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The conclusions of inductive reasoning are inherently uncertain. It only deals with the extent to which, given the premises, the conclusion is "credible" according to some theory of evidence. Examples include a many-valued logic, Dempster–Shafer theory, or probability theory with rules for inference such as Bayes' rule.
Various aspects of the premises are important to ensure that they offer significant support to the conclusion. In this regard, the sample size should be large to guarantee that many individual cases were considered before drawing the conclusion. [60] [73] An intimately connected factor is that the sample is random and representative. This means ...
Most conclusions drawn in surveys and carefully controlled experiments are arguments by example and generalization. Studies that analyze past speeches also draw conclusions by taking specific examples of communication and inferring generalizations from them. [1]
Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure".
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions, yet only weakly buttress the conclusions, hence a faulty generalization is produced. The essence of this inductive fallacy lies on the overestimation of an argument based on insufficiently-large samples under an implied margin or ...
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.
Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.