Talk:Modus ponens

message: One of the "conversation" chapters in Gödel, Escher, Bach is by Lewis Caroll, and is about MP and how it can be extended to absurdity. -- Tarquin 05:58 Aug 27, 2002 (PDT)
It's not correct to put "sic" after "premiss."  That's not a spelling error, it's an archaic spelling.  — Preceding unsigned comment added by 64.199.25.9 (talk) 20:00, 1 May 2012 (UTC)
replies: text: It's a type of syllogism.  — Gwalla | Talk 21:07, 16 Sep 2004 (UTC)
thread_title:  Miscellaneous 

message: Should the truth tables of modus ponens be added to this article? --Vince.Buffalo 05:41, 19 August 2006 (UTC)
thread_title: Truth Tables

message: I stated this incorrectly in the history page - modus ponens is just a form, and as such truth-value assignments are irrelevant. My real justification for deleting the link is that it really is too unrelated to an article on modus ponens (it would go well in an article on conditional statements). [Prior unsigned comment from  2006-11-03T00:01:47 130.64.31.145]
Note also that there are systems with modus ponens that do not have the property that falsity implies everything. Nahaj (talk) 19:00, 27 October 2008 (UTC)
thread_title:  eliminated link to "falsity implies anything" 

message: isn't this called hypothetical syllogism as well?
    If P, then Q.
    If Q, then R.
    P.
    Therefore, R.  —Preceding unsigned comment added by Michael miceli (talk • contribs) 14:17, 1 October 2007 (UTC)
thread_title:  (P->Q ^ Q->R) -> P->R 

message: :P \to Q, \neg P \vdash true
Does this argument form have a name? Thanks, --Abdull (talk) 16:01, 8 January 2010 (UTC)
replies: text: This isn't really a rule. I mean, if you have "true" on the right, typically you could have anything at all on the left and it would be a valid inference. Knorlin (talk) 17:13, 5 November 2022 (UTC)
thread_title:  Another rule 

message: Should we say something about the converse not necessarily being true? I.e., in the example,
:If today  is Tuesday, then I will go to work.
:Today is  Tuesday.
:Therefore, I will go to work.
Just because you go to work doesn't mean it is Tuesday; it could be Wednesday. Tisane (talk) 04:56, 9 March 2010 (UTC)
replies: text: I agree, but I'm not an expert. There's also the fellacious argument "today is not Tuesday, therefore I will not go to work" which does not follow from the previous argument. This error, I  believe, has been catalgogued elsewhere according to some vague recollection I have--143.210.122.139 (talk) 14:18, 8 April 2011 (UTC)

text: So, "If today is Tuesday, then I will go to work. I will go to work. Therefore it is Tuesday." That's called the fallacy of affirming the consequent. Knorlin (talk) 17:15, 5 November 2022 (UTC)
thread_title:  The converse 

message: Section titles may be changed and removed in whatever way, but I do not think that this propositional theorem [ is off-topical]. Incnis Mrsi (talk) 05:54, 19 April 2013 (UTC)
thread_title:  ((P → Q) ∧ P) → Q 

message: The sentence near the beginning saying that modus ponens "must not be confused with a logical law" is potentially confusing. It depends upon exactly what you mean by "logical law". I would think that most logicians would be happy to call it a logical law. I think that the distinction being made in the texts referred to is between an axiom or theorem (a necessarily true formula) and an inference rule. Modus ponens is an inference rule rather than an axiom. But it still could be called a logical law, since, as far as I know, "logical law" does not have a precise technical meaning. Sifonios (talk) 11:03, 6 November 2014 (UTC)
replies: text: You are entirely correct about this, and I've wondered how to approach your point. Since the early 1800's "modus ponens", under a different name Principle of sufficient reason and not formalized as an "inference rule" as it is today, was considered a "law" by both Hamilton (1830's) and Russell (1900 to 1910). But see in particular the quote at footnote #10 in this article; also more at Laws of thought where Hamilton identifies the two. Somewhere along the line between his Principles of Mathematics and Principia Mathematical Russell singled out his expression of the "principle of sufficient reason" (he never called it that in anything he wrote, to my knowledge; he was abysmal at footnoting and sourcing so we can't trace how his ideas evolved) and adopted it/singled it out in Principia Mathematica as "Anything implied by a true elementary proposition is true", the very first of his "Primitive propositions (Pp)" *1.1 to which he added *1.2 through *1.7 to form his axiom-set, or if you prefer "laws of thought" (by this time the moniker "laws of thought" seemed to be passé by the mathematicians but still used by philosophers -- cf Russell 1912 for example. By the time of Hilbert and Gödel (1920's-1930's), modus ponens had been reclassified as a "rule" as opposed to an axiom. It would seem that the contemporary literature starting in particular with Gödel separates his axioms from his "sentence formation rules", the "rule of inference (modus ponens)", "rule of substitution", and a tacit "rule of specification". Unfortunately I don't have enough sources to make sense of exactly what's happened here. BillWvbailey (talk) 15:43, 6 November 2014 (UTC)
thread_title: Comment

message: I am not a specialist in this domain, but the article doesn't seem to be explicit concerning the issue that, when attempting to use MP in an argument, the responsibility of establishing soundness will be primarily dependent on establishing the antecedent: This be complex in areas of eg implied causality:"if it rains, flowers will bloom" may at first glance appear reasonable, even coherent,  But what is missing are all the intermediary logical steps to determine that raining implies flowering - and yet to be established at all is that "A implies B" can ever be coherent beyond some hermeneutic stance. (20040302 (talk) 11:30, 30 July 2016 (UTC)
thread_title:  Responsibility in MP of establishing the antecedent - not so clear in the article. 

message: In the following sentence, the author of Principia Mathematica has been abridged to be "Russell."  Whitehead is a co-author of the work, so the absence seems conspicuous.  Is this intentional?  Is there any objection to adding Whitehead as well? modify 18:45, 17 July 2020 (UTC)
thread_title:  Reference to Principia Mathematica 

message: See Talk:Boolean_algebra#CS_guy_tackles_modus_ponens_with_mixed_results — MaxEnt 02:23, 14 October 2022 (UTC)
thread_title:  Boolean algebra section added 

message: Treating \Pr(Q|P) as the probability of a conditional sentence is a dubious move; see Lewis's triviality result. The cited observation by Hailperin is about \Pr(P \rightarrow Q), not \Pr(Q|P). So I cut one paragraph and corrected the other. Knorlin (talk) 07:47, 20 November 2023 (UTC)
thread_title:  Probability calculus material trimmed back