I've done Aristotelian, first order, set theory, and modal logic like broke my brain. someone on Reddit suggested I watch this video and I'm so happy I did. you really made my life a lot less stressful ty.
okie this is actually super cool, this is much more like kants thing on reasoning, always felt a huge gulf between logic and my experience, this is definitely tightening up like to like "reality"
okie cool i think diamond q does follow: D: ◻ p → ◊ p 5: ◊ p → ◻ ◊ p q v q => (q -> q) V q => q, tho in the world the context is different. not sure we can evaluate like that
i'm a little confused on how implication exists for the world, are we moving states? ie for world S5, obviously the other "states" which exist all have q as true, which implies w(5) -> [ ] q given arrow is like travel to, but would we not just simplify q V q as q? i'm also confused if q means (for some propositions in this world this is true and for some it's false) or if it means (all available states of movement have the quantification of the state q as being less than or equal to true : [ ] q -> q) please continue your series :)
Hi Dr. Jago, thank you so much for starting this series on modal logic - something I've wanted to learn for a long time. I just wanted to say that the font was a little bit too small to see in my phone. (And a little too cursive). Nevertheless I eagerly anticipate the next video in the series!
Thank you for the amazing introduction. Short and straight to the point. I come from a different field (foundations of quantum mechanics), and what's driven me to modal logic was Aumann's theorem about "agreeing to disagree". We are here struggling to write up a meaningful version of Aumann's result in the quantum world, and we noticed that what matters there is the "logic" (in a very loose sense now) behind the argument. One thing led to another, and here I am, commenting on your (excellent) video. I got a question, though. Suppose you run and go through all the possible truth values of all possible propositions given a particular graph. Isn't possible to define a propositional logic having just "one world" and as propositions, say, objects like p(s_1) such that (i) you know their truth value and (ii) all the possible modal modifications are now pre-codified in/are part of the propositions? Sorry for the silly question, but I am learning on the fly. Cheers, C.
Thanks Cristhiano! What you're doing sounds really interesting. Not quite sure I get your question. In modal logic, with just one world, there are basically two options: (i) it has a loop to itself or (ii) it doesn't (so no arrows). In (i), each sentence A is materially equivalent to []A and A (ie they have the same truth value in that model). In (ii), A is always false and []A always true. So in one-world models, the [] and don't really do much!
Thank you for giving my question a go. Very much appreciated. Let me try to make my question a bit more precise. Let me start with an example from category theory: forgetful functors basically strips away any underlying structure and takes you back to ordinary set theory. Another example, the set of integers and the set of rational numbers are nothing but the same, as there's a bijection between them. Forgetful functors are too radical, and sets of numbers are too poor structurally-wise, but I wonder if it's possible to fit modal logic within propositional logic while preserving its structure. If the question is still too cloudy, nevermind - sometimes I miss the good and old whiteboard interaction.
Thanks! There’s this one, have a look at the videos on QML & existence: ua-cam.com/play/PLwSlKSRwxX0qXTZKnIT7l4_YAIWpJcZJ9.html I haven’t done anything on the metaphysics of possible worlds yet.
Modal logic builds on truth-functional (aka propositional) logic, so it’s best to learn that first. But you don’t strictly need first-order logic to understand modal logic, and in fact, some courses teach modal before first-order logic.
Its really astonishing, how often it is thought, that possibility and Truth could be different, in Order for there to be necessary truths and only possible ones, often called Contigent. But thus is Not true for it cannot be. What is possible is Not Impossible and vice versa. That is clear. Now what is true is also not False and vice versa. But what is true, is, and what is false, is Not. But all that is, must be possible, and only what is possible, is. Therefore, There is nothing, that is possibly False, in the Sense, that there cannot be what cannot be. Error is of course possible. It Makes No Sense to speak of necessary Truth, as If there could be a Truth, that is Not true, hence necessary. Of whatever is thought, it is Either either true or False about it. There cannot be anything Contigent, for contingencies are contradictory, and the contradictory is the False, and the False is Impossible. By necessity. Necessary and possible Fall together as one Like Truth too. For anything else is contradictory or begging the Question, Like in the Talk of possible worlds in contrast to an actual one, for there cannot be other possible worlds in comparison to the actual, scince this means, that they are actually Impossible, because they are Not actual. And even If one bends ones mind further to absurdity rather then simple understanding, by suggesting that all possible worlds are in fact actual, then nothing would have Changed about the conclusion from above, scince all is in all worlds necessary and also everything about all worlds. They would furthermore be either nothing, scince nothing can deviate from the fact of States in 'this' world directly, or would be other Spaces of this one world.
I have to think, hearing him, about Eric Idle from Monty Python. It's a certain British accent and not unpleasant at all. For the rest, it's too difficult for me although I notice some resemblance with Feynman diagrams, which I understand neither.
I know you aren't a fan of deontic logic, and I'm not really one either, but I feel like you should have at least given it a passing mention when you talked about the different modalities.
Furthermore, what is this Split between worlds supposed to mean and bring? If i have p, and negate it, i could say, that there is a world for both cases, but what is this supposed to say more, then what is already Said in First order Logic, namely, that both States of p can be Put forth by simple Negation? And If one speaks of p and q, it Turns Out to be the Same, scince i say the Same by saying that both or non or either one is true, when i say the Same by naming a different world for any Option. But what is this supposed to Bring, and why bother with this Talk? I assume it is due to the understanding of possibility and necessity, that one takes IT to be somewhat meaningfull to speak of different worlds, since one Thing only of all Options can happen in one world Respectively. But this is again nothing more then using the word possibility in an obscure way, by saying that possibility and necessity can Go apart. But how, scince all Division of worlds describes only the necessary States in each one which are already implied by the Connectors of Logic? Does one get what i mean? The Talk of many worlds is irritating, because it only amounts, If at all to anything, to the different Options by differentiation through logical Operators. Like in a Truth table, where als stand next to each other. No need there to Talk of different worlds, scince one talkes about all of them in Respect to one world, namely the world. The Talk of possible worlds will rather be a relic of past Times, invented with the Goal to indeed think about different worlds as either existing or valid Options, apart from what is then called our world. Really a destinction in an ontological Sense. If Not, please correct me sufficiently, for i Hope it became otherwise clear, that there is Something very shady about that all.
Another way to think of it: try to make sense of modal logic without using possible worlds. Logicians struggled with this for about 50 years, nobody came up with any really good suggestions, until Kripke introduced possible world semantics.
@AtticPhilosophy thank you again for your Answer. I would Like Go make Sense of modal Logic without the semantics of possible worlds, but i dont seem capable of it. I will have to watch the Rest of your Playlist, for which i thank you for having produced it. It becomes difficult to me to understand, why a specific Logic is needed to describe the differences of possibility and Impossibility, but i guess, that there is No Problem in making one either. Or else, i think i could get along with one that speaks of General and particular Relations, as i tried to hint to, where i can make Sense of the semantics of necessity and 'contigency' by referring to Something Like this: A Cat is a mamal. Therefore it is necessary, that If there is a Cat, that it is a mamal, and above an animal and so on. But of the colors of Cats one can speak of one Cat being colored one way, and another another way. Therefore it might not be necessary of all Cats, that they are black, although they will be colored somehow. But how can a Modal Logic Help in this. Or what is it supposed to do now, that i dont understand until now? For i cannot see further. Greetings.
@AtticPhilosophy P.P.S: and with what exactly have they struggeld? Maybe their struggle was Not warented as i suspect so, for there is maybe No need or possibility for a Modal Logic of their imagination.
This is horrible, you didnt explain stuff, you told us the things that you know about modal logic and how can you give examples about types of modal logic.
Yup, this is what I was looking for. I know this playlist is old, but it’s great.
I've done Aristotelian, first order, set theory, and modal logic like broke my brain. someone on Reddit suggested I watch this video and I'm so happy I did. you really made my life a lot less stressful ty.
Thanks! (And thanks Reddit!) To me, modal makes a lot more sense than first-order. You can do so much of it just by drawing nice diagrams!
This is the best channel for learning logic and its diramations.
Loved the video!
Modal logic is by far the best.
Yes, modal logic is great! More coming soon.
Thank you! Always on time for a subject I'm reviewing!
Any time!
This is amazing! You made learning it fun :)
Thanks!
Wow what a great video!!
Thanks!
okie this is actually super cool, this is much more like kants thing on reasoning, always felt a huge gulf between logic and my experience, this is definitely tightening up like to like "reality"
okie cool i think diamond q does follow:
D: ◻ p → ◊ p
5: ◊ p → ◻ ◊ p
q v q => (q -> q) V q => q, tho in the world the context is different. not sure we can evaluate like that
i'm a little confused on how implication exists for the world, are we moving states? ie for world S5, obviously the other "states" which exist all have q as true, which implies w(5) -> [ ] q given arrow is like travel to, but would we not just simplify
q V q as q?
i'm also confused if q means (for some propositions in this world this is true and for some it's false) or if it means (all available states of movement have the quantification of the state q as being less than or equal to true : [ ] q -> q)
please continue your series :)
Hi Dr. Jago, thank you so much for starting this series on modal logic - something I've wanted to learn for a long time. I just wanted to say that the font was a little bit too small to see in my phone. (And a little too cursive). Nevertheless I eagerly anticipate the next video in the series!
Glad you like them! Do you mean my handwriting? Yes good point, I'll try to make it bigger in future videos
Super clear
Thanks!
well explained
Thank you for your help. Greetings from Ecuador
You’re welcome!
Thank you for the amazing introduction. Short and straight to the point. I come from a different field (foundations of quantum mechanics), and what's driven me to modal logic was Aumann's theorem about "agreeing to disagree". We are here struggling to write up a meaningful version of Aumann's result in the quantum world, and we noticed that what matters there is the "logic" (in a very loose sense now) behind the argument. One thing led to another, and here I am, commenting on your (excellent) video.
I got a question, though. Suppose you run and go through all the possible truth values of all possible propositions given a particular graph. Isn't possible to define a propositional logic having just "one world" and as propositions, say, objects like p(s_1) such that (i) you know their truth value and (ii) all the possible modal modifications are now pre-codified in/are part of the propositions?
Sorry for the silly question, but I am learning on the fly.
Cheers,
C.
Thanks Cristhiano! What you're doing sounds really interesting. Not quite sure I get your question. In modal logic, with just one world, there are basically two options: (i) it has a loop to itself or (ii) it doesn't (so no arrows). In (i), each sentence A is materially equivalent to []A and A (ie they have the same truth value in that model). In (ii), A is always false and []A always true. So in one-world models, the [] and don't really do much!
Thank you for giving my question a go. Very much appreciated. Let me try to make my question a bit more precise. Let me start with an example from category theory: forgetful functors basically strips away any underlying structure and takes you back to ordinary set theory. Another example, the set of integers and the set of rational numbers are nothing but the same, as there's a bijection between them. Forgetful functors are too radical, and sets of numbers are too poor structurally-wise, but I wonder if it's possible to fit modal logic within propositional logic while preserving its structure. If the question is still too cloudy, nevermind - sometimes I miss the good and old whiteboard interaction.
At 12:19, wouldn't diamond P also be true since there IS in fact a world it can see where P?
That’s right, you’ve got it!
This is wonderful! Is there a playlist that goes deeper into possible worlds theories?
Thanks! There’s this one, have a look at the videos on QML & existence:
ua-cam.com/play/PLwSlKSRwxX0qXTZKnIT7l4_YAIWpJcZJ9.html I haven’t done anything on the metaphysics of possible worlds yet.
@@AtticPhilosophy Thank you!
Does the graph formed by this necessarily need to be connected? All the examples in the videos seemed to have that property?
No, any directed graphic is good. But unconnected areas of a graph make no difference, because box and diamond can take you only to connected states.
Great vid!
Thanks!
13:23 could it be an exclusive or?
Always inclusive 'or' (unless it explicitly says otherwise)
So, just to clarify, modal logic is inductive?
No, deductive. Good modal arguments preserve truth (at a world).
Good vid
Thanks!
can I learn modal logic without background in basic logic ?
Modal logic builds on truth-functional (aka propositional) logic, so it’s best to learn that first. But you don’t strictly need first-order logic to understand modal logic, and in fact, some courses teach modal before first-order logic.
@@AtticPhilosophy Yeah, I currently have an elective called Modal Logic but I have not taken Propositional Logic before lol
Missing my logic classes since I joined my masters, the prescribed book skipped so many details, finally it feels like I may pass
I was wondering if you could do a video on Epistemic and Doxastic Logic? I've got a test in 2 days and I'm still struggling.. Great video btw!
Sure, I love epistemic logic! Won't be in time for your test tho .. good luck!
@@AtticPhilosophy please do some epistemic logic ! Perhaps relate it to Game Theory? Thanks for your videos :)
How did the test go? :)
Thanks!
You’re welcome!
Its really astonishing, how often it is thought, that possibility and Truth could be different, in Order for there to be necessary truths and only possible ones, often called Contigent.
But thus is Not true for it cannot be. What is possible is Not Impossible and vice versa. That is clear. Now what is true is also not False and vice versa. But what is true, is, and what is false, is Not. But all that is, must be possible, and only what is possible, is. Therefore, There is nothing, that is possibly False, in the Sense, that there cannot be what cannot be. Error is of course possible.
It Makes No Sense to speak of necessary Truth, as If there could be a Truth, that is Not true, hence necessary. Of whatever is thought, it is Either either true or False about it. There cannot be anything Contigent, for contingencies are contradictory, and the contradictory is the False, and the False is Impossible. By necessity.
Necessary and possible Fall together as one Like Truth too. For anything else is contradictory or begging the Question, Like in the Talk of possible worlds in contrast to an actual one, for there cannot be other possible worlds in comparison to the actual, scince this means, that they are actually Impossible, because they are Not actual. And even If one bends ones mind further to absurdity rather then simple understanding, by suggesting that all possible worlds are in fact actual, then nothing would have Changed about the conclusion from above, scince all is in all worlds necessary and also everything about all worlds. They would furthermore be either nothing, scince nothing can deviate from the fact of States in 'this' world directly, or would be other Spaces of this one world.
really cool
Thanks!
I have to think, hearing him, about Eric Idle from Monty Python. It's a certain British accent and not unpleasant at all. For the rest, it's too difficult for me although I notice some resemblance with Feynman diagrams, which I understand neither.
Always look on the bright side of life.
I know you aren't a fan of deontic logic, and I'm not really one either, but I feel like you should have at least given it a passing mention when you talked about the different modalities.
He Kant.
Furthermore, what is this Split between worlds supposed to mean and bring? If i have p, and negate it, i could say, that there is a world for both cases, but what is this supposed to say more, then what is already Said in First order Logic, namely, that both States of p can be Put forth by simple Negation? And If one speaks of p and q, it Turns Out to be the Same, scince i say the Same by saying that both or non or either one is true, when i say the Same by naming a different world for any Option. But what is this supposed to Bring, and why bother with this Talk?
I assume it is due to the understanding of possibility and necessity, that one takes IT to be somewhat meaningfull to speak of different worlds, since one Thing only of all Options can happen in one world Respectively. But this is again nothing more then using the word possibility in an obscure way, by saying that possibility and necessity can Go apart. But how, scince all Division of worlds describes only the necessary States in each one which are already implied by the Connectors of Logic?
Does one get what i mean?
The Talk of many worlds is irritating, because it only amounts, If at all to anything, to the different Options by differentiation through logical Operators. Like in a Truth table, where als stand next to each other. No need there to Talk of different worlds, scince one talkes about all of them in Respect to one world, namely the world.
The Talk of possible worlds will rather be a relic of past Times, invented with the Goal to indeed think about different worlds as either existing or valid Options, apart from what is then called our world. Really a destinction in an ontological Sense.
If Not, please correct me sufficiently, for i Hope it became otherwise clear, that there is Something very shady about that all.
Another way to think of it: try to make sense of modal logic without using possible worlds. Logicians struggled with this for about 50 years, nobody came up with any really good suggestions, until Kripke introduced possible world semantics.
@AtticPhilosophy thank you again for your Answer. I would Like Go make Sense of modal Logic without the semantics of possible worlds, but i dont seem capable of it. I will have to watch the Rest of your Playlist, for which i thank you for having produced it.
It becomes difficult to me to understand, why a specific Logic is needed to describe the differences of possibility and Impossibility, but i guess, that there is No Problem in making one either. Or else, i think i could get along with one that speaks of General and particular Relations, as i tried to hint to, where i can make Sense of the semantics of necessity and 'contigency' by referring to Something Like this: A Cat is a mamal. Therefore it is necessary, that If there is a Cat, that it is a mamal, and above an animal and so on. But of the colors of Cats one can speak of one Cat being colored one way, and another another way. Therefore it might not be necessary of all Cats, that they are black, although they will be colored somehow.
But how can a Modal Logic Help in this. Or what is it supposed to do now, that i dont understand until now? For i cannot see further.
Greetings.
@AtticPhilosophy P.S: please excuse my English, as i am no native speaker.
@AtticPhilosophy P.P.S: and with what exactly have they struggeld? Maybe their struggle was Not warented as i suspect so, for there is maybe No need or possibility for a Modal Logic of their imagination.
first order logic>>>>>>
you resemble daniel radcliffe
probably just cuz you're an white young british adult
This is horrible, you didnt explain stuff, you told us the things that you know about modal logic and how can you give examples about types of modal logic.