KNOLmnc 0 The translation of On Interpretation, chapter 7 by Professor Gohlke leads to the logical hexagon, the bilateral possible, the formula of strict implication : L p ≡ Lq. To the Verlag Walter de Gruyter.

Cliquer sur le lien: Du carré logique à l’hexagone

DU CARRÉ LOGIQUE À L’HEXAGONE.RTF

By Jean-François Monteil

Download

The formula of strict implication is: L p ≡ Lq

The fact p strictly implies the fact q

if it is certain that the possible fact p is equivalent to the certainty of the fact q.

The developed form of L p ≡ Lq is

L p & Lq w ~p & M ~q.

This developed form L p & Lq w ~p & M~q

is to be read

It is one thing or the other,

either p and then Lq, the certainty of q,

or not-p and then M~q, the possibility of not-q.

The question of strict implication was raised by Clarence Irving Lewis in 1916.

If one types Strict implication, the paper

KNOLmnc 1 Modal logic. The three ingredients of strict implication. Calcutta

appears in a flattering position.

La formule de l’ implication stricte est: L p ≡ Lq

Le fait p implique strictement le fait q

s’il est certain que le possible fait p équivaut à la certitude du fait q.

La forme développée de L p ≡ Lq est

L p & Lq w ~p & M~q.

Cette forme développée L p & Lq w ~p & M~q

est à lire

De deux choses l’une,

ou bien on a p et dans ce cas on a la certitude de q,

ou bien on a non-p et dans ce cas on a la possibilité de non-q.

Le problème de l’implication stricte fut posé par Clarence Irving Lewis en 1916.

Allemands et Français s’adonnaient alors à des jeux violents et la logique ne retenait guère leur attention !

About the paradoxical sign of Jean-François Monteil and its importance for logic and linguistics.

Le signe paradoxal de Jean-François Monteil et son importance …

These are two major works produced by the German scholarship:

1- Gohlke, P., 1951: Aristoteles, Die Lehrschriften; hrsg., übertragen und in ihrer Entstehung erlaütert von Paul Gohlke. Kategorien und Hermeneutik, Paderborn 1951.

2- Die Hermeneutik des Aristoteles: in der Übersetzung des Ishak Ibn Honain, Auteur: Isidor Pollak, Editeur: Leipzig: in Commission bei F.A Brockaus, 1913, Collection: Abhandlungen für die Kunde des Morgenlandes, 13, 1.

Thanks to Paul Gohlke and Isidor Pollak, the text of die Hermeneutik des Aristoteles second book of the Aristotelian Organon can be at last established. In the light of their works, the problem raised by the indeterminate propositions of De interpretatione chapter 7 is at last solved.

Establishing the text of De interpretatione, chapter 7 brings about a chain reaction. It leads first to the replacement of the square of opposition by the hexagon of Robert Blanché.

The logical hexagon represents 6 values, the traditional square of opposition only 4. The hexagon is a more potent figure than the square. The hexagon is something obviously complete, the square something obviously deficient.

The main result of the substitution of the logical hexagon for the traditional square of opposition is this: applied to modal logic, the hexagon shows the existence and importance of the bilateral possible. The notion of bilateral possible conducts to the formula of the strict implication of a fact q by a fact p:

L p ≡ Lq

A fact p strictly implies a fact q, if it is established that the fact p is equivalent to the certainty of the fact q.

The problem of strict implication was posed in 1916 by one C.I Lewis. The point was to remove the two unpleasant paradoxes of the so called material implication.

In the framework of material implication, a proposition p, if false, implies any other proposition, that is, q as well as not-q.

In the framework of material implication, a proposition q, if true, is implied by any other proposition, that is, by p as well as by not-p.

For those who have in view a cause and effect relationship, between a fact p and a fact q, the paradoxes in question are excruciating !

So L (p ≡ Lq) is a formula of strict implication, to be read:

It is certain that the possible fact p is equivalent to the certainty of the fact q.

It represents the content of the complex sentences of natural language:

If p, then q and If and only if p, then q.

The developped form of L (p ≡ Lq) is

L( p & Lq) w (~p & M~q).

This developed form L( p & Lq) w (~p & M~q)

is to be read

It is one thing or the other,

either p and then Lq, the conditional certainty of q,

or not-p and then M~q, the possibility of not-q.

The developed form of our formula of strict implication manifests the three ingredients of strict implication

– 1 The developed form indicates that the conjunction of p and not-q is impossible and that one has ~M (p & ~q). So is retrieved the content of the so called material implication.

– 2 L( p & Lq) w (~p & M~q) implies the bilateral possible Mp & M~p and so disposes of the first paradox of material implication, the fact that a false proposition implies anything.

– 3 (~p & M~q), the second alternative, disposes of the second paradox, the fact that a true proposition is implied by anything.

Useful links:

KNOLmnc 1 Modal logic. The three ingredients of strict implication. Calcutta

KNOLmnc 1 A German exception: the translation of On Interpretation by Professor Gohlke. His tenth note on indeterminate propositions. To Mind a Quarterly Review of Philosophy.

Isidor pollak et les deux traductions arabes differentes du De interpretatione

FR MNC The paradoxical sign of JF Monteil, the German exception of Professor Gohlke and the formula of strict implication L p ≡ Lq. To the Verlag Walter de Gruyter.

FR MNC Premier courriel à la maison Walter de Gruyter. Establishing the text of Die Hermeneutik des Aristoteles leads to the formula of strict implication L p ≡ Lq.

FR MNC Deuxième courriel à la maison Walter de Gruyter. Establishing the text of Die Hermeneutik des Aristoteles leads to the formula of strict implication L p ≡ Lq. The tenth note on the Aristotelian indeterminates of De Interpretatione, chapter 7.

FR MNC Troisième courriel à la maison Walter de Gruyter. Establishing the text of Die Hermeneutik des Aristoteles leads to the formula of strict implication: L p ≡ Lq. Hermann Weidemann should have taken into account the works of two absentees of his bibliography: Isidor Pollak and the Paul Gohlke commenting on the Aristotelian indeterminates of De Interpretatione, chapter 7.

FR MNC Liste des articles dédiés à Mind a quarterly review of philosophy

Ceci est une disposition testamentaire.

En pleine occupation, ma mère, bonne musicienne, excellente Germaniste me rattacha à l’Allemagne. Que si un jour au vu de l’usage que j’ai fait de l’érudition allemande, telle ville universitaire d’outre-Rhin voulait honorer ma mémoire, je demande de la façon la plus expresse qu’au-delà du Rhin mon nom soit exclusivement associé au prénom de Madeleine Marquetoux.

Jean-François Monteil

Cestas, le 3 Mars 2019

Cliquer sur le lien: Du carré logique à l’hexagone

The formula of strict implication is: L p ≡ Lq

The fact p strictly implies the fact q

if it is certain that the possible fact p is equivalent to the certainty of the fact q.

The developed form of L p ≡ Lq is

L p & Lq w ~p & M ~q.

This developed form L p & Lq w ~p & M~q

is to be read

It is one thing or the other,

either p and then Lq, the certainty of q,

or not-p and then M~q, the possibility of not-q.

The question of strict implication was raised by Clarence Irving Lewis in 1916.

If one types Strict implication, the paper

appears in a flattering position.

La formule de l’ implication stricte est: L p ≡ Lq

Le fait p implique strictement le fait q

s’il est certain que le possible fait p équivaut à la certitude du fait q.

La forme développée de L p ≡ Lq est

L p & Lq w ~p & M~q.

Cette forme développée L p & Lq w ~p & M~q

est à lire

De deux choses l’une,

ou bien on a p et dans ce cas on a la certitude de q,

ou bien on a non-p et dans ce cas on a la possibilité de non-q.

Le problème de l’implication stricte fut posé par Clarence Irving Lewis en 1916.

Allemands et Français s’adonnaient alors à des jeux violents et la logique ne retenait guère leur attention !

These are two major works produced by the German scholarship:

1- Gohlke, P., 1951: Aristoteles, Die Lehrschriften; hrsg., übertragen und in ihrer Entstehung erlaütert von Paul Gohlke. Kategorien und Hermeneutik, Paderborn 1951.

2- Die Hermeneutik des Aristoteles: in der Übersetzung des Ishak Ibn Honain, Auteur: Isidor Pollak, Editeur: Leipzig: in Commission bei F.A Brockaus, 1913, Collection: Abhandlungen für die Kunde des Morgenlandes, 13, 1.

Thanks to Paul Gohlke and Isidor Pollak, the text of die Hermeneutik des Aristoteles second book of the Aristotelian Organon can be at last established. In the light of their works, the problem raised by the indeterminate propositions of De interpretatione chapter 7 is at last solved.

Establishing the text of De interpretatione, chapter 7 brings about a chain reaction. It leads first to the replacement of the square of opposition by the hexagon of Robert Blanché.

The logical hexagon represents 6 values, the traditional square of opposition only 4. The hexagon is a more potent figure than the square. The hexagon is something obviously complete, the square something obviously deficient.

L p ≡ Lq

A fact p strictly implies a fact q, if it is established that the fact p is equivalent to the certainty of the fact q.

The problem of strict implication was posed in 1916 by one C.I Lewis. The point was to remove the two unpleasant paradoxes of the so called material implication.

In the framework of material implication, a proposition p, if false, implies any other proposition, that is, q as well as not-q.

In the framework of material implication, a proposition q, if true, is implied by any other proposition, that is, by p as well as by not-p.

For those who have in view a cause and effect relationship, between a fact p and a fact q, the paradoxes in question are excruciating !

So L (p ≡ Lq) is a formula of strict implication, to be read:

It is certain that the possible fact p is equivalent to the certainty of the fact q.

It represents the content of the complex sentences of natural language:

If p, then q and If and only if p, then q.

The developped form of L (p ≡ Lq) is

L( p & Lq) w (~p & M~q).

This developed form L( p & Lq) w (~p & M~q)

is to be read

It is one thing or the other,

either p and then Lq, the conditional certainty of q,

or not-p and then M~q, the possibility of not-q.

The developed form of our formula of strict implication manifests the three ingredients of strict implication

– 1 The developed form indicates that the conjunction of p and not-q is impossible and that one has ~M (p & ~q). So is retrieved the content of the so called material implication.

– 2 L( p & Lq) w (~p & M~q) implies the bilateral possible Mp & M~p and so disposes of the first paradox of material implication, the fact that a false proposition implies anything.

– 3 (~p & M~q), the second alternative, disposes of the second paradox, the fact that a true proposition is implied by anything.

Useful links:

Share this:

Related

Leave a comment Cancel reply