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:
“If the Christ were content with humble toilers for disciples, that wasn’t good enough for our Bert. He wanted dukes’ half sisters and belted earls wiping his feet with their hair; grand apotheosis of the snob, to humiliate the objects of his own awe by making them venerate him.”
—Angela Carter (1940–1992)
“Philosophy is written in this grand book—I mean the universe—
which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it.”
—Galileo Galilei (1564–1642)
“A picture whose pictorial form is logical form is called a logical picture.”
—Ludwig Wittgenstein (1889–1951)
“But the quality of the imagination is to flow, and not to freeze.”
—Ralph Waldo Emerson (1803–1882)