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I’m confused by this jump to the natural world: > could you encode in pure logic how a dog behaves Assuming we knew enough about how a dog behaves (or less am
by bazoom42 7mo ago
I’m confused by this jump to the natural world:
> could you encode in pure logic how a dog behaves
Assuming we knew enough about how a dog behaves (or less ambitiously, a more primitive organism) I would assume this could be described in a formal language. But why would Principia be needed for this? Math have been used to model natural phenomena a long time before Principia.
- ergonaught 7mo ago> I would assume this could be described in a formal language The assumption is the first problem, no? If the formal language is complete, it must be inconsistent. If it is consistent, it must be incomplete. If the language is incomplete or inconsistent, you may be unable to encode dog behavior in it.
- bazoom42 7mo agoThe article use “describing the behavior of a dog” as something people began to think was possible because of Principia. This is what I don’t get. Was this thought impossible before Principia? On what grounds? What about describing an electrical circuit formally? Surely this was thought possible before Principia was published.
- roxolotl 7mo agoThe assumption made by many in the early 20th century, spurred on by the recent successes of unification and formalization, was essentially that we could formally describe the entire universe. Godel’s proof shows that if you attempt to formally describe something there’s either an inconsistency or it’s incomplete. That doesn’t mean you cannot describe the behavior of a dog formally but it does mean the same formula which encodes the behavior will either be inconsistent or incomplete. It might only be inconsistent or incomplete when applied outside of defining the behavior of a dog though. That’s why the little preamble about unification exists in this post but it’s not very well tied into the rest of the post.
- bazoom42 6mo ago> Godel’s proof shows that if you attempt to formally describe something there’s either an inconsistency or it’s incomplete. The “something” Gödels proof talks about is axiomatic systems. It doesn’t talk about physical objects.
- coldtea 7mo ago>This is what I don’t get. Was this thought impossible before Principia? On what grounds? Even the full formalization of mathematics wasn't considered certain (*) before Hilbert/Principia and those 20th century attempts. Much less the formalization being applied everything in the physical world or even animal behavior. * in retrospect rightly so, because it wasn't, at least not without inconsistency/incompleteness.
- coldtea 7mo ago>Assuming we knew enough about how a dog behaves (or less ambitiously, a more primitive organism) I would assume this could be described in a formal language. But why would Principia be needed for this? It explains this directly before that phrase: "Their language was dense and the work laborious, but they kept on proving a whole bunch of different truths in mathematics, and so far as anyone could tell at the time, there were no contradictions. It was imagined that at least in theory you could take this foundation and eventually expand it past mathematics: could you encode in pure logic how a dog behaves, or how humans think?" >Math have been used to model natural phenomena a long time before Principia. Which means little in this context. The question posed wasn't if you can use some math to describe some natural phenomenon. The question posed was whether one could model the whole thing (e.g. how a dog behaves) in a formal language - not just take some isolated equations and apply it to this or that aspect of phenomenon (especially if it's a mere approximation). That they already knew, e.g. the equations for planetary motion.
- bazoom42 7mo agoSo would it be just as correct to use an electrical circuit as example, i.e. before Principia it was not believed possible to model an electrical circuit in a formal language?