Disjunctive Syllogism

An explanation of the Rule of Implication referred to as Disjunctive Syllogism in Propositional Logic (90 Second Philosophy and 100 Days of Logic).
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!
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!

[@HBSKATE]

thank you so much for these videos, learning formal logic seemed like a daunting task before I found this, but ur videos have boosted my confidence in my own capacities to understand and learn significantly. Thanks again man

[@lorenespanola8399]

it's year 2022 and your videos helped me a lot with my school works. especially during this time of pandemic/online classes.

[@wailmohamed8412]

Quarantine day 96: learning formal logic at carneades, reached 17

[@tuxino]

I hope you will get into soundness and fallacies in this series as well. From your examples in this video I immediately thought of false dichotomies.

[@CarneadesOfCyrene]

I've been meaning to do a "Fallacy Week" for a long time. I'll make sure to include false dichotomies.

[@CarneadesOfCyrene]

There were too many fallacies so I extended it from a single week to a whole month: Fallacy February. Check it out.

[@EngGear]

Salam Cardeades, I hope that you are fine. Why disjunctive syllogism is classified as a syllogism?

[@robert2real]

Great video although it sound like someone is tickling you throughout

[@CarneadesOfCyrene]

Thanks, I strive for videos which are educational and entertaining. :)

[@bartonsmith-johnson9721]

Hi Carneades.org, I love your videos. I have a question about how you can prove disjunctive syllogism using only elimination and introduction rules. I have seen this proof in a number of places but am very confused by it. My problem is with line (6) where a negation of ~Q is introduced by negation introduction. I don't know how the assumption (04) ~Q is "blamed" for the contradiction in (5) and thus must be discarded it seems irrelevant to the formation of the contradiction. Equally could one not assume Q in (4) and by the same contradiction and negation elimination conclude ~Q? Hope I have explained myself clearly and that you can help. Thanks.
1 (01) P ∨ Q Premise
2 (02) ~P Premise
3 (03) P Assumption
4 (04) ~Q Assumption
2,3 (05) P&~P Conjunction Introduction: 2,3
2,3 (06) ~~Q Negation introduction: 4,5
2,3 (07) Q Negation elimination 6
8 (08) Q Assumption
1,2 (09) Q Disjunction Elimination: 1,3,7,8,8

[@bartonsmith-johnson9721]

Thanks a lot thats very helpful!

[@PaChamFoodies]

Thanks sir I got it:-)

[@CarneadesOfCyrene]

alee swanson Thanks for watching! Glad I could help.

[@RaduSamanc]

Seems like Double Negation is missing from the playlist.

[@CarneadesOfCyrene]

+Gratis Negatur Which playlist are you watching on? The 100 Days of Logic Full should have it (czcams.com/play/PLz0n_SjOttTcjHsuebLrl0fjab5fdToui.html). The Propositional Logic one had it, it was just in the wrong place (czcams.com/play/PLz0n_SjOttTd0nC-t2Usgbk54oayqkkNg.html) but I just fixed that. Thanks for the heads up.

[@Nicoder6884]

+Carneades.org It's missing from the 18 rules of inference playlist.

[@PaChamFoodies]

I am an I.t student and my instructor give us a problem set including this rule of inference, but since I can't catch up with one example given by my teacher, may I ask your help to solve this.
A-> (B v~C)
D-> C
A
~B \~D

[@CarneadesOfCyrene]

alee swanson Whenever you have a conditional and it's antecedant, Modus Ponens is the best way to go. This will give you a disjunction and the negation of one of it's parts, therefore you need Disjunctive Syllogism. Finally you have a conditional and the denial of it's consequent so Modus Tollens is your best bet. Here's how I would do it. P1) A>(Bv~C) P2) D>C P3)A P4)~B //~D P5) Bv~C (P1, P3 MP) P6) ~C (P4,P5 DS) P7) ~D (P2,P6 MT) Hope that helps.

[@variennecloete3962]

oky I get what you saying about either and or statements but where are the inclusive and exclusive parts of the argument as well as validity. that's complex!

[@muhammadabdullahqureshi1941]

isn't this affirming the disjunct

[@elcaricaturable]

Nice video. However, the examples that use the word "either" are not normal disjunctions but exclusive disjunctions. Exclusive disjunctions are not necessary for Disjunctive Syllogisms to work.

[@CarneadesOfCyrene]

True. I mentioned earlier in the series that the logical "or" is an inclusive "or". I suppose that examples with "and/or" might have been more accurate, but also less common in normal speech.

[@elcaricaturable]

@@CarneadesOfCyrene I see your point. It would be nice to include a normal disjunction in your examples though. What about something like this: 1) to put out the fire you have to remove the oxygen or lower the temperature (you could also do both) 2) you can't lower the temperature 3) so you must remove the oxygen.

[@joanbarrosguerra8841]

it's good. jajja you make some teachers look bad.

[@atpTUBE]

Where is Desctructive dilemma here sir? Did you miss or was it intentionally?
Actually there are 19 rules of inference in Copi's rules but someone replaces the rule(6) absorption to destructive dilemma.
But you discard two of them, could you explain please?
And in some pages I see the "resolution" rule also
Could you look at it:
egyankosh.ac.in/bitstream/123456789/34741/1/Unit-3.pdf