What is Quantified Modal Logic? | Attic Philosophy
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- เผยแพร่เมื่อ 8 ก.ค. 2024
- Modal logic lets us reason about possibility and necessity. Adding quantifiers, 'for some' and 'for all', allows us to reason about how things have to be and how they could have been. In this tutorial video, we'll introduce the basics of quantified modal logic (QML), setting the stage for more in-depth tutorials.
00:00 - Intro
00:57 - What is QML?
01:28 - Language
02:38 - De Re vs De Dicto
03:22 - De Re possibility and necessity
04:14 - De Re/De Dicto comparison
05:00 - Essential properties
05:56 - Accidental properties
07:14 - Descartes & the Mind
10:33 - QML = logic of philosophy
More videos on modal logic coming next! If there’s a topic you’d like to see covered, leave me a comment below.
Links:
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Thank you so much! This channel is a true gem. You’re helping us understand these really deep topics. Really a breath of fresh air in sea of none sense that passes itself off as philosophy on TH-cam. Keep it up!
I'll try! Glad you enjoyed so far.
Thank you for that English language example! It had the "accidenta"l effect of making me realize the difference between Px and necessarily Px!
Excellent! Glad it helped.
Damn, this helped a ton, its similar to algebra in the sense that letters represent number were as in this case symbols represent letters. Thats atleast how I see it and it helps me understand it better. W work.
Great! Yes, logic is a lot like algebra on abstract values rather than numbers.
I loved the FML joke lol. And also, this is just great content, so thank you.
Thanks!
wow, the FML joke was so unexpected lmao
Really great and helpful! Could you talk more about evaluating validity of arguments or doing proofs/tableau in quantified modal logic? Thanks for all your great videos!
Thanks for the suggestion! I've just added a video on QML semantics, which covers reasoning form the point of view of possible worlds models. (That's how I find it easiest to reason in QML.) For QML proof theory, we can combine first-order and modal natural deduction or proof trees/tableau. I've covered FOL natural deduction & modal proof trees, but not both in one style! I'll add this to the list.
@@AtticPhilosophy Thanks for letting me know! I will def watch it. And that makes sense. I don't think I've watched your FOL natural deduction vids so I'll check that out too
I tried to type Descartes argument into the Tree Proof Generator to validate the argument, but i failed, perhaps because i wasn't able to type the ≠ symbol, and i was not able to find the logical equivalent of ≠ using the available characters. What would be the logical equivalent of ≠ in this situation?
The not-equals symbol abbreviates ~(x=y)
This man is the logical equivalent of Superman
If only!
Can you please make a video example/practice proofs in QML, like you did with PL & FOL? (preferably using natural deduction). Alternatively, are there any free books/PDFs for learning more about/practicing QML? I only managed to find ones about regular modal logic.
Good question - I don't actually know of a textbook with a proof system for QML. Ted Sider's Logic for Philosophers is great on QML, but reasons semantically, not with trees or ND. Constant-domain QML is basically FOL + K + the Barcan sentence. So a ND system would be all the rules for FOL + K, plus a new rule for the Barcan sentence, allowing you to infer []AxB from Ax[]B. And, if you have identity in the language, you also need a 'necessity of distinctness' rule, allowing you to infer []a=/b from a=/b. That's constant-domain K-QML. You can then add the additional rules for B, T, 4, 5, etc.
@@AtticPhilosophy That's great information, thank you! By the way, I also remember you saying that ND for modal logic has []Intro and []Elim rules that use a special kind of assumption (similarly to -->I and vE); do you think you could elaborate more on that?
Great videos. Greetings from Ecuador. I have a question, maybe you can help me. Looking for what is neccesary, we should consider every possible world--a collection of worlds to which I am going to refer as the realm of possiblity. It seems to me that there are stances on the metaphysics of time, where whatever that corresponds to the actual stuff (objects+situations) change. This as well as the realm of possibility. For instance, if we adopt a presentist view, at ta we would have an actual world Wa and a corresponding set of possible worlds (the other possible worlds) Pa, where some of such worlds could be whatever that was actual (or will be actual) at previous times tjta), right? Being so, when we look for what remains the same across possible worlds, we could be looking for what remains the same across time. And doing so would amount to look for something within the realm of possibility Ra={Wa U Pa}. Now, at a different time tb the actual world is Wb, and what is non-actual at such time are elements of the other possible worlds which belongs to the set Pb. That is, at tb the realm of possibility is Rb={Wb U Pb}. My question is: Is there some study about the relations between Ra and Rb? Thank you in advance for your attention and time.
The usual way to combine 2 kinds of modality (temporal and alethic) is by using multiple accessibility relations. So: you have a bunch of points in the model, thought of as temporal stages of possible worlds, plus 2 accessibility relations, T and R. Tsu means s and u are temporally related: u is a future stage relative to stage s. Rsu means u is possible, relative to u. 'Possible worlds' extended over time can be thought of as maximally T-related stages, in order.