The Principle of Relevant Propositions states that unless the truth value (be it true or false) of some fact or proposition logically entails or negates the truth value of any facts or proposition(s) in an argument, or negates any logical operators (negation, conjunction, disjunction, implication, biconditional, etc.) in or among the premises of the argument, or anything necessary for the truth or falsity of such premises, the fact is not relevant to the argument.
By contraposition, if a proposition is relevant to a given argument, then (to grossly oversimplify this principle) the proposition logically entails or negates something in the argument or something necessary for anything in the argument.
Below is a picture that further explicates the criteria for relevancy.
But what does this all have to do with evaluating arguments?
Arguments are all about premises, conclusions, and assumptions. A necessary condition for a criticism to successfully refute or undermine an argument is that the criticism must be relevant to the argument. Something which is utterly irrelevant to an argument’s premises, assumptions, or conclusions will clearly be something which cannot have a bearing on the argument’s rational force. Hence, two ways to evaluate arguments manifest themselves in discussing relevancy: one can bolster or critique an argument by emphasizing the irrelevance of a claim in relation to another claim; or, one can bolster or critique an argument by pointing out the relevance of a claim in relation to another claim.
It stands to reason, then, that a systematic analysis of what it means for a proposition to be relevant will be wholly invaluable for one’s conceptual toolkit.
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@rational_inquiry (Caleb) has created and eloquently expounded The Principle of Relevant Propositions on Instagram.
There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.