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Venn diagram for "A or B", with inclusive or (OR) Venn diagram for "A or B", with exclusive or (XOR). The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively.
would commit the complex question fallacy because while it assumes there is a place called France (true), it also assumes France currently has a king (false). But since answering this question does not seem to incriminate or otherwise embarrass the speaker, it is complex but not really a loaded question. [6] When a complex question contains ...
(3) "Either you tell the truth, or you lie". Therefore "[y]ou are an immoral person (whatever choice you make in the given situation)". [1] This example constitutes a false dilemma because there are other choices besides telling the truth and lying, like keeping silent. A false dilemma can also occur in the form of a disjunctive syllogism: [6]
14, OR, Logical disjunction; 15, true, Tautology. Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
Affirming a disjunct – concluding that one disjunct of a logical disjunction must be false because the other disjunct is true; A or B; A, therefore not B. [ 10 ] Affirming the consequent – the antecedent in an indicative conditional is claimed to be true because the consequent is true; if A, then B; B, therefore A .
An example: we are given the conditional fact that if it is a bear, then it can swim. Then, all 4 possibilities in the truth table are compared to that fact. If it is a bear, then it can swim — T; If it is a bear, then it can not swim — F; If it is not a bear, then it can swim — T because it doesn’t contradict our initial fact.
The general form of McGee-type counterexamples to modus ponens is simply , (), therefore, ; it is not essential that be a disjunction, as in the example given. That these kinds of cases constitute failures of modus ponens remains a controversial view among logicians, but opinions vary on how the cases should be disposed of.
The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that