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A formal consequence must be true in all cases, however this is an incomplete definition of formal consequence, since even the argument "P is Q ' s brother's son, therefore P is Q ' s nephew" is valid in all cases, but is not a formal argument. [1]
The consequent in a hypothetical proposition is not necessarily a consequence of the antecedent. If monkeys are purple, then fish speak Klingon. "Fish speak Klingon" is the consequent here, but intuitively is not a consequence of (nor does it have anything to do with) the claim made in the antecedent that "monkeys are purple".
Affirming the consequent can also result from overgeneralizing the experience of many statements having true converses. If P and Q are "equivalent" statements, i.e. P ↔ Q {\displaystyle P\leftrightarrow Q} , it is possible to infer P under the condition Q .
Logical consequence, also known as a consequence relation, or entailment; Consequent, in logic, the second half of a hypothetical proposition or consequences; Consequentialism, a theory in philosophy in which the morality of an act is determined by its effects; Unintended consequences; Consequence, in operant conditioning, a result of some behavior
In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. While it is not generally used in formal writing, it is used in mathematics and shorthand.
The normative status of an action depends on its consequences according to consequentialism. The consequences of the actions of an agent may include other actions by this agent. Actualism and possibilism disagree on how later possible actions impact the normative status of the current action by the same agent.
The double turnstile is a binary relation. It has several different meanings in different contexts: To show semantic consequence, with a set of sentences on the left and a single sentence on the right, to denote that if every sentence on the left is true, the sentence on the right must be true, e.g. .
The material conditional (also known as material implication) is an operation commonly used in logic.When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false.