A use-based semantic theory can accommodate mathematical discourse without positing abstract objects or fictional surrogates, making the platonist/fictionalist framework theoretically unnecessary.
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Theoretically unnecessary(describing what the statement claims about the platonist/fictionalist framework)
Not needed as part of a theory's explanation—the theory works just fine without it.
Use-based semantic theory(as the main subject of the statement)
A theory of meaning that says words and concepts get their meaning from how we actually use them, rather than from what they refer to in the world.
abstract objects(The target of Platonist ontological claims)
Objects referred to by singular terms in literally true sentences that cannot be paraphrased away; includes mathematical objects (e.g., numbers), propositions, properties, relations, sentence types, possible worlds, logical objects, and fictional objects.
framework(Carnap's philosophy of language and logic)
A structured system of rules or language that must be in place for rational discourse to be possible.
positing(Fichtean model of self-consciousness)
The act by which the I establishes or asserts being — both its own being and, through limitation, the being of the non-I
semantic theory(Davidsonian semantics)
A theory that states all the facts about the meanings of expressions in a language