Significance
Intensional languages cannot be given an adequate semantics in terms of the extensions of expressions in them, since the extensions themselves do not suffice to determine a logical value. (If they did, then one could not change the logical value by substituting co-extensive expressions.) On the other hand, for the first half of the 20th century the only known systems of formal semantics worked by assigning extensions to expressions and used a Tarski-style truth-definition of statements constructed from the primitive expressions of the language under analysis. Hence, these semantical methods were pathetically inadequate for understanding the semantics of any but a few small artificial languages or mutilated fragments of natural languages.
This situation changed in the 1960s with the invention of possible-world or "intensional" semantics, the main form of which is due to Saul Kripke. Though this has enabled improvements in the semantic modelling of natural languages, much work remains to be done.
Read more about this topic: Intensional Statement
Famous quotes containing the word significance:
“Of what significance the light of day, if it is not the reflection of an inward dawn?—to what purpose is the veil of night withdrawn, if the morning reveals nothing to the soul? It is merely garish and glaring.”
—Henry David Thoreau (1817–1862)
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—Joyce Maynard (20th century)
“It is necessary not to be Christian to appreciate the beauty and significance of the life of Christ.”
—Henry David Thoreau (1817–1862)