Making Do With A Single Logical Quality
Logical quality has become much less central to logical theory in the twentieth century. It has become common to use only one logical quality, typically called logical assertion. Much of the work previously done by distinguishing affirmation from denial is typically now done through the theory of negation. Thus, to most contemporary logicians, making a denial is essentially reducible to affirming a negation. Denying that Socrates is ill, is the same thing as affirming that it is not the case that Socrates is ill, which is basically affirming that Socrates is not ill. This trend may go back to Frege although his notation for negation is ambiguous between asserting a negation and denying. Gentzens notation definitely assimilates denial to assertion of negation, but might not quite have a single logical quality, see below.
Read more about this topic: Logical Quality
Famous quotes containing the words making, single, logical and/or quality:
“The organization controlling the material equipment of our everyday life is such that what in itself would enable us to construct it richly plunges us instead into a poverty of abundance, making alienation all the more intolerable as each convenience promises liberation and turns out to be only one more burden. We are condemned to slavery to the means of liberation.”
—Raoul Vaneigem (b. 1934)
“There is no single face in nature, because every eye that looks upon it, sees it from its own angle. So every mans spice-box seasons his own food.”
—Zora Neale Hurston (1891–1960)
“The sensual and spiritual are linked together by a mysterious bond, sensed by our emotions, though hidden from our eyes. To this double nature of the visible and invisible world—to the profound longing for the latter, coupled with the feeling of the sweet necessity for the former, we owe all sound and logical systems of philosophy, truly based on the immutable principles of our nature, just as from the same source arise the most senseless enthusiasms.”
—Karl Wilhelm Von Humboldt (1767–1835)
“The quality of American life is an insult to the possibilities of human growth ... the pollution of American space, with gadgetry and cars and TV and box architecture, brutalizes the senses, making gray neurotics of most of us, and perverse spiritual athletes and strident self-transcenders of the best of us.”
—Susan Sontag (b. 1933)