Just to add, I think the big break between Peirce and the nominalists is because a general can’t be limited to any collection of actual entities. This is obvious in mathematics if we talk about a general like “even integers.” Clearly that’s an infinite collection. But if you say something like “white horses” you don’t just mean all white horses but all possible white horses. You can limit things more, but generals by their very nature have this connection to continuity.
While I said in practice there isn’t as big a practical effect between nominalists and Peirce’s realism it’s because nominalists are fine to potentially quantify over future experienced entities. That is the way they conceive of possibilities is much more in an Aristotilean fashion. Potential is just an openness to new finite entities. Peirce is thinking much more logically. So it’s with his pragmatic maxim that I think you see his thinking regarding nominalism develop most. The original pragmatic maxim starts with meaning be how you do measure something. But that’s clearly problematic as a rock is hard whether you measure it or not. He then moves to a moderate realism by invoking counterfactuals. It’s hard if I could measure it. But he keeps thinking through these questions of potentialities and realizes he has to deal with a continuous set of possibilities. Further that an entity’s properties are independent of what I think about it. That is when I ask about a property scientifically I’m not merely making a claim about a future measurement but a claim about the entity itself. It’s at that point that I think the traditional nominalistic tendencies, especially within science, start to split off. In one sense it doesn’t matter because all we can test are potential measurements. Yet the significance of those measurements are the properties of the thing itself. This is also where I think Peirce (and later Dewey) chart a third way between the traditional poles of realism and idealism such as were found in the early 20th century. Especially in the United States. I bring all this up because my sense is that it’s to the pragmatic maxim we have to look for all these terms.
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