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Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems:
In classical logic, disjunctive syllogism [1] [2] (historically known as modus tollendo ponens (MTP), [3] Latin for "mode that affirms by denying") [4] is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]
Philosophy of logic is the area of philosophy that studies the nature of logic. [1] [2] Like many other disciplines, logic involves various philosophical presuppositions which are addressed by the philosophy of logic. [3]
Logic studies valid forms of inference like modus ponens. Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and ...
Science of Logic (SL; German: Wissenschaft der Logik, WdL), first published between 1812 and 1816, is the work in which Georg Wilhelm Friedrich Hegel outlined his vision of logic. Hegel's logic is a system of dialectics , i.e., a dialectical metaphysics : it is a development of the principle that thought and being constitute a single and active ...
In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order ...
In this sense, propositional logic is the foundation of first-order logic and higher-order logic. Propositional logic is typically studied with a formal language, [c] in which propositions are represented by letters, which are called propositional variables. These are then used, together with symbols for connectives, to make propositional formula.