Combining Philosophers

Ideas for Friedrich Schlegel, Hilary Putnam and Stephen Houlgate

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2 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Before the late 19th century logic was trivialised by not dealing with relations [Putnam]
     Full Idea: It was essentially the failure to develop a logic of relations that trivialised the logic studied before the end of the nineteenth century.
     From: Hilary Putnam (Philosophy of Logic [1971], Ch.3)
     A reaction: De Morgan, Peirce and Frege were, I believe, the people who put this right.
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Asserting first-order validity implicitly involves second-order reference to classes [Putnam]
     Full Idea: The natural understanding of first-order logic is that in writing down first-order schemata we are implicitly asserting their validity, that is, making second-order assertions. ...Thus even quantification theory involves reference to classes.
     From: Hilary Putnam (Philosophy of Logic [1971], Ch.3)
     A reaction: If, as a nominalist, you totally rejected classes, presumably you would get by in first-order logic somehow. To say 'there are no classes so there is no logical validity' sounds bonkers.