I just want to say a big big thank you for these videos! I have a pass for progression formal logic university module which I just resat yesterday, I have to say you saved me, I went from not understanding modal logic to being able to do it pretty well! Your videos essentially have hopefully saved me from wasting a year as a external student resitting this module.
Thanks for this video. It really helped me. The exercises you added at the end of the video are great but where are the solutions? I will appreciate if you add a document or make a video to that effect. Nice one!
I don't see why we are able to close a whole branch by finding a contradiction in only one opened world. I've asked this question on Philosophy Stack Exchange: philosophy.stackexchange.com/q/57135/29944 Thank you for the video. It has been very helpful.
Dear Kane B, I hope you could help me out here. I'm not getting why you have to stack the worlds if they are derived from the same branch. Or actually why do you evalueate worlds from the same branch together? And thanks for the uploads!
I had some confusion that, specifically why close the whole branch, read this: tinyurl.com/ybkgrz4r Basically if a contradiction follows from a claim in any world, it closes all of them. Possibly opens world, if you say possibly x and then it follows that if x is true y and not y is true, the original claim possibly x is not true, x must be false. You don’t have to consider the branch where x is false, you have to get rid of the false claim that x is possibly true.
Note that doesn’t mean you have to not consider x being false, just you don’t have to consider it as a consequence of the false claim that x is possibly true. X will either be false or the whole original claim will be a contradiction.
Ok, surely i'm missing something important. Sorry for asking such a dumb question: what does waiting for a new world mean? Can you, please, state the difference between "already having access to a new world from the actual world" and "creating a new world"? in other words, it is unclear to me when i make use of / when it is the case that "i already have an arrow to another world" and "i draw a new arrow and a new world". Thanks!
i think it means that, if u know box(A), u can confidently say that in any world w1 accessible from w0, A will hold in w1, but u cant assume that such a world exists: as far as u know, there could be no w1 accessible from w0, so you cant just create one; and this isnt in conflict with knowing box(A): this only says that if a w1 exists, then A will hold, it doesnt say anything about such a world existing. its different with diamond, in that if u know diamond(A) in w0, u can confidently say that at least 1 world w1 accessible from w0 exists, and in w1, u can confidently say that A holds. thats how i understood it, im not an expert but i think i am right on this
i dont understand how the last example works, i did it a bit differently and got a positive result, maybe you could help me understand where i did wrong :) after u get the implication not(box(q)) -> not(box(p)), i just rewrote that in the OR version as box(q) OR box(not(p)) from that, since i have diamond(p), i create a new w1 in which p holds (but where i dont specify that not(q) also holds: my reasoning was that, yes, there must be a world in which p holds and a world in which not(q) holds since we have those formulae in possibility in w0, but these worlds dont have to be the same one; note that i did this just by reasoning, so this might be where i'm wrong). going back to w1, i can say that, since i have box(q) OR box(not(p)) in w0, i must have q OR not(p) also in w1, and this doesnt generate a contraddition: i know p holds so not(p) cant also hold, but i assumed i can say that p holds in w1, thus leaving the world open. this works the same in a w2 created from the fact that diamond(not(q)) holds in w0, so not(q) holds in w2: in w2 also q OR not(p) holds, and again, p cant hold because i know not(q) holds, but this just leaves a world in which i decided that q holds, and so also w2 is left open. if u can help me understanding where is my mistake i'd appreciate it a lot, thanks :) also, very good series, i have to write my uni thesis on modal logics and this guide is proving to be very clear and informative
No, because w1 and w2 are both on the same branch, which is closed because of the contradiction in w2. The whole tree is closed because all of its branches are closed.
Poor and informal introduction. It is supposed to be logic. All I see are adhoc rules and explanations, without prior justifications or even axioms presented.
I just want to say a big big thank you for these videos! I have a pass for progression formal logic university module which I just resat yesterday, I have to say you saved me, I went from not understanding modal logic to being able to do it pretty well!
Your videos essentially have hopefully saved me from wasting a year as a external student resitting this module.
I'm reviewing ML basics, and as your long-term follower, it is fun to hear the /young/ Kane B at it :)
taking a class on Modal logic now and this helped so much (even if in 2022)! thank you!!!!
The movie The Counselor has dialogue influenced by Modal logic.
It starred Brad Pitt, Cameron Diaz, Xavier Bordem.
Thank you so much for sharing these videos.
Gracias por estos videos, sirven de mucho para mi parcial de Logica 2. Thanks, you should make more like these.
Your videos are so helpful, thanks so much!
Thank you Kane B, your videos are really helpful
Thanks for this video. It really helped me. The exercises you added at the end of the video are great but where are the solutions? I will appreciate if you add a document or make a video to that effect. Nice one!
Thank you for your sharing :)
Can it be demonstrated that necessity is NOT distributed over disjunction, just as it is here demonstrated to BE distributed over implication?
I don't see why we are able to close a whole branch by finding a contradiction in only one opened world. I've asked this question on Philosophy Stack Exchange: philosophy.stackexchange.com/q/57135/29944 Thank you for the video. It has been very helpful.
Thank you so much
Dear Kane B, I hope you could help me out here. I'm not getting why you have to stack the worlds if they are derived from the same branch. Or actually why do you evalueate worlds from the same branch together?
And thanks for the uploads!
I had some confusion that, specifically why close the whole branch, read this:
tinyurl.com/ybkgrz4r
Basically if a contradiction follows from a claim in any world, it closes all of them. Possibly opens world, if you say possibly x and then it follows that if x is true y and not y is true, the original claim possibly x is not true, x must be false. You don’t have to consider the branch where x is false, you have to get rid of the false claim that x is possibly true.
Note that doesn’t mean you have to not consider x being false, just you don’t have to consider it as a consequence of the false claim that x is possibly true. X will either be false or the whole original claim will be a contradiction.
What software do you use to create these truth trees?
It's just powerpoint.
Ok, surely i'm missing something important. Sorry for asking such a dumb question: what does waiting for a new world mean? Can you, please, state the difference between "already having access to a new world from the actual world" and "creating a new world"? in other words, it is unclear to me when i make use of / when it is the case that "i already have an arrow to another world" and "i draw a new arrow and a new world". Thanks!
See from min 3:00
This also is not clear to me.
i think it means that, if u know box(A), u can confidently say that in any world w1 accessible from w0, A will hold in w1, but u cant assume that such a world exists: as far as u know, there could be no w1 accessible from w0, so you cant just create one; and this isnt in conflict with knowing box(A): this only says that if a w1 exists, then A will hold, it doesnt say anything about such a world existing.
its different with diamond, in that if u know diamond(A) in w0, u can confidently say that at least 1 world w1 accessible from w0 exists, and in w1, u can confidently say that A holds.
thats how i understood it, im not an expert but i think i am right on this
@@bobgreenfield9158 i wrote an answer, see if its clearer
i dont understand how the last example works, i did it a bit differently and got a positive result, maybe you could help me understand where i did wrong :)
after u get the implication not(box(q)) -> not(box(p)), i just rewrote that in the OR version as box(q) OR box(not(p))
from that, since i have diamond(p), i create a new w1 in which p holds (but where i dont specify that not(q) also holds: my reasoning was that, yes, there must be a world in which p holds and a world in which not(q) holds since we have those formulae in possibility in w0, but these worlds dont have to be the same one; note that i did this just by reasoning, so this might be where i'm wrong).
going back to w1, i can say that, since i have box(q) OR box(not(p)) in w0, i must have q OR not(p) also in w1, and this doesnt generate a contraddition: i know p holds so not(p) cant also hold, but i assumed i can say that p holds in w1, thus leaving the world open.
this works the same in a w2 created from the fact that diamond(not(q)) holds in w0, so not(q) holds in w2: in w2 also q OR not(p) holds, and again, p cant hold because i know not(q) holds, but this just leaves a world in which i decided that q holds, and so also w2 is left open.
if u can help me understanding where is my mistake i'd appreciate it a lot, thanks :)
also, very good series, i have to write my uni thesis on modal logics and this guide is proving to be very clear and informative
I still can't get #4 & #8. Anyone care to show me the solutions?
@15:29 If I'm not mistaken, you say that the whole tree is closed. w1, however, is still open.
No, because w1 and w2 are both on the same branch, which is closed because of the contradiction in w2. The whole tree is closed because all of its branches are closed.
Why bother writing down w1 if w1 and w2 are analysed together and w2 invalidates w1? Why not just ignore w1 and save on time?
hes doing this to explain how this works, not prove how fast he can do it
I'd be damned if this thing is not isomorphic to pure type systems
Poor and informal introduction. It is supposed to be logic. All I see are adhoc rules and explanations, without prior justifications or even axioms presented.