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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 the type of object that declarative sentences denote. For instance, the sentence "The sky is blue" denotes the proposition that the ...
It deals with propositions [1] (which can be true or false) [10] and relations between propositions, [11] including the construction of arguments based on them. [12] Compound propositions are formed by connecting propositions by logical connectives representing the truth functions of conjunction, disjunction, implication, biconditional, and ...
The logical NAND is an operation on two logical values, typically the values of two propositions, that produces a value of false if both of its operands are true. In other words, it produces a value of true if at least one of its operands is false. The truth table for p NAND q (also written as p ↑ q, Dpq, or p | q) is as follows:
A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water is boiling." expresses a proposition since it can be true or false. The sentences "Is the water boiling?"
It is possible in logic to make well-constructed propositions that can be neither true nor false; a common example of this is the "Liar's paradox", [15] the statement "this statement is false", which is argued to itself be neither true nor false. Arthur Prior has argued that The Paradox is not an example of a statement that cannot be true or ...
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). [1] [2]
A proposition (true or false) asserting an atomic fact is called an atomic proposition. — Russell, "Introduction to Tractatus Logico-Philosophicus" See also [2] and [3] especially regarding elementary proposition and atomic proposition as discussed by Russell and Wittgenstein; Note the distinction between an elementary/atomic proposition and ...
Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its logical constants).