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| I see stuff from Mental Floss from time to time. As I'm sure I've noted before, I don't really trust their fact-checking (if, indeed, any takes place). And I'm entirely too lazy to fact-check things point by point. But sometimes, something catches my eye enough to share; I just feel like I have to throw in the disclaimer. Okay, well, my mind remains firmly un-boggled after reading this, but that may be because I'm familiar with the ideas. Or it could be because I've become jaded, cynical, and almost completely out of shits to give. In any case, as the headline notes, there are 20 of them here. The URL says 10, but apparently, that's because they updated the article at some point. I'm not going to bore you with all 20, but I have comments on some of them. A paradox is a statement or problem that either appears to produce two entirely contradictory (yet possible) outcomes, or provides proof for something that goes against what we intuitively expect. A fair enough definition, I think. Delving into the details of what makes a paradox paradoxical can give us new insights, and often shows that "common sense" is bullshit. But most paradoxes that I've encountered aren't paradoxes after all, or have a very simple solution, or result from the imprecision of language. There might be exceptions. Take, for example, the sentence: "This sentence is false." It's a pretty famous example of a paradox (and shows up on the linked list at #7), because if the sentence is false, then it's true; while if it's true, it's false. Hell, Spock used it in the original Star Trek to make an AI run around in mental circles until it exploded. But here in reality, it's merely a reminder that things aren't always either heads or tails, one or zero, true or false, no matter how much we might want things to be that simple. So, some of the other examples: 1. The Paradox of Achilles and the Tortoise The Paradox of Achilles and the Tortoise is one of a number of theoretical discussions of movement put forward by the Greek philosopher Zeno of Elea in the 5th century BCE. As far as I know, all of Zeno's paradoxes are essentially the same idea. What's interesting about them now isn't the paradoxes themselves, but that it took 2000 years for someone to come up with a compelling reason (other than "common sense," which is not compelling at all) why they're not paradoxes. The trick here is not to think of Zeno’s Achilles Paradox in terms of distances and races, but rather as an example of how any finite value can always be divided an infinite number of times, no matter how small its divisions might become. Well, kind of. What it took was Newton and Liebniz developing (mostly independently) a new system of math that addressed the infinitesimal. 2. The Grandfather Paradox This, along with a few other time-travel paradoxes (another is noted in the article), has a simple way out: perhaps time-travel, at least as it's presented in popular fiction, is flat-out impossible. I've often said that imagining the impossible is one of our great superpowers, but like all superpowers, it can be used for good or evil. Or, in the spirit of what I said above, something else entirely. 4. The Ship of Theseus Paradox One of the more famous paradoxes, thanks in part to the Marvel show WandaVision, is the Ship of Theseus Paradox. Here’s a brief summary. In the interest of time and space (specifically, my time and space in this blog), if you're not familiar with this one, go to the article or, better yet, find it on Wikipedia.  I'm including this one because I don't really consider it a paradox. Though I think of myself as a materialist, I can think of an analogy: our own bodies. It's been bandied about that all of our cells replace themselves every seven years. This isn't really true; some cells replace faster, some slower, and some do, indeed, hang in there for life (though their individual sub-components may be replaced). And yet, I remember things that happened to "me" as a kid, and I feel continuity with Kid Me, through memory and experience. The point being that, in my view, the key to identity isn't physical components, but pattern. As kind of an aside, I sometimes imagine a band whose members individually swap out, until none of the original band members remain, but the band plays on, with the same name. I'm sure this has happened, and yet no one has named themselves "Band of Theseus." 5. and 6. The Sorites Paradox and The Horn Paradox These being not nearly as famous as the previous paradoxes, I was tempted to skip them. But then I realized that the list item includes something I've been saying all along: The Sorites Paradox is all about the vagueness of language. Because the word heap doesn’t have a specific quantity assigned to it, the nature of a heap is subjective. It also leads to false premises. Sometimes, paradoxes are easily resolved once we remember that language is imprecise. 7 through 10 are really the same paradox. I referred to it above: "This sentence is false." 11. Newcomb’s Paradox We can safely dismiss any "paradox" that hinges on the existence of an omniscient entity. Not that we shouldn't think about it, but don't expect to find a definitive answer. 12. The Dichotomy Paradox Lazy bastards. This is just a restated Zeno paradox, and has the same solution: calculus. Same with #14 (well, the first #14; they flubbed and presented two #14s). I'm skipping #13 entirely because it relies on people not understanding probability theory, which, well, I think more people understand the basics of calculus, if that tells you anything. (the second)14. Galileo’s Paradox of the Infinite I don't pretend to understand everything about mathematics, myself, but I do know that this one was made obsolete by set theory in, like, the 19th century or something. 15. The Potato Paradox Also fixed by understanding mathematics. 16. The Raven Paradox Also known as Hempel’s Paradox, for the German logician who proposed it in the mid-1940s, the Raven Paradox begins with the apparently straightforward and entirely true statement that “all ravens are black.” Yes, yes, I know. Albino or leucistic ravens exist, and they're not black. This is not the way out of the paradox, though. Assume, for the sake of argument here, that all ravens are black. This is matched by a “logically contrapositive” (i.e. negative and contradictory) statement that “everything that is not black is not a raven”—which, despite seeming like a fairly unnecessary point to make, is also true given that we know “all ravens are black.” By "fairly unnecessary," I think they mean "tautological." 17. The Penrose Triangle This is more of an optical illusion than a "paradox," leading me to believe that maybe these word-logic paradoxes should be considered "cranial illusions" or something, to emphasize that they take advantage of our limited mental capacity the way optical illusions take advantage of our limited optical capacity. You know the famous duck-rabbit illusion?  No one calls that a paradox, as far as I know. And yet, it shares traits with some of the more wordy paradoxes.Apparently to make up for repeating #14, they skip #18. So there's still 20 here. The last two are just reminders that math can't always be described using plain language, which we should already know, because if it could, they wouldn't have come up with precise mathematical notations. So, yeah, congratulations if you made it this far, or skipped down to here. To summarize: most paradoxes aren't paradoxes at all, but if they make us think, well, mission accomplished. |
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