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For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P. (Equivalently, it is impossible to have P without Q , or the falsity of Q ensures the falsity of P .) [ 1 ] Similarly, P is sufficient for Q , because P being true always implies that Q is true, but P not being ...
On the other hand, one can affirm with certainty that "if someone does not live in California" (non-Q), then "this person does not live in San Diego" (non-P). This is the contrapositive of the first statement, and it must be true if and only if the original statement is true. Example 2. If an animal is a dog, then it has four legs. My cat has ...
A mixed hypothetical syllogism has two premises: one conditional statement and one statement that either affirms or denies the antecedent or consequent of that conditional statement. For example, If P, then Q. P. ∴ Q. In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent.
The example in the previous section used unformalized, natural-language reasoning. Curry's paradox also occurs in some varieties of formal logic.In this context, it shows that if we assume there is a formal sentence (X → Y), where X itself is equivalent to (X → Y), then we can prove Y with a formal proof.
Late in the 20th century, criticism of both the motif and the theory continued from a number of other perspectives, e.g. Daniel J. Harrington, a former professor at the Weston Jesuit School of Theology, argued that even the term "Messianic Secret" is a misnomer, has lumped together multiple issues and some of the Biblical terms used have been ...
The hypothesis of Andreas Cellarius, showing the planetary motions in eccentric and epicyclical orbits. A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or ...
The Farrer hypothesis (also called the L/M hypothesis, the Farrer–Goulder hypothesis and the Farrer–Goulder–Goodacre hypothesis) is a possible solution to the synoptic problem. The theory is that the Gospel of Mark was written first, followed by the Gospel of Matthew and then by the Gospel of Luke , with Matthew and Luke using the earlier ...
Thus, there is an explosion of true statements. In a different solution to the problems posed by the principle of explosion, some mathematicians have devised alternative theories of logic called paraconsistent logics, which allow some contradictory statements to be proven without affecting the truth value of (all) other statements. [7]