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List of paradoxes. Outline of public relations – Overview of and topical guide to public relations. Map–territory relation – Relationship between an object and a representation of that object (confusing map with territory, menu with meal) Mathematical fallacy – Certain type of mistaken proof.
Formal proof. In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence, according to the rule of inference. It differs from a natural language ...
Validity (logic) In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. [1] It is not required for a valid argument to have premises that are actually true, [2] but to have premises that, if they were ...
One valid argument form is known as modus ponens, not to be mistaken with modus tollens, which is another valid argument form that has a like-sounding name and structure. Modus ponens (sometimes abbreviated as MP) says that if one thing is true, then another will be. It then states that the first is true. The conclusion is that the second thing ...
Formal fallacy. In logic and philosophy, a formal fallacy[a] is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. [2] It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still ...
Premise. A premise or premiss[a] is a proposition —a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. [1] Arguments consist of a set of premises and a conclusion. An argument is meaningful for its conclusion only when all of its premises are true.
The cut-elimination theorem for a calculus says that every proof involving Cut can be transformed (generally, by a constructive method) into a proof without Cut, and hence that Cut is admissible. The Curry–Howard correspondence between proofs and programs relates modus ponens to function application : if f is a function of type P → Q and x ...
The exception proves the rule is a phrase that arises from ignorance, though common to good writers. The original word was preuves, which did not mean proves but tests. [4] In this sense, the phrase does not mean that an exception demonstrates a rule to be true or to exist, but that it tests the rule, thereby proving its value.