What is the Barcan Sentence? | Attic Philosophy
ฝัง
- เผยแพร่เมื่อ 24 ก.ค. 2024
- Two logical sentences are central to quantified modal logic - the Barcan and Converse Barcan Sentences. Here, we look at what they are, why they're philosophically contentious, and when they're valid or invalid.
00:00 - Intro
01:25 - Ruth Barcan Marcus
02:25 - Barcan Sentence
02:52 - Converse Barcan Sentence
03:47 - Are they true?
04:01 - Exercise
04:22 - Worked Answer
05:30 - Why it’s controversial
07:19 - When is BS valid?
10:06 - Nested domains model
10:43 - Shrinking domains model
11:12 - When is CBS valid?
11:30 - Summing up
More videos on modal logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
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I was expecting this one! So happy!
Hi Attic, are you planning to do videos on predicate logic? Enjoying your vids btw
Sure, there's some up already (on quantifiers, identity) and more to come soon.
Very helpful! Thanks so much!
You're welcome! Glad you found the videos useful.
Thank you so much for this breakdown.
No worries!
What are the necessary limitations on the Necessitation Rule given that the Converse Barcan Sentence can be proven using it?
This is a difficult issue in modal logic, probably without an ideal solution. To prove CBF, you need the necessitation rule + classical quantifier rules. The usual move is to change the quantifier rules, rather than the necessitation rule. For if something is a theorem, it's logically required, so how could it fail to be necessary? For example, you can change the quantifier rules from classical to free logic, in effect only allowing instantiation and elimination for existing entities. There's a good explanation here: plato.stanford.edu/entries/logic-modal/#QuaModLog
Thanks for mentioning the Kripke controversy, very interesting/disturbing
Also, do you think that actualists should accept the Barcan Formula? Or should we abandon either actualism or the Barcan Formula? Thanks
Where do you weigh-in on the credit between the tag theory and Kripke's causal-historical theory?
I've read 'Modality and Intensional Languages' and Naming and Necessity, it strikes me that Naming and Necessity is generally a more accessible and slightly more developed work. Marcus tends to stage her 'tag theory' as a response to Quine's interpretation challenge, but Kripke responded explicitly to topics of wider interest; descriptivism, analyticity and a priority, I imagine, cast a wider net over philosophical interests. Not that I don't doubt for a second that sexism was a huge hindrance for Marcus, and mention of Marcus' work should at least preface discussion of Kripke's in my opinion (and also, I have no clue why Kripke didn't mention Marcus in his lectures.)
I always mention Barcan Marcus before Kripke when teaching this. Kripke should have done too - I’m sure he knew her work. So at best, it’s poor scholarship.
I know I'm late to the party, but it seems to me the rule ¬∀xF ⊨ Ǝx¬F, is problematic. I mean... what if there are no x's at all? It could still be true (perhaps trivially) that ¬∀xF, without there existing an x which is not-F, no?
There's always at least one thing (in logic, the domain is never empty), and it's either F or not-F. So if not everything is F, then at least something is non-F. You're right that, if the domain was allowed to be empty, then the equivalence between the quantifiers disappears.
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Interesting. That makes perfect sense. So then... Couldn't the untoward consequences of the Barcan formula (like the one you mentioned in your video about your daughter having a sibling) actually be a result of this no-empty-domain rule?
I find the Bacon Sentence tastier and more filling than the Barcan Sentence.
What about the converse bacon?
"If it's possible that there exists a married bachelor, then there exists someone who is possibly a married bachelor". That one seems fine to me, however,
"If a married bachelor could have existed, there there exists someone who could be a married bachelor". Oh yeah, that one sounds weird.
These are strange cases, because they're about impossible situations. In classical logic, with the material conditional, all these sentences are true, simply because they have a false antecedent. It's very interesting to think abut what to do with impossible cases - but maybe not the best case to think about for the Barcan sentence!