Talk:Syllogism

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There, cleaned it up a bit and wrote the stuff about majors and minors. Removed cleanup tag, but it still needs tender loving attention from a father-figure logician, the poor thing. I just don't know enough about the subject. saturnight 22:53, Sep 3, 2004 (UTC)

Note that Term logic and Talk:Term logic contain even more about syllogisms than this article does. Things need to be moved from there to here. I'd do it if I knew anything about syllogisms (which I don't at present). mark 15:07, 2 Mar 2005 (UTC)

Looking for Something about Square of opposition[edit]

This is a relatively important logical construct, and needs to be added as a link, along with the logical relationships of contraries, subalterns, subcontraries, and contradictions. I recently took a course in logic that was heavy into syllogism, and we used the square of opposition a lot. Thought or feelings? Is there a place within the article that would best describe and illucidate this concept, or am I really best just to put a link in the "see also" section? Thanks. Asday85 (talk) 17:07, 30 January 2008 (UTC)

Question[edit]

Any relationship to "JISM"? —Preceding unsigned comment added by 68.96.213.27 (talk) 23:42, 1 October 2007 (UTC)

Not that I know of... can you be more clear? 129.93.16.77 (talk) 21:04, 14 January 2008 (UTC)

A Philosopher Professor[edit]

Come on. Is there seriously no professor in logic who has taken to editing this article? Get with the program, academia. "...deductive reasoning, where facts are determined by combining existing statements, in contrast to inductive reasoning where facts are determined by repeated observations." Who on earth wrote that? existing statements? Denito 16:26, 25 August 2007 (UTC)

OK, here's your answer, from a logic professor, like it or not. Aristotelian logic is a clumsy cack-handed system that no modern logician would remotely bother with; to achieve what it does we now have a system that is both much simpler and more powerful. That one can have it both ways is testimony to the astronomical crapulence of Aristotle. Wait, it gets worse. Via the "doctors" of the church and the efforts of Aquinas, aristotelian logic is still viewed as the one and only correct system in Roman-Catholic seminaries. That is testimony to the astronomical stupidity of the RC church. No one in the know would touch this page. One visits this only out of morbid curiosity, a bit like scat porn.81.178.147.159 (talk)

men (will) die[edit]

This piece is, pedantically speaking, wrong.

Men die. (general principle)
Socrates is a man. (specific statement)
Socrates will die. (application of major to minor)

The correct conclusion would be "Socrates dies." The problem is that semantics and syntax are funnily linked, such that for semactic equivalence "will" has to be included in the conclusion. Solutions I can think of:

  • men die -> men will die; probably wrong though
  • Socrates will die -> Socrates dies; probably equally wrong semantically as the previous option
  • die -> die some day
  • die -> have finite lifespan
  • men die -> Every human will die; Good and also makes the implied "every" which is needed for this to be valid reasoning, explicit.

Comments? --MarSch 12:38, 2 September 2005 (UTC)

Actually the next sentence in the article hints that the major used to be "All men are mortal", which is probably even better. I will reinstate this. --MarSch 12:41, 2 September 2005 (UTC)

I added a bit about this, too, to explore the relationship of time in syllogisms  :-) Ted 18:41, 17 January 2006 (UTC)

Made some additions[edit]

I added a good bit to the syllogisms page. I thought it would be nice to have something more accessible than formal logic normally gets. Comments and revisions are (of course) welcome. Twrigley 18:58, 15 January 2006 (UTC)

WHY is it called the Barbara Syllogism?[edit]

I just searched the net, and found not a single explanation of why it's called the Barbara Syllogism.

Anyone here know? That definitely should be included in the article.Kaz 16:52,

I used to work for Barbara Syllogism. Full of fallacies, that woman.

19 January 2006 (UTC)

According to Bertrand Russell, it is an acronym from Greek. That ought to help you in your search. The book was in my high school library, so now you have an even short search list, meaning that it couldn't have been a very esoteric title by Russell, but one of his popularizations. --Ancheta Wis 17:56, 19 January 2006 (UTC)
It's part of a medieval mnemonic. Each syllogism involves three propositions labelled "A", "E", "I" or "O", and so each syllogism is given a word that contains those three letters in order. Hence the syllogism deriving an All conclusion from two All premises needs a word with three As as its first three vowels: Barbara was chosen, but it could have been calamari. --- Charles Stewart(talk) 18:00, 19 January 2006 (UTC)
So that explains why celarent was another of those mnemonics. --Ancheta Wis 18:13, 19 January 2006 (UTC)

In fact the whole mnemonic is given and explained at Term logic#Conversion and reduction. Should this page should be merged there? --- Charles Stewart(talk) 19:04, 19 January 2006 (UTC)

I'm not certain about merging - I'm still trying to get a handle on the over-all structure of wikipedia, while Wittgenstein laughs at me from the back of my head (hierarchical knowledge structures; please!!!). for a pro-tem solution, though, I'll add your explanatory link.  :-) Ted 18:54, 20 January 2006 (UTC)
I came here looking for an explanation of the consonants in the mnemonic words for syllogisms, and apparently that text no longer exists on this page or Term logic. I was able to get some information from historical versions of Term logic but it seems like it should be on an active page. Gimmetrow 20:54, 15 May 2006 (UTC)

well, I went and looked through the Term logic page, and there is a lot of overlap. certainly the sections on syllogisms parallel what is given here. it seems our choices (aside form leaving things exactly as they are - lol) are these:

  1. bring the sections on syllogisms from term logic and integrate them here, leaving a link
  2. create a single combined page under the heading term logic
  3. create a single combined page under the heading syllogisms

personally, I think 'syllogism' is the more common term, but what do I know? at any rate, we'd need to link the unused term back to the new term; does anyone know how to do that? Ted 19:58, 20 January 2006 (UTC)


There's an answer to this. The medieval mnemonic (attributed to Peter of Spain, is hardly a secret. It encodes, not just which pairs of premises in each figure give a conclusion and what that conclusion is, but also how Aristotle proves the validity of that syllogism in Prior Analytics I.4-6. Names are constructed like this:

  1. The vowels "a","e","i", and "o" are used for the four types of categorical sentence:
    • "a" = universal affirmati
    • "e" = universal negative
    • "i" = particular affirmative
    • "o" = "particular negative"
    Allegedly, the vowels are chosen because "a" and "i" (for the affirmative types) are the first two vowels in "affirmo" ("I affirm") and "e" and "o" the vowels in "nego" ("I deny").
  2. The names for the four first-figure forms begin with the first four consonants of the alphabet: B, C, D, F
  3. Consonants then get added for euphony (but note that "r" and "l" dominate and that there's no "s", "m", "c", "p"): Barbara, Celarent, Darii, Ferio
  4. The four first-figure forms are "perfect" and need no proof
  5. For the second and third figure moods (Aristotle does not recognize a fourth figure), the name is an encoding of Aristotle's method of proof. His proofs consist of what he calls "reduction" to a first-figure form, which is a matter of (1) replacing premises by other sentences they imply until a pair of first-figure premises is reached, (2) drawing the conclusion of that pair, (3) if needed, drawing a further consequence of that conclusion to get a form that fits the original figure. For these replacements, Aristotle only uses "conversion", which is interchanging subject and predicate of a sentence. An "e" or "i" sentence implies its converse, and an "a" sentence implies the sentence you get by converting it and changing to an "i". The mnenomic calls the first of these "simple conversion" (conversio simplex, abbreviated by "s" after the premise's letter) and the second "conversion per accidens" (conversio per accidens, abbreviated by "p" after the premise's letter). Sometimes, major and minor premise must be swapped to get to the first figure; "m" is used to abbreviate this. We then get mnemonics like these:
    • Camestres (2nd fig.): (1) convert the "e" premise (Camestres); (2) swap major and minor premises (Camestres); (3) this gives you Celarent in the first figure (Celarent), with an "e" conclusion; (4) convert the conclusion (Camestres) to get the second-figure conclusion you need
    • Felapton (3rd fig.): (1) convert the "a" premise (Felapton); (2) this gives you Ferio in the first figure (Felapton), with an "o" conclusion/li>

    In some cases, it's impossible to get a proof using the conversion methods (second-figure Baroco, third-figure Bocardo). So, Aristotle uses indirect proof (assume the contrary of the desired conclusion, which with one of the premises will give you a first-figure form; the conclusion of this is the contradictory of the other premise; infer the desired conclusion by reductio ad absurdum). The mnemonics mark such cases with a "c" (for per contradictionem) after the premise that's contradicted. So:

    • Baroco 2nd. figure): Given premises "all Bs are As" and "some Cs are not As", assume "All Cs are Bs"; with the first premise, this gives (via Barbara) "All Cs are As, which contradicts the second premise; therefore, infer the denial of the assumption "All Cs are Bs" to get "Some Cs are not Bs".

    That at any rate is a brief account of the mnemonics. Aristotle of course knew nothing about them.

For a more detailed discussion of the significance of these names, see Paul Spade, <a href="http://pvspade.com/Logic/docs/thoughts1_1a.pdf">Thoughts, Words, and Things: An Introduction to Medieval Logic and Semantic Theory</a>, pp. 21-25.

--Robin Smith (Actually, my translation of the Prior Analytics is cited in the bibliography for this page) 128.194.75.5 (talk) 14:32, 25 August 2008 (UTC)

Major Change[edit]

I've integrated the Term Logic and Syllogism pages, and redirected the former to the latter. I've still got itchy little stuff to do (formatting and highlighting, and checking related pages to restructure things) but I think this works. let me know if you disagree. Ted 04:24, 5 February 2006 (UTC)

I'm uncomfortable with the change. There's more to term logic that the syllogism, even if syllogistic inference is the center of term logic. For example, there are two forms of inference in Aristotelian logic that are non syllogisms: axioms such as "A is A", and those that are recorded in the square of oppositions, such that the inference of contradiction from All As are B and Some As are not B.
Let's not hurry about reversing the change: I like the gathering together of all the scraps of content into one article. We should figure out what differences we mean between:
1. Term logic
2. Aristotelian logic, and
3. Syllogistic logic
--- Charles Stewart(talk) 18:36, 5 February 2006 (UTC)
ok. I'll confess it wasn't clear to me exactly what 'term logic' referred to. sometimes it seemed to be an alternate phrase for syllogisms, sometimes to be a broader term for aristotelian logic (but only to the parts that dealt with syllogisms, since it never seems to apply to propositional logic). perhaps I was a bit over-aggressive in my integration.  :-) tentative breakdown, along your lines:
  • Aristotelian Logic: everything discussed in the Prior Analytics and On Interpretation (to distinguish it from Organon proper)
  • Term Logic: the system of logical deduction dealing with internal categorical structures that developed (over a millennium or two) from Aristotelian Logic.
  • Syllogisms: the particular symbolic form that Term Logic takes.
By this breakdown, section 1 would clearly go on a term logic page, sections 3 and 4 on a syllogism page. section 2 is less clear: parts go one way, parts go another, and some are just stuck in the middle, spinning. comments or ideas? Ted 22:05, 5 February 2006 (UTC)

Excessive subtext[edit]

  • JA: Could active editors put all but routine editorial comments and communications on the discussion page instead of enscouncing sotto voce asides in the article, as the latter are really hard to follow what's going on for interested bystanders watching the diff and hist displays. Gratia in futuro, Jon Awbrey 18:28, 5 February 2006 (UTC)
sure thing, sorry. Ted 22:03, 5 February 2006 (UTC)

I'm concerned about some of this authorial bias or intention--I think I saw, "We shall discuss..." Who's we? I'm not familiar enough with wiki rules but this seems problematic. Is that portion literally ripped off a syllabus or a paper? Wishelephant (talk)wishelephant —Preceding undated comment added 23:57, 25 September 2011 (UTC).

oh dear[edit]

Oh no! I wrote the original article "Term Logic". I've just noticed the change that incorporates Term Logic into "Syllogism". This was not the right thing to do. Broadly:

• "Term logic" signifies the crucial feature of Aristotelian logic that analyses propositions into two terms, with the logical constants "all" "some" &c. Thus "All/some/no A's are / aren't B's". • "Aristotelian logic" signifies the logic developed by Aristotle in the books collectively known as the Organon. This happens to be a form of term logic. • "Syllogistic" refers to the form of inference that is connected with term logic. It is a much narrower concept, in fact is a part of term logic.

Thus Term logic = semantics of terms + theory of the proposition + syllogistic

Aristotelian logic = a version of term logic ( the only version as it happens, but the two should not be confused. An alien civilisation might develop a form of term logic, but it wouldn't properly be 'Aristotelian' logic).


I will have to change all this back in a way that is logical. Dbuckner 11:20, 6 March 2006 (UTC)

yes, this is acceptable. Charles made a similar comment some time back, and I see the point. the only difficulty I've had (which is why I haven't effected such a change myself - still pondering) is that there's a certain overlap in the content that's difficult to parse. as far as I can see it, the original distinction between propositional logic and syllogistic logic was Aristotle's: he split the analysis of the relationship between propositions from the analysis of the internal structure of a singular proposition. term logic developed as an elaboration and refinement of syllogistic logic, which (despite it's sophisitication) never seems to step beyond the bounds of Aristotle's original construct. in terms of structure, your equation holds; in terms of historical development, term logic is derivative of syllogisms; in pragmatic terms there are certain things (like mood and figure) that it would seem need to be discussed on both articles, thus creating a good bit of redundancy.
options:
  • rewrite and restructure to make the distinction clearer, but keep the content on one page
this may involve renaming the page Term Logic and redirecting syllogisms there
  • split the page into two, dividing content appropriately
how then to divide some of the mutually relevent content? Ted 14:47, 6 March 2006 (UTC)

Personal essay[edit]

I've reverted to an earlier version because this seems to have turned into a personal essay, which is not to say that nothing good had been added (some of it is worth keeping, for sure), but the tone is unencyclopedic in places e.g. "Note, however, that the decline was a protracted affair. It is simply not true that there was a brief "Frege Russell" period 1890-1910 in which the old logic vanished overnight." These phrases "Note, however ..." and "It is simply not true ..." are POV. We report what reputable publications have written and no more, and the material has to be sourced. See WP:NOR, WP:V, and WP:RS. SlimVirgin (talk) 19:08, 6 March 2006 (UTC)

Twrigley, I have no problem with some of the good material being restored, but it needs to be built up slowly and sourced properly. As it stands, it looks like someone's personal essay. SlimVirgin (talk) 19:26, 6 March 2006 (UTC)
Slim, thanks, but please consider two things:
  1. the other editors and I are about to restructure the page again, to separate term logic from syllogisms; this should eliminate your 'personal essay' concerns. (you should also know that the part you are marking as a personal essay wasn't my work, but that of another editor that I worked into this article at his request)
  2. the current version is a substantial improvement over the earlier; I believe the other editors would agree that editing is preferred to reversion at this point.
I was expecting your visit, though it makes me sad. please feel free to edit without destroying the structure of the page. Ted 19:29, 6 March 2006 (UTC)

Charles, Dbuckner: SlimVirgin is pissed at me because I gave her a hard time on a different page. this is payback, I suppose... I'm going to go report her for vandalism right now; please, if one of you would revert the page to it's established form? I see know reason why you or the page should suffer because of her bad temper.

Thanks Ted 19:33, 6 March 2006 (UTC)

I saw some of your work here, for example, [1] which is why I'm concerned. We can't include edits such as "Formal logic is a complex game. And I do mean game ..."
As for this being "payback," please AGF. I'm not here because I'm "pissed" at you, but because I'm not convinced you're familiar with our content policies, and so I've looked at your edits. As I said, I have no trouble with some of the good material being added back, but you'll need to provide at least some sources, and they have to be published professional philosophers. You also need to keep your own personal comments and opinions out of the article. SlimVirgin (talk) 19:38, 6 March 2006 (UTC)

SlimVirgin you have violated another standard of wikipedia by disrupting the work of several editors to make a point. [2] The reversion took place after your discussion with the before-said editor over similiar inappropriate behavior elsewhere. This is further proof of your violation of wikipedia rules, and the violation of your position. I request you ceast and desist in your harassment here and let the editors who have put many hours into this page, alone. To revert an entire article is un-called for and I DEMAND a verifiable reason for what you have done. --Northmeister 02:13, 8 March 2006 (UTC)

  • More specifically, what do you SlimVirgin consider to be Original Research, please indicate here so Ted has a chance to state his case.
  • Second, what do you consider not verifiable according to the policy on such?
  • Third, what sources do you challenge on this subject? Please show this community what particular parts of this article you consider to violate the above, since you seem to indicate that the above rules were somehow violated.
Civility is a cornerstone of understanding and respect. Good Faith presumes that Ted was acting as such when editing this article. Good Faith should be shown by yourself and any others who wish to challenge this article. Therefore present your case so Ted knows what your talking about and then let CONSENSUS determine what is to be changed or what is not right. --Northmeister 02:51, 8 March 2006 (UTC)
I further find it offensive that you bring material from a previous edit up as if it were a recent edit to scold an editor. This is not proper. The edit in question by you (SlimVirgin):
  • "Formal logic is a complex game. And I do mean game ..."
The above sentence was changed by Kazvorpal on 19 January 2006 [3]to:
  • "Formal logic is a complex game. Literally a game,"
This was accepted by Twrigley until an improvement was made by him on 05 February 2006 [4]to read:
  • "A syllogism's ability to explore errors of reasoning, however, relies on its structural validity. Not every trio of propositions creates a valid syllogism, and often - particularly when variant moods and figures are involved - the validity of a syllogism becomes ambiguous and difficult to ascertain. e.g.:"
This reading has been accepted since it was added into the article on that before said date. Since then the following users have helped to edit the article: Ancheta_Wis, Chalst, Mhss_en, Brian0918; including the following anonymous users: 66.26.38.109, 71.136.83.144, 70.242.141.195; and did not dispute the change made by Ted.

I ask that you present reasonable instances to the community of error in this article or that you stop your efforts at disruption and allow those editors mentioned earlier to edit as they were in the wiki fashion of collaboration and consensus. I am sure this article is not perfect, but no article at Wikipedia is. --Northmeister 04:27, 8 March 2006 (UTC)

Rewrite[edit]

Sorry if I've seemed to bull in and do a major rewrite without consultation, but as it stood the article was in dire need of help. The term "Barbara", for example, was introduced with no explanation or context, and I doubt whether an intelligent reader who was ignorant of the subject would have been any the wiser (actually, even someone who did know something of the subject would have been puzzled at points). The last section, on validity, is also a bit of a mess (confused, obscure, bitty), but I ran out of time. I'll be back soon, though if anyone else wants to pitch in... --Mel Etitis (Μελ Ετητης) 22:17, 6 March 2006 (UTC)

Thank you, Mel. That's a huge improvement. SlimVirgin (talk) 22:38, 6 March 2006 (UTC)

Where did Baralipton go from the list? — 0918BRIAN • 2006-03-6 22:46

Baralipton is an indirect mood (like Frisesomorum, Fapesmo, Dabitis, etc.); I'll add a section on those, but this was a first go, and meant to be simple and straightforward. --Mel Etitis (Μελ Ετητης) 23:04, 6 March 2006 (UTC)
After double edit conflict:
Ah, I've just looked at the History, and found this version. It's better than what I replaced in many respects, though it too often reads like a (somewhat facetious) personal (and PoV) essay, and goes into rather too much detail for an encyclopædia article on some matters (History pf logic would be a good place for a lot of it). If this had been in place when I came along, I'd have still wanted to subject it to a good shave and haircut, though I'd have been less inclined to replace it wholesale. Perhaps some compromise can be found, adding material from the version in history to what's now in place?
As this is specifically and only about the syllogism, though, we need to be careful not to overdo the general history-of-logic stuff. --Mel Etitis (Μελ Ετητης) 22:56, 6 March 2006 (UTC)

hey, Mel, Slim. Suit yourselves. if you want this page, it's yours. might as well start renaming this place crapipedia... later. Ted 22:58, 6 March 2006 (UTC)

oops. We need a process, that is clear. Some civility is called for here. It is probably discomfitting when the electric fence shows up, but we eventually reveal ourselves when we edit here long enough. When the articles reach stability, all too often the consensus is unspoken although real. This could all have been avoided with a general call for approval on the talk page, periodically. Please don't feel too aggrieved; it would probably be best if you simply retracted the above. If you do so, you have my permission to delete my statement as well. Peace. But we have just crossed a line here. Perhap we need some breathing room as well. --Ancheta Wis 23:11, 6 March 2006 (UTC)
OK, perhaps I was wrong about compromise, and thinking that we could all work together. Still, if other editors would care to join in? --Mel Etitis (Μελ Ετητης) 23:04, 6 March 2006 (UTC)

Mel, please, neither you nor Slim showed any interest in this page until after I got in a tiff with her. and I really don't want the to badger either of you about. it saddens me that the two of you would go out of your way to muck up a page just to try to punish me, so I'm hoping that if I stop participating for a while you guys will come to your senses. drop me a line if you care to discuss things, otherwise I'll check back in in a month or so.

Ted 23:09, 6 March 2006 (UTC)

No one's "punishing" anyone. It was just that the version that was on the page before I reverted was too much of a personal essay, and the one that I reverted to was inadequate. As Mel says, somewhere in between would be ideal, being careful to leave out personal opinions, or else attributing them to a published source. SlimVirgin (talk) 23:12, 6 March 2006 (UTC)
No, you have violated Wikipedia rules of civility by reverting hours of work by an editor. You have disrupted this page to make a point, among other things. As above you are in violation of [5] and I ask you stop harassing Twrigley because he mediated a case in which you would not participate. It is uncalled for. If an editor has a problem with a portion of this article, let that individual editor present his case here and with civility work out the problem with Twrigely who has put hours into this. --Northmeister 02:27, 8 March 2006 (UTC)

What's happened?[edit]

We have now lost the whole of the original article on term logic - here is a recent version.

[[6]]

At some point it was turned into a rambling essay, then got merged with syllogism, then SlimVirgin cut it down completely. I agree some that some reduction was necessary, but now we have lost all the stuff on why there are two terms in the proposition, what terms are and so on. Dbuckner 12:30, 7 March 2006 (UTC)

Would it be acceptable to revert to the term logic Revision as of 03:41, 20 January 2006 and disconnect from this article, for now? Anyone? --Ancheta Wis 13:38, 7 March 2006 (UTC)
Well not really, as Mel's rewrite of this article is quite good, and the old Term logic did overlap a lot. I need to think of a way to bring in the material that was lost. Dbuckner 13:57, 7 March 2006 (UTC)
Twrigley, by all means start merging back some of the old version (in consultation with the other editors), but please don't delete Mel's additions, because they really are improvements. SlimVirgin (talk) 13:29, 8 March 2006 (UTC)
I agree with "Slim Virgin". I wrote the article "Term Logic" some years ago when WP style was chattier. Since then additions were made that were stylistically awful, and I'm happy to see it go in the dustbin. Plus, Mel's rewrite is high quality stuff and we should keep it. So, Ted, please be constructive about this. Dbuckner 08:54, 9 March 2006 (UTC)

Versions[edit]

this page has been reverted to it's state before this argument began. please see my discussion with Mel Etitis on my talk page, here. Mel, since you agree that the original version was superior to the version you found on your first edit, I suggest that we begin revisions (however extensive you would like those to be, beginning here.

I agree with your comments on wordiness, and while I disagree in strong terms with SlimVirgin's claims about personal essays, I'm willing to discuss the matter. her actions, however, destroyed far too much new and worthwhile content to be considered appropriate.

shall we discuss a plan for revisions, or simply feel our way through the process? as I said, I've had ongoing discussions with two other established editors of this page about changes, and there's no need for particular hurry in the matter. —Preceding unsigned comment added by Twrigley (talkcontribs)

Ted, your discussion with Mel on his talk page shows that he agrees some of the old version should be merged into this one, but not all of it, because as he said some of the old had POV problems and parts were written in an unencyclopedic style. Mel has said that once his busy period is over, he'll be able to start collaborating on transferring material from one version to the other. I think you should wait for him to do that, because you'll probably end up with a great article as a result. SlimVirgin (talk) 13:42, 8 March 2006 (UTC)

SV... thank you: I'm more than happy to collaborate with Mel. however, I personally feel it's much better to start with a relatively complete page and pare it down, than to begin with a skeletal page and build it up. you are free to disagree, and we can discuss this if you like.

but it appears from the immediate reversion that you've marshalled people to make sure that we do it your way. that's cool. very bad faith on your part, but none of my business. Ted 13:56, 8 March 2006 (UTC)

  • I've just seen that User:Twrigley has reverted the page (twice) with the extremely misleading edit summary "rv. per discussion with Mel. please see discussion on talk page". Even if he's using "per" in an extremely non-standard way, I find it very difficult to assume good faith with regard to this; nothing in what I've said here or on his Talk page comes close to justifying a reversion (quite the contrary). I shall continue to make use of his material when expanding and up-dating the article, but it seems clear that he's not in fact interested in collaboration. I think that that's a pity, but it's silly for me to use up further time and energy trying to achieve an amicable joint approach given his behaviour, so I'll leave it there, and spend the time trying to improve Wikipedia. --Mel Etitis (Μελ Ετητης) 21:55, 8 March 2006 (UTC)
I reverted originally and just now, because SlimVirgin broke rules of civility and her administrator discretion by reverting an entire page she has never engaged in or had been asked to look at. She did this after a mediation case in which she was accused of breaking other rules and defining wikipedia arbcom cases against the wishes of Jimbo Wales. She refused the mediation. Ted got involved in that indirectly as the one who chose to mediate as he was on the Mediation Cabal as it is called. He was attacked by SlimVirgin for his decision done in fairness and honesty. SlimVirgin immediatly came here and reverted days! of edits. You arrived after this and put in hours. I appreciate your work Mel, and offered a suggestion you work with Ted from his original version which did need work. SlimVirgins explanations for reverting an entire work of material were not appropriate as I've shown above. She has failed to answer my legitimate questions. As a wikipedia editor I have every right to question anyone who acts in this manner. I expect answers from her abuse of Ted still. You have been hostile towards me, understandable if you thought I was directing the reversion against your edits...I was not. I actually approve of your edits, but I had to right a wrong when it came to Ted from SlimVirgin who was abusing her role here and continues to do so. My suggestion again, is to work together with Ted, the both of you could put together a wonderful and accurate article. I will continue to uphold his version and insist according to procedures here at wikipedia, that you show sentences you disagree with and show us here in the community your changes with citations, if you refuse to collaborate with Ted who has spent days on this before the unwarranted reversion. --Northmeister 00:38, 9 March 2006 (UTC)
Northmeister, you're trolling, pure and simple, and have no knowledge of or interest in the subject matter, so please give it a rest. SlimVirgin (talk) 02:36, 9 March 2006 (UTC)
SlimVirgin, I am trying to defend someone who tried to help wikipedia out through mediation and who was 'punished' by yourself through reversion. Please answer my questions above. I have every right to discuss this article since your reversion, since that is the topic here, unneccessary reversion. You should of discussed why you wanted to revert before you reverted. You should know this, and the fact you have been around awhile, makes this doubly so. I want civility here. I request in all good faith that you stop 'harassing' Ted and allow this page alone to be edited by those who were working on it before your reversion. I remind you in this official manner: I see you have been experimenting with Wikipedia. Your change was determined to be unhelpful, and has been reverted or removed. Please use the sandbox for any tests you want to do. Take a look at the welcome page if you would like to learn more about contributing to our encyclopedia. Thanks., that reverting an entire page without prior notice or any Good Faith observations of Ted is wrong. You should know this. My interest in this page will end when the 'harassment' and abuse ends. It looks as if Ted left because of what you did, and what Mel has done since your reversion. I extend good faith to Mel, maybe he is an innocent bystander who decided to edit just at the wrong time, not sure, so he should understand that my reversion was done to fix a wrong, and work from the original article with Ted to improve it. We both (you and I SlimVirgin) should stay out of it. --Northmeister 02:45, 9 March 2006 (UTC)
None of this protracted ad hominem addresses the important question of the relative quality of Mel's work versus the quality of the work he replaced. My judgment is that Mel's work is better (I have studied syllogistic and traditional logic for nearly thirty years). By a long way (see my comments below). I'm sorry if anyone has been offended or upset, but at the end of the day we are trying to write a quality encyclopedia, and the sections on logic and philosophy need all the quality they can attract. So please: chill out. Dbuckner 09:26, 9 March 2006 (UTC)
Yes, I agree a quality article is the most important. Your statement below is incorrect. SlimVirgin reverted an entire article and Mel came in right after that. Mel's contributions are excellent, but the work of Twrigley was also well done. I've seen no real explanation that Twrigley's work on the article was wrong. The first standard of an encyclopedia is getting it right. The second is writing it straight. Everyone says Twrigley got it right, including SlimVirgin. Even Mel acknowledged a better version that was interestingly Twrigley's. The point then is to restore that better version by his own admittance and then include the changes Mel wishes to make. First we right the wrong done by SlimVirgin. Then we collectively replace any material that Mel has done better into the article to improve it. Thus we have structure, fairness, and cohesion to the entire process. I restored Twrigley's version. Mel now may edit that original article that was vandalised with any better material. Let's do this paragraph by paragraph as a starting remedy. The end results will clearify all disorder and restore vitality and accuracy to wikipedia and this article. Let us engage. --Northmeister 14:43, 9 March 2006 (UTC)

Suggestion[edit]

Some more thoughts. I've read again through the edit that "Ted" and "Northmeister" want to revert. Their complaint is that a lot of material has been deleted by Mel's rewrite, which is true.

Bit I would NOT want to lose Mel's rewrite, as this deals with the syllogism in a compact and efficient way. He introduces the syllogism with a short definition, moreover in a way that defers to Aristotle in the medieval style. Then he introduces the idea of major and minor premiss in an economical way, by the key concepts of major, minor, minor and middle term. Nearly all you need to know about the syllogism is in the introductory paras, which is the essence of good writing. So, well done Mel.

However, the problem is that 'Traditional Logic' is a far wider area than just the syllogism, and the original article 'Term Logic', which was (cursory) attempt to deal with the wider subject, is now completely lost. Can I therefore suggest that this issue is dealt with in the upcoming rewrite of all the logic pages, which Charles Stewart ((talk) ) (an accomplished logician) and myself (a not so accomplished logician, but I do have a detailed knowledge of the history of logic). Rather than get into a protracted edit war, can I suggest that solution.

I.e. in SUMMARY: keep Mel's rewrite, but work towards a proper organisation of the logic pages, and moreover work together without these protracted and silly arguments. Yes? Dbuckner 09:26, 9 March 2006 (UTC)

Speaking for the bystanders, thank you for your precis. Might we see a sketch of a roadmap for the logic pages at some time? That might even attract others to the pages. --Ancheta Wis 10:27, 9 March 2006 (UTC)

Yes. At the top we have the article on Logic. The idea of the recent rewrite as proposed here User:Dbuckner/logic was to emphasise the elements that 'traditional' logic have in common with 'mathematical' logic (of schema and logical form, of inference and validity and so on).

The article Organon should cover precisely what Aristotle covered in the books now called by that name. I have done some work on the sub-articles such as Posterior Analytics, but I slapped on a 'developed or reviewed' notice on Organon itself as there are numerous inaccuracies.

There should be an article Aristotelian Logic. This should cover the 'Peripatetic' logic of the Middle Ages, including the additions (such as the theory of consequences, supposition theory, the theory of mental language and so on).

There ought to be something on Traditional logic, covering the period from Arnauld to Mill, as this is fairly distinct and leads naturally into modern logic.

Regarding modern logic, there are already some very good articles, e.g. Mathematical logic, on the mathematical logic side. It is less good in the area of Philosophical logic however. I have contributed ad hoc articles – a complete rewrite of Existence for example, plus Plural quantification and some others, but there needs to be more work here. Enough? Dbuckner 11:53, 9 March 2006 (UTC)

A further problem is that any of the more general subjects such as Truth will come under attack from the Usenet fringe. I'm surprised Existence hasn't yet. I'm hoping that Logic is enough of a specialist subject to avoid detection by elements who imagine that generality of subject matter is an excuse for ignorance of it. A notable casualty of this is the Philosophy article, which genuine philosophers such as Mel have avoided (end of sermon). Dbuckner 11:53, 9 March 2006 (UTC)

As per by latest statement[edit]

Let us engage. Paragraph by paragraph, Mel offer your rewording here for the community to consider both paragraphs and to work with yours and Twrigley's for accuracy and detail. Together much can be accomplished. --Northmeister 14:46, 9 March 2006 (UTC)

I will start with the first two opening paragraphs which in my opinion are much better for their historical background and for lay-person wishing to understand this page, like myself works better. Here is the paragraphs:

"Syllogisms are the cornerstone of the logical tradition, known as term logic or Aristotelian logic, that originated with Aristotle (see Prior Analytics, Book I, c. 1.) and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. A syllogism (Greek sullogismos, meaning deduction) consists of three interrelated propositions, in which the last proposition is shown to be necessary if the first two propositions are true. Occasionally these are called categorical syllogisms because the propositions they contain involve relatively simple declarations about categories, objects, and the properties that apply to these categories and objects. Syllogisms are usually considered to be a form of inference, but the inferences drawn in syllogisms are generally viewed by nominalists as trivial and tautological. Instead, syllogisms are used to examine the validity of reasoning involved in a given statement by exposing questionable assumptions and incorrect category relations. This article provides an introduction to syllogisms (categorical syllogisms, term logic), giving some historical background, a description of the basic use and structure of syllogisms, an analysis of common errors in reasoning, and suggestions for further reading.

Non-categorical syllogisms deal with the truth values of proposition in relation to other propositions, rather than looking at their internal structure of propositions as is done here. Propositions are taken as single, non-decomposable elements in non-categorical syllogisms, each with a given truth value, without considering internal validity or derivation. See disjunctive and hypothetical syllogisms."

Considering the above two paragraphs, what within them needs changing to improve these two. Let us engage in discourse and improvement. --Northmeister 14:52, 9 March 2006 (UTC)

1. In the tradition referred to the conclusion is not 'shown to be necessary' it 'results of necessity'.

2. The explanation 'These are called categorical syllogisms because the propositions they contain involve relatively simple declarations about categories, objects, and the properties that apply to these categories and objects.' is not a very good explanation. It presupposes understanding of 'categorical'. (Actually Mel's is not much better here).

3. 'inferences drawn in syllogisms are generally viewed by nominalists as trivial and tautological' – there is a grain of truth in this, but presupposes a much wider debate which it would not be wise to bring in at this point.

4. " Non-categorical syllogisms deal with the truth values of proposition in relation to other propositions, rather than looking at their internal structure of propositions as is done here. Propositions are taken as single, non-decomposable elements in non-categorical syllogisms, each with a given truth value, without considering internal validity or derivation. See disjunctive and hypothetical syllogisms." This is incomprehensible.

5. Much of the rest of the article comes from the article I wrote in September 2003 which is [here], and which is much broader in scope. I have already said I do not mind if it falls by the wayside for now.

6. Northmeister: please stop this mindless reverting. You left a message on talk page saying "my sense of justice precludes me from starting anywhere than Twrigley's original article". Most of this is not Twrigley's, and my view, if you forgive my saying, is that he did not improve what I had originally written (quite the reverse). Dbuckner 15:28, 9 March 2006 (UTC)

As evidence of this, Twrigley wrote in a previous edit. "Formal logic is a complex game. And I do mean game - in its intricacies it resembles the world's best crossword puzzle. For the most part, these intricacies develop from difficulties with variant category constructions: subsets, negations, exclusions. e.g." Dbuckner 15:34, 9 March 2006 (UTC)

Dbuckner, I didn't have time to photoshop an LCD monitor into Rembrandt's picture. But I can see a phone on the desk and a printer in the window. Please reconsider leaving the encyclopedia. Regards, the lot of us.

In fact if any more of this nonsense goes on it will be me who leaves Wikipedia. I've had enough of it. Philosophy was bad enough. My professional work involves drafting complex documents using teams of people. To do this we hire people with proven ability by a complex system of exams and work experience. This works. The idea that you can do the same except without the qualifications is completely mad. Wikipedia was a brave social experiment. It has failed. Dbuckner 15:34, 9 March 2006 (UTC)

I actually share your sympathies above. The social experiment of wikipedia is failing and the example of what has happened to me (per history articles-my field of expertise) is sad. My attempt to defend an innocent bystander from disruptions and ill-will seems also to be failing. That is all true. As I have stated often, I do not debate the contents, but the wrong done. There is no need to bring the above statement up again, I already questioned SlimVirgin for doing so, since this statement was changed after it was written weeks ago. My proposition that we -right the wrong done by SlimVirgin and work from there, is out of sense of justice. Then as a community, Mel, yourself, Ted (if he ever returns) can work together to improve this article. That is how wikipedia works, to get it right through collaboration and consensus. I do not wish to argue continuously. It is as if no one listens, but simply responds. No war exists here. Simply a struggle to right the original wrong, use Mel's improvements, and your thoughts on the subject to improve the article. I got involved here because of what SlimVirgin did. This is your range of expertise, and when the wrong is righted and the community works together, achievement can result. Only the few make it harder on the rest of us. But the many, united together in common hope, with evidence and facts, can through the rule of consensus progress toward works of excellence. That is what we came here for. You came here and I, to offer our expertise, to engage with the community at large to put together a free-encyclopedia that the world could turn to and gather information from for their studies; to build together and work out our problems through citations and fact. We came because we love knowledge, we are pushed around by the few, who have ruined our experience. But they are the few, that very small few, and once recognized for their actions, the many who want harmony and truth, can united to prevail for that truth, that justice, that Wiki-way. Let us not turn back but forward and face this situation with all that brought us here. Let us work together and as a community and overcome the small molehills that like a mirage in the blinding sun of the desert, looks as if it were a mountain. --Northmeister 15:52, 9 March 2006 (UTC)
Northmeister, it appears that Mel, Dbuckner, Charles Stewart, and Ancheta Wis have the expertise needed to write a good article based on Mel's version, while retaining the good material in the previous version. Please allow them to get on with that. SlimVirgin (talk) 16:11, 9 March 2006 (UTC)
Nonetheless Then I leave Wikipedia, after many years of work, and many articles on philosophy. Just to be clear, it is because of people like you [Northmeister], who say (your words) "I do not debate the contents, but the wrong done". It's not clear that any wrong was done here. Mel, who is a professional philosopher and a good writer, reverted an edit by someone who is not a professional philosopher, and is not a good writer. What's wrong with that? And in any case, the most important thing is the contents. I'm fed up with working with people like you. Dbuckner 16:19, 9 March 2006 (UTC)
I'll come back when there is a decent editorial policy. It's unfair that people who have some sort of respect within their peer group, have to put up with this constant low level of aggregation. It was not like this when I started on WP. The lunatics will eventually take over the asylum. Dbuckner 16:19, 9 March 2006 (UTC)
ME? Mel did not revert first. Check the edit history. It was SlimVirgin. Your arguments continue to state fallacies. You have the personal choice to leave. To blame my defense of someone who was wronged by SlimVirgin (who has wrong others in the past), on your leaving based on your false assumptions above, is specious at best. People like me? What sort of person am I to defend a fellow editor from abuse? What sort of person am I to right a wrong done to Ted after SlimVirgin was ruled against in a mediation case and responded in kind here to revert his entire work? What does that make me? I concur about editorial policy, there is actually a decent one, just the few like SlimVirgin who abuse their positions by what she has caused and done here at this page. Look at the results of it. Had she not violated 'don't disrupt to make a point' this whole thing would not be occuring, as I would not be here trying to defend a good and honest editor who was abused by her. Am I a lunatic by your accusation? If defending others from abuse is lunatic then I am guilty. If attempting to defend wiki-policy on decency and 'do not disrupt' makes me a lunatic, then am I am guilty. If attempting to right a wrong done by SlimVirgin here makes me a lunatic, then guilty. Why are you so hostile towards me? I've never been hostile towards you? It doesn't make any sense. I've called for harmony and working together and I am accused of being a lunatic, once again guilty as charge, if that is the definition. --Northmeister 16:45, 9 March 2006 (UTC)

last comments before I leave for good[edit]

I am finding this entire experience exceedingly unpleasant, and so I have decided to leave the Wikipedia community. I'm just waiting for some responses on a couple of issues before I finalize that. I would, however, like to make a few last comments re: this page before I go, which will hopefully settle some disagreements.

Dbuckner, Mel
I wouldn't disagree with you on most of your points. My issue is not with Mel's rewrite, or with DBuckner's desire to re-separate the Syllogism and Term Logic pages. My objection is to SlimVirgin's crass exportation of a personal vendetta into article content. It's a pity that the syllogism page got caught up in that. I will say that the one line you keep bringing up "Formal logic is a complex game. And I do mean game - in its intricacies it resembles the world's best crossword puzzle. For the most part, these intricacies develop from difficulties with variant category constructions: subsets, negations, exclusions. e.g." is one I probably would have cut out myself, except I forgot I put it in. Well... the second half is actually true, if maybe a little on the NOR side... but in itself this was not grounds for reverting the entire article. Frankly, under other circumstances I would have loved to work on the article with both of you, but... I just don't like it here.
Northmeister
If you respect me, and respect that I honestly tried to help you on the other page, please do not bring the fight with SlimVirgin here. Let it be, and let the people who really want to reconstruct the page get to work. I will not be working here, and if you leave as well, SlimVirgin will have no further reason to be here either. She won't control herself (she's not capable of it), so it's up to you to be the responsible one. Ok?
Ancheta, and other observers
My apologies for all this. I got some crap stuck on my shoe in a different context and it dragged itself in here after me. Not much I can do about it, but I do feel bad.
SlimVirgin
Since I'm leaving, I feel free to tell you that you are one of three people in the world that I have reason to disrespect utterly. You have no perspective, no self-discipline, no sense of context, and no sense of decency or propriety. Go away, you're useless.

Administrator trolls, I swear... and you wonder why the social experiment is failing here? Ted 18:29, 9 March 2006 (UTC)

  • Thank you for bringing this talk page to the level of MySpace. It is what we have been striving to accomplish. Wikipedia is not a social experiment. It is a site that uses social software to create an encyclopedia. If you want a social experiment, check out MySpace or LiveJournal. I highly doubt the staff of Encyclopaedia Britannica throws nearly as many "hissy fits" as those on Wikipedia. — 0918BRIAN • 2006-03-9 19:29

<shrug...> I play the cards I'm dealt, my friend. I wish that Wikipedia were what you hope for, and I hope it reaches that state some day, but I recognize a fold hand when I see it.

I do Ted, and I will not intervene here any longer. Sorry to see you leave. Good wishes and luck in the future. --Northmeister 22:09, 9 March 2006 (UTC)

Four and a half years later, 2010, reading the above I remember the high hopes we had for Wikipedia. Our cult of the amateur, as someone has called it, failed. When you empower everyone equally, the people with the biggest grudges and the most time on their hands outlast anyone who "has a life," as the saying is. By 2010 one expects this and one enjoys Wikipedia more than one did in 2006. Profhum (talk) 04:54, 11 September 2010 (UTC)

Merge/rewrite project[edit]

For those who want to work on the article using the version before the version before my rewrite, I've moved it here. My feeling is that a lot of the material would better moved to Term logic or even to Mediæval logic, but some of it certainly belongs in this article. --Mel Etitis (Μελ Ετητης) 10:03, 13 March 2006 (UTC)

That's well done, Mel. There had almost been an edit war here

Patrolling the ocean called Wikipedia|Tell me about vandals, violations and more... 13:38, 13 March 2006 (UTC)

Types of ... Gibberish?[edit]

Sorry to tell you folk, but, at the moment, everything from "Another classification" in Syllogism#Types of syllogism until the start of Syllogism#The place of the syllogism in logic is unexplained, out-of-context, near-gibberish. What is the table for? What is being explained? Who are Barbara and her friends? Please tell us, in plain english please, what you are hoping to tell us here.

After a bit of Googling I think I've been able to clarify it. What seems to be being explained is that there are a finite number of types of syllogism and the article discusses the categorisation scheme for them. Barbara and so forth are mnemonics for the types of valid (logically correct) syllogism. I'll add an example of each type if I can find the time.
It would be nice to have an explanation of why A, E, I and O.

--Ekaterin 12:37, 7 August 2006 (UTC)

The article explains what you were able to find using Google. As for why A, E, I and O, according to Irving M Copi, Introduction to Logic, third edition, The Macmillan Company. (1960):
The letter names are presumed to come from the Latin words "AffIrmo" and "nEgO," which mean "I affirm" and "I deny," respectively.
I've added a note to this effect to the article.
Paul August 19:01, 7 August 2006 (UTC)

Doesn't sound right to me. Was the choice of A,E, I, and O random? Could any of the other letters of the Latin words have been chosen? It would be different if they were the first letters of the Latin words. But, the letters of the first Latin word are the first and fourth letters. The letters of the second Latin word are the second and fourth letters. There is not even a pattern. It is more likely that they were primarily chosen simply because they are the vowels in well-known order. The Latin words are merely a mnemonic, as an afterthought.

The vowel letters … are symbols or abbreviated names, which are always used to denote the four kinds of proposition; and here will be no difficulty in remembering their meaning if we observe that A and I occur in the Latin affirmo, I affirm, and E and O in nego, I deny.

William Stanley Jevons, Elementary Lessons in Logic, Lesson VIII

Lestrade

Alternative syllogy[edit]

What about the famous parody on these logical examples:

One cat has one tail more than no cat.
No cat has nine tails.
Thus, one cat has ten tails.

What is this an example of? 惑乱 分からん 23:13, 15 September 2006 (UTC)

The negative phrase "No cat" is being misused as a positive concept. Happens all the time.Lestrade 13:40, 19 September 2006 (UTC)Lestrade

inconsistent opening paragraphs[edit]

Hi, I can see that there has been a lot of discussion in this page here, and that the page has gone through numerous rewrites. However, this opening part is blatantly inconsistent and very confusing:

"In Aristotle, each of the premises is in the form "Some/all A belong to B", where "Some/All A' is one term, and "belong to B" is another, but more modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in the case of the major premise this is the major term, i.e., the predicate of the conclusion; in the case of the minor premise it is the minor term, the subject of the conclusion. For example:

Major premise: All men are mortal. Minor premise: Socrates is a man. Conclusion: Socrates is mortal. "

So we read that "each of the premises is in the form "some/all A belong to B," and then we are given the example premise "Socrates is a man." Uhhh, what???? Fix this please. It may just take something as simple as "Socrates is a man is actually technically rendered in a syllogism as 'All things that are Socrates are men," but please clear this up.


One serious problem with this language is that it completely reverses the sense of "belongs" (inherited from Aristotle's terminology in Greek). When Aristotle says, "A belongs to B" (or more precisely what's usually translated as that), what it means is "A is true of what B is true of", or if you like "Things that are B are also A", or to be absolutely traditional, "Bs are As". In other words, in "A belongs to B", A is the predicate term and B is the subject term. It would be accurate to say "each of the premises is of the form "A belongs/does not belon to all/some B" (if a little awkward), but it is actually nonsense to say something like "Some A belong to B" (that would be equivalent to "Bs are some As").

For purposes of exemplification, the example given is also very misleading. The categorical syllogistic requires that every term be a general term, i.e. something that can be used as a predicate. "Socrates" is not such a term: it's a singular term, i.e. a name. The sentence "Socrates is mortal" can't easily be classified as universal ("All Socrates is mortal"?) or as particular ("Some Socrates is mortal"?). There's a long history of discussion about just where to put singular terms in any version of the syllogistic, but in any event "All men are mortal, Socrates is a man, therefore Socrates is mortal" is actually a poor example of a categorical syllogism,---Robin Smith

May I second the above -- as a visitor who also found that passage obscure in an otherwise illuminating article.

A second inconsistency appears in the baroco (A-O-O) example:
All informative things are useful.
Some websites are not useful.
Some websites are not informative.

Surely, the minor premise and conclusion need to be reversed here?! In the major, 'informative' is a subset of 'useful' but not (necessarily) vice versa. So while uninformative websites are not useful, there is no reason to believe that useless websites might not still be informative. Syllogistically speaking. 212.248.167.53 22:35, 24 January 2007 (UTC)Estragon

I agree with the original comment - in default of a detailed explanation about how singular nouns ("Socrates", in the example) are considered to refer to their entire extension in a syllogism, perhaps a change to "All humans are mortal, All philosophers are human, All philosophers are mortal" might be in order. On Estragon's point, this is in fact how Baroco works - a perennial problem with all the second, third, and fourth-figure syllogisms. We can reduce it to a first-figure syllogism (Ferio) by contraposition of the major:

No non-useful thing is informative
Some websites are non-useful
Some websites are not informative.

Tevildo 11:38, 22 April 2007 (UTC)

I also propose to change the "Basic structure" section to just include a canonical example of a perfect syllogism. The "All greeks are human, all humans are mortal, hence all greeks are mortal" would be a viable candidate. This article discusses Aristotle's syllogism, and Aristotle just admits universal terms in his system. Let's shift the discussion the use of singular terms like "Sokrates" in syllogisms into later section, since it is an extension to Aristotelian logic. Łukasiewicz who is mentioned as reference in this article makes a big point in making clear that there are no singular terms in Aristotelian Syllogistic.

Further the opening section would more accessible, if just gave a short description of a syllogism without discussing special cases. Der lunz (talk) 16:09, 14 August 2008 (UTC)

Hi. I came here to ask a specific question, but Robin Smith has already asked it;So we read that "each of the premises is in the form "some/all A belong to B," and then we are given the example premise "Socrates is a man." Uhhh, what???? Fix this please. It may just take something as simple as "Socrates is a man is actually technically rendered in a syllogism as 'All things that are Socrates are men," but please clear this up.

I see from the discussion here that alternative examples have been suggested, but not implemented. I also see that the exact status of singular terms is contested - so why complicate things for a general reader such as myself by introducing a singular term premise in the very first example of the article ? Especially since none of the 19 examples of valid syllogisms contain a singular term premise - this means that for me as a beginner, I'm unable to decide exactly what form of syllogism the Socrates example is. Which is most unhelpful.

I think that if all the examples of the 19 valid syllogisms are going to be universals, then so should all the other examples in the article. There should then be a separate section devoted to singular terms and their classification. I'm sorry I can't help write it myself. Regards Gnu Ordure (talk) 16:03, 4 March 2009 (UTC)

agreed, do not use singular terms in examples. They create much smoke and no light for the general reader. --Philogo (talk) 00:11, 5 March 2009 (UTC)

Hi Philogo - That's great, nice edit. I guess I could have just done it myself, but I'm new here, and it seemed presumptuous, given my very limited understanding of logic (not to mention the rather heated nature of the discussions above).

Anyway, as I said, the article is still lacking - I think I'll start a new section here with a specific request, if that's OK. Cheers, Gnu Ordure (talk) 18:52, 5 March 2009 (UTC)

Frege[edit]

The logic that Frege invented was second-order not first-order. Both he and Pierce produced second-order logics at around the same time. That students are now taught a first-order variant of Frege's logic is because it was subsequently discovered that second-order logic has certain limitations that are not present in first-order logic. One of the key benefits of Frege's logic was its ability to deal with the problem of multiple generality in a way that Aristotelian logic could not. As a starting point, Wikipedia articles on multiple generality and quantification touch on this point.

Ok, it was corrected! Cyb3r (talk) 17:58, 25 May 2008 (UTC)

Datisi type explanation[edit]

Hello,

First of all I'd like to third' the above statements and mention that the opening is indeed confusing and possibly wrong.

Secondly I believe that Datisi under the paragraph Types of syllogism is wrongly stated. Currently is stands as following:

Datisi

   All the industrious boys in this school have red hair.
   Some of the industrious boys are boarders.
   Some boarders in this school have red hair. 

Doesn't this give of the wrong conclusion. This example assumes that there are red haired boarders in the school.

If it sais "Some of the industrious boys IN THE SCHOOL are boarders." than the conclusion would be valid.

A valid point - appropriate changes have been made. Tevildo 16:18, 13 May 2007 (UTC)

Set diagrams and four dimensional structure[edit]

The fifteen syllogisms valid in modern logic, represented in the diagrams below, correspond with a four element sets non empty subsets. Is anyone able to explain this curious matter?

Error between language and logic[edit]

Consider the following claims: "All humans are not perfect / No humans are perfect." In my opinion, they are different or at least can be interpreted differently. When P is "the object is perfect" and A is "for all humans", the first sentence says -A: P (A = "for all", P is a statement), in other words "it is not true for all humans that they are perfect". The second says -E: P, "there is no human for which holds: he/she is perfect" which has the same value in logic as A: -P. Careful consideration: is there an error or is it just me?86.50.9.167 (talk) 21:30, 27 April 2008 (UTC)

I understand "All humans are not perfect" as ∀x H(x)→¬P(x) and "No humans are perfect" as ¬∃x H(x)∧P(x) where H(x) means "x is human" and P(x) means "x is perfect". Now, assuming the law of excluded middle and that (¬∃x ¬A(x))↔(∀x A(x)), then the two are equivalent. bungalo (talk) 13:16, 27 October 2012 (UTC)

Request for a new section in this article...[edit]

Hi. I admit I know very little about logic. I came to this article looking for an answer to a specific question, and was confused by what I found. After reading the discussion above (section 20), I saw that others were similarly concerned, and after I raised the point again, Philogo has made an appropriate edit.

My question remains; why does Aristotle's syllogistic system exclude singular premises ?

This raises supplementary questions. What is the implication of composing a syllogism with a singular premise ? Is the conclusion still valid ? If so, why ? If not, why not ?

This raises another question. If singular premises are disallowed, why does the most famous syllogism in the world contain a singular premise ?

I've just spent half an hour trying to find out who first used the Socrates example, and failed. The Stanford Encylopedia of Philosopy sources it back to (at least) the 14th century :

So far as syllogistic was concerned, some logicians, such as Lambert of Auxerre (or Lagny) gave a standard account of the Aristotelian syllogism which is centered on the universal and particular quantification of general terms at the same time as they gave examples with singular terms, such as “Every man is an animal, Socrates is a man, therefore Socrates is an animal.”

I find this fascinating. Someone creates a system which disallows singular premises, and then for hundreds of years, other people use syllogisms with singular premises as examples of it.

I mean, Doh (as another famous greek said).

But to recapitulate: what I think the article now needs is a short additional section devoted to singular premises; this should include a definition of them, an explanation of their exclusion from Aristotles's system, and another explanation of why they have historically (and erroneously ?) been used as examples of said system (e. the Socrates example).

This would be very, very, helpful to the general reader (ie me).

Cheers,

Gnu Ordure (talk) 20:58, 5 March 2009 (UTC)

It is categorical sylogisms (the usual sort) that do not allow singular terms, only categorical terms. Look here for a neat defintion/explanation of "categorical" [7]. Hence a syllogism in using "Socrates is a man" is NOT a categorical syllogism (because "Socrates" is not a categorical term) and is a poor example of it, now corrected in this article I am not sure how Aristotle dealt with singular terms (it's been a while), but you can use the categorical syllogisms in the following way.

"Construe" "Socrates is a man" in one of the following two ways. (a) "Something is a man" (b) "All that is Socrates is a man" (or cf as I have seen "Pegasus is a horse" as "All that pegasizes is a horse". No I am not making it up, its Quine (I think)!)
Having "construed" in this way, we can reason for example either (a) "Some thing is a man, All Men are Mortal, therefore Some thing is Mortal." or (b) (BABARA) "All that is Socrates is a man, All Men are Mortal, therefore All that is Socrates is Mortal." Hope this helps! PS Normally after studying Categorical Syllogisms, the student goes on to study Logic post Frege (who made the theory of Syllogism, for all practical purposes, redundant, RIP) in particular First Order Predicate Logic, in which all the valid Syllogisms can be proven (as well as a WHOLE lot more.)

It would be possible to show in this article for each syllogism their expression in modern first order predicate logic. As an exercise a proof of one any of them could be constructed in first order predicate logic. I think you would be impressed. --Philogo (talk) 14:42, 6 March 2009 (UTC) Eg starting by:

A: a universal affirmative proposition--All S is P [(x)(Sx -> Px)].
E: a universal negative proposition--No S is P [(x)(Sx -> -Px)].
I: a particular affirmative proposition--Some S is P [(Ex)(Sx & Px)].
O: a particular negative proposition--Some S is not P [(Ex)(Sx & -Px)].
--Philogo (talk) 14:51, 6 March 2009 (UTC)

Hi Philogo. Thanks for the links, very helpful. I've been thinking about your two alternative construels, and I admit I don't understand how the re-phrasings avoid the singular. The original goes : All men are mortal. Socrates is a man. So Socrates is mortal. The minor premise refers a single entity (points at scruffy bearded philosopher, who for the purposes of this argument is somehow alive and well).

First you suggest re-construing as follows:

All men are mortal. Some thing is a man. So some thing is mortal.

But now we've lost Socrates, the syllogism no longer refers to him at all. (Unless the "some thing" in the minor premise actually refers to the man (points at scruffy philosopher) - but if that's the case, the minor premise should more accurately be written : This-thing-here is a man. But we can't write that without abandoning the structure of categorical syllogism (A E I or O).

So, this structure is fundamentally different to the original - ie it leads to a different conclusion.

The second re-construel goes like this :

All men are mortal. All that is Socrates is a man. So, all that is Socrates is mortal.

The problem here is that if "All that is Socrates" refers to a single entity (points at etc etc), then one might as well write "Socrates". What difference does it make ? And then we're back to the disallowed form.

May I suggest a solution ? We simply pluralize Socrates. Not the scruffy philospher himself, of course, we can't clone him - we simply call other things by his name, so then there's more than one 'Socrates'. First, I've bought a dog, which I've called Socrates. Second, I've written a play, which features a character named Socrates.

So there are now 3 things-named-Socrates : a person, a dog and a fiction.

(Note that the minor premise of your second re-construel, All that is Socrates is a man, now becomes untrue, so the conclusion is untrue).

So, we can re-write the syllogism to deal with the existence of 3 socrates, by making the distinction between 'socrates' and 'a thing named socrates':

All men are are mortal. Some things-named-Socrates are men. Some things-named-Socrates are mortal.

That seems to work. It distinguishes between the man and the dog and the fiction (and allows for other people to be named Socrates, as there undoubtedly are).

And it provides the conclusion we want, referring to the man himself, now identified as 'a-thing-named-Socrates'.

And this is the form of valid syllogism known as Darii:

All kittens are playful. Some pets are kittens. Some pets are playful.

Imagine that my dog dies and I burn my play. There is now only one thing-named-Socrates again. The syllogism remains sound.

What do you reckon, Philogo ?

Gnu Ordure (talk) 20:29, 6 March 2009 (UTC)

I think you are enjoying this (I hope you are). It's been a while since I looked at syllogisms (they are obsolete you realize). Lets say we want to use our categorical sylogisms, to show that the following is a valid argment "Socrates is a man, all men are mortal ergo Socrates is mortal". We know it is valid intuitively, but it is not in the form a a categorical syslogism, so the latter cannot be used to demonstrate the former, ergo categorical sylogisms are inadequate. The best we can do to keep the motor running, so to speak, is to "construe" the first premis as being somehow equivalent to a categorical proposition, by susstituing (as we must) a categorical term for "Socrates". You don't buy my two suggestions i.e. substiture (a) "Something" for "Socrates" (b) "that is Socrates" and you suggest (c) "things-named-Socrates". I feel that (c) suffers from the same defect as (a) - the conclusion "Some things-named-Socrates are mortal" is not really equaivalent to "Socrates is mortal" is it, because your dog is called Socrates as well. Lets say we can come up with (what in the trade is called "a definite description which fits our sage and no one else, say, Greek philosopher, teacher of Plato, bad tempered wife drank hemlock etc. For shorthand we could agree that anyone who fits that description is said to "socritose", i.e, by definition Socarates and nobody else socratises. Now we have a categorical term and can write "All that socratises is a man, all men are mortal ergo all that socratises is mortal".
PS I lied to you when I said if we substitute the FOPL shown above for AEIO cat props, all the 24 valid syslogisms can be shown to be valid. In fact on these substitutions of the 24 valid sylogisms only 15 turn out valid and nine invalid. Notshelling. the reason is that (i) All S are P in sylogism entails (ii) Some S are P, whereas (iii) (x)(Sx -> Px) in FOPL does not entail (iv) (Ex)(Sx & Px)]. (i) is said to construe All As are Bs as having "existential import" whereas (iv) does not.

The justification for this long conversation on talk page is that perhaps some of the matters discussed might find their way into the article to make it clearer and more interesting for one such as you who self-describes himself as "I know very little about logic" If however you are really pullng a Socrates on me and you're really a bored prof of logic winding me up, I will find find a way of reaching you through cyber-space and a foot will come though your screen. --Philogo (talk) 23:03, 6 March 2009 (UTC)

Heh-heh. I'll take that as a compliment, Philogo !! I do indeed know very little about logic. For example, no, I didn't know that syllogisms are obsolete. I'm not even sure what obsolete means in this context.

Furthermore, I don't understand logical symbols, I hadn't heard of Frege until 3 days ago, and I know nothing about FOPL, so feel free to carry on lying about substituting "the FOPL shown above for AEIO cat props", I won't be contradicting you anytime soon !!

This also means that your sentence

"the reason is that (i) All S are P in sylogism entails (ii) Some S are P, whereas (iii) (x)(Sx -> Px) in FOPL does not entail (iv) (Ex)(Sx & Px)]. (i) is said to construe All As are Bs as having "existential import" whereas (iv) does not.

... might as well be in Latin for all the sense it makes to me.

You say : The justification for this long conversation on talk page is that perhaps some of the matters discussed might find their way into the article to make it clearer...

Absolutely. But we're only having this long conversation because the information that I came to wiki to find, isn't here. Which is why I created this section of discussion to suggest a new section in the wiki article, which would address the issues related to single-term premisses, which no longer feature in the article at all.

And yet, the most famous syllogism in the world, which dates back at least 800 years, contains a single-term premise.

This is a remarkable fact. Surely it deserves comment ?

I will come back to the actual discussion later. Cheers. Gnu Ordure (talk) 00:44, 7 March 2009 (UTC)

And yes, Philogo, I am enjoying this discussion, I am also learning stuff, which is mainly due to your courteous responses to my naive questions, so thank you (except for the slightly discourteous bit about the foot, of course). I hope you're happy to educate me. Gnu Ordure (talk) 01:10, 7 March 2009 (UTC)

It seems to me, Philogo, that 'All that socratises' isn't a categorical term, not because it only has one member, but because it only can have one member - by your definition of the word 'socratize' ("Socrates and nobody else socratises").

I can point at various examples of my category, things-named-Socrates, either the man, or the dog, or the fictional character. You can only point at one example of things-that-socratize, and you'll never be able to point at another.

A category that can have only one member does not deserve to be called a category, surely ? A category might have only one member (as things-named-socrates does after my dog dies and my play burns) - but it must be theoretically possible for it to have more. It is not theoretically possible for things-that-socratize to have more than one member, by definition.

So 'All that socratizes' is functionally equivalent to 'Socrates', and we're back with a single-term proposition.

You say : I feel that (c) suffers from the same defect as (a) - the conclusion "Some things-named-Socrates are mortal" is not really equivalent to "Socrates is mortal", is it?.

Agreed, because the conclusion also needs to be a categorical proposition; but this conclusion concerns a subset of a category (things-named-socrates who are also men) to which the man himself belongs, which is why we can use the syllogism to say something about him, but not about dogs-named-socrates, nor fictional-characters-named-socrates.

More accurately, we're using Socrates the man as an example of the minor premise, to verify that it is true. Once we've done this, we know for a fact that the resulting conclusion, though expressed as a conclusion about categories, will also apply to Socrates specifically, since we've already used him as justification for the truth of the minor premise.

All men are mortal. (True) Some things-named-socrates are men. (True - points at the man himself as an example). This is Darii, so the conclusion must be true: Some things-named-socrates (such as the man himself, but not Socrates-the-fictional-character) are mortal. Gnu Ordure (talk) 18:47, 7 March 2009 (UTC)

I have checked up on my Aristotle, and he says, Prior Analytics, Chap 1, second sentence we must define 1. premiss 2. term 3. syllogism. Torwards the end of the chapter he says "I call a term that into which the premis is analsysed (subejct and predicate) , 'is' or 'is not' being tacked onto one of the terms. John Warrington (ed & trans, Everyman, 1964) in his intro p ix says "Terms may be other singular (e.f. Pericles) or general (man). When two such terms are linked ..there is a simple proposition which is singular if its subject is singular, general if general. General propositions are .. 'universal' or 'particular'" Later p x, he writes "We come now to syllogisms..,. Aisrstotle assumes that that all the terms involved are general". I cannot say that I find in Prior A. much is made of the distinction, nor basis for Warrington's assertion that A. assumes all terms are general. At the end of Prior A. chap-m27, A. however says "Of all existing things some, such as Cleon and Callia, or any sensible particualr, are not predicable of anything truly and universally, while othere are predicable of them". It follows immedaitely that no singular term can be the major or middle terms in a syllogism, because they cannot be used to predicate. It does not however prevent a singular term being the minor term, since it is never used to predicate.

If despite that we wish to insist that ALL terms in a syllogism be general terms, i.e. categorical terms, i.e sets, then we canot use 'Socrates' as a term since it is singfular, not general and not a set. We can works round this issue however providing only that we can allow a term to be general depeite its only having one member, and to this you have objected above, wihtout really saying why. There is certianly no rule to say that a set should have more than one member, I cannot think why a general term, or category should be so limited either. If terms must refer to more that one individual either contingently or necessarily. If that were to be a requirmeent, then All As or Bs would be false in case that there were not at least two As. Thus All Men are Mortal would have been false when uttered by Adam, and will be false when uttered by the last man to shake off this mortal coil. Surely in the latter case his dying words would not be false but "too true". If on the other hand we will allow as general terms which refer to sets that may have but one member, then we can as suggested above use the terms "things that are socrates", "that which socrateses", "that which drank the hemlock" or succinctly 'the set of all things that are identical to socortes'. Such a set, I believe would be written in set notation by enumeration as the set {socrates}. --Philogo (talk) 13:23, 9 March 2009 (UTC)

This article http://plato.stanford.edu/entries/singular-terms-medieval/#7 discusses singular terms, in particular see para 7:

7. Singular Terms in Logic The use of singular terms in inferences raised various issues. So far as syllogistic was concerned, some logicians, such as Lambert of Auxerre (or Lagny) gave a standard account of the Aristotelian syllogism which is centered on the universal and particular quantification of general terms at the same time as they gave examples with singular terms, such as “Every man is an animal, Socrates is a man, therefore Socrates is an animal.”

--Philogo (talk) 11:17, 10 March 2009 (UTC)

Without Auschwitz, there would be no Israel[edit]

Or "without the jews, there would be no holocaust". Are any of those statements syllogistic in nature? I heard this one guy say that the Soviet Union collapsed because of the Cold War, while in a way the Soviets started that Cold War along with the US. Then I thought, the Soviets made themselves collapse. The same structure as the jew-statement I guess. I was wondering if that was syllogistic. Mallerd (talk) 00:46, 6 March 2009 (UTC)

Fallacious Fesapo[edit]

I'm no expert on syllogisms, but isn't the following incorrect?

Fesapo:
No humans are perfect.
All perfect creatures are mythical.
Some mythical creatures are not human.

Shouldn't the conclusion be "No mythical creatures are human?" JDCAce (talk) 09:41, 23 March 2009 (UTC)

Yes. Cf. van Eick. — Charles Stewart (talk) 10:04, 23 March 2009 (UTC)
That would have to be fesapE, since "No mythical creatures are human?" is type E not O.--Philogo (talk) 12:00, 23 March 2009 (UTC)
see the following at [8] para 5:-

Here is an example of a fourth figure EAO (Fesapo) syllogism:

  • No dog is a bird.
  • All birds are winged.
  • --------------------------------------------------------------------------------
  • Some winged animals are not dogs.


It seems like a perfectly valid argument. It is valid, because there are birds. However, suppose we replace birds by purple three winged mountain goats and winged by border collie. We get

  • No dog is a purple three winged mountain goat.

All purple three winged mountain goats are border collies.

  • --------------------------------------------------------------------------------
  • Some border collies are not dogs.


In mediaeval times, people might have said that the second premise is false because there are no purple three winged mountain goats. Today we see both premises as true, the conclusion as false. We don't discard poor Fesapo altogether; we just say that Fesapo, which follows the scheme

  • No P is M
  • All M are S
  • --------------------------------------------------------------------------------
  • Some S are not P


is valid as long as M does not describe some non-existent class of objects. To put it in the form of an answer to exercise 5 of Section 5.5 of the textbook, if the (set of objects corresponding to the) middle term is not empty.

  • -------------
  • -------------

The form is

  • PeM : No P is M
  • MaS : All M is S
  • *SoP : Some S is not P

From

  • PeM : No P is M

we may deduce by conversion

  • PoM : Some P is not M


and with this new premis the conclusion then follows intuitively

  • PoM : Some P is not M : Some dog is not a purple three winged mountain goat.
  • MaS : All M is S : All purple three winged mountain goats are border collies.
  • *SoP : Some S is not P : Some border collies are not dogs.

Thus Fesapo is a strengthened form,

  • PeM : No P is M : No dog is a purple three winged mountain goat.

being "stronger" than

  • PoM : Some P is not M : Some dog is not a purple three winged mountain goat.


--Philogo (talk) 12:09, 23 March 2009 (UTC)

Existential import[edit]

I tidied up the section "Existential import", primarily adding punctuation (there was almost none) but much remains to be done:

(1) What are "forms Ahab, Abe, Ail and Alb"?
(2) Is it acceptable to use the abbreviations "AaB" etc in a section that aims to be comprehensible to non-specialists?
(3) 'If "No men are fire-eating rabbits" is true, then "There are fire-eating dragons" is false', apparently. Even ignoring the rabbits/dragons discrepancy, I don't see how this follows from the preceding section.
(4) Apparently, Strawson (does he have a first name?) claims the answer to question (a) is no. Question (a) is "Which statements of these four forms have existential import and with regard to which terms?" It does not admit of a yes/no answer. 91.105.5.246 (talk) 16:31, 18 May 2009 (UTC)

If "No men are fire-eating rabbits" is true, then "There are fire-eating dragons" is false. Is that correct? BTW I presume this is P. F. Strawson? Groomtech (talk) 17:42, 11 March 2010 (UTC)

Not for nothing[edit]

Not for nothing, but this entire article seems to be an expanded definition. Is it possible this is best done on Wiki Dictionary?

Jbaker071 (talk) 07:53, 24 December 2009 (UTC)

Basic Structure; some variation[edit]

Under Basic Structure, there is this statement: "In Aristotle, each of the premises is in the form "All A are B," "Some A are B", "No A are B" or "Some A are not B", where "A" is one term and "B" is another. More modern logicians allow some variation."

What is "some variation" supposed to mean? Sometimes A and B are the same term? Sometimes A or B actually means a third term, c?

Broadcaster101 (talk) 08:03, 8 August 2010 (UTC)

Monty Python Syllogism sketch[edit]

The "A witch?" sketch of the movie 'The Holy Grail" seems an ideal example of syllogisms at play. The album "The Album of the Soundtrack of the Trailer of the Film of Monty Python and the Holy Grail" perhaps offers the only example in popular culture of an explanation through comedy of syllogisms in Track 8, 'A Lesson In Logic'.

e.g. "The last scene was interesting from the point of view of a professional logician because it contained a number of logical fallacies; that is, invalid propositional constructions and syllogistic forms, of the type so often committed by my wife. 'All wood burns,' states Sir Bedevere. 'Therefore,' he concludes, 'all that burns is wood.' This is, of course, pure bullshit. Universal affirmatives can only be partially converted: all of Alma Cogan is dead, but only some of the class of dead people are Alma Cogan. " (http://www.montypython.net/scripts/logician.php)

Could this not be linked as an example? (180.183.8.220 (talk) 05:59, 18 January 2011 (UTC))

What syllogisms are about[edit]

The structure of syllogisms, if you accept the formalism of representing the "terms" in the premises and the conclusions as a simple and single symbol is the same as the problems of sorting three items. Based on their appearance two items are compared, then it is concluded that one is greater than the other, so you have a sequence, a, b. If next you have a new item to be placed in that sequence or pair on the same principle, meaning size, then you may find that c is greater than a, but smaller than b, so the right sequence will a,c,b. In other words you place c by halving the sum of a+b or dividing the separator between the two items (whole, integer) into two fractions, which will be the Middle term. So what you do is, you duplicate and reverse the relation between A and B (making C > A) and then you get the conclusion (C > B) right. Of course, you do not want to work with irrational numbers, so you make M to become an integer too as represented by the literals. Check out that when you look at the terms in term of being more, or more numerous or greater, you will get the same arrangement as by sorting in the above fashion, which is widely in use in algebra. For instance:

Major premise A < B
Minor premise C > A
Conclusion    C > B
A(1) < B(2) C(3) > A(1) C(3) > B(2)
A B C 


Notice also:

Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.

Here the scope of mortal is wider than that of humans The scope of Greeks is narrower than that of humans.

So you get: Greeks, Humans, Mortals sorted.


Just for fun[edit]

Major Premise: 2 + 3 = 5
Minor Premise= 1 + 2 = 3
_________________________
Conclusion:    1 + 3 = 4

Or see it as spatial semantics: A B C

A is on the left of B
C is on the right of A
C is on the right of B

Genezistan (talk) 12:40, 12 February 2013 (UTC)


Help with a syllogism[edit]

Hello guys. I made a syllogism and i am asking your help to improve it.
Als following the rules of wikipedia - can i post the conclusion of a syllogism in an article?
Please have a look - the editors of the page dont agree with me and i dont trust them - i would like to hear a second oppinion.

Criticism of the Federal Reserve

Thanks, Alextoader (talk) 10:29, 2 January 2014 (UTC)

Wrong predicate logic version of Barbara syllogism (and possibly others)?[edit]

The picture for the Barbara syllogism formalizes it in modern predicate logic as follows:
Ex: Mx & Px
Ex: Sx & Mx
thus
Ex: Sx & Px

(in words: "there is an M that's also P, there is an S that's also M, thus, there is an S that's also P"; it seems this is not even just wrong, but also false.)

It should read:
Ax: Mx --> Px
Ax: Sx --> Mx
thus
Ax: Sx --> Px

EelkeSpaak (talk) 10:07, 13 January 2014 (UTC)

The bars over the top negate. not(Ex: Mx & not-Px) is equivalent to Ax: Mx --> Px. Vaughan Pratt (talk) 10:43, 13 January 2014 (UTC)