Academic journal article International Journal on Humanistic Ideology

Real World Semantics

Academic journal article International Journal on Humanistic Ideology

Real World Semantics

Article excerpt

According to the principles of logic, a proposition is true or false in relation to a certain context. If a proposition is true in any imaginable context, it is called tautology, and a false proposition in any imaginable context is called contradiction. Factual propositions are true in certain contexts and false in others. Tautology, contradiction and factuality represent logical values of propositions which, in contrast to truth values, are invariable relatively to context.

In addition to the truth and the logical values, propositions are characterized through their modal value, namely, a proposition can be necessary true, possible true, necessary false or possible false. The modal value of propositions has an epistemological importance. A proposition is certain in a justified way only if it is necessary. The acceptance of contingent propositions is uncertain as they can be false. Certitude is founded on necessity, while opinions are relative to contingent propositions.

Because the modal values are reducible to one of them and negation, it is sufficient to define one modal value in order to determine the meaning of all modal values. However, for many times, the attempts to define modal values lead to vicious circle. One of the first attempts to define modalities so that vicious circle is avoided belongs to Aristotle. He defines necessity in relation to the consequence relation between propositions. For him, the conclusion of a correct inference necessarily follows from the premises.1 According to Aristotle, if "Pl-Q" is a correct inference then, if P is true, then Q is necessary true (it can not be possible to be false). In other words, a proposition, g, is necessary true if and only if:

1) There is a proposition P so that ß is a consequence of P;

2) P is a true proposition.

According to Aristotle's definition, the modal value of a proposition depends on the truth value of another proposition and on the consequence relation between them.

The attempt of Logic to symbolize the consequence relation through material implication has generated the paradoxes of material implication: there are propositions connected through material implication, but which are not in a relation of consequence. In order to surpass the paradoxes of the material implication, C. I. Lewis suggests the representation of consequence relation using another connector, different from material implication, called by him strict implication. The American logician argues that material implication cannot render the dimension of necessity of the consequence relation, noticed by Aristotle. Because of this, in order to obtain a correct representation of consequence, we must add necessity to material implication. In this way, a proposition P strictly implies another proposition Q if and only if P materially implies Q with necessity (Lewis CL, Langford C.H., 1959, p. 124).

From Aristotle's definition it results that the proposition P is necessary true if it is the consequence of another true proposition, Q. In order for the modal value of P not to depend on another proposition but only on itself, the truth value of the proposition Q must depend only on the truth value of P. Thus, the proposition Q must be a truth function of the proposition P. At the same time, in order to be in accordance with Aristotle's definition, Q is not a necessarily true proposition. Because the only truth function that fulfils these conditions is negation, we find the definition of necessary propositions given by CJ. Lewis: a proposition P is necessary true if it is strictly implied by its negation. Starting from the definition of necessity, the definitions for the other modal values are obtained. For instance, a proposition is possible true if and only if it is compatible with itself (Lewis CL, Langford C.H., 1959, p. 161).

Although it surpasses the inconvenient of paradoxes of material implication, C.I. Lewis' analysis of modalities generates other paradoxes called the paradoxes of strict implication (Lewis CL, Langford CH. …

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