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Abstract: Russell's understanding of implication in The Principles of Mathematics (1903) is dual. At the heart of this understanding we find two concepts: material and formal implication. In the paper I give the reasons why Russell had to introduce the distinction between formal and material implications. I then draw the consequences of the distinction with special attention to their direct effect on logical affirmation and logical conclusion.
Key words: proposition, propositional function, material implication, formal implication, logical conclusion.
Platonic Realism and the Project of Philosophical Logic
The article is based on the main problems that the Russel's onthology (platonic realism) generates. The extreme realism that the philosopher allows is a fundament of his philosophical logic. From another point of view, persisting on this kind of realism leads to unsolvable problems on the field of philosophical logic.
Key words: Russell, philosophical logic, Platonic realism, logical form, Wittgenstein