Take a look at the circle diagram we saw at 4:05. For P->Q to be true, P has to be inside Q. For the second row of the truth table, It says a dot is inside P but not inside Q, which cannot be possible because P is supposed to be inside Q. Therefore P->Q is false. For the third row, it says a dot is not inside P but inside Q, which can be possible because the Q circle is bigger than P so a dot can be outside P but inside Q. Therefore P->Q is true. For the fourth row, it says a dot is not inside P nor Q, so the dot is irrelevant to P->Q, therefore P->Q can be true.
I will give you a short intuitive explanation. The expression p->q simply affirms q. So in the table, whenever q is true (T) then the expression p->q will be true. And the only other time it can be true is when p and q are both false (F) since we are simply affirming something that we know is false.
+Marko Savic It's exactly the same thing. Remember that the proofs are basically conditional proofs (well, actually, you will get to that later) where we assume that the premises are true and see what follows as well. Put differently, IF premises THEN conclusion. So you have P arrow Q and P as premises ((P arrow Q) ^ P) and have Q as a conclusion. Or ((P arrow Q)^P) arrow Q. Clear?
With modus ponens, can i interchange premise 1 and premise 2? Like Premise 1: I am Miley Cyrus. Premise 2: If I am Miley Cyrus, then I am crazy. thanks
First of all, saying I do not believe x exists is not really an "if then" statement. So logical notation would just be ~b (not believe in x). Saying "you believe/not believe" simply means "it is the case/not the case" So, ~b ~b Is equivalent. For future reference, it's somewhat ambiguous to use the word "believe" especially when we're dealing with logic, because logic doesn't measure opinion just true and false.
The first two columns are the premises which we are using to prove that the third column, the conclusion, is true. -F and -T is a separate premise to F and T, so -F and -T should be a separate premise column. We didn't add that column because the conclusion does not contain -F or -T therefore we have no need to add it in as a column.
@@ChristopherKim I think that is close! I think in this case, the first two columns (P and P => Q) are the premises, and then Q is the conclusion. I am guessing that William wrote the table that way so that the simple sentences P and Q would be in the leftmost columns.
I love you William this saved my live.
excellent video! better than uni!
How did the rest of uni go?
Could you recommend any good books (that aren't massive textbooks) for learning about the topics you cover here? Thank you!
2:32 hearing at this while Flowers sounds in the background 😆😂
Bon Iver - 00000 Million
"In oh, the old modus:
Out to be leading live
Said comes the old ponens
Demit to strive"
Struggling with this unit in math, but now I understand. Thanks.
How did the rest of your math class go?
how did you fill last three rows of the truth table?? (counting from top) 0:05:50
Take a look at the circle diagram we saw at 4:05. For P->Q to be true, P has to be inside Q.
For the second row of the truth table, It says a dot is inside P but not inside Q, which cannot be possible because P is supposed to be inside Q. Therefore P->Q is false.
For the third row, it says a dot is not inside P but inside Q, which can be possible because the Q circle is bigger than P so a dot can be outside P but inside Q. Therefore P->Q is true.
For the fourth row, it says a dot is not inside P nor Q, so the dot is irrelevant to
P->Q, therefore P->Q can be true.
I will give you a short intuitive explanation. The expression p->q simply affirms q. So in the table, whenever q is true (T) then the expression p->q will be true. And the only other time it can be true is when p and q are both false (F) since we are simply affirming something that we know is false.
Thank you, this is very understandable 👍💯
((P->Q)^P)->Q is the "extended" form of Modus Ponens, according to Wikipedia and other resources. Can you explain it in this form?
+Marko Savic It's exactly the same thing. Remember that the proofs are basically conditional proofs (well, actually, you will get to that later) where we assume that the premises are true and see what follows as well. Put differently, IF premises THEN conclusion.
So you have P arrow Q and P as premises ((P arrow Q) ^ P) and have Q as a conclusion. Or ((P arrow Q)^P) arrow Q. Clear?
+William Spaniel Yes, thanks.
@William Would this be correct?
p-->q
q
---------
p
or does it have to be in the standard form? I did the truth table for my example it was true twice
The goal of the use of Modus Ponens is to affirm something, being 'q' true doesn't implies that p will be true.
That would be the formal fallacy known as affirming the consequent. See video 48 of this series.
Nice vid, better than my prof
How did the rest of your class go?
thank you so much for this!
With modus ponens, can i interchange premise 1 and premise 2? Like Premise 1: I am Miley Cyrus. Premise 2: If I am Miley Cyrus, then I am crazy. thanks
Thanks this is helpful
that was very helpful thanks
What about
1. If im a pen, i am crazy
2. Im not a pen
... i am not crazy
This sounds invalid but i couldnt figure out how
Thank you 😌
What if the problem is
If p then not q
not p
therefore q?
Denying the antecedent logical fallacy
According to this rule, would these premises mean the same?
I do not believe X exists.
and
I believe X does not exist.
Thank u!
First of all, saying I do not believe x exists is not really an "if then" statement. So logical notation would just be ~b (not believe in x). Saying "you believe/not believe" simply means "it is the case/not the case" So, ~b ~b Is equivalent. For future reference, it's somewhat ambiguous to use the word "believe" especially when we're dealing with logic, because logic doesn't measure opinion just true and false.
0:05:50 Why can't we have F-F-F or T-F-T on last three rows???
The first two columns are the premises which we are using to prove that the third column, the conclusion, is true.
-F and -T is a separate premise to F and T, so -F and -T should be a separate premise column. We didn't add that column because the conclusion does not contain -F or -T therefore we have no need to add it in as a column.
@@ChristopherKim I think that is close! I think in this case, the first two columns (P and P => Q) are the premises, and then Q is the conclusion. I am guessing that William wrote the table that way so that the simple sentences P and Q would be in the leftmost columns.
Man, you know you're talking about something important when Rihanna made a whole song about it...
Ponen de replay 😎
1. P=>Q
2. P
therefore, Q
1. if I think, I am
2. I think
... I am
Solving logic puzzles with modus ponens and modus tollens: ua-cam.com/video/DKioUaN3be4/v-deo.html
dissing poor miley cyrus