Talk:Disjunctive syllogism

Self-contradictory redirections?

The second paragraph of Disjunctive syllogism's section Related argument forms claims that

Modus tollendo ponens should also not be confused with modus ponendo tollens.

but modus tollendo ponens and modus ponendo tollens both redirect to Disjunctive syllogism. Doesn't this contradict the above quoted passage?

192.102.214.6 16:58, 4 January 2007 (UTC)

I admit to not being proficient in logic or Latin, however I don't think it contradicts itself. What it is effectively saying is that by disputing a trait confirms the other, and that it can occur in two forms, one being the opposite of the other.

Eg. The cat is not black, therefore it is white. vs. The cat is not white, therefore it is black.

Both examples use the same form of logic, but prove the opposite logical conclusion.

It must be noted that this is my own personal judgement based on my own reasoning, therefore I may be overlooking missing information.

I suspect the last line was added by a different author to the first paragraph. I must also comment that there are no references to confirm the sources of the information. This would help to identify accurate information.

I do suggest providing an example in this section to help users understand it better.

--Minotaur500 17:49, 6 February 2007 (UTC)

Modus tollendo ponens should also not be confused with modus ponendo tollens They are not the same.

Modus tollendo ponens:

A v B ~A

---

B

modus ponendo tollens

~(A & B)

A

---

~B

it is just that in an exclusive or( A or B but not both)

((A v B) & ~(A & B)) They are both valid.

Hope this helps.

___________________________________________________________________________________________________ I am in a logic class. Both ponendo tollens and tollendo ponens are forms of disjunctive syllogisms, in fact they are also forms of conjunctive sylogisms. Anyway, the definitions are as follows...

Tollendo Ponens......Ponendo Tollens

Valid Syllogisms.........Invalid Syllogisms

1)............................1)

Either P or Q..............Either P or Q

Not P........................P

Therefore Q................Therefore not Q

2)............................2)

Either P or Q..............Either P or Q

Not Q........................Q

Therefore P................Therefore not P

Invalid Syllogisms.........Valid Syllogisms

3)............................3)

Not both P and Q.......Not both P and Q

Not P........................P

Therefore Q................Therefore not Q

4)............................4)

Not Both P and Q.......Not Both P and Q

Not Q........................Q

Therefore P................Therefore not P

There is no contradiction

Relevance logic

Shouldn't there be a section on how some logics, like relevance logic, deny DS in at least some cases? (Paraconsistent logics have to deny that DS applies in inconsistent situations on pain of having to admit the Principle of explosion, avoidance of which is usually one of the motivations for going paraconsistent in the first place).

There is at least one relevant logic in which DS is valid: the Intuitionistic Relevant Logic defined by Neil Tennant. (See : http://people.cohums.ohio-state.edu/tennant9/publications.html ) By the way the article says that the DS is classically valid, but it is also intuitionistically valid, not only classically.

Merge

I propose merging Modus tollendo ponens into this article (Disjunctive syllogism), since their usual representations in modern classical logic are identical and having two articles necessitates redundancy. — Charles Stewart (talk) 06:04, 12 June 2009 (UTC)

The disjunctive syllogism is classically valid. So much the worse for classical logic.

I totally agree with the discusser who points out that disjunctive syllogism is invalid in relevant logics. In fact, it suffers from a fallacy of ambiguity. See Anderson and Belnap, Entailment, Vol. 1, p. 165ff. They provide a proof of the invalidity of ~A&(AvB)->B. This should be fixed. —Preceding unsigned comment added by Rsamstag (talk • contribs) 23:48, 10 July 2010 (UTC)

I've added a link to paraconsistent logic, which was indeeed missing. This could probably be expanded, but we'd need to be clear about the assumptions (see WP:NPOV). Kingdon (talk) 12:16, 15 July 2010 (UTC)

Disjunctive syllogism does not work for all P and Q in classic logic

Shouldn't this be pointed out on the page? I worked this out for myself, but can't find a reference to it online unfortunately. 88.203.90.14 (talk) 22:03, 16 December 2013 (UTC)

P: All men are mortal

Q: French men are mortal

~P: All men are immortal

Therefore French men are mortal.

However, French men cannot be both mortal (Q) and immortal (~P).

It doesn't work when Q is a subset of P. 88.203.90.14 (talk) 21:20, 16 December 2013 (UTC)

No contradiction. ~P is "Some men are immortal." None of them are French. Vaughan Pratt (talk) 19:24, 26 December 2013 (UTC)