1059:). In the first paragraph he writes, "McGee (1985) showed that there is good reason to take seriously the possibility that Modus Ponens (MP) is false. . . ." I did not mean to exaggerate the significance of McGee's position, and I don't think I did exaggerate it. He's a person of note in the discipline (who still teaches at MIT), he took this stance on MP, most of the discipline thinks he's wrong, but there's no consensus on where he went wrong. That's why his 1985 paper and a 1989 follow-up piece in The Philosophical Review continue to get referenced and discussed.
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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. Bill
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was the other. Where this analysis fails is by assuming that the other premises would still hold if it is suddenly discovered that
Shakespeare was not the author. We can only say premise 1 is true because Shakespeare DID write Hamlet. If that were not the case, the argument would still be valid - the conclusion would still follow from the premises - but the first premise would be false and therefore the conclusion could not be determined.
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good reference for the infinite valued calculus is: A. Tarski and J. Lukasiewicz, "Investigations into the
Sentential Calculus" appearing as Chapter IV in Tarski's "Logic, Semantics, and Metamathmatics" And for the multiple valued logic is probably: Lukasiewicz J. (1913) Die logishen Grundlagen der Wahrscheinichkeitsrechnung. What would be a reference for the truth table given applying to anything other than classical two valued logic?
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865:'If today is Tuesday, then I will go to work and today is Tuesday' means symbolically 'A imp B, A'. The whole judgement is based on the the implication. If we do the correct conversion by denying of the conclusion, i. e. not B (I won't go to work), then we know securely, that musn't be Tuesday and premises are denied, too (denied is at least the second). The judgement is therefore correct.
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moon orbits the earth, then I am wearing white carpenter's pants. Again, the first premise, P, is true. And take my word for it that the second premise, Q, is also true. Given the foregoing, the conclusion is valid. But why? It doesn't seem like the moon orbiting the earth should have any bearing on what I am wearing today, does it?
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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. (
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I'm happy to entertain suggestions about how the section might be improved, although I think anyone who would set out to explain where McGee goes wrong should first spend some time thinking about the problem and reviewing the literature. In the meantime, please un-comment the section. There's nothing
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Let me address this, as the author of the offending material. The intent was not to make any actual claims about the validity of modus ponens, just to document some debate about it among philosophical logicians. McGee's 1985 article, appearing in one of academic philosophy's leading journals, caused
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I recommend this entire passage is rewritten in a way that explicitly states these apparent "counterexamples" are fallacious and explains why. I would do it myself but I'm new to
Knowledge and am not sure if it would constitute original research. I'm going to comment it out for now, however, because
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Emphasis mine. This is such a blatant contradiction I'm surprised that it made it into a
Knowledge article, let alone was apparently published by an actual philosopher. If indeed it is the case that the set of authors is only Shakespeare or Hobbes, then it obviously follows that if it was not one it
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Enderton, for example, observes that "modus ponens can produce shorter formulas from longer ones", and
Russell observes that "the process of the inference cannot be reduced to symbols. Its sole record is the occurrence of ⊦q ... an inference is the dropping of a true premise; it is the dissolution
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McGee's article features an example about the 1980 presidential election involving Carter, Reagan and
Anderson. There are also examples about someone sighting a fish (possibly a lungfish) and someone digging for gold but possibly finding silver. All of those examples require a bit of setup, whereas
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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
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I give you A), while the "modus tollens" is something that needs reflection first. I don't exactly know if this is true/unargued, but this should be mentioned perhaps. Also I've heard that the full name of the modus is "modus ponendo ponens" (and his 'counterpart' "modus tollendo tollens"), if this
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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
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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).
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But there is a problem once you start filling in the variables. The usual example is If one is a man, then one is mortal. Socrates is a man, hence
Socrates is mortal. That works. P is true, Q is true, and the conclusion, by the magic of modus ponens comes out true. But what about this: If the
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Just pick any paper on a three valued logic with truth tables and Modus Ponens for examples of some of the various truth tables other than the one in the article. Lukasiewicz's
Multivalued logic and his infinite valued logic are, for example, are not two valued but have the rule of modus ponens A
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So I think I have a second answer that works better. Because basic propositional logic doesn't account for time, modality, probability, etc. Given that, propositional logic describes a world in which all true propositions are necessarily related to each other (or necessarily not related to each
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There are only two ways I have to deal with this, and I hope someone can help. First is simply to say that propositional logic doesn't account for modalities--whether the moon necessarily or possibly orbiting the earth has any impact on my choice of pants. Granted, modal logic, temporal logic,
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I think you misunderstand the notion of a logically valid argument. A valid argument is one in which the conclusion is *guaranteed* simply by virtue of the form of its premises. In your example, you seem to just be assigning truth-values to propositions. It makes no sense to say "given that the
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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
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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.
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fuzzy logic, and some applications of predicate logic capture all of that. But as to basic bone-headed propositional logic, the conclusion seems odd, because it leaves open the possibility of a modus ponens sentence returning an invalid result--which it shouldn't be able to do.
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In this case, 3 is guaranteed by 1 and 2. Whether or not the argument is *sound* has to do with the truth of 1 and 2, and what I believe you are saying is that 2 is absurd (false). This does prevent the argument from being sound, but the argument itself is still valid.
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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
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The apparent implication being that McGee has somehow torn a massive hole in the foundations of propositional logic which has stumped the eminent professors of the field, when in fact it is a very basic conflation of natural language with formal reasoning.
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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
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earlier two propositions are true, the conclusion is valid," since validity is a property of arguments, not of individual propositions (a common category mistake people make when first learning about logic). "Validity" just means "truth-preserving."
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is a necessary truth.” I have tried to address these problems and in doing so have switched to a more narrative style of exposition. Someone else might see room for further improvement. Or perhaps MaxEnt will take exception to my changes—let's see.
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the Shakespeare/Hobbes example doesn't, and so that keeps the section from being any longer than it already is. That was my thinking, although I would have preferred not to introduce a new example (the whole "original research" rule).
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quite a stir. There continues to be discussion about it. See, for instance, a piece by Mandelkern in Philosophy and Phenomenological Research, so new it is not yet in print but is viewable online if you have access (
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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
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The section on relation to other mathematical frameworks is something of a bag of odds and ends. The “Subjective logic” framework developed by user Josang and presented here (and also more fully in a separate
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I've heard that the "modus ponens" is considered something every man is born with (in order to be able to make transactions, like: - "I give you A, if you give me B" - you give me B -: -->
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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?
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And to lead into this modus ponens with "instances of its use may be either sound or unsound" is pure genius since this instance may indeed (or ininterpretation) be either.
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Addendum: Actually, it might not be a bad idea to add a few sentences outlining the different reactions to McGee by other philosophers. This would be good added info.
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That these kinds of cases constitute failures of modus ponens remains a minority view among logicians, but there is no consensus on how the cases should be disposed of.
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on Knowledge. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the
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other.) For instance, in the world that propositional logic can describe--every time a butterfly flaps its wings, there either must or must not be a hurricane.
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are to be addressed explicitly at this point. However, the use of the definite article over the possessive pronoun suggests that the author is not referring to
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The first premise seems reasonable enough, because Shakespeare is generally credited with writing Hamlet. The second premise seems reasonable as well, because
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It should probably have a disclaimer that the given truth table applies ONLY to classical two valued logic, while Modus Ponens applies to a good deal more.
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845:'If today is Tuesday, then I will go to work and today is Wednesday' means symbolically 'A imp B, C'. By this way can't be already contrived modus ponens.
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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.
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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
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If the argument is modus ponens and its premises are true, then it is sound. The premises are true. Therefore, it is a sound argument.
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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. --
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I'm putting in an article about that. To help, can someone clarify if "modus ponens" is the correct term to use with this argument:
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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
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I assume "the premises are true" in the second line refers to the the premises mentioned in the first line, the premises of
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It seems like the passage should at least mention that although "If Shakespeare didn't write Hamlet, Hobbes did it" may
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with the set of Hamlet's possible authors limited to just Shakespeare and Hobbes, eliminating one leaves only the other
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Note also that there are systems with modus ponens that do not have the property that falsity implies everything.
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Underneath the main (conclusion) operator, all lines of the truth table are true, hence the argument is valid.
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1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 *
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Section titles may be changed and removed in whatever way, but I do not think that this propositional theorem
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I don't want to change this by myself, because I'm not really sure whether it's true or not, as mentioned.
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are not well premised as true by the second line due to expectations of the reader that the premises of
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It's not correct to put "sic" after "premiss." That's not a spelling error, it's an archaic spelling.
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In other words, does the existence of the quantifiers prevent me from calling this "modus ponens"?
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which follows from 1 by specialization. Then the remainder of the argument would be modus ponens.
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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appear in both the object language and the metalanguage. He may also be aware that his use of “
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This is in fact a perfectly valid argument. The article's analysis of it, however, is fraught.
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Should we say something about the converse not necessarily being true? I.e., in the example,
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If either Shakespeare or Hobbes wrote Hamlet, then if Shakespeare didn't do it, Hobbes did.
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That's about all I have to describe it, but I'd love to hear what anyone else has to say.
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But the conclusion is dubious, because if Shakespeare is ruled out as Hamlet's author,
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Responsibility in MP of establishing the antecedent - not so clear in the article.
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Just because you go to work doesn't mean it is Tuesday; it could be Wednesday.
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2. If the moon orbits the earth, then I am wearing white carpenter pants.
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where Hamilton identifies the two. Somewhere along the line between his
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In standard form the modus ponens argument similar to yours would go:
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3. Therefore, I am wearing white carpenter pants. (1,2 modus ponens)
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as the probability of a conditional sentence is a dubious move; see
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Should the truth tables of modus ponens be added to this article? --
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Could someone include some discussion of the following problem ...
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to be false, it is actually a true statement according to how the
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Therefore, if Shakespeare didn't write Hamlet, Hobbes did it."
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the information it presents is totally misleading to readers.
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https://onlinelibrary.wiley.com/doi/abs/10.1111/phpr.12513
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so majorly wrong with the section to warrant removing it.
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If P, then Q. If Q, then R. P. Therefore, R.
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there are many more plausible alternatives than Hobbes
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In short, I just realized you're messing with people.
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1318:{\textstyle x}
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886:is off-topical
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840:symbolic logic
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661:Michael miceli
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512:155.101.224.65
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271:the discussion
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1279:is true” and
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1125:
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609:
606:
603:
600:
595:
592:
589:
585:
581:
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570:
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559:
554:Trivial Truth
553:
551:
550:
546:
542:
536:
535:
531:
527:
522:
521:
517:
513:
508:
507:
504:
503:Vince.Buffalo
496:
494:
491:
483:
481:
478:
475:
472:
470:
466:
462:
461:this argument
458:
457:this argument
454:
446:
445:this argument
442:
440:
437:
434:
432:
431:this argument
429:
428:
427:
418:
413:
409:
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402:
398:
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390:
382:
381:
380:
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375:
370:
364:
361:
358:
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356:
352:
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346:
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331:
329:
322:Miscellaneous
321:
306:
302:
296:
293:
292:
289:
272:
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264:
263:
255:
249:
244:
242:
239:
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224:
221:
218:
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198:
190:
186:
185:
182:
180:
175:
174:
169:
165:
161:
157:
151:
148:
147:
144:
127:
126:
121:
117:
116:
108:
97:
95:
92:
88:
87:
83:
76:
71:
68:
65:
61:
56:
52:
46:
38:
37:
27:
23:
18:
17:
1344:
1191:acknowledges
1183:
1170:
1160:
1148:
1146:
1086:
1039:
1035:
1031:
1027:
1023:
1019:
1013:
1011:
1006:
1004:
1000:
991:
986:
965:
942:
937:
933:
906:
883:
864:
847:
844:
837:
788:
774:
771:The converse
739:
683:Another rule
649:
626:
622:
613:
610:
607:
604:
601:
597:
593:
590:
586:
582:
578:
574:
566:
563:
560:
557:
537:
523:
509:
500:
497:Truth Tables
492:
487:
479:
476:
473:
468:
464:
460:
456:
452:
450:
444:
438:
430:
425:
394:
386:
378:
371:
368:
354:
335:— Preceding
332:
325:
301:Mid-priority
300:
260:
226:Mid‑priority
155:
123:
113:
51:WikiProjects
34:
890:Incnis Mrsi
673:Q_^_Q-: -->
655:—Preceding
643:Q ^ Q-: -->
341:64.199.25.9
276:Mathematics
267:mathematics
223:Mathematics
41:Start-class
1476:Categories
567:((P : -->
484:Psychology
131:Philosophy
120:philosophy
70:Philosophy
1345:Treating
1305:meaning “
1259:meaning “
855:1 0 false
674:R)_-: -->
644:R) -: -->
401:syllogism
389:AxelBoldt
39:is rated
969:20040302
948:Wvbailey
910:Sifonios
861:0 0 true
858:0 1 true
852:1 1 true
675:_P-: -->
669:contribs
657:unsigned
642:(P-: -->
337:unsigned
1460:Knorlin
1328:Knorlin
1129:Knorlin
1109:Knorlin
1073:Knorlin
903:Comment
867:Chomsky
825:Knorlin
757:Knorlin
676:R": -->
645:P-: -->
374:Ryguasu
328:Tarquin
303:on the
158:on the
1421:, not
1177:MaxEnt
1153:modify
1107:Done!
1087:appear
805:have--
791:Tisane
742:Abdull
408:Gwalla
47:scale.
1187:entry
629:Nahaj
594:Thx.
541:Nahaj
526:yayay
365:∴ a=b
197:Logic
75:Logic
28:This
1464:talk
1332:talk
1171:See
1133:talk
1113:talk
1099:talk
1077:talk
1045:talk
973:talk
952:talk
936:and
914:talk
894:talk
871:talk
829:talk
811:talk
795:talk
761:talk
746:talk
665:talk
633:talk
545:talk
530:talk
516:talk
412:Talk
345:talk
150:High
1009:.
295:Mid
1478::
1466:)
1429:Pr
1403:→
1394:Pr
1353:Pr
1334:)
1201:→
1175:—
1135:)
1115:)
1101:)
1079:)
1047:)
979:)
975:)
954:)
916:)
896:)
888:.
873:)
842:.
831:)
823:.
813:)
797:)
763:)
748:)
713:⊢
707:¬
698:→
671:)
667:•
635:)
569:Q
547:)
532:)
518:)
410:|
406:—
403:.
372:--
347:)
177:/
73::
1462:(
1446:)
1443:P
1439:|
1435:Q
1432:(
1409:)
1406:Q
1400:P
1397:(
1370:)
1367:P
1363:|
1359:Q
1356:(
1330:(
1313:x
1293:1
1290:=
1287:x
1267:x
1247:1
1244:=
1241:x
1221:=
1131:(
1111:(
1097:(
1075:(
1043:(
1016:.
971:(
950:(
912:(
892:(
869:(
827:(
809:(
793:(
759:(
744:(
725:e
722:u
719:r
716:t
710:P
704:,
701:Q
695:P
663:(
646:R
631:(
543:(
528:(
514:(
343:(
307:.
162:.
53::
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