Assertion
Assertion
Frege introduced the assertion sign, in 1879, as a means of indicating the difference between asserting a proposition as true and merely naming a proposition (e.g., in order to make an assertion about it, that it has such and such consequences, or the like). Thus, with an appropriate expression A, the notation |-A would be used to make the assertion, “The unlike magnetic poles attract one another,” while the notation -A would correspond rather to the noun clause, “that the unlike magnetic poles attract one another.” Later Frege adopted the usage that propositional expressions (as noun clauses) are proper names of truth values and modified his use of the assertion sign accordingly, employing say A (or -A) to denote the truth value thereof that the unlike magnetic poles attract one another and |-A to express the assertion that this truth value is truth.
The assertion sign was adopted by Russell, and by Whitehead and Russell in Principia Mathematica, in approximately Frege’s sense of 1879, and it is from this source that it has come into general use. Some recent writers omit the assertion sign, either as understood, or on the ground that the Frege-Russell distinction between asserted and unasserted propositions is illusory. Others use the assertion sign in a syntactical sense, to express that a formula is a theorem of a logistic system (q.v.); this usage differs from that of Frege and Russell in that the latter requires the assertion sign to be followed by a formula denoting a proposition, or a truth value, while the former requires it to be followed by the syntactical name of such a formula.
In the propositional calculus, the name law of assertion is given to the theorem
p ? [[p ? q] &sup q].
(The associated form of inference from A and A ? B to B is, however, known rather as modus ponens.) — A.C.
The act of declaring a proposition or propositional form to be true (or to be necessarily true, or to be a part of a system).