Underdetermination: The Big Picture Kareem Khalifa Department of Philosophy Middlebury College Overview • • • • What is Underdetermination? Holistic Underdetermination Contrastive Underdetermination Why Underdetermination Matters: Rationality General Structure of Underdetermination Output 1 Output 2 Input 1 Rule/ Process … Output n In words… • Suppose we have input of type A. • Furthermore, we have a rule that is consistent with the following: – If A, then B, C, D, … or Z. • Then the input and the rule underdetermine the outputs. • Sometimes the “blame” is assigned to the inputs; sometimes to the rules; sometimes to both. Simple (Non-Scientific) Example 10 apples, 0 oranges Total Expenditure on apples and oranges = $10 8 apples, 1 orange Total expenditure = ($1 x #apples) + ($2 x #oranges) 6 apples, 2 oranges 4 apples, 3 oranges 2 apples, 4 oranges So your total expenditure (input) plus the price of fruit (rule) underdetermines the exact quantity of apples and oranges that you purchase (output). 0 apples, 5 oranges Scientific Underdetermination: Basic Structure Theory 1 Theory 2 Empirical Evidence “Scientific Method” … Theory n Scientific Underdetermination: Simple Example Correlation between video games, violent behavior Video games cause violence Causal Inference Violence causes video games … Some third factor causes both Five ways of fleshing out underdetermination 1. Clarify the kinds of evidence that underdetermine (e.g. correlations, experimental, census, ethnographic, etc.) 2. Clarify the kinds of rules that underdetermine (e.g. significance tests, crucial experiments, Mill’s Methods, etc.) 3. Clarify the kinds of hypotheses/theories that are underdetermined (causal hypotheses, those concerning unobservables, qualitative, etc.) 4. Determine the strength of the underdetermination a. b. Nonuniqueness: more than one hypothesis is acceptable Egalitarian: any hypothesis is acceptable 5. Clarify if the underdetermination is transient or permanent. Two Kinds of Underdetermination • Holist Underdetermination (HU): – Input: evidence – Rules: Best fit/coherence – Output: theories to accept, rules • Contrastive Underdetermination (CU) – Input: evidence and hypotheses available at a given time – Rules: any that identify which available hypothesis “best fits” the evidence – Output: hypotheses to accept (available and unavailable) Holist Underdetermination 1. If evidence E disconfirms hypothesis H, then auxiliary hypotheses A1, …, An must be assumed. 2. If A1, …, An must be assumed, then E does not contradict H alone, but contradicts the conjunction of H & A1 & … & An. 3. So, if E is true, then either H is false OR A1 is false OR … OR An is false. 4. So any disconfirming evidence underdetermines the hypothesis (auxiliary or otherwise) to be rejected. Comparison of Standard View and HU Theory: Aux. Hyp: Concrete apparatus is measuring an F. All F’s are G’s Aux. Hyp.: Concrete apparatus is measuring a not-G Falsifying Experiment: This F is not a G Aux. Hyp.: Scientist did not make a mistake. HU Which hypothesis do we reject? Aux. Hyp.: Concrete apparatus is not malfunctioning Standard View Contrastive underdetermination 1. Suppose that, at time t, H is the available hypothesis that “fits” best with the evidence E. 2. Throughout the history of science, there has always been a hypothesis H* that is unavailable at t (but available at t+1) that would have fit E at least as well as H had it been available at t. 3. So at any given time, the evidence underdetermines the hypothesis that best fits with it. HU without CU • Suppose, contra CU, that there is only one conjunction of hypotheses H & A1 & … & An that could possibly fit with the evidence. • However, HU could still apply: if there is a contradiction then should we reject H or A1 or…? CU Without HU • Conversely, suppose, contra HU, that we knew that A1 & … & An should be accepted and H should be rejected. • However, CU could still apply: is there a currently-unavailable alternative to H, H*, that better fits the evidence? Why Underdetermination Matters 1. A sufficiently strong form of underdetermination implies that non-rational factors always play a role in how scientists accept theories. 2. But if scientists are (semi-)irrational in how they accept theories, then few beliefs are (fully) rational. 3. So sufficiently strong form of underdetermination implies few beliefs are (fully) rational. Does Underdetermination Imply Irrationality? 1. If evidence and the rules of scientific method underdetermine the theory to be accepted, then something else (call it X) needs to be added to “pick up the slack” or “cover the difference.” 2. Evidence + scientific method exhaust the rational bases of theory acceptance. 3. So X must be a non-rational basis of theory acceptance. Recap • Underdetermination occurs when inputs and rules fail to provide a unique output. • In science, the paradigmatic case is when evidence and the rules of scientific method fail to provide a unique “best theory” to accept. • There are many ways of refining this basic idea, though HU and CU have been the most prominent. • Certain forms of underdetermination suggest that science is not as rational as it appears.