Fallacies of relevance in the context of Inductive fallacy

Informal fallacies are a type of incorrect argument in natural language. The source of the error is not necessarily due to the form of the argument, as is the case for formal fallacies, but is due to its content and context. Fallacies, despite being incorrect, usually appear to be correct and thereby can seduce people into accepting and using them. These misleading appearances are often connected to various aspects of natural language, such as ambiguous or vague expressions, or the assumption of implicit premises instead of making them explicit.

Traditionally, a great number of informal fallacies have been identified, including the fallacy of equivocation, the fallacy of amphiboly, the fallacies of composition and division, the false dilemma, the fallacy of begging the question, the ad hominem fallacy and the appeal to ignorance. There is no general agreement as to how the various fallacies are to be grouped into categories. One approach sometimes found in the literature is to distinguish between fallacies of ambiguity, which have their root in ambiguous or vague language, fallacies of presumption, which involve false or unjustified premises, and fallacies of relevance, in which the premises are not relevant to the conclusion despite appearances otherwise.

A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. It is an example of jumping to conclusions. For example, one may generalize about all people or all members of a group from what one knows about just one or a few people:

• If one meets a rude person from a given country X, one may suspect that most people in country X are rude.
• If one sees only white swans, one may suspect that all swans are white.

Expressed in more precise philosophical language, a fallacy of defective induction is a conclusion that has been made on the basis of weak premises, or one which is not justified by sufficient or unbiased evidence. 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 of error.