On the Role of Auxiliary Assumptions in the Production of Evidence - - PowerPoint PPT Presentation

Introduction Counterexamples Conflation Implications References

On the Role of Auxiliary Assumptions in the Production of Evidence

Corey Dethier

University of Notre Dame Philosophy Department corey.dethier@gmail.com

• Nov. 3, 2018

PSA 2018

Introduction Counterexamples Conflation Implications References

Introduction

Introduction Counterexamples Conflation Implications References

Traditional (Duhemian) view of auxiliary hypotheses

No (logical) difference between an auxiliary hypothesis and the hypothesis-to-be-tested. Consequence: theories are tested as a whole. Under attacked for decades (see, e.g., Azzouni 2000; Hacking 1983; Longino 1990; J. Norton 2008). Implications for auxiliary hypotheses have been underdeveloped.

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Duhem’s argument

(P1) Hypotheses are (only) tested via the comparison of derived consequences with the world (Duhem 1914/1951, 180). (P2) In the derivation of consequences, there is no logical difference between the hypothesis and the auxiliary hypotheses (Duhem 1914/1951, 182). (P3) The auxiliary hypotheses relied on in actual testing scenarios are “science ... taken as a whole” (Duhem 1914/1951, 187). (C) In actual testing scenarios, the “science ... taken as a whole” is tested.

Introduction Counterexamples Conflation Implications References

A problem

I think the Duhemian conclusion is false. Specifically, in any case in which (known) idealizations are employed in the derivation of consequences, it would be unreasonable to say that the truth of the idealization and hypothesis are both tested. – we already know the idealization is false! In the first part of the talk, I run through two such cases.

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Saying something positive

Diagnosis: the argument turns on a conflation between the assumptions necessary for the derivation of an empirically testable consequence from a hypothesis and the assumptions necessary to test the theory. Upshot: the role of auxiliary hypotheses in testing is more akin to that of reliability-apt tools than it is to truth-apt premises. (And then some implications.)

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Counterexamples

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The shape of the earth

Fge Fgp p

x-section of a rotating sphere

If you can measure differences in acceleration by latitude, you can distinguish between different theories of gravity.

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Measuring differences in acceleration

Pendulum lengths (ℓ) and periods (T) can be related to acceleration by: a “ 4ℓπ2 T 2 According to the traditional view, the use of the pendulum as an instrument to measure acceleration requires assuming that this equation is true. Can only test universal gravity insofar as we’re simultaneously testing this relationship.

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A problem

The pendulum equation isn’t actually true; it’s an idealization in that it fails to account for the effects of amplitude. Practically speaking, this effect is negligible when the amplitude is small, but it does exist. The problem: the pendulum data serves as a test of universal gravity even though the theory as a whole is false.

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HW model of allele distribution

Gen 1 Gen 2 freq(A1) = p freq(A2) = q G 1

A1A1 = p2

G 1

A1A2 = 2pq

G 1

A2A2 = q2

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HW assumptions

Assumptions of the HW model include: infinite population; no mutation; no differential fitness; no organization of mating within the population; no genetic exchange with other populations; no genetic exchange between generations. Clearly, these assumptions are never literally satisfied by an actual population; at best, there’s effective approximation.

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Heretozygote advantage

Heterozygote advantage occurs when the heterozygote (A1A2) has a fitness advantage over the homozygotes. In testing, the application of the HW model is crucial: we can only measure the advantage by means of the deviation from HW equilibrium. Essentially: the HW model acts like a (“vicarious”) control population (compare S. D. Norton and Suppe 2001).

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Conflation

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What’s gone wrong?

Why are these two cases tests? Roughly: the observable data can be used—in combination with certain theories or models—to discriminate between two hypotheses. Clearly, we don’t need to assume that theories or models are true

• r “perfect” (c.f. Teller 2001) in order to use them (in this way).

Instead, we must assume that the equation or model is reliable in the context of use.

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Reliability

What does “reliable” mean in the context of the prior slide? Roughly, a model or theory is reliable to the degree that it allows for (something like) truth-preserving inferences in the context of use: given accurate data and a model or theory that is reliable to degree x, we should correctly pick out the true hypothesis x% of the time. Obviously, truth is not necessary for reliability. And note the parallel here with instruments.

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The alleged conflation

My claim, then, is that the argument given above conflates the assumptions necessary to derive consequences from a hypothesis (assumptions about truth) with those necessary to use those consequences as a test (assumptions about reliability). As such, we should reject the claim that theories are tested (only) via their derived consequences. Instead, the connection between them is secured by theories and models that allow for more-or-less reliable (in a context) use of the data.

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Why not simply re-write the argument?

Why not simply claim that the mistake lies in the account of which auxiliary hypotheses are employed in a derivation? – i.e., instead of the hypothesis that Newtonian theory is true, the hypothesis that it is reliable. Allows us to maintain the connection between derivation and testing. Doesn’t allow us to maintain the idea that anything even approximating the “whole theory” must be assumed to be true in each test, however.

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The role of auxiliary assumptions

Traditional view: the primary role of auxiliary hypotheses in testing is as (truth-apt) premises in the derivation of consequences. My view: the primary role of auxiliary hypotheses in testing is as (reliability-apt) tools that are used in combination with empirical data to distinguish between hypotheses.

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Implications

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First: Models as epistemic tools

As just noted, my view is that the theories and models that we employ as auxiliary hypotheses are epistemic tools, in a sense similar to the sense in which physical instruments are. This view fits well with the position recently advocated by a number of authors (e.g., Edwards 2010; Lloyd 2012; Morrison 2015) who argue that experiments and evidence production inevitably involves both theoretical and physical aspects.

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Models as epistemic tools (continued)

The analysis so far suggests a further conclusion. Not only are both models and instruments involved in testing, they play essentially the same epistemic role: both are “tools” in the production of evidence in the sense that (a) their role is to secure a connection between theoretical question and world; (b) what matters is their (in-context) reliability for this task. Asking whether our pendulum equation is “true” is therefore much like asking whether a thermometer would give accurate readings on the sun—it’s completely irrelevant to determining whether the answer is a good one.

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Second: Idealizations and confirmation theory

Suppose we know that a model, M, is an idealization; there’s some way in which it misrepresents the phenomenon. On a straightfoward interpretation of PpMq, then, we can’t conditionalize on M: PpH|Mq “ PpHqPpM|Hq PpMq So even if M ( H, we cannot formally say that M supports H.

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Idealizations and confirmation theory (continued)

I’ve spent this talk giving independent reasons for thinking that this is the wrong way to interpret PpMq. Instead, we should interpret PpMq as the probability that M is reliable in the context of use. No principled reason for rejecting the use of these context-sensitive judgments of reliability in confirmation given that we already need to make them when we’re using instruments.

Introduction Counterexamples Conflation Implications References

Azzouni, Jody (2000). Knowledge and Reference in Empirical

• Science. London: Routledge.

Duhem, Pierre (1914/1951). The Aim and Structure of Physical

• Theory. Trans. by Phillip P. Wiener. Princeton, NJ: Princeton

University Press. Edwards, Paul (2010). A Vast Machine: Computer Models, Climate Data, and the Politics of Global Warming. Cambridge, MA: MIT Press. Hacking, Ian (1983). Representing and Intervening: Introductory Topics in the Philosophy of Natural Science. Cambridge: Cambridge University Press. Lloyd, Elisabeth (2012). The Role of “Complex” Empiricism in the Debates about Satellite Data and Climate Models. Studies in History and Philosophy of Science Part A 43.2: 390–401. Longino, Helen (1990). Science and Social Knowledge: Values and Objectivity in Scientific Inquiry. Princeton, NJ: Princeton University Press.

Introduction Counterexamples Conflation Implications References

Morrison, Margaret (2015). Reconstructing Reality: Models, Mathematics, and Simulations. Oxford: Oxford University Press. Norton, John (2008). Must Evidence Underdetermine Theory? In: The Challenge of the Social and the Pressure of Practice: Science and Values Revisited. Ed. by Martin Carrier, Don Howard, and Janet Kourany. Pittsburgh, PA: University of Pittsburgh Press: 17–44. Norton, Stephen D. and Fredrick Suppe (2001). Why Atmospheric Modeling Is Good Science. In: Changing the Atmosphere: Expert Knowledge and Environmental Governance. Ed. by Clark A. Miller and Paul N. Edwards. Cambridge, MA: The MIT Press: 67–105. Teller, Paul (2001). Twilight of the Perfect Model Model. Erkenntnis 55.4: 393–415.