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Full Description
This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work.
Contents
The Basic Assumptions of Propositional Logic.- Classical Propositional Logic - PC -.- Relatedness Logic: The Subject Matter of a Proposition - S and R -.- A General Framework for Semantics for Propositional Logics.- Dependence Logics - D, Dual D, Eq, DPC -.- Modal Logics - S4, S5, S4Grz, T, B, K, QT, MSI, ML, G, G* -.- Intuitionism - Int and J -.- Many-Valued Logics - L3, Ln, L?, K3, G3, Gn, G?, S5 -.- A Paraconsistent Logic: J3.- Translations Between Logics.- The Semantic Foundations of Logic.- Summary of Logics.
