Logic, Reason and Critical Thinking, Class 13: Period 4, Thursday, December 10
Miss Bennet's mood was greatly improved from that a week previous. Her appearance was much its usual, with no trace of an elf costume to be found. It helped that Miss Bennet did not concern herself much with weapons, nor would she be terribly saddened to learn of their candy-cane fate.
"This week," Miss Bennet said, "I should like for us to discuss a logical state known as paradox. Paradox can perhaps best be shown by example."
She turned to write two sentences on the board.
The sentence below is false.
The sentence above is true.
"If the first sentence is true," she said, "then that means the second statement is false. But the second statement declares the first sentence to be true. The second statement being false means the first statement is likewise false, and not true at all. The two contradict one another in ways that do not easily resolve themselves; they comprise a paradox."
"Some situations appear to be paradoxical, based on unclear assumptions or tricks to language. If the problem can be resolved with a touch more information, so that the premises no longer contradict one another, then it is not a true paradox. Furthermore, the term paradox is frequently applied to situations which are not contradictory, but are unexpected based on our current understanding of the world. The birthday paradox, for example, states that in any group of twenty-three or more people, there is a greater than fifty percent chance that two will have the same birthday. Surprising, but the mathematics behind the principle are perfectly logical.
"Finally, there is a subset of paradox known as the dialetheia -- that which is true and false at the same time. Dialetheias are found in philosophical settings which allow for contradictions: many backgrounds do not."
Miss Bennet smiled, warmly, at her class. "And so. We shall discuss paradox, today. Its place in the study of logic, what paradox can teach us, and whether an island such as this makes paradox into child's play."
"This week," Miss Bennet said, "I should like for us to discuss a logical state known as paradox. Paradox can perhaps best be shown by example."
She turned to write two sentences on the board.
The sentence below is false.
The sentence above is true.
"If the first sentence is true," she said, "then that means the second statement is false. But the second statement declares the first sentence to be true. The second statement being false means the first statement is likewise false, and not true at all. The two contradict one another in ways that do not easily resolve themselves; they comprise a paradox."
"Some situations appear to be paradoxical, based on unclear assumptions or tricks to language. If the problem can be resolved with a touch more information, so that the premises no longer contradict one another, then it is not a true paradox. Furthermore, the term paradox is frequently applied to situations which are not contradictory, but are unexpected based on our current understanding of the world. The birthday paradox, for example, states that in any group of twenty-three or more people, there is a greater than fifty percent chance that two will have the same birthday. Surprising, but the mathematics behind the principle are perfectly logical.
"Finally, there is a subset of paradox known as the dialetheia -- that which is true and false at the same time. Dialetheias are found in philosophical settings which allow for contradictions: many backgrounds do not."
Miss Bennet smiled, warmly, at her class. "And so. We shall discuss paradox, today. Its place in the study of logic, what paradox can teach us, and whether an island such as this makes paradox into child's play."