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18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
Full Idea: To get any advantage from moving to second-order logic, we need to assign to second-order variables a role different from merely ranging over collections made up of things the first-order variables range over. | |
From: Vann McGee (Logical Consequence [2014], 7) | |
A reaction: Thus it is exciting if they range over genuine properties, but not so exciting if you merely characterise those properties as sets of first-order objects. This idea leads into a discussion of plural quantification. |