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This answer will focus on two references that may be useful to understand the issues dividing realism and anti-realism. Rather than looking at this from the perspective of logic it may be more useful to see it from the perspective of various metaphysical disputes such as platonism in mathematics versus intuitionism, realism of the physical world versus ...


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For Dummett, there is a tension between the certainty of deductive inference (the guarantee of the truth of the conclusion licensed by the truth of the premisses) and its usefulness or fruitfulness, that is, the ability of deductive arguments to yield new information. We have to consider the context : Wittgenstein with the well-know Tractarian slogan ...


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If I understand your question correctly, you are asking in effect how do we distinguish logic from non-logic? Logical expressions give rise to valid arguments and logical truths, that is, arguments where if the premises are true it is impossible for the conclusion to be false, and truths such that there is no way for them to come out as false. But this ...


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Here are the questions: What is the most general way to define and separate "the rules of logic" from "the things to which the rules are applied" ? The following definition of "theory" from Wikipedia may help clarify the separation: A theory about a topic is usually a first-order logic together with a specified domain of discourse over which the ...


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1) What is the most general way to define and separate "the rules of logic" from "the things to which the rules are applied" ? The basic distinction is obtained by the definition of propositions and of the logical operations done on them. "Separation" is achieved in the sense that only the truth of the propositions is relevant to the way the operations work....


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The "rules of logic" are the object of study of formal logic and mathematical logic. They define languages and proof systems, like e.g. predicate calculus, that are "applicable" to any topics whatever. The so-called "laws of logic" are formulas that are true irrespective of any possible interpretation, i.e. they hold in every interpretation. In this ...


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Patrick Suppes provides an example of an inference rule in section 2.1 that satisfies the soundness Criterion I but does not satisfy the completeness Criterion II: From any sentence P we may infer P. If the antecedent of the conditional, P, is true, then the consequent, P, is also true and so the rule is sound. However, it does not allow us by itself to ...


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