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In modern formal logic and type theory, the term is mainly used instead for a single proposition, often denoted by the falsum symbol ; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition).
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.
Presupposition. For other uses, see Presupposition (disambiguation). In linguistics and philosophy, a presupposition is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. Examples of presuppositions include:
For the information science concept, see Ontology (information science). Ontology is the philosophical study of being. As one of the most fundamental concepts, being encompasses all of reality and every entity within it. To articulate the basic structure of being, ontology examines what all entities have in common and how they are divided into ...
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. [1][2] It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. [3][4] A paradox usually involves contradictory-yet ...
Proposition. A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as being the kind of thing that declarative sentences denote. For instance the sentence "The sky is blue" denotes the ...
A different meaning of the term hypothesis is used in formal logic, to denote the antecedent of a proposition; thus in the proposition "If P, then Q", P denotes the hypothesis (or antecedent); Q can be called a consequent. P is the assumption in a (possibly counterfactual) What If question.
Propositional calculus. Not to be confused with Propositional analysis. The propositional calculus[a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4][5] It deals with propositions [1] (which can be true or false) [6] and ...