I’m not interested in more rigorous methods because I am interested in bridging the gap between the rationalist and, let’s say, those who have a propensity of demanding lower levels of evidence for beliefs.
There’s no bridging this gap because the non-rationalists (e.g., honestly religious people) are ultimately uninterested in objective truth.
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.
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.
It’s wrong. There is no difference in principle between “absence of evidence” and “evidence to the contrary”. You can’t use “faith” “in absence of evidence”, you can only use intuition knowing that you expect it to come to the right conclusions because of the evidence that your mind processed but you don’t see consciously; also, you always start from some priors, including the priors as rules for reacting to new evidence. P!=NP is a bad example, we have lots of explicit evidence. No one is entitled to take beliefs on faith.
This is true, but I don’t think DA was arguing that is is OK to take beliefs on faith. His point was that the following two statements display significantly different and distinct types of faith:
(A)”I don’t have much evidence to decide between A and ~A, but I like A, so I believe A is true.”
(B)”I have substantial evidence that ~A is true, but I want A to be true, so I will believe in A and consider myself virtuous for believing A in spite of the evidence.”
Neither is properly justified, but (A) is only slightly harmful, so long as you are open to new evidence and willing to reupdate on it accordingly, and so long as you aren’t making important decisions based on this false certainty. (B) is insidious, for once you take this stance, reality and reason are forever your enemies. This sense of faith is entirely contradictory to that used by AK.
Yet, this is exactly what the religious mind-set insists must be done.
Is it the case that this tendency will spill over into other areas of life, and in their desire to either explain, or explain away phenomenon for which they have no experience?
My personal intuition says yes.
As for absence of evidence I see on the Richard Dawkins and Sam Harris websites all the time, people who insist that absence of evidence allows them to retain beliefs which are highly doubtful (that tendency to have beliefs that are not allowed to be challenged because they must be respected).
I guess what I am saying is that I agree with you, but that you have only nicked the top of the iceberg.
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’s no bridging this gap because the non-rationalists (e.g., honestly religious people) are ultimately uninterested in objective truth.
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.
It’s wrong. There is no difference in principle between “absence of evidence” and “evidence to the contrary”. You can’t use “faith” “in absence of evidence”, you can only use intuition knowing that you expect it to come to the right conclusions because of the evidence that your mind processed but you don’t see consciously; also, you always start from some priors, including the priors as rules for reacting to new evidence. P!=NP is a bad example, we have lots of explicit evidence. No one is entitled to take beliefs on faith.
This is true, but I don’t think DA was arguing that is is OK to take beliefs on faith. His point was that the following two statements display significantly different and distinct types of faith:
(A)”I don’t have much evidence to decide between A and ~A, but I like A, so I believe A is true.”
(B)”I have substantial evidence that ~A is true, but I want A to be true, so I will believe in A and consider myself virtuous for believing A in spite of the evidence.”
Neither is properly justified, but (A) is only slightly harmful, so long as you are open to new evidence and willing to reupdate on it accordingly, and so long as you aren’t making important decisions based on this false certainty. (B) is insidious, for once you take this stance, reality and reason are forever your enemies. This sense of faith is entirely contradictory to that used by AK.
Yet, this is exactly what the religious mind-set insists must be done.
Is it the case that this tendency will spill over into other areas of life, and in their desire to either explain, or explain away phenomenon for which they have no experience?
My personal intuition says yes.
As for absence of evidence I see on the Richard Dawkins and Sam Harris websites all the time, people who insist that absence of evidence allows them to retain beliefs which are highly doubtful (that tendency to have beliefs that are not allowed to be challenged because they must be respected).
I guess what I am saying is that I agree with you, but that you have only nicked the top of the iceberg.
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.