# Talk:Logical hexagon

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## The article is good because it reads the logical propositions of the logical square as such

(Jean KemperNN (talk) 08:32, 18 November 2010 (UTC)) The article is good. It reads the logical propositions of the square: A E I O as such. For instance A is read "Whatever x may be, if x is a man, then x is white." conformably to the algoritmic expression (x)(M(x) → W(x))of modern logic. Jean-François Monteil, the author of the present remarks, thinks that it is not legitimate to identify A that is (x)(M(x) → W(x)) with the marked universal affirmative of natural language All men are white (or Everyman is white). In his opinion,the logical proposition A Whatever x may be, if x is a man, then x is white exactly represents the common referent of two semantically different universals of natural language: Every man is white on the one hand and Man is white, Men are white on the other. The author of these remarks thinks that if Every man is white and Man is white have the same referent, still they have not the same sense.

They have the same referent in so far as they both make known the same reality: the fact that Whatever x may be, if x is a man, then x is white ,in other words, that the quality 'white'is ascribed to the totality of mankind. It goes without saying that when I examine the expressions: Whatever x may be, if x is a man, then x is white, Men are white, All men are white, I'm acting as logician and linguist and that I don't adhere to their obviously false content.

They have not the same sense in so far as they do not contradict the same antithetic proposition. Man is white, Men are white contradicts Man is not white, Men are are not white whereas All men are white (or Everyman is white)contradicts Not all men are white, Some men are not white. The fact that Some men are not white refers to and the fact that Man is not white refers to are different. What we want to explain is this : the sense of an assertive proposition of natural language is made of two elements: its referent of course but also its power to contradict. References:Tract Eight-8,"knol 000" (Jean KemperNN (talk) 13:09, 19 November 2010 (UTC))

## About the representation of the third subcontrary U as A v E

(Jean KemperN (talk) 03:49, 28 December 2010 (UTC)) The article presents U as the disjunction A v E. Hence what one finds in the article to represent U analytically by means of modern algoritmic symbolization: (x)(M(x) → W(x)) v (x)(M(x) → ~W(x)) The statement U may be interpreted as Whatever x may be, if x is a man, then x is white or whatever x may be, if x is a man, then x is non-white. I cannot object to the representation of U as a disjunction A v E that is to say (x)(M(x) → W(x)) v (x)(M(x) → ~W(x)) since it is what we find in Structures intellectuelles of Robert Blanché. However in this talk page I want to explain soon why it would be good to translate U by A w E instead of A v E. A w E or (x)( M(x) → W(x)) w ((x) M(x) → ~W(x)) is to be read something like this: One of two things, either Whatever x may be, if x is a man, then x is white or Whatever x may be, if x is a man, then x is NOT white. (84.100.243.244 (talk) 23:35, 12 January 2011 (UTC)) (84.100.243.244 (talk) 09:01, 28 January 2011 (UTC))

(84.100.243.244 (talk) 02:33, 28 February 2011 (UTC))The great presupposition as far as the logical square and the logical hexagon, the more complete figure, are concerned is this: A and E are necessarily, a priori incompatible. That means that the facts they represent cannot coexist and can be both excluded from reality. The exclusion both of A and E is the conjunction of I (i.e not-E) and O (i.e not-A), which constitutes the third contradictory of Robert Blanché's hexagon symbolized by Y. When U is the case, it means that Y is not the case and that you have not the conjunction: not-A & not-E. On the other hand, you cannot have A & E and that a priori. Therefore, U is equivalent to ~ ( A & E) & ~ (not-A & not-E). Now, p w q (one of two things either p or q) signifies first that one has not both p and q , second that one has not both not-p and not-q. Consequently, if with U you have ~ ( A & E) & ~ (not-A & not-E), you have A W E and not A V E. In my opinion, the drawback of A V E consists in the fact that the form A V E does not exclude explicitly the forbidden conjunction A & E. —Preceding unsigned comment added by 84.100.243.244 (talk) 02:50, 28 February 2011 (UTC) (86.75.111.161 (talk) 22:07, 19 April 2012 (UTC))mindnewcontinent

If the equivalent formulas listed on the page are correct, then A and E have no existential import and so both can be true. For example, the statements ″All unicorns are white" and "All unicorns are not white" are both true, so long as there are no unicorns. If the hexagon is supposed to represent contradiction between U and Y then U must mean an inclusive "or" so as to include the case where A and E are both true. Dezaxa (talk) 12:43, 4 June 2013 (UTC)

## From the square of opposition to the logical hexagon of Robert Blanché. The two triads

(84.101.36.19 (talk) 22:15, 2 July 2013 (UTC)) The logical hexagon of Robert Blanché adds two values to the four values A, E, I, O represented in the square of opposition or square of Apuleius. The value Y represents a third contrary constituting with A the universal affirmative and E the universal negative a triad of contraries. Y represents the conjunction of the subcontrary I called particular affirmative and the subcontrary O called particular negative. Between I particular affirmative and E universal negative, there is a relation of contradictoriness due to the fact that they differ in quantity and quality. For the same reason, there is a relation of contradictoriness between A the universal affirmative and O the particular negative. It follows that Y, conjunction of I and O, excludes both the content of A and that of E. As to the other value U added by Robert Blanché, it is to Y what I is to E and what O is to A. This third subcontrary constitutes with the two traditional subcontraries I and O a triad of subcontraries. The subcontrary U can be represented as the exclusive disjunction of A and E. If U contradicts Y, if, in other words, it rejects the fact that the universals A and E might be both false, that means that one of two things, either A or E is true. Hence the fact that U can be represented by the exclusive disjunction: A w E. (84.101.36.131 (talk) 15:13, 10 July 2013 (UTC))