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pragmatist comments on [Poll] Less Wrong and Mainstream Philosophy: How Different are We? - Less Wrong
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For most Platonists, an object is something we quantify over. So, for instance, numbers are objects, because we say things like "There is one even prime" (existential quantification), and "All multiples of 6 are also multiples of 2" (universal quantification). Any domain over which we quantify is a domain of objects.
Then what does it mean for an abstract object like 2 to "exist"?
There are many different answers to this question. One common answer is that we should believe an object exists if a theory we accept quantifies over that object. If quantum field theory requires quantification over the integers then 2 (and other integers) exist. Since contemporary physics doesn't quantify over a domain containing phlogiston, phlogiston does not exist.
There's something wrong when smart people argue and disagree over a question when there are many different ideas as to what the words in the question actually mean...