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In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
[1] Being a valid argument does not necessarily mean the conclusion will be true. It is valid because if the premises are true, then the conclusion has to be true. This can be proven for any valid argument form using a truth table which shows that there is no situation in which there are all true premises and a false conclusion. [2]
Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water ...
Intermediate conclusions or sub-conclusions, where a claim is supported by another claim that is used in turn to support some further claim, i.e. the final conclusion or another intermediate conclusion: In the following diagram, statement 4 is an intermediate conclusion in that it is a conclusion in relation to statement 5 but is a premise in ...
1] A relation of inference is monotonic if the addition of premises does not undermine previously reached conclusions; otherwise the relation is non-monotonic. Deductive inference is monotonic: if a conclusion is reached on the basis of a certain set of premises, then that conclusion still holds if more premises are added.
A false dilemma is an informal fallacy based on a premise that erroneously limits what options are available. [1] [2] [3] In its most simple form, called the fallacy of bifurcation, all but two alternatives are excluded. A fallacy is an argument, i.e. a series of premises together with a conclusion, that is unsound, i.e. not
An argument is valid if and only if it would be contradictory for the conclusion to be false if all of the premises are true. [3] Validity does not require the truth of the premises, instead it merely necessitates that conclusion follows from the premises without violating the correctness of the logical form.
The claim "I am definitely a British citizen" has a greater degree of force than the claim "I am a British citizen, presumably". (See also: Defeasible reasoning .) The first three elements, claim , ground , and warrant , are considered as the essential components of practical arguments, while the second triad, qualifier , backing , and rebuttal ...
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