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.
Often when talking with people of faith about the issue of atheism, a common response I get is:
Any atheist who has ever talked to a theist has likely encountered this line of reasoning. There is a distinction to be made between the glorifying of faith as evidence of truth, as theists do, and the desire to become less faithful in our understanding, as the rational truth seeking person does.
As has been discussed previously, realistically P = 1 is not attainable, at least for the foreseeable future. Nor is P=1 necessary to be comfortable in the universe. Richard Feynman and Carl Sagan among others, feel the same way. We know that heuristics “fill the gaps” in knowledge of recognizable scenarios such that we can comfortably demand less evidence and still come to a reasonable conclusion about our surroundings in most cases. We also know the myriad of ways in which those heuristics fail. Much has been written about uncertainty in the decision making process and I would imagine it will be the focus of much of the future research into logic. So, I have no problems concluding that there is some level of faith in all decision making. How much faith in a claim am I comfortable with? The way in which I have been thinking about the different levels of "faith" recently is as a sliding bar:
On the left side, natural evidence is indicated in blue which is comprised of data points which indicate to the observer the natural proof of the argument. On the right, faith is indicated in red which is comprised of either counter evidence for the claim or a lack of information. The bar’s units can be anything (probability, individual records) so long as both sides are measured in equal parts.
A few examples:
Claim: Natural and sexual selection as described by Charles Darwin accurately describes the processes which develop biological traits in separate species.
I agree with this claim with 99% natural evidence in the form of observed speciation and fossil and geologic discoveries and accept 1% faith because, well, anything can happen:
Claim: The price of Human full DNA sequencing will fall below $1000.00 before 2012.
I agree with this at 80% natural evidence based on the projection that the price will continue to fall at the same rate that it has and accept 20% faith based on the fact that predictions failed for 2008 and 2009
You get the idea.
I started noticing a few years back that most rational people, and in general people within scientific and analytic communities, generally needed to slide their evidence meter pretty far to the right before they would accept a premise, even tentatively. After all, even frequentists, as flawed as their methodology may be, still chose 95% as the conventional level of significance. Conversely with a meter far to the left, demanding much faith, most rational people I have found choose to reject those claims.
It’s not a perfect method, nor is it terribly rigorous. However 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. I think the scale method is a grounding point for discussion between two people who hold different views on a subject. I am of the mind that this helps the average person who has never heard of probability theory grasp the idea and why one person's cause for faith is another person's cause for natural evidence. This way, the faithful can discuss why the incorruptibles are a miracle and proof of faith and another can point to the evidence of embalming, mummification or preservation like burying environment in which they were buried.
One question I have myself about the methodology: would the most rational individual restrict themselves to two scales for all claims; one for acceptance and another for rejection?
Any refinements are welcome – it’s an open source methodology.
My scale of trust in my scale method is 50% evidence and 50% faith.