Following Wittgenstein's rule-following considerations, the determinacy of length relations depends on normative practices of application, not on platonic structures that fix their own extensions independently of human activity.

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1 reason against

Reasons For

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Reason for

1.Mathematical rules like length measurement have no intrinsic meaning apart from communal agreement on how to apply them in practice.
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2.If Platonic objects existed independently, they couldn't causally explain why humans converge on identical measurement standards.
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3.The same physical object receives different length descriptions across measurement systems, showing length facts depend on normative frameworks.
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Reasons Against

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Reason against

1.Normative practices themselves must track something objective, else disagreement over measurement would be meaningless rather than mistaken.
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2.Length relations hold counterfactually even when no humans practice measurement—suggesting independence from actual normative activity.
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3.If determinacy requires only social agreement, then any consistent measurement community would be equally correct, making science epistemically arbitrary.
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Key Terms

Extensions(what FO allegedly cannot express according to the claim): In logic, the set of all things that a property actually applies to—for example, the extension of 'red things' is everything that is red.
Normative practices(as used in social philosophy): The shared rules, standards, or habits that a group of people follow about what is right, proper, or acceptable.
Platonic structures(the alternative view being rejected—the idea that abstract structures exist on their own): Abstract, timeless perfect forms or ideals (from Plato's philosophy) that exist independently of the physical world and human minds.
Wittgenstein: Ludwig Wittgenstein was an Austrian-British philosopher who fundamentally changed how people think about language and meaning in the 20th century. He argued that many philosophical problems arise from misunderstanding how words actually work in everyday life, rather than from deep metaphysical mysteries. His ideas influenced not just philosophy but also mathematics, logic, and even how people approach psychology and artificial intelligence today.
a priori(Frege treats 'analytic' as entailing 'a priori' for arithmetic.): Knowable independently of empirical experience; here treated as a consequence of analyticity.
determinacy(Game theory, infinite games): The property that for any game property φ, either player i has a strategy to force a set of histories satisfying φ, or player j has a strategy to force ¬φ; formally: {i}φ ∨ {j}¬φ
rule-following considerations(in philosophy of language): Wittgenstein's famous puzzle about how we know what rule to follow next: if you learn a rule by seeing examples, how do you know you're applying it correctly to new cases you've never seen before?

Connections

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Truth & Knowledge1 linked Perception1 linked

If Platonic objects existed independently, they couldn't causally explain why hu...If determinacy requires only social agreement, then any consistent measurement c...

Details

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