Begin here and read up to part 5 inclusive. On the margin, getting a basic day-in, day-out wardrobe of nice well-fitting jeans/chinos (maybe chino or cargo shorts if you live in a hot place) and t-shirts is far more valuable when you start approaching fashion than hats. Hats are a flair that come after everything else in the outfit you’re wearing them with. Maybe you want to just spend a few hours one-off choosing a hat and don’t want to think about all the precursors. But that can actually make you backslide. If you look at their advice about hats, you’ll see that pork pies and fedoras are recommended, but it’s well-known how badly a fedora can backfire if you aren’t very careful.
(For example, I’m still in the ‘trying new t-shirts/shirts/jeans/chinos/shoes with an occasional jumper purchase’ phase after about a year, 18 months. Still haven’t even got to shorts. You might progress faster if you do shops more often or have a higher shopping budget. But suffice to say hats are a long way in.)
There is a known phenomenon of guys walking around with a fedora or brimmed hat or whatever with a poorly coordinated outfit, dirty clothes, odour, bad fit, etc. basically not having the basics down before going intermediate. In these cases you will lose points with a lot of people because they will cringe or think you’re trying to compensate. You may or may not have been engaging in similar thinking when making this thread, but watch out for that failure mode.
Supplementary reading and good to get a yay or nay before buying something, or to get recommendations within a type of garment: /r/malefashionadvice/
Fashionability and going for safety helmets/caps might be divergent strategies though. If you were purely optimizing the former, what I say above might be relevant. If the latter, just getting some Crasches and calling it a day might be enough.
Why can’t the deduction be the evidence? If I start with a 50-50 prior that 4 is prime, I can then use the subsequent observation that I’ve found a factor to update downwards. This feels like it relies on the reasoner’s embedding though, so maybe it’s cheating, but it’s not clear and non-confusing to me why it doesn’t count.