Talk:Syllogism

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Help with a syllogism

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)[reply]

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

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)[reply]

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)[reply]

Yes, the bars negate, and I know that, but not everyone will know that. I added the following text that I hope will make that clearer: "In the predicate logic expressions, a horizontal bar over an expression means to negate ("logical not") the result of that expression." Dwheeler (talk) 13:40, 3 September 2016 (UTC)[reply]

Thanks

Just had occasion to refer to the article, and I want to say that I found it well organized and comprehensive - at least it covered whatever I want to know. Thank you for the article. You know who you are. Mp1233 (talk) 21:50, 22 May 2016 (UTC)[reply]

I agree, this Syllogism article was really helpful. Thanks everyone Dwheeler (talk) 13:40, 3 September 2016 (UTC)[reply]

Which source was used for the existence statements in their predicate logic forms?

Some of the syllogisms include a third required existence statement when expressed as predicate logic. For example, statements like $\exists xS(x)$ (note the lack of an "and"). THANK YOU, whoever included that information!! However, I'm trying to track down the source for those existence statements. Which source specifically provided the third existence statements? There are a lot of sources & it's not obvious which one was used for that. Thanks. Dwheeler (talk) 13:26, 31 August 2016 (UTC)[reply]

strict logic by Walther Brüning

Hello!

I already have written in German Wikipedia; There is a german logician (Walther Brüning), who is able to explain syllogistik in a ("strict") "mechanical" way, like a calculation. It is nearly as easy as the calculation used to be in truth tables. I made a tutorial about it (1 hour [and with at least one mistake]). The book of Walther Brüning ("Grundlagen der strengen Logik") is only available in German (it is also on google books). The reason why i write this here is, because his thinking about syllogistic would change half of the article and this change I dont dare now. I would be curious about your opinions.

Tutorial: (https://www.youtube.com/watch?v=2esURv_dtBk&vl=en old, broken link, new one: https://www.youtube.com/watch?v=KuB_vAPrUvA --123qweasd (talk) 16:57, 29 October 2019 (UTC))[reply]

--123qweasd (talk) 17:09, 14 May 2017 (UTC)[reply]

nevermind. Maybe i will write an article about strict syllogistic in german wikipedia 123qweasd (talk) 16:49, 16 May 2017 (UTC)[reply]

Maybe I will dare it though --123qweasd (talk) 09:45, 3 November 2017 (UTC)[reply]

Have a look please, at my simplified Venn diagrams and reduction to short list of 7 essential syllogisms, all others are trivial modifications. The aims could be similar. hgwb 20:42, 3 November 2017 (UTC) — Preceding unsigned comment added by Skeptiker (talk • contribs)

I wrote an article in german wikipedia: strenge Logik. Sorry, but i dont understand, why there should be exactly seven syllogisms. For any questions about strict logic you can ask me. Here is a short introduction (again): https://www.youtube.com/watch?v=2esURv_dtBk&vl=en 123qweasd (talk) 13:36, 12 November 2017 (UTC)[reply]

For those who are interested: Here a version of an old attempt to change the article, redirects to section "Strict syllogistic": Syllogism (from 21.May,2018) # Strict syllogistic 123qweasd (talk) 15:51, 20 May 2019 (UTC)[reply]

A project of a python-application to train strict syllogism [1]--123qweasd (talk) 08:57, 11 August 2022 (UTC)[reply]

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Creationism is not an argument it is a view

There is a clear difference. No source calls it an argument.,Apollo The Logician (talk) 18:53, 31 May 2017 (UTC) Apollo The Logician (talk) 18:53, 31 May 2017 (UTC)[reply]

Stoic syllogistic

The statement is made that "In antiquity, two rival theories of the syllogism existed: Aristotelian syllogistic and Stoic syllogistic" but then only Aristotelian syllogistic is described. I know nothing about this, but could some put in at leas a single sentence to describe the alternative, Stoic syllogistic? — Preceding unsigned comment added by 106.69.175.42 (talk) 00:23, 30 July 2017 (UTC)[reply]

Simplified Venn Diagrams For Syllogisms And Reduction To Seven (7) Essentially Distinct Syllogisms.

The three-circle Venn diagrams for the Syllogisms are much too complicated (absurdly so). As a retired maths prof and logician/philosopher, I would NEVER use the ones shown now in one of my classes. Below, I submit examples of vastly simpler Venn diagrams, or Euler diagrams — geometric "proofs" — with two twists or clarifying devices:

REDUCTION TO SEVEN (7) ESSENTIALLY DISTINCT SYLLOGISMS

     (1.)  The boxes are given  characteristic borders. 
     (2.)  Diagram has boxes labeled with example predicates.  
        ……………
   S = /     \
       \_____/

         ……………
   M =  |     |
        |_____|

         …………… 
   P =  {     }
        {_____}

The joint presence of three boxes in a syllogistic diagram below implies three pairs of two boxes, the configuration of each pair illustrating one of the three propositions of the syllogism.

REDUCTION TO SEVEN (7) ESSENTIALLY DISTINCT SYLLOGISMS:

As probably is fairly well-known, we can reduce the count of syllogisms from 24 to 11 by

 (1.) dropping five "weak" syllogisms Barbari (AAI-1), Celaront   
      (EAO-1), Cesaro (EAO-2), Calemos (AEO-4), Camestros (AEO-2);
 (2.) identifying equivalent propositions due to the symmetries
            AeB <=> BeA,    AiB <=> BiA.

Thus for example all four EIO syllogisms, through the 4 figures are really the same or at least equivalent, and all four may be represented by FERIO (EIO-1). This leads to the following table of eleven (11) "reduced" syllogisms or equivalence classes.

However, even 11 syllogisms is too many, there are really only seven (7) essentially truly distinct syllogisms: Barbara, Darii, Felapton, Ferio, Celarent, Bocardo and Baroco. Please see below for discussion ("Homework").

To simplify reading of diagrams, premises are stated next in non-traditional order:

  First premise (=minor premise)
  Second premise (=major premise)

However,for the three-letter codes we retain the traditional form, placing the major premise first, before minor premise:

 1.  Barbara (AAA-1): SaM,MaP:SaP 
 2.  Darii (AII-1): SiM,MaP:SiP         
 3.  Felapton (EAO-3):  MaS,MeP,SoP      
 4.  Ferio (EIO-1): SiM,MeP:SoP         
 5.  Celarent (EAE-1): SaM,MeP:SeP      
 6.  Bocardo (OAO-3):  MaS,MoP:SoP 
 7.  Baroco (AOO-2):SoM,PaM:SoP

It is interesting to exhibit the seven (7) simplified Venn or Euler diagrams for this list with examples showing both, similarities and changes, as we pass from one to the next

DIAGRAMS OF SEVEN REDUCED SYLLOGISMS.

- - - - -

1. Barbara (AAA-1): SaM,MaP:SaP

 all S is M; all M is P: all S is P

 S:Greeks M:Men P:mortal

    All Greeks are men.    (SaM)
    All men are mortal.    (MaP)
  ∴ All Greeks are mortal. (SaP)

   …………………………………………………………………………
  {     mortals               }
  {    …………………………………………       }  
  {    |     men       |      }
  {    |   ………………………   |      }   
  {    |  / Greeks  \  |      } 
  {    |  \_________/  |      }
  {    |_______________|      }
  {___________________________}

- - - - -

2. Darii (AII-1): SiM,MaP:SiP  (=Datisi (AII-3), 2 in class)

 some S is M; all M is P: some S is P

 S:fragrant; M:flower; P:lifeform
 
       Some fragrant things are flowers  (SiM)
       All flowers  are lifeforms         (MaP)
     ∴ Some fragrant things are lifeforms (SiP)

         …………………………………………………………………
        {                         } lifeforms
        {   ………………………………………………    }   
        {   |  flowers        |   }
        {   |     ………………………………|………}………………     
        {   |    /  ($)       |   }  ?    \                              
        {   |    \____________|___}_______/                               
        {   |_________________|   }  fragrant things  
        {_________________________}

- - - - -

3. Felapton (EAO-3):MaS,MeP:SoP (=Fesapo (EAO-4), 2 in class)

 all M is S; no M is P: some S is not P

 S:lifeform; M:flower; P:heavy weight

     All flowers are lifeforms.         (MaS)
     No flowers are heavy weight.       (MeP)
  ∴ Some lifeforms are not heavy weight. (SoP)

    …………………………………lifeforms  
   /  ……………………      \     
  /  |        |  …………\…………………
 /   |  ($)   | {  ?  \      }
 \   |flowers | {_____/______} 
  \  |________|      / heavy weight things  
   \________________/

The symbol ($) means that set S of flowers is not empty, there is stuff in it (flowers) . .!!

- - - - - 
4. Ferio (EIO-1):SiM,MeP:SoP (=Festino (EIO-2)=Ferison(EIO-3)=Fresison (EIO-4), 4 in class)

 some S is M; no M is P: some S is not P

 S:mammal; M:carnivore; P:ruminant

     Some carnivores are mammals. (MiS)
     No herbivores are carnivores. (PeM)
  ∴ Some mammals are not herbivores. (SoP)

       ……………………………………
      |             |
     …|…..…….…………………|………………  mammals 
   /  |             |       \     
  /   |             |    …………\……………
 /    |   ($)       |  {      \  ?  }
 \    | carnivores  |  {______/_____} 
  \   |_____________|        /  herbivores
   \________________________/

- - - -
5. Celarent (EAE-1): SaM,MeP:SeP (=Cesare (EAE-2), 2 in class)

 all S is M; no M is P: no S is P

 S:flowers; M:lifeforms; P:fulgurite

     All flowers are lifeforms.   (SaM)
     No lifeforms are fulgurites. (MeP)
   ∴ No flowers are fulgurites.   (SeP) 
   
    ………………………………………………          
    |                 |       …………………
    |   …………………       |      {        }  fulgurite
    |  /flowers \     |      {________} 
    |  \________/     |     
    |_________________| 
               lifeforms 
 
- - - - - 
6. Bocardo (OAO-3): MaS,MoP:SoP

 all M is S; some M is not P: some S is not P

 S:plant; M:flower; P:fragrant

    All flowers are lifeforms.     (MaS)
    Some flowers are not fragrant.  (MoP)
  ∴ Some lifeforms are not fragrant. (SoP)

    …………………………………  lifeforms
   /  ……………………………  \     
  /  |        ………|……\………
 /   | ($)    {  |   \  ?}
 \   |flowers {__|___/___} 
  \  |___________|  / fragrant things
   \_______________/

- - - - -

7. Baroco (AOO-2): SoM,PaM:SoP

 some S is not M; all P is M: some S is not P

 S:fragrant; M:lifeform; P:flower

    Some fragrant things are not lifeforms. (SoM)
    All flowers are lifeforms.             (PaM)
  ∴ Some fragrant things are not flowers.  (SoP)

   …………………………………………………… lifeforms
  |    ………………………………    |  
  |   {   flowers  }   |       
  |   {     …………………}………|……………….      
  |   {    /       }   |        \      
  |   {   /    ?   }   |  ($)    \      
  |   {   \        }   |         /    
  |   {    \_______}___|________/    
  |   {____________}   |  fragrant things
  |____________________|

List of the seven (7) essential ones, with the above examples in short form "syllogism (P S)":

  Barbara (Mortal Greeks) 
  Darii (Lifeform Fragrants) 
  Felapton (Non-Heavy Weight Lifeforms) 
  Ferio (Non Herbivore Mammals)
  Celarent (Fulgurite Non Flowers)
  Bocardo (Non-Fragrant Lifeforms)  
  Baroco (Non-Flower Fragrants)

Homework For Syllogism Tutorial: Please convince yourself that only these seven (7) syllogisms are truly distinct, as in two pairs there is no actual distinction in the inference:

   Darrii & Disamis are identical inferences.
   Celarent & Camestres are identical inferences.

Furthermore, two additional syllogisms can be eliminated, being weakened forms:

Frst, Bamalip AAI is weaker than Barbara AAA, having a weaker conclusion.

    Bamalip:  If MaS & PaM, then SiP.  
    Barbara:  If SaM & MaP, then SaP.

Perform a substitution of variables in Barbara:

    Barbara:  If PaM & MaS, then PaS.

But PaS for nonempty P implies SiP, hence Bamalip is weaker than Barbara. If P is empty, then Bamalip is invalid, as is well-known.

Second, Darapti is weaker than Darii, having stronger premises:

     Darapti: If MaS & MaP, then SiP.  
     Darii: SiM, MaP: SiP.

For Darapti to be true, M must be nonempty, as is well-known. If so, the premises imply SiM & MaP, hence SiP by Darii.

hgwb 22:12, 8 November 2017 (UTC) hgwb 12:17, 8 August 2018 (UTC)

I took the liberty to put this long section in a box. See also v:Talk:Syllogisms for context. Watchduck (quack) 00:37, 4 August 2020 (UTC)[reply]

Why Socrates and not Aristotle (as it should be)?

Can anyone tell me why a bust of Socrates is shown on the page, rather than Aristotle's? Thanks--80.147.11.76 (talk) 10:41, 25 November 2021 (UTC)[reply]

I'm guessing the picture goes less with the page and more with the example ("All men are mortal. Socrates is a man. Therefore Socrates is mortal.") 2601:49:8400:392:F87F:40C9:D833:6AAD (talk) 02:48, 20 September 2024 (UTC)[reply]