One Man's Modus Ponens (Is Another Man's Modus Tollens)

An explanation of the phrase "One Man's Modus Ponens is another Man's Modus Tollens" as well as definitions of the logical forms of modus ponens and modus tollens and an example from G.E. Moore.

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Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!
(#Logic, #ModusPonens)

[captain_outis]

One person’s Modus Pwnens is another person’s Modus Trollens

[valdembergnobre]

I know it doesn't have anything to do with the content of the video, but it was odd that the title of one of the slides was "Judo flip", but the "images" on the side are composed by the word "Karate". Anyway it's just a funny thing, great video as always and I love the "Dumbfounding definitions, (and a whole bunch of d-words haha)".

[paulk]

The end of the video can be expressed with a new modis ponens:
p and not q
p and not q implies not (p implies q)
therefore, not (p implies q)

[HeyHeyHarmonicaLuke]

Damn, that was a good one! Nice work Carneades.org

[zsoltnagy]

Hm, interesting interpretation of the phrase "One Man's Modus Ponens is another Man's Modus Tollens.".
I have quite the different interpretation of the same phrase "One Man's Modus Ponens is another Man's Modus Tollens.".
Generally speaking the material conditional P>Q is logically equivalent to these other three statements:

1) P>Q
2) ~Q>~P 1, contraposition
3) ~P∨Q 1, material implication
4) ~(P&~Q) 3, De Morgan's law

Contraposition, material implication and De Morgan's law are actually logical equivalences, so the above inferences could be done from the conclusions to the premises backwards.

Suppose the material conditional P>Q as premise P1 and P as premise P5, then the following argument and inference can be made from those two premises:

P1) P>Q
P5) P
C) Q 1, 5, *modus ponens*

But since there are three othere logically equivalent formulations of that material conditional and premise P1 another inferences and with that arguments can be made with the same premise P5 deriving the same conclusion C:

P2) ~Q>~P 1, contraposition
P5) P
C) Q 2, 5, *modus tollens*

Or

P3) ~P∨Q 1, material implication
P5) P
C) Q 3, 5, *disjunctive syllogism*

Or

P4) ~(P&~Q) 3, De Morgan's law
P5) P
P6.1) ~Q indirect proof assumption
P6.2) P&~Q 5, 6.1, conjunction introduction
P6.3) ~(P&~Q)&(P&~Q) 4, 6.2, conjunction introduction
C) Q 6.1- 6.3, *indirect proof*

All four inferences *modus ponens*, *modus tollens*, *disjunctive syllogism* and *indirect proof* and the associated arguments with them are logically equivalent to each other and since *modus ponens* and *modus tollens* are the more common ones, I guess then, therefore the phrase "One Man's Modus Ponens is another Man's Modus Tollens.".
But the following phrase would be more appropriate to reflect this logical equivalences and subject matter of arguments:
"One Man's Modus Ponens is another Man's Modus Tollens, another Man's Disjunctive Syllogism and another Man's Indirect Proof."

[Pfhorrest]

I'm almost always taking the third way, denying that some P and Q held by opposing sides are actually in opposition. No wonder everybody seems to hate my philosophical views. (But guys, I'm trying to say you're both right! You can have P and Q! It's just the "if P then not-Q" part that's tripping you both up! Can't we all just get along?)

[zsoltnagy]

I'm using mostly the "Third Way" denying and rejecting the implication in apologetic arguments.
For example there is this nonsense from Wade A. Tisthammer alias Maverick Christian:

_1. If it is raining, then my car is wet._
_2. It is raining._
_3. Therefore, my car is wet._
from his blog *"Introductory Logic, Part 1"*

I mean, what else is here to say than, that it might be raining and his car still might be not wet, because it might be in a garage, when that rain might occur?

[JonSebastianF]

Is this "Judo Flip" the same as a _reductio ad absurdum_ argument?
*P1:* _p_
*P2:* _p_ implies _q_
*C1:* therefore _q_
*P3:* _not-q_
*C2:* therefore P1 or P2 or both are false

[Ansatz]

It's foolish to flip an argument around like that since the whole point of giving an argument is to convince people of the argument's conclusion, and to do that we need to use premises that people are likely to accept. A person who just gave an argument for q is highly unlikely to accept not-q as a premise.