What is the Paradox of Linguistic Elegance? (Ockham's Razor)
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- čas přidán 25. 07. 2024
- An explanation of the paradox of linguistic elegance, a more general version of the Grue Paradox, also known as Nelson Goodman's New Riddle of induction.
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While it's a good point that linguistic simplicity isn't necessarily an objective measure of simplicity, it does not follow that there is no objective measure of simplicity, or that it's all arbitrary. While perhaps not the best example, we have objective measures of simplicity such as Kolmogorov complexity. There is also an interesting new field of Assembly Theory which studies complexity of systems as the number of steps needed to construct them.
This is a fantastic argument against those who are into game design that want to make simple interfaces yet avoid sophistication and intellectualism of the engine.
He should do another series like 100 days of Logic. 90 days of Nelson Goodman? 90 days of Neurath? 100 days of Wittgenstein (or Whitehead). 500 days of Phillipa Foot. 50 days of G.A. Cohen. The possibilities are endless.
I feel like the section on risk is aimed at me specifically :D
So, I don't quite follow how exactly the principle of explosion is useful in a counterargument to parsimony as epistemic efficiency and thus prudence, because even setting explosion aside, if a theory posits any one thing that turns to be false... the theory is just false, strictly speaking (although another very similar theory, another "version of this theory", could still be possibly true). What we're trying to minimize is the chance of anything the theory posits turning out false at all. It's fine that "one hit kills" via explosion, because that's true anyway, and that's just all the more reason to limit the odds of getting hit even that once.
As for the matter of picking one assumption that's very unlikely versus many assumptions that are jointly more likely than the one, that's where the part about equally-well explaining the observations comes in. Nobody says that a simpler theory is always more likely to be true regardless of anything else; getting all the observations correct comes first, and then within that limit, simplicity is preferable. This is like how minimizing cost is not the overriding criteria for a pragmatic endeavor, because if you spend too little to get the job done you've failed; it's only when you spend more than necessary to get the job done that you needlessly take on risk of loss if the endeavor fails.
But, of course, the exact threshold for how much expenditure will in fact get the job done successfully is not certain, there's a fuzzy boundary there, so really what we're looking for in practical strategizing is to spend when the spending's increase to your odds of success outweighs its increased exposure of you to loss in the case of failure. The epistemic analogue of that fuzzy boundary of success is probability, so adding complexity when it increases the overall probability of your theory -- the odds of the theory successfully explaining all the observations -- is worth it. But then needlessly adding more complexity that doesn't justify itself by increasing the probability of the theory, that isn't needed to make the theory adequately explain the observations, just exposes it to greater risk of turning out to be wrong.
And as for the broader topic of this video and the third point about language, that's why I've made the point on many previous videos that it's about information content, not number of statements or anything like that, so yeah I basically agree that merely linguistic elegance is not worth anything; although, see my previous comment on Grue for a little more on that topic.
Before you even said the word "grue", I was already thinking "ugh this sounds like that grue nonsense".
Grue is a more "complicated" (not certain that's the best adjective but lets go with it) concept than green (or blue) because in order to teach someone the word green from scratch, like you teach a child, you just need to show them sets of things that differ in only one phenomenal aspect, their color, so they can infer that the word green refers to that one property that things in one set have and things in the other set lack; while to teach someone what "grue" means in that same regard, you have to show them sets of pairs of colored things and dates, where the colors don't reliably differ between the members of the two sets, and the dates don't reliably differ between the members of the two sets, but the relationships between color and date do reliably differ between the members of the two sets.
This video is missing from the Ockham's Razor playlist.
I'm writing a thesis on Modal Meinongianism and part of it discusses paraphrasing and choices between ontological and linguistic simplicity and the relation between these two sides. May i ask you for more references and resources on this matter?
"A pint's a pound
the world around"
The Tamil Journal of Mathematics will have a field day with thia.
Elegance in theories is a very old idea... That comes from the Greeks (at least, as far as we know) and we can see (read) how much presence it has throughout the history of ideas
There is a lot room in the section about “preference” to talk about “utility” instead. Finding a useful language demands a lot more than changing a number of rules and conventions for a single discrete sentence or claim. Science should be in the business of building language that is useful for navigating phenomena, and the same rules apply like any other language: you’re not going to change all the rules to describe one phenomena if the new rules aren’t more useful overall. You’ll still have unavoidable issues with the community using the language, but I’m a pragmatist, so this is par for the course for me anyway.
"Elegance" is pretty subjective. Some proofs are "Beautiful". I think you have to study math for a long time to understand. Some proofs are simple, and those are often elegant and even clever. In the end a proof is a proof even if it's an ugly duckling
How is it a paradox?
This is why saying things mathematically is always more elegant than using a natural language - in addition to all the other benefits of stating theories mathematically.
Hi Carneades, I'm an atheist living in a Muslim society. Often when I debate with them about things that are immoral for me, such as killing apostates or slavery, they tell me that as an atheist I don't have any source of morality, and so, I can't tell what's right and wrong, good and evil. And the example they often say is as an atheist "What is your reference to say that incest is bad or evil, or that zoophilia is bad or evil, if harm is your unique reference then when it's with consent is it still immoral?", can you please help me answer this?
Ok: Given a topology on the set of all possible worlds, a proposition is “simple” if the subset of worlds in which it is true is simply connected.
This needs elaboration I feel
I'm getting a sense that this doesn't work just due to how many different reasons something could be true