Your Proving Too Much disproves too much: If we only allow reasoning steps that always work, we never get real-world knowledge beyond "I think, therefore I am.". Some of these reasons for belief make their belief more likely to be true, and qualitatively that's the best we can get.

I did all the exercises above. Here's what I wrote down during the timed sections. (It's a stream of consciousness account, it may not be very clear/understandable.)

Some general thoughts

• I found doing the exercises very enjoyable.
• I think that the answers here could’ve been more to-a-format. These aren't very open-ended questions, and I think that if I’d practiced matching a format that would’ve drilled a more specific tool better. But not clear that's appropriate.
• I didn’t like how all the examples were of the “don’t believe a dumb low-status thing”. Like I think people often build epistemologies around making sure to never be religious, endorse a failed startup idea, or believe homeopathy, but I think that you should mostly build it around making sure you will make successful insights in physics, or building a successful startup, which is a different frame. I would’ve liked much more difficult examples in areas where it’s not clear what the right choice is purely based on pattern-matching to low-status beliefs.
• The post tells people to sit by a clock. I think at the start I would've told people to find a timer by googling ‘timer’ (when you do that, one just appears on google) else I expect most folks to have bounced off and not done those exercises.
• I really liked the ‘reflect on the general technique’ sections, they were excellent and well-placed.

Ex. 8: I believe in a soul because I have a really strong gut feeling.

OTOH, thinking without any intuitions or assumptions at all remains an unsolved problem.

Regarding example 4. Believing something because a really smart person believes it is not a bad heuristic, as long as you aren't cherry-picking the really smart person. prepriors, then everyone says, you had the misfortune of being born wrong, I'm lucky enough to be born right. If you were transported to an alternate reality, where half the population thought 2+2=4, and half thought 2+2=7, would you become uncertain, or would you just think that the 2+2=7 population were wrong?

The argument about believing in Cthulhu because that was how you were raised proving too much, itself proves too much.

Regarding example 4. Believing something because a really smart person believes it is not a bad heuristic, as long as you aren't cherry-picking the really smart person. If you have data about many smart people, taking the average is an even better heuristic. As is focusing on the smart people that are experts in some relevant field. The usefulness of this heuristic also depends on your definition of 'smart'. There are a few people with a high IQ, a powerful brain capable of thinking and remembering well, but who have very poor epistemology, and are creationists or Scientologists. Many definitions of smart would rule out these people, requiring some rationality skills of some sort. This makes the smart people heuristic even better.

"If a tree falls in the woods, but no one is around to hear it, does it make a sound?" doesn't sound like an argument, but a question. "Yes, because the presence of a person with ears doesn't affect the physical behavior of the air" or "No, because air waves shouldn't be considered sound until they interact with a mind" are arguments.

Or do you mean "argument" in the sense of a debate or discussion (as in "we're having an argument about X")?