Search Results

This book presents a history of modern logic from the Middle Ages through the end of the 20th century. In addition to a history of symbolic logic, the book also examines developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837–1936. The book contains a section on the development of mathematical logic from 1900–1935, followed by a section on main trends in mathematical logic after the 1930s. The book goes on to discuss modal logic from Kant till the late 20th century, and logic and semantics in the 20th century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the 20th century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic.

The Logic of Language opens a new perspective on logic. Seuren first argues that the logic of language derives from the lexical meanings of the logical operators. These meanings, however, prove not to be consistent. To solve this problem, the author distinguishes between a default ‘basic‐natural’ and two nondefault ‘strict‐natural’ versions of natural predicate logic, all different from standard modern logic. Basic‐natural logic is shown to derive from an ontology of entities and properties, combined with a basic‐natural set theory, reflecting the way humans deal cognitively with plural sets. A new measure for ‘logical power’ shows the extreme weakness of standard predicate logic as against the maximal power of one version of strict‐natural logic, traditional, post‐Aristotelian predicate logic, or the ‘Square of Opposition’. It is shown that Aristotle's original logic as reconstructed by Abelard is logically faultless (unlike the Square, which suffers from ‘undue existential import’) and also more powerful than standard logic, though less so than the Square or basic‐natural logic. The latter two are shown to be maximally functional for natural linguistic interaction. In the last five chapters, a general theory of discourse‐bound interpretation is developed, covering discourse incrementation, anaphora, presupposition (with its logic) and topic—comment structure. The ‘donkey‐anaphora’ problem is solved by an appeal to discourse structures. The great defect of the Square, its ‘undue existential import’, is remedied by means of a protecting presuppositional ‘mantle’ creating a third truth value of radical falsity, assigned to propositions suffering from presupposition failure and causing inconsistency with preceding true discourse. Finally, topic—comment structure is shown to correspond to a question—answer game directing the building up of discourse domains and to be not of a pragmatic but of a truth‐conditional, hence semantic, nature. Anaphora, presupposition, and topic—comment structure are thus seen to form the ‘cement’ of discourse structure.