On Propositions

Abstract

Propositional assertions as the store of knowledge, which may be true, false or both at once 41 – Mathematical equations are definitions lacking truth-values 41 – So-called particular and individual propositions are also definitions lacking truth-values 41 – Only proposition-forming connectors can properly join concepts or expressions to form propositions 42 – Propositional truth-values appear plainly in the pyramid: Truth and falsity as flowing from the regular as opposed to the irregular use or reading of the connectors within the pyramid 42 – Contradictory propositions are simultaneously true and false 42 – The logical tradition - that they are “logically or analytically or a priori” false - is itself false 42 – In paradoxical propositions truth and falsity are fused and reciprocally dependent 43 – Alternative and disjunctive propositions are likewise simultaneously true and false, not “logically or analytically or a priori” true, as the tradition holds 43 – On assertions and probable propositions and their relation to truth and falsity 46 – Logical probability is generally considered as a third truth value. In fact, it has the structure of a contradiction, combining truth and falsity 45 – It combines true general knowledge with specific ignorance about instances 45 – The logical structure of the mathematical probability 45 – But its contradictory structure is neglected thereby: Even the “most probable” or the “least probable” will either occur or not 46 – “Fuzzy logic” as a kind of probability-logic 46