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    Trains, under the simple account using abstraction princi... — Carmelics
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    Home/Modality & Possibility
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    Trains, under the simple account using abstraction principles, are abstract entities rather than concrete physical objects.

    Modality & Possibility
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.A train is defined as a maximal string of railroad carriages all connected to one another.
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    • 2.The expression 'the train of x' is defined via an abstraction principle: the train of x equals the train of y if and only if x and y are connected carriages.
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    • 3.x is a train if and only if for some carriage y, x is the train of y.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Abstraction principles define equivalence classes over concrete relata, but equivalence classes can themselves be spatiotemporally located where their members are located.
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    • 2.The train of x, defined as the maximal connected string containing x, inherits causal and spatiotemporal properties from its concrete carriages, satisfying paradigm criteria for concreteness.
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    • 3.Hale and Wright's own neo-logicist framework distinguishes between logical abstracts like numbers and sortal abstracts grounded in physical relations, where the latter retain concrete status.
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    Reason against 2 of 2
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    • 1.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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    • 2.Trains, unlike numbers or directions, admit of physical destruction, occupy determinate regions of spacetime, and exert gravitational force, which are criteria Kit Fine and Michael Dummett treat as definitive of concreteness regardless of definitional method.
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    Modality & Possibility

    Related

    A train is defined as a maximal string of railroad carriages all connected to on...Abstraction principles define equivalence classes over concrete relata, but equi...Entities defined by abstraction principles of this form are reckoned as abstract...Hale and Wright's own neo-logicist framework distinguishes between logical abstr...
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    The expression 'the train of x' is defined via an abstraction principle: the tra...The form of an abstraction principle alone is insufficient to determine the onto...The train of x, defined as the maximal connected string containing x, inherits c...Trains, unlike numbers or directions, admit of physical destruction, occupy dete...x is a train if and only if for some carriage y, x is the train of y.

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    Source

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    SEP: abstract-objects
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    where the \(F\text{s}\) cover the \(G\text{s}\) if and only if every part of every \(G\) has a part in common with an \(F\). Similarly, suppose a train is a maximal string of railroad carriages, all of which are connected to one another. We may define a functional expression, ‘the train of \(x\)’, by means of an ‘abstraction’ principle: The train of \(x\) = the train of \(y\) if and only if \(x\) and \(y\) are connected carriages. We may then say that \(x\) is a train if and only if for some car
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    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit