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:
“However, the danger in [socially unbalanced relationships] is that the subjection of the woman temporarily calms the man’s jealousy but also renders it more demanding. He ends up making his mistress live like those prisoners on whom light is shone day and night in order for them to be better watched. And things always end in tragedy.”
—Marcel Proust (1871–1922)
“His virtues walked their narrow round,
Nor made a pause, nor left a void;
And sure the Eternal Master found
The single talent well employed.”
—Samuel Johnson (1709–1784)
“Nature’s law says that the strong must prevent the weak from living, but only in a newspaper article or textbook can this be packaged into a comprehensible thought. In the soup of everyday life, in the mixture of minutia from which human relations are woven, it is not a law. It is a logical incongruity when both strong and weak fall victim to their mutual relations, unconsciously subservient to some unknown guiding power that stands outside of life, irrelevant to man.”
—Anton Pavlovich Chekhov (1860–1904)
“A quality is something capable of being completely embodied. A law never can be embodied in its character as a law except by determining a habit. A quality is how something may or might have been. A law is how an endless future must continue to be.”
—Charles Sanders Peirce (1839–1914)