A few questions:Physics Guy wrote: ↑Fri Jan 30, 2026 9:44 amLike the guy at the party who's been asleep on the couch for a little while and wakes up, I want to come back to the Sorites "heap" paradox that some people keep invoking.
One standard resolution to the Sorites paradox is just to allow a continuum of intermediate states between "heap" and "not a heap", which can be assessed as being more or less heap-ish. Past a certain point, that collection of grains is a darn good heap; below another point, those few specks are definitely not a heap. In between, though, it's just not right to call the collection of little bits as "heap" or "not heap" and leave it at that. At the least you have to assign a rough number to how far along they are between clear heap and clear not-heap.
Even if this intermediate zone is in practice quite narrow, with few instances lying within it, it eliminates the paradox, that was based on the common-sensical axioms that taking one grain away from a heap cannot instantly eliminate its heap status, and neither can adding one grain to a non-heap suddenly make it a heap. If "heap" and "non-heap" are the only options, then these axioms imply the paradox (along with the additional axioms that one object is not a heap, and that an arbitrarily large pile of things is one). What the add-or-subtract-one-grain principle is really getting at, though, is precisely the fact that heap-ness is not actually a binary condition. Removing or adding a grain cannot make the full difference between heap and non-heap, but it may well make something slightly more or less heap-ish.
One interpretation of the heap-to-non-heap continuum is that every collection of little bits has a probability P to be considered a heap, so that it also has a probability (1-P) to be a non-heap. A little pile smack-dab in the middle between heap and non-heap is something for which, if you had to call it heap or non-heap, you could go either way. This perspective on the continuum is an example of what is called "fuzzy logic", where statements are not necessarily true or false, but can have some probability for each.
Fuzzy logic may just found like fuzzy thinking, but there's a lot to be said for it as a practical tool for situations in which we have too little evidence to be completely sure what is true. These are most situations. Fuzzy logic is a natural fit for Bayesian inference. And in Bayesian inference, just as people like MG would seem to want, one is allowed to retain high confidence in a conclusion in spite of strong evidence against it, without even being irrational. One simply needs to have a strong prior.
Bayesian inference reduces logic to a learning rule, which tells you how to revise your previous probability estimates in light of new evidence. The rule is multiplicative, but in a slightly complicated way that ensures that the total probability of all cases together must always be one. Perfectly consistent Bayesian inference allows stubbornness: if one is really, really sure of something, then one is allowed to retain most of that confidence even in the face of seemingly powerful counter-evidence. And it's really not bad that it lets us do that. This feature is the Bayesian justification for not being too fazed by occasional coincidences.
So, yeah, it's not necessarily irrational for a conservative Mormon to just shrug off all kinds of awkward evidence and keep insisting that the Mormon stuff is all true. The conservative Mormon just needs to have a prior probability for it being true that is very close to 100%. In the heap-of-sand analogy, they need a definition of "heap" that barely concedes that the whole Sahara is a little bit heap-ish, and won't give a firm vote of "heap" to anything less than the planet Dune. That position may not be unassailable, but what is wrong with it is not exactly that it's illogical.
In case anyone has read this far, though, here is what I actually want to say about Bayes and Sorites.
These are not high cards to play. They are not sophisticated and subtle grounds that automatically make conservative viewpoints respectable. The Sorites "paradox" is elementary analysis of language, and Bayes's theorem is two lines of basic arithmetic. "Sorites" and "Bayes" may seem like good names to drop if one isn't familiar with them, but the ideas involved are quite basic.
Saying, "From my perspective your pile of evidence does not make a heap," or, "My prior is so strong that your evidence hardly budges my needle," is only a fancy-sounding way of saying, "BLAH-BLAH-BLAH I CAN'T HEAR YOU BECAUSE MY EARS ARE COVERED!"
Sometimes it's smart to cover one's ears and ignore things. One is not obliged to debate every soundbite, or throw away all the science textbooks every time somebody posts a weird TikTok. Invoking Sorites or Bayes is not an argument, though. It's just stonewalling.
Yes, we can all stonewall, and sometimes we should. But everyone knows that. So you don't get any respect or credit just for exercising your right to ignore things. If you want credit for anything more than that, you have to make an actual case of some kind. Invoking your personal freedom to believe as you wish is not making a case. And name-dropping Sorites or Bayes doesn't make it into making a case, because those are just fancy-sounding ways to say that you are free to cover your ears.
Where would you say that epistemology enters into this?
What would you consider to be a “strong prior”?
Is “fuzzy logic” another way of expressing ambiguity that might be more acceptable to logicians?
How did your own epistemology enter into the substance of your post? What is your epistemology? In your opinion as you consider types of knowledge, sources of knowledge…what are your own “priors”? As you consider the branches of epistemology…naturalized epistemology, social epistemology, and historical epistemology…do you place a higher preference on one over another?
As a matter of fact, let me say I really enjoyed your post. Food for thought.
Regards,
MG
