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Comment by Jtsummers | Hacker News Reader

> It's just people having trouble understanding counterfactuals.

You've just described most paradoxes. From the definition of "paradox":

> a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true.

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How odd, I've never come across that definition of paradox. I've always understood it to be purely self-contradictory, like: This sentence is false. If I take it to be false, it's true; if I take it to be true, it's false. The proper understanding is that it actually has no semantic meaning, but it certainly doesn't prove to be well-founded or true.

Using "paradox" for something like this concept though is along the lines of also using it for the phenomenon of people appearing to vote against their self-interest. They keep doing it, we don't understand why - it might be that they're stupid, it might be that we don't understand enough of their perspective, but it just doesn't strike me as a paradox. Not unless every phenomenon we don't understand is also a paradox. Are software bugs paradoxes?

Yeah, this is something that has always bugged be a tiny bit. I was more familiar with the idea of a paradox as something like your definition -- containing an actual contradiction. But it seems to be used instead to describe any initially counterintuitive situation.

It is tempting to attribute this to a technical/non-technical difference (similar to fallacy, which in non-technical discussion has been expanded to basically include almost any bad argument). But somehow the Birthday "Paradox" has managed to stick in probability.

Paradox isn't synonymous with contradiction. Some paradoxes are, or contain, logical contradictions (i.e. they effectively say both X and not X are true) but the term is much broader.

Some of the earliest paradoxes are Zeno's, and they were referred to by that term at the time. For example the paradox that an object that moves towards a point must first cover half the distance, and then half the remaining distance, then half of the remainder, etc. Since this is an infinite number of steps, Zeno playfully argued that motion is impossible. There's no logical contradiction there, just a way of pointing out something counterintuitive about reality and maths.

That's fair, the thing I'm looking for isn't quite a contradiction.

What I like about Zeno's motion based paradoxes is they have this aspect of "here's a reasonable model of motion, and here's the ridiculous result you get from it." There's clearly something wrong in the model, but working it out takes a while, you need someone to come around and invent series first.

After a little reading, I think I just like falsidical paradoxes and don't like veridical paradoxes.

i always heard it called the birthday problem: https://en.wikipedia.org/wiki/Birthday_problem

[weirdly, someone discovered an birthday overlap today at work and i just re-google/wiki'd this today]

Huh, what are the odds that the same mathematical concept will come up in conversation twice on one day? We have invented the Synchronicity paradox, er, problem.

Baader–Meinhof phenomenon or frequency illusion.

Sadly nobody called it baader-meinhof paradox.

Your notion of paradox is more precisely known as an antinomy:

https://en.wikipedia.org/wiki/Antinomy

Yes, all antinomies are paradoxes but not all paradoxes are antinomies.

An antinomy that isn't a paradox would be paradoxical indeed.

>How odd, I've never come across that definition of paradox. I've always understood it to be purely self-contradictory, like: This sentence is false.

That's just one kind of paradox in one domain (say, logic). There are well known named paradoxes of several different types, belonging to several different domains...

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