Past exam of the philosophy of science supplementary subject of the University of Oxford / 2019 / 7

Scientific underdetermination limits what evidence alone establishes, but its practical consequences depend on the strength of the equivalence being claimed. Rival theories fitting present data need not agree on future observations. Rival formulations agreeing on every observable in a specified domain present a more persistent limitation within that domain.

With finitely many data points $(x_i,y_i)$, suppose an interpolation polynomial $p$ fits all $n$ measurements. Thenalso fits them for every $\lambda$. This proves nonuniqueness for a deliberately broad model class. It does not prove that all these functions are equally plausible physical theories. Constraints from independently tested mechanisms, bounds on derivatives, symmetries and the measurement process can sharply restrict the class. A new observation at a different point can also distinguish the displayed alternatives.

The Duhem problem concerns an additional kind of latitude: a prediction tests a theory together with auxiliary hypotheses. A mismatch can be assigned to different components. This is a reason to vary apparatus, calibrate independently and use multiple kinds of evidence. It is not a demonstration that any preferred theory can be made equally well supported by arbitrary repairs.^[ref]

Exact empirical equivalence requires more. If two accounts supply identical probability distributions for all observations allowed by a stated setup, observations of that kind cannot favour one through their likelihoods. Bayesian inference makes the limitation explicit: posterior odds equal prior odds when the likelihood ratio is one. Declaring a prior preference does not transform it into new experimental discrimination.

Theories can nevertheless differ in explanatory organization, computational usefulness or how they connect with a larger domain. Those are legitimate questions, provided their role is stated. If a proposed new intervention distinguishes them, the equivalence did not cover that enlarged domain. If the difference is instead only a change of redundant description, treating it as two competing physical worlds may create a spurious dispute; gauge symmetry provides an important case requiring care.

For scientific practice, the appropriate response is model comparison with explicit assumptions, searches for discriminating tests and honest limits on what has been established. For scientific realism, enduring empirical equivalence challenges any claim that the evidence uniquely fixes a full ontology. It does not make precise predictions or experimental decisions impossible. Underdetermination is consequently a constraint on inference whose seriousness must be demonstrated case by case, rather than a general proof that all scientific reasoning is arbitrary.

A commitment to testing claims against experience is a defensible scientific norm. A strict account according to which every meaningful scientific statement must be conclusively verified, or translated into a fixed vocabulary of theory-free observations, is much harder to sustain. Logical empiricism should also be understood as a changing family of projects, not reduced without qualification to its strongest early formulations.

An unrestricted universal scientific law concerns cases beyond a finite observation record. No finite list of favourable cases deductively entails all of them. Requiring conclusive verification would therefore exclude much ordinary theoretical science. Replacing that demand with scientific confirmation retains a relation to evidence while accepting that support is fallible. This is a substantive revision, rather than proof that universal laws were conclusively verified after all.^[ref]

A second difficulty concerns observations. A detector count relies on assumptions about sensitivity, background and the production of a signal. Theory-ladenness makes a sharp division between completely neutral observations and theoretical claims implausible. But dependence on some assumptions does not imply dependence on the truth of the target theory. A calibration can be supported independently, and agreement across instruments using different mechanisms can make a putative effect less vulnerable to one shared error.

Nor should unobservable vocabulary be dismissed merely because its referents cannot be seen directly. A theory of electrons and electromagnetic fields can organize measured currents, spectra and scattering through a common model. What matters scientifically is how the theoretical commitments constrain observations and survive attempts to discriminate them from alternatives. Insisting that each term independently translate into an observation report can miss the role of a whole theoretical structure.

An empiricist can accept much of this. Constructive empiricism permits literal theoretical discourse and commitment to using a theory while restricting belief to empirical adequacy. It separates withholding a stronger ontological belief from refusing to reason with theoretical models.^[ref] Whether this restraint is preferable to selective scientific realism remains an argument about what successful testing warrants.

The strongest sustainable empiricism is consequently methodological and fallible: demand explicit empirical consequences, scrutinize calibration and preserve the possibility of correction. The stricter verificationist reduction does not adequately describe how laws, theoretical terms and measurement actually work. Rejecting that reduction need not weaken the central demand that scientific claims remain accountable to evidence.