Inconsistency and Peculiarity of Conceited Reasoners
A reasoner of type 1 is faced with the statement "I will never believe this sentence." The interesting thing now is that if the reasoner believes he or she is always accurate, then he or she will become inaccurate. Such a reasoner will reason: "If I believe the statement then it will be made false by that fact, which means that I will be inaccurate. This is impossible, since I'm always accurate. Therefore I can't believe the statement: it must be false."
At this point the reasoner believes that the statement is false, which makes the statement true. Thus the reasoner is inaccurate in believing that the statement is false. If the reasoner hadn't assumed his or her own accuracy, he or she would never have lapsed into an inaccuracy.
It can also be shown that a conceited reasoner is peculiar.
Read more about this topic: Doxastic Logic
Famous quotes containing the words peculiarity, conceited and/or reasoners:
“The peculiarity of sculpture is that it creates a three-dimensional object in space. Painting may strive to give on a two-dimensional plane, the illusion of space, but it is space itself as a perceived quantity that becomes the peculiar concern of the sculptor. We may say that for the painter space is a luxury; for the sculptor it is a necessity.”
—Sir Herbert Read (1893–1968)
“We are so conceited and so unproud.”
—D.H. (David Herbert)
“Those who have handled sciences have either been men of experiment or men of dogmas. The men of experiment are like the ant; they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes the middle course; it gathers its material from the flowers of the garden and of the field, but transforms and digests it by a power of its own. Not unlike this is the true business of philosophy.”
—Francis Bacon (1561–1626)