Since empirical evidence underdetermines theory, the choice between empirically equivalent but incompatible theories cannot be made on purely empirical grounds. Scientists must appeal to pragmatic criteria like simplicity and fruitfulness, or potentially embrace relativism about which theory is true.
Your prerequisite — the Duhem-Quine thesis — showed that individual hypotheses cannot be tested in isolation: whenever an experiment goes against expectations, we can always pin the failure on some auxiliary assumption rather than the central hypothesis. Underdetermination takes this a step further, from the local level (any single test is inconclusive) to a global level (the total body of evidence cannot uniquely determine which theory is true).
The core logical point is simple: for any finite set of observations, there are in principle infinitely many theories consistent with those observations. Geometry provides the classic illustration. Pre-Einsteinian physicists assumed Euclidean geometry and built mechanics accordingly. When astronomical anomalies appeared — like the perihelion precession of Mercury — they could have modified the mechanics (as Einstein eventually did), or they could have modified the geometry, or they could have modified some auxiliary assumption about how light travels. All three adjustments could be made consistent with the same observations. These are empirically equivalent theories: they make identical predictions for every possible observation yet describe metaphysically different worlds.
The most discussed historical case is Newtonian absolute space. Newton's mechanics with a preferred rest frame (absolute space) is empirically equivalent to Newton's mechanics with any uniformly moving frame — no mechanical experiment can distinguish them, because uniform boosts don't affect any measurable quantity. The two theories describe different objective realities (one posits absolute rest, the other doesn't), yet no observation can adjudicate between them. What should we do? Einstein resolved this by reformulating the theory so that the underdetermined choice (which frame is "really" at rest) vanishes entirely.
When theories are empirically equivalent, scientists inevitably appeal to theoretical virtues: simplicity, fruitfulness, internal coherence, breadth of scope, consistency with background knowledge. The underdetermination thesis raises the question of whether these virtues are *truth-tracking* or merely pragmatic. The scientific realist argues they are evidence: if one theory is simpler and more fruitful, that's reason to believe it's closer to the truth, not just more convenient for us. The empiricist or instrumentalist counters: theoretical virtues reflect our cognitive preferences, not the world's structure; they select for good tools, not true descriptions of unobservables. Underdetermination is thus a central pressure point in the realism debate — it's not merely a curiosity about theory choice but a fundamental challenge to the idea that science converges on a unique, true description of unobservable reality.
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