[44140] in linux-announce channel archive
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daemon@ATHENA.MIT.EDU (Paypal)
Mon Nov 20 04:21:56 2023
Date: Mon, 20 Nov 2023 08:52:21 +0100
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The second premise of the indispensability argument states mathematical objects are indispensable to our best scientific theories. In this context, indispensability is not the same as ineliminability because any entity can be eliminated from a theoretical system given appropriate adjustments to the other parts of the system. Therefore, dispensability requires an entity is eliminable without sacrificing the attractiveness of the theory. The attractiveness of the theory can be evaluated in terms of theoretical virtues such as explanatory power, empirical adequacy and simplicity. Furthermore, if an entity is dispensable to a theory, an equivalent theory can be formulated without it. This is the case, for example, if each sentence in one theory is a paraphrase of a sentence in another or if the two theories predict the same empirical observations.
According to the Stanford Encyclopedia of Philosophy, one of the most influential arguments against the indispensability argument comes from Hartry Field. It rejects the claim that mathematical objects are indispensable to science; Field has supported this argument by reformulating or "nominalizing" scientific theories so they do not refer to mathematical objects. As part of this project, Field has offered a reformulation of Newtonian physics in terms of the relationships between space-time points. Instead of referring to numerical distances, Field's reformulation uses relationships such as "between" and "congruent" to recover the theory without imply
Field's alternative to platonism is mathe
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<span style="color:#FFFFFF;font-size:5px;">The second premise of the indispensability argument states mathematical objects are indispensable to our best scientific theories. In this context, indispensability is not the same as ineliminability because any entity can be eliminated from a theoretical system given appropriate adjustments to the other parts of the system. Therefore, dispensability requires an entity is eliminable without sacrificing the attractiveness of the theory. The attractiveness of the theory can be evaluated in terms of theoretical virtues such as explanatory power, empirical adequacy and simplicity. Furthermore, if an entity is dispensable to a theory, an equivalent theory can be formulated without it. This is the case, for example, if each sentence in one theory is a paraphrase of a sentence in another or if the two theories predict the same empirical observations. According to the Stanford Encyclopedia of Philosophy, one of the most influential arguments against the indispensability argument comes from Hartry Field. It rejects the claim that mathematical objects are indispensable to science; Field has supported this argument by reformulating or "nominalizing" scientific theories so they do not refer to mathematical objects. As part of this project, Field has offered a reformulation of Newtonian physics in terms of the relationships between space-time points. Instead of referring to numerical distances, Field's reformulation uses relationships such as "between" and "congruent" to recover the theory without imply Field's alternative to platonism is mathe</span><br />
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