Logic 101 (#27): Modus Ponens

Rules of inference allow us to take two or more true inputs (sometimes called premises) and output a new statement which must be true as a consequence of the inputs. Unlike replacement rules, rules of inference allow us to reach new conclusions and learn something we did not know before.

This lecture starts our unit on rules of inference with modus ponens. Modus ponens says that if P implies Q is true and P is true as well, then Q must follow as a result.

For example, suppose

"If I am in California, I am in America."

and

"I am in California."

Then it must be true that you are in America.

[lucascorea]

I love you William this saved my live.

[NickKizirnis]

Could you recommend any good books (that aren't massive textbooks) for learning about the topics you cover here? Thank you!

[ryank]

Struggling with this unit in math, but now I understand. Thanks.

[erikabenavidez]

2:32 hearing at this while Flowers sounds in the background 😆😂

[michaeltebele]

Bon Iver - Million
"In oh, the old modus:
Out to be leading live
Said comes the old ponens
Demit to strive"

[parizer]

((P->Q)^P)->Q is the "extended" form of Modus Ponens, according to Wikipedia and other resources. Can you explain it in this form?

[ledamariefrancisco]

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

[DrStrangeLove]

how did you fill last three rows of the truth  table?? (counting from top)  0:05:50

[boluwatifeogunnowo]

Thank you, this is very understandable 👍💯

[sundusyawar]

@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

[Woshii]

What if the problem is
If p then not q
not p
therefore q?

[keaco]

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!

[DrStrangeLove]

 0:05:50   Why can't we have  F-F-F  or  T-F-T  on last three rows???

[dosto_viski]

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

[PunmasterSTP]

Man, you know you're talking about something important when Rihanna made a whole song about it...











Ponen de replay 😎

[GeorgeLeroux]

1. if I think, I am
2. I think
... I am