The form of an abstraction principle alone is insufficient to determine the ontological category of its output, as Frege's own Grundlagen distinguishes directions (abstract) from aggregates (concrete) despite both being definable by abstraction.

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Reasons For

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Reason for

1.Frege explicitly treats directions and aggregates differently despite both arising from equivalence relations, showing form alone underdetermines ontology.
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2.Multiple abstraction principles can yield outputs with identical formal structure but different metaphysical status (abstract vs. concrete).
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3.The identity conditions and modal properties of abstract objects differ systematically from concrete ones, requiring additional principles beyond abstraction form.
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Reasons Against

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Reason against

1.Frege's own theory suggests that the *content* of an equivalence relation (not mere form) determines whether outputs are abstract or concrete objects.
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2.If form alone were insufficient, we'd lack principled criteria for individuating abstraction principles—undermining the entire neo-Fregean project.
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3.The distinction between directions and aggregates may reflect different *domains of application* rather than proof that form fails to determine ontological category.
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Key Terms

Concrete: Concrete refers to a building material made by mixing cement, water, sand, and gravel together. When these ingredients combine, they harden into a strong, durable substance that can be shaped into almost any form before it sets. Concrete is one of the most commonly used materials in construction because it's affordable, long-lasting, and can be used for everything from sidewalks and bridges to buildings and dams.
Frege(as a major historical figure in philosophy): Gottlob Frege (1848-1925) was a German logician and philosopher who founded modern logic and did groundbreaking work on how language relates to meaning and existence.
Grundlagen(as a key philosophical text): A famous 1884 book by Frege titled 'The Foundations of Arithmetic' where he explored how numbers and mathematical objects come to exist through logical rules.
Ontological category(as used in metaphysics): A fundamental type or kind of thing that exists; like how 'physical objects,' 'numbers,' or 'ideas' might be different categories of what exists.
abstract(in Zalta's definition, contrasted with primitivism): Not merely the negation of being concrete; rather, abstract objects are those that could not possibly be concrete (e.g., numbers, sets)
abstraction principle(Used to introduce abstract entities such as trains from concrete relata such as carriages): A principle that defines a functional expression by specifying an equivalence condition: f(x) = f(y) iff x and y stand in relation R.
aggregate(Avicenna's argument for a necessary existent): The totality of all currently existing contingent individual things, each of whose existence is accounted for by its causal antecedents.

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Modality & Possibility1 linked

Frege explicitly treats directions and aggregates differently despite both arisi...Frege's own theory suggests that the *content* of an equivalence relation (not m...If form alone were insufficient, we'd lack principled criteria for individuating...Multiple abstraction principles can yield outputs with identical formal structur...

Details

Type: claim
Perspectives: 2 (1 for, 1 against)
Edits: 1 edit