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The project of PM is to reduce mathematics to logic, and part of the view of logic behind this project is that logical truths are all completely general.
In the process, important elements of his "Pythagorean" view of logic were abandoned.
Despite their differences, Russell and Frege were alike in taking an essentially Platonic view of logic.
This is different from the traditional view of logic, in which the conditional has a material implication truth table, in which the conditional is true for these three cases and just false for p not q cases.
This method of teaching logic, variously known as critical thinking or informal logic, had already been embraced by a few teachers of philosophy who wanted to get away from the essentially mathematical view of logic taken by famous thinkers like Bertrand Russell and make it a more practical instrument for analyzing the questions of everyday life.
While much prior work on vagueness considers it from the point of view of logic and metaphysics, we will be looking at it as philosophers of language, asking in particular what a theory of meaning must look like if it is to explain how we communicate as we do using vague language.
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Soc., Providence, 1984, ix + 360 pp. Three Views of Logic: Mathematics, Philosophy, and Computer Science.
"And we realized we had to come from that point of view of irrefutable logic, that it's wrong and it's child abuse to not lock up your gun".
Section 2 focuses on negation as a unary connective from the point of view of philosophical logic.
Russell observes that "from the point of view of formal logic" it is impossible to derive an Ought from an Is.
This may not be very significant from the point of view of modern logic, which does not distinguish between basic and non-basic judgements in this way, but it may have a considerable ontological significance.
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