The empirical adequacy of comparativism about mass in Newtonian Gravity Niels C.M. Martens DPhil candidate Philosophy of Physics Oxford University 4 th Tübingen Summer School in HPS 2015 Idealizations in Physics Slides available at http://users.ox.ac.uk/~corp2044 29 July 2015
Outline Absolutism vs. Comparativism about mass 1 Dasgupta’s argument for Comparativism 2 Counter-argument: Empirical Inadequacy 3 Responses 4 Bonus: Ontological Parsimony 5
Outline Absolutism vs. Comparativism about mass 1 Dasgupta’s argument for Comparativism 2 Counter-argument: Empirical Inadequacy 3 Responses 4 Bonus: Ontological Parsimony 5
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Absolutism vs. Comparativism Counter-argument: Empirical Inadequacy Assumptions Responses Bonus: Ontological Parsimony “ The property of having mass is a determinable that appears to have two kinds of determinates. On the one hand, we naturally think that something with mass has a determinate intrinsic property, a property it has independently of its relationships with other material bodies. But we also think that things with mass stand in various determinate mass relationships with one another, such as x being more massive than y or x being (Dasgupta, 2013, p.105) ” twice as massive as y. Niels Martens Comparativism about mass 4/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Absolutism vs. Comparativism Counter-argument: Empirical Inadequacy Assumptions Responses Bonus: Ontological Parsimony Absolutism vs. Comparativism (Weak) Absolutism The most fundamental facts about material bodies vis-à-vis their mass are intrinsic properties (i.e. intrinsic masses). The mass relations hold in virtue of these intrinsic masses. (Weak) Comparativism The most fundamental facts about material bodies vis-à-vis their mass just concern how they are related in mass. All other facts about their mass, if any, hold in virtue of those relationships (and a convention). (Dasgupta, 2013) Niels Martens Comparativism about mass 5/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Absolutism vs. Comparativism Counter-argument: Empirical Inadequacy Assumptions Responses Bonus: Ontological Parsimony Collectively exhaustive? Strong Absolutism Strong Comparativism Weak Comparativism Weak Absolutism 1 1 Intrinsic masses are Mass relations are 2 2 fundamental fundamental Eliminativism / Reductionism / Emergentism Mass is not fundamental 1 → Compatible with Weak Abs & Comp Niels Martens Comparativism about mass 6/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Absolutism vs. Comparativism Counter-argument: Empirical Inadequacy Assumptions Responses Bonus: Ontological Parsimony Assumptions Newtonian Gravity Mass ratios (Baker, manuscripts) Equivalence between gravitational and inertial mass Niels Martens Comparativism about mass 7/34
Outline Absolutism vs. Comparativism about mass 1 Dasgupta’s argument for Comparativism 2 Counter-argument: Empirical Inadequacy 3 Responses 4 Bonus: Ontological Parsimony 5
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Dasgupta’s Razor Responses Bonus: Ontological Parsimony The argument for comparativism Dasgupta’s Razor P u Empirical adequacy of comparativism. All other things being equal (i.e. P u ), P o Occamist norm: we should favour theories that are ontologically more parsimonious. P p Comparativism about mass is ontologically more parsimo- nious than absolutism. C c Comparativism about mass is favoured. (Dasgupta, 2013) Niels Martens Comparativism about mass 9/34
Outline Absolutism vs. Comparativism about mass 1 Dasgupta’s argument for Comparativism 2 Counter-argument: Empirical Inadequacy 3 Responses 4 Bonus: Ontological Parsimony 5
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Defining Empirical Adequacy Counter-argument: Empirical Inadequacy Initial Variable Problem Responses Argument against Empirical Adequacy of Comparativism Bonus: Ontological Parsimony Empirical adequacy Empirical Adequacy: T 1 (absolutism) T 2 (comparativism) The comparativist laws of nature pick out a set of dynamically possible P 1 (possible models) P 2 (possible models) models from the set of possible S 1 (dynamically possible models) models such that all empirically distinct models generated by the absolutist theory are included (i.e. completeness ) and all models that S 2 (dynamically possible models) are empirically distinct from each of the absolutist solutions are excluded (i.e. soundness ). Niels Martens Comparativism about mass 11/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Defining Empirical Adequacy Counter-argument: Empirical Inadequacy Initial Variable Problem Responses Argument against Empirical Adequacy of Comparativism Bonus: Ontological Parsimony Empirical adequacy Laplacean Determinism: T 1 (absolutism) T 2 (comparativism) A model m is deterministic iff, for any time t , there is only one P 1 (possible models) P 2 (possible models) empirically possible world whose S 1 (dynamically possible models) state at t is identical to m ’s. → Unique solution to the Initial Value Problem S 2 (dynamically possible models) Niels Martens Comparativism about mass 11/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Defining Empirical Adequacy Counter-argument: Empirical Inadequacy Initial Variable Problem Responses Argument against Empirical Adequacy of Comparativism Bonus: Ontological Parsimony Empirical adequacy Empirical Adequacy: T 1 (absolutism) T 2 (comparativism) The laws of nature uniquely (i.e. deterministically) evolve each set P 1 (possible models) P 2 (possible models) of initial conditions allowed by the S 1 (dynamically possible models) theory into a dynamically possible model, such that the whole set of empirically distinct dynamically possible models generated by the S 2 (dynamically possible models) absolutist theory is reproduced (i.e. completeness ) and no models that are empirically distinct from each of the absolutist solutions are generated (i.e. soundness ). Niels Martens Comparativism about mass 11/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Defining Empirical Adequacy Counter-argument: Empirical Inadequacy Initial Variable Problem Responses Argument against Empirical Adequacy of Comparativism Bonus: Ontological Parsimony Empirical adequacy T 1 (absolutism) T 2 (comparativism) P 1 (possible models) P 2 (possible models) E 1 E 1 E 2 E 2 Niels Martens Comparativism about mass 11/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Defining Empirical Adequacy Counter-argument: Empirical Inadequacy Initial Variable Problem Responses Argument against Empirical Adequacy of Comparativism Bonus: Ontological Parsimony Empirical adequacy For comparativism to be T 1 (absolutism) T 2 (comparativism) empirically adequate, we need to find a map φ : P 1 → P 2 , such that P 1 (possible models) P 2 (possible models) ∀ m E ( m , φ ( m )) 1 φ Niels Martens Comparativism about mass 11/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Defining Empirical Adequacy Counter-argument: Empirical Inadequacy Initial Variable Problem Responses Argument against Empirical Adequacy of Comparativism Bonus: Ontological Parsimony Empirical adequacy For comparativism to be T 1 (absolutism) T 2 (comparativism) empirically adequate, we need to find a map φ : P 1 → P 2 , such that P 1 (possible models) P 2 (possible models) ∀ m E ( m , φ ( m )) 1 S 1 S 2 Completeness: 2 φ ∀E i ( E i ∩ S 1 � = ∅ → ( ∃ m ∈ E i : φ ( m ) ∈ S 2 )) Niels Martens Comparativism about mass 11/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Defining Empirical Adequacy Counter-argument: Empirical Inadequacy Initial Variable Problem Responses Argument against Empirical Adequacy of Comparativism Bonus: Ontological Parsimony Empirical adequacy For comparativism to be T 1 (absolutism) T 2 (comparativism) empirically adequate, we need to find a map φ : P 1 → P 2 , such that P 1 (possible models) P 2 (possible models) ∀ m E ( m , φ ( m )) 1 S 1 S 2 Completeness: 2 φ ∀E i ( E i ∩ S 1 � = ∅ → ( ∃ m ∈ E i : φ ( m ) ∈ S 2 )) Soundness: 3 ∀E i ( E i ∩ S 1 = ∅ → ( ¬∃ m ∈ E i : φ ( m ) ∈ S 2 )) Niels Martens Comparativism about mass 11/34
Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Defining Empirical Adequacy Counter-argument: Empirical Inadequacy Initial Variable Problem Responses Argument against Empirical Adequacy of Comparativism Bonus: Ontological Parsimony How to find φ Recipe for φ : m { m i ,α 2 ,...,α n } , abs → m { mi mj ,α 2 ,...,α n } , comp For instance: φ : m { m i , r ij , v ij } , abs → m { mi mj , r ij , v ij } , comp T 1 (absolutism) T 2 (comparativism) P 1 P 2 S 1 S 2 φ m { m i , r ij , v ij } m { mi mj , r ij , v ij } Niels Martens Comparativism about mass 12/34
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