The " ~ " signifies logical negation; it simply reverses the truth value of any statement (simple or compound) in front of which it appears: if the original is true, the ~ statement is false, and if the original is false, the ~ statement is true. Thus, its meaning can be represented by the truth-table at right.
The symbol p represents here a conceivable fact like the conceivable fact considered by Bertrand Russell in An inquiry into meaning and truth, chapter 20, the conceivable fact that it snowed on Manhattan Island on the first of January in the year 1 Anno Domini.
The symbol ~p to be read not-p represents here a conceivable fact consisting in excluding the fact p from reality. The conceivable fact not-p in question is the conceivable fact that it did not snow on Manhattan Island on the first of January in the year 1 Anno Domini.
Let the symbol (l) represent a priori necessity. (l) p w ~p means that the fact p and the fact not-p are a priori necessarily contradictory. On the one hand, they are necessarily in-compatible in reality, on the other hand they cannot be both excluded from reality. Hence the fact p ≡ ~~p. That means that the fact p is the fact excluding the fact not-p as the fact not-p is the fact excluding p. The author of these lines refers the potential reader to the following papers : KNOLmnc 1 To defend his views about modal logic and strict implication, Jean-François Monteil utilizes the chapter of Bertrand Russell’s An inquiry into meaning and truth entitled The law of excluded middle. and KNOLmnc 1 Modal logic. The three ingredients of strict implication. Calcutta.
If we consider the assertive sentence The Anglo-American Normandy landing took place on Tuesday, 6 June 1944 and identify it with a proposition p, we say that the proposition p is true because it makes known a fact, which is certain and belongs to the realm of reality. It is obvious that the proposition not-p represented by the assertive sentence whose form is negative The Anglo-American Normandy landing did not take place on Tuesday, 6 June 1944 is false because the conceivable fact that such an assertive sentence is intended to make known is excluded from reality by the p The Anglo-American Normandy landing took place on Tuesday, 6 June 1944 being true. If (l) p w ~p, p ≡ ~~p. If the proposition ~p to envisage now is Harry is not married and if this not-p is true because Harry is notoriously a bachelor, the corresponding p Harry is married is false. All seems quite simple. If a proposition p is true, the proposition not-p is false, if a proposition not-p is true, the proposition p is false. The temptation which must be resisted is to add too fast: if p is false, not-p is true, if not-p is false, p is true.
The law of excluded middle must be defined in terms of facts. It consists in stating that the conceivable facts p and not-p are a priori contradictory. This is representable by (l) p w ~p.
Let us imagine that Jupiter has become so old, so doting that he does not have any knowledge of the recent events of human history. He knows vaguely that a landing was to take place. When and where, he does not know. Who won, who lost, he does not know either. The poor god in his state of dotage
The law of excluded middle must be defined in terms of facts. It consists in stating that the conceivable facts p and not-p are a priori contradictory. This is representable by (l) p w ~p.
On Tuesday 6 June, Anglo-American troops land on the coast of Normandy. France Actualités condemns the battle, which bathe France in blood.
The law of excluded middle states that for any proposition, either that proposition is true, or its negation is true.
In logic, the law of excluded middle (or the principle of excluded middle) is the third of the three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is true.
The founding a priori necessary fact: (l) p w ~p ,that is to say,the law of excluded middle.
Let the symbol (l) represent a priori necessity. (l) p w ~p means that the fact p and the fact not-p are a priori necessarily contradictory. On the one hand, they are necessarily in-compatible in reality, on the other hand they cannot be both excluded from reality. Hence the fact p ≡ ~~p. That means that the fact p is the fact excluding the fact not-p as the fact not-p is the fact excluding p. The author of this remark refers the potential reader to An inquiry into meaning and truth, chapter 20 by Bertrand Russell and to what is devoted to the said chapter entitled The law of excluded middle in the following papers:
KNOLmnc 1 To defend his views about modal logic and strict implication, Jean-François Monteil utilizes the chapter of Bertrand Russell’s An inquiry into meaning and truth entitled The law of excluded middle.
KNOLmnc 1 Modal logic. The three ingredients of strict implication. Calcutta.
