First, consider the common definition for "faith." Though they vary, perhaps the best one I've seen is
Faith (n.): Belief without evidence or in spite of contradictory evidence.Of course, this "or" is inclusive, as in it could account for both at the same time, and it provides for us a very clear understanding of what faith is doing when it comes to the (Bayesian) reasoning process. Indeed, it does exactly what I claimed it does (by claiming that the OTF has the goal of undoing these effects) in my previous posts about Bayes's theorem and the OTF.
So this article can stand alone, allow me to provide a very quick recap of the meaningful numbers in Bayesian analysis.
- P(h|b): the probability that the hypothesis h is true given background knowledge b, but not including the role of evidence. This is called the "prior probability," because it is an evaluation or guess made prior to examining the evidence obtained by testing the hypothesis against some body of evidence, e.
- P(e|h,b): the probability that the body of evidence e is explained by the combination of our background knowledge b on the assumption that our hypothesis h is true, called a "consequent." I will call this the "positive consequent," for convenience. In a sense, this is an estimate of how well the body of evidence is actually explained by the hypothesis.
- P(e|~h,b): the probability that the body of evidence e is explained by the combination of our background knowledge b on the assumption that our hypothesis h is false (the tilde ~ means "not" in logical shorthand), also called a "consequent." I will call this the "negative consequent." In a sense, this is an estimate of how well the body of evidence is explained by other hypotheses than the one we are testing.
- P(h|e,b): the probability that our hypothesis is true after weighing background knowledge b and the evidence e, called the "posterior probability." The goal of most Bayesian analysis is to obtain this number (so it is, usually, "the answer").
I want to define faith according to these numbers, then, using the definition I gave above:
Faith (n.): A cognitive bias in which a person overestimates the prior probability, overestimates the positive consequent, and/or underestimates the negative consequent in a Bayesian analysis.Indeed, I argue that "overestimating the positive consequent" and "overestimating the prior probability" are technical ways to say "believe without evidence" and that "underestimating the negative consequent" is likewise a technical way of saying "believe in the face of contradictory evidence," although it's certainly not so cleanly cut since these categories overlap somewhat.
(Though the overestimate of the prior is more obviously the way to go with "believe without evidence," overestimating the positive consequent means "believing on false evidence," which is seeing evidence that isn't actually evidence, which implies of believing without actually having evidence since belief follows what is believed to be evidence.)
The effect is pretty straightforward:
- Overestimates to the positive consequent will have the effect of overestimating the posterior probability, which measures the likelihood that the hypothesis is true after evaluating the body of evidence.
- Underestimates to the negative consequent will also have the effect of overestimating the posterior probability.
- (Incidentally, overestimating the prior probability also overestimates the posterior probability.)
The advantage of this definition is that it puts the cognitive bias of faith into clear contrast in terms of how it impacts the reasoning capacity of a person that holds it. In this light, it makes it very difficult to accept, at least in general, that this cognitive bias can be considered a "virtue."
N.b.: Skepticism is often attacked at this point as being a particular perspective that engages in its own cognitive biases (specifically to lower the posterior probability by whatever means necessary), but indeed, skepticism is functionally the attempt to remove all sources of cognitive bias from these sorts of analysis and to accept the (unbiased) posterior probability for what it is. Specifically and importantly, skepticism does not attempt to raise or lower the "real" posterior probability, but rather it seeks to come as close to that number as possible and then accept it (though new efforts at refinement are always welcomed). In that sense, one could say that skepticism is a bias against biases, but ample evidence (e.g. all of the accomplishments of science in terms of predictive power) support the claim that a tendency to avoid biases provides accurate, trustworthy information vastly more often than does biased information. Thus, calling it a "bias" really misses the meaning of the word "bias" and comes off, at best, as prevaricating.
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