Sanity check: If I’m understanding Eleizer and D’Anna correctly, step 8 is valid in PA but not in classical (= first order?) logic. The deduction theorem only applies to proofs in classical logic, therefore this part:
“Applying the Deduction Theorem to Löb’s Theorem gives us, for all C:
((◻C)->C)->C"
is incorrect; you can’t use the deduction theorem on Lob’s Theorem. Everything after that is invalidated, including 2=1.
Is that more or less the point here? I have a good head for math but I’m not formally trained, so I’m trying to be sure I actually understand this instead of just thinking I understand it.
Incidentally: Godel’s Theorem inspired awe when I was first exposed to it, and now Lob’s has done the same. I actually first read this post months ago, but it’s only going back to it after chasing links from a future sequence that I think I finally get it.
Greetings. I am Error.
I think I originally found the place through a comment link on ESR’s blog. I’m a geek, a gamer, a sysadmin, and a hobbyist programmer. I hesitate to identify with the label “rationalist”; much like the traditional meaning of “hacker”, it feels like something someone else should say of me, rather than something I should prematurely claim for myself.
I’ve been working through the Sequences for about a year, off and on. I’m now most of the way through Metaethics. It’s been a slow but rewarding journey, and I think the best thing I’ve taken out of it is the ability to identify bogus thoughts as they happen. (Identifying is not always the same as correcting them, unfortunately) Another benefit, not specifically from the sequences but from link-chasing, is the realization that successful mental self-engineering is possible; I think the tipping point for me there was Alicorn’s post about polyhacking. The realization inspired me to try and beat the tar out of my akrasia, and I’ve done fairly well so far.
My current interests center around “updating efficiently.” I just turned 30; I burnt my 20s establishing a living instead of learning all the stuff I wanted to learn. I figure I only have so many years left before neural rigor mortis begins to set in, and there’s more stuff I want to learn and more skills I want to aquire than time to do it in. So, how does one learn as much truth as possible while wasting as little time as possible on things that are wrong? The difficulty I see is that a layperson to a subject (the C programming language for purposes of this example) can’t tell the difference between K&R and Herbert Schildt, and may waste a lot of time on the latter when they should be inhaling the former or something similar. The “Best Textbooks” thread looks like it will be invaluable here.
A related concern is that some subjects in science don’t lend themselves to easy verification. How does one construct an accurate model of a thing when, for reasons of cost or time, you can’t directly compare your map (or your textbook’s map) to the territory? I can read a great deal about, say, quantum mechanics, but without an atom smasher in my backyard it’s difficult to check if what I’m reading is correct. That’s fine when dealing with something you know is settled science. It’s harder when trying to draw accurate conclusions about things that are politically charged (e.g. global warming), or for which evidence in any direction is slim. (e.g. cryonics)
Something else I’m interested in is the Less Wrong local meetups. There’s one listed for my area (Atlanta) but it doesn’t appear to be active. Finding interesting people is hard when you’re excessively introverted. I’ve tried Mensa meetings, but most of the people there were nearly twice my age and I found it difficult to relate. Dragoncon worked out better (well, almost), but only happens once a year.
A fair number of intro posts seem to include religious leanings or (more frequently) lack thereof, so I’ll add mine: I was raised mildly Christian but it began to fade out of my worldview around the time I read the bit about how disobedient children should be stoned to death. In retrospect my parents probably shouldn’t have made me read the Bible on days that we skipped church. Churches leave that stuff out. Now I swing back and forth between atheism, misotheism, and discordianism, depending on how I’m feeling on any given day, and I don’t take any of those seriously.
Is it still acceptable/advisable to comment in the Sequences, even as old as they are? It looks from the comment histories in them that some people still watch and answer in them. I doubt I’ll muck around too much elsewhere until I’ve finished them.