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Colin McGinn on Wittgenstein's ontology

Colin McGinn, a contemporary philosopher of some importance, (google "new mysterians") often discusses the history of the discipline in his blog. I'm fascinated by his recent comment on "Wittgenstein's Ontology," which you can find by clicking here.  Wittgenstein’s Ontology - Colin McGinn    Let us start our consideration of it with a simple question: what is ontology? By standard definition, it is the study of being, discussing for example what types of thing constitute the furniture of the universe. Sample questions: Are numbers real?  Are only the numbers we call "real numbers" real or are "imaginary" numbers also real? This is distinct from questions about cosmology or the mind-body problem, which are puzzles ABOUT certain of the pieces of furniture in the universe. These inquiries all fit under the broader framework of metaphysics.  Anyway, McGinn's first point is that Wittgenstein sets out his own ontology clearly in the opening...

Inflated Ontology

This illustration is making its way around the more philosophical corners of the interwebs. In case I've given you an illegible variant of it, here are the captions, in sequence: 1. Shop for a new tie 2. Make macaroni 3. Do cardio 4. Don't inflate your ontology 5. Don't do it. 6. Vacuum the rug. The fifth cell includes an illustration of a unicorn and the square root of -1 as thoughts in the mind of the character doing various quotidian things. The warning, then, is not to attribute reality either to imaginary beings or to imaginary numbers. Leaving unicorns aside, I think there is something odd about the warning as it applies to numbers. The value of any number system, including the numbers we call real and those we call imaginary, consists entirely of its utility. So, for a pragmatist as to math, the square root of -1 stands on the same "ontological" footing as does -1, or as does 1. But I do like the cute minimalism of the illustrations here. ...