Philosophy - Assignment Example

If an “E” statement is false, that means the “I” version of the statement is true. “I” and “O” are subcontrary, which means that while both cannot be false at the same time, they may still be true at the same time, making the argument valid. How do you know? The premise is a false “E” statement while the inference is a false “O” statement. A false “E” statement is equivalent to a true “I” version of the statement, and a false “O” statement is equivalent to a true “I” version of the statement as well.

Therefore, the argument becomes that some trees bear fruit, therefore some trees bear fruit, which is a tautology and is valid. How do you know? The premise is a false “I” statement while the inference is a true “O” statement. A false “I” statement is equivalent to a true “O” statement, which re-words the argument as some berries are not beans, therefore some berries are not beans. The result is a tautology and is valid. How do you know? The premise is a true “A” statement while the inference is a false “O” statement.

A false “O” statement is logically equivalent to a “I” statement. An “A” statement leading to an “I” statement is a subalternation, in which the premise implies the truth of the inference. Valid or invalid? Valid. The premise is a true “I” statement. The inference is a false “E” statement. We know by the contradictory relation that the “E” statement must be false, which is what the conclusion indicates. Valid or invalid? Valid. The premise is a false “A” statement.

The inference is a false “I” statement. The premise is logically equivalent to a true “O” statement (i.e. that some soccer balls are not round objects) while the inference is logically equivalent to a true “E” statement (i.e. that no soccer balls are round objects). The truth of the premise does not lead to the truth of the inference, which is how subalternation