There’s been an interesting conversation at UD over self-evident truths lately. I think I’ve run up against the Uncommon Descent policy on dissent (don’t dissent), and the whole thing has devolved into “we are right” and “they are liars and also dumb.” But the underlying conversation was interesting, and I’d like to get some outside opinions on it. Especially KN, or anyone else with actual training in philosophy. I’m going to number positions for the sake of convenience, so that people with an opinion can react to any that interest them without feeling the need to engage them all. I’d love to hear where I’m wrong.
So as to my position:
- I make mistakes. I know this as certainly as I know anything—certainly enough not to doubt it in practice. This shows that I do not have the ability to perfectly perceive error in my own thinking.
- I cannot therefore be logically, absolutely certain of anything—not even that A=A. Because the faculties I would use to be perfectly, logically certain of that are the same ones that are not perfect.
- I think the trickiest question here is whether I can be certain that “I think, therefore I am.” But even there, is the fact that I cannot imagine any counter-example because it’s perfectly true, or because I have an imperfect and limited mind? I can’t know without a perfect, limitless mind, so I have to say even here, it’s not logically absolutely certain. (But obviously practically certain, and I don’t doubt it in practice.)
Does that make sense?
Now as to StephenB and Barry Arrington’s position.
- I think one major motivator of the “you’re a liar!” style of debate they’ve adopted is community identification. I’ve been thinking of this as building a wall. The point of the conversation is largely, not entirely, to show that “we think like this:” and “they think like that:”, or more pointedly, “look how stupid and ugly they are.” It makes it very easy to avoid questioning beliefs, because we cling particularly to those notions that separate us from them. It identifies and strengthens the community of us by redefining it in opposition to the ugliness and stupidity of them. And once that wall is built, it’s extremely hard to dismantle. Why on earth would you stop and seriously consider something a stupid and dishonest person says? And what would it say about you if you agreed with them? The wall exists to separate.
- This is not to say their positions are dishonest—I think they’re very upfront with their beliefs, and mean what they say.
- I think this is demonstrated particularly by BA’s habit of bailing out of a conversation and posting a new thread that very explicitly says look at how stupid and ugly those people are!
- I think I’m doing the same thing right now. I think that wall-building is wrong, but I don’t know how not to do it—especially as observing that someone else is building a wall is as good as laying a brick in your own.
- I can try to fight back against that by observing that walls exist to keep people in as well as out; the point is largely to have a bulwark against having to reconsider one’s beliefs and identity. So it’s important to ask, “Am I wrong?” Which I’m doing here, and attempting with some success to do in my own head.
And now the conversation itself. This is tricky because they’re cagey about answering questions. I suspect they know they’re on uncertain ground, and don’t want to commit to a position whose implications they can’t perfectly predict. I think they’re leery of inadvertently contradicting each other, too, because they’re aware that it would be awkward for two people professing infallibility to disagree. So gathering dribs and drabs of what they’ve said, I think this is a reasonably fair representation of their position. I’m not confident that it is, but I’m doing my best.
- Self-evident truths (SETs) exist.
- People can perceive SETs. I refer to the faculty for doing so as “SET-sense,” because it’s alliterative.
- People do not use reason to perceive SETs. If one needs reason to arrive at a truth, it is not a SET.
- People can be uncertain about whether a SET exists.
- People cannot be wrong when they identify something as a SET. No false positives are possible.
- This is some guesswork on my part; SB started calling me a liar rather than answer, and I didn’t bother to ask BA. I think he’s said in the past that no such error is possible, but I can’t recall where.
- I think their position entails “no false positives.” If you can falsely believe that something is a SET, then the very existence of undoubtable SETs is out of reach.
- I’m not certain whether false negatives are possible.
- BA and SB have both suggested in the past that anyone who disagrees with them that it is self-evident that certain moral truths are objectively wrong must be lying, which suggests that the answer is “no.”
- On the other hand, uncertainty is possible for them, which suggests that false negatives might be too.
- Mathematical operations can be SETs.
- 2+2=4 is a SET.
- 17*45=765 is not a SET.
- I don’t think the operation itself, + or *, makes a difference.
- Things that have to be reasoned out aren’t SETs. I think that must include calculation, and I think BA at least agreed with that.
- There is no grey area, in which it’s impossible to tell whether a truth is self-evident or just a possibly flawed intuition.
- This is BA’s position, at least.
- For n+n=2n, we know that:
- If n=2, we have a SET.
- If n+n has to be calculated to get the answer, we don’t have a SET.
- So for those values where n>2 and n+n can be known without reasoning through the addition, we may or may not have a SET.
- Pursuant to F, there are no false positives.
- Pursuant to J, there are no grey areas. It’s a SET or it isn’t.
Whoo! This is improbably great fun. So with all that as background, let’s do a thought experiment. Let’s increment n and see what happens!
If we tested one million people by asking them to solve the iterations (what’s 2+2, 3+3, 4+4, etc.) we could chart out the percentage that got it right. For n=2 and probably 3 and 4 and 5, we’d get pretty much 100%. But that number would start to decline pretty quickly!
Some people, especially uneducated people, would start being unable to answer without doing a calculation. And remember, if you have to calculate it, you aren’t using SET-sense. Others will be uncertain, so also not using their SET-sense. They’re out of the sample—we only care about people who are arriving at an answer without having to guess or calculate it. That means we’re at 100% getting the problem right… or are we?
Some number of people are going to get the problem wrong. As n increases, more and more will do so. At some point, say n=17, we’ll have two groups of people left in the study: those who were confident they were right and answered 34, and those who were confident they were right and answered something else.
Uh oh. Now we have people believing they’ve arrived at a self-evident truth, but being wrong about it. False positives.
It’s possible to be in error about at least some apparent SETs. SteRusJon escaped this by identifying all math problems as SETs, but that’s not BA’s or SB’s position, and I don’t think they’ll back down. That’s one consequence of building a wall: you can’t leave the walled-in area very easily. Having belittled and insulted those who doubted them, it’ll be very difficult for them to consider whether their confidently-asserted positions had inconvenient entailments.
Another escape, and the one I think they’d prefer to use, is to mind-read. Those people who got n=17 wrong didn’t really believe that 17*2=38. They just thought they believed it. I’m dubious of any solution that requires redefining someone else’s belief, and this again introduces the possibility of error. If you can think you’re using your SET-sense, then how do you ever know for a fact that you are?
I think probably BA regrets trying to use math to show how obviously right he is, and will rely in the near future on simpler, more aggressive tactics to build the wall.
But! Maybe I’m wrong. Maybe my logic is off, in one way or many. What do you guys think?