they’re not rational, and why any discussion with them is usually unproductive as long as it doesn’t touch on the concepts of rationality and belief.
That was my point in response to the OP: that there’s no rapprochement or agreement to be had on this subject between rationalists and such anti-rationalists.
Strictly speaking, P=1 never attains, even with math
Correction accepted. You can always doubt your computing hardware, your sense and brain, your memory of the proof (induction problem), etc.
No it doesn’t. You don’t have to believe in the hypotheses to act on them, it’s everyday decision-making under uncertainty.
The way you use the word “believe”, it’s as if no-one ever believes in anything. When I act as if a hypothesis was true despite uncertainty, and do so in all circumstances (which don’t provide new evidence against that hypothesis), that’s what I call believing in that hypothesis.
Of course, whenever I act on a hypothesis I get new evidence that relates to it, but as long as that evidence supports the hypothesis the above definition holds.
There seems to be a fundamental misunderstanding here. By “absence of evidence” I mean our lack of knowledge. I don’t mean that “we checked and there’s no evidence”, as you seem to be suggesting—I mean “we haven’t checked because we don’t know how yet”. We have no evidence either way, that’s a complete absence of any kind of evidence.
I wouldn’t normally use the word “faith” like this, but it’s the meaning given in the OP: faith is what you have whenever your evidence is less than P=1 (P=1 is possible with math proofs).
We have evidence, yes, but not as much as we would like (no formal proof). The remaining uncertainty, small as it may be, requires the exercise of “faith” if we’re going to assume P!=NP in practice.
That’s what I meant too. Not having observed evidence is not a privileged state. You can be right or wrong in your beliefs, overconfident or not confident enough, and it may be correct to hold a belief with certainty, all when you haven’t “observed any evidence”, just as well as after you’ve seen a ton of evidence.
Strictly speaking, P=1 never attains, even with math, although with math (or algorithms) you can hoard as much certainty as you want. A class of beliefs with the level of certainty less than, say, 200 bits, is just a bad category to consider, suffering from fallacies of gray and compression.
No it doesn’t. You don’t have to believe in the hypotheses to act on them, it’s everyday decision-making under uncertainty. The opposite side of the coin should too be taken into account, except when the limited resource of attention rules to not think of lesser detail.
I agree with all that.
You disagreed when I said:
How about this reformulation: rationalists act despite having incomplete information and P<1 on their best theories (and sometimes P<<1). The quantity 1-P was called by the OP “faith” (and as I noted it’s not precisely the standard usage). In this sense, rationalists act “on faith”: it means nothing more than that they act as if some theories were true although they can’t be sure from the evidence.
Non-rational people, however, use “faith” (this time the ordinary sense of the word) to discount evidence. IOW, they refuse to update on new evidence that contradicts their faith-supported theory. That’s why they’re not rational, and why any discussion with them is usually unproductive as long as it doesn’t touch on the concepts of rationality and belief.
That was my point in response to the OP: that there’s no rapprochement or agreement to be had on this subject between rationalists and such anti-rationalists.
Correction accepted. You can always doubt your computing hardware, your sense and brain, your memory of the proof (induction problem), etc.
The way you use the word “believe”, it’s as if no-one ever believes in anything. When I act as if a hypothesis was true despite uncertainty, and do so in all circumstances (which don’t provide new evidence against that hypothesis), that’s what I call believing in that hypothesis.
Of course, whenever I act on a hypothesis I get new evidence that relates to it, but as long as that evidence supports the hypothesis the above definition holds.