A false premise is an incorrect

proposition A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...

that forms the basis of an argument or

syllogism A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defin ...

. Since the

premise A premise or premiss is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. Arguments consist of a set of premises and a conclusion. An argument is meaningf ...

(proposition, or assumption) is not correct, the conclusion drawn may be in error. However, the logical validity of an argument is a function of its internal consistency, not the

truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in ...

of its premises. For example, consider this syllogism, which involves a false premise: * If the streets are wet, it has rained recently. (premise) * The streets are wet. (premise) * Therefore it has rained recently. (conclusion) This argument is logically valid, but quite demonstrably wrong, because its first premise is false — a street cleaner may have passed, the local river could have flooded, etc. A simple logical analysis will not reveal the error in this argument, since that analysis must accept the truth of the argument's premises. For this reason, an argument based on false premises can be much more difficult to refute, or even discuss, than one featuring a normal logical error, as the truth of its premises must be established to the satisfaction of all parties. Another feature of an argument based on false premises that can bedevil critics, is that its conclusion can in fact be true. Consider the above example again. It may well be that it has recently rained and that the streets are wet. This does nothing to prove the first premise, but can make its claims more difficult to refute. This underlies the basic

epistemological Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowled ...

problem of establishing causal relationships.

Large language models A large language model (LLM) is a language model trained with Self-supervised learning, self-supervised machine learning on a vast amount of text, designed for natural language processing tasks, especially Natural language generation, language g ...

often fail to appropriately answer questions based on false premises, but can be trained to respond correctly.

References

See also