Past exam of the philosophy of science supplementary subject of the University of Oxford / 2017 / 5

The covering-law model explains a phenomenon by subsuming it under scientific laws and specified circumstances. Its deductive-nomological model requires the event to follow by valid deduction, with a law used essentially, empirical content and true premises. For example, a dynamical law and appropriate initial conditions can explain a body's later trajectory.^[ref]

This captures an important feature of many physical explanations: the event is shown to fit a wider, independently supported pattern. It makes assumptions explicit and connects explanation with prediction. However, derivability alone does not ensure the right explanatory direction. With a pole, a known solar elevation and a measured shadow, geometry lets us calculate either height from shadow or shadow from height. The explanatory asymmetry remains: under the ordinary causal setup, the pole and illumination explain the shadow, rather than its measured length causing the pole's height.

Irrelevant information also exposes a weakness. From a general law plus an unnecessary fact one may still derive the result; logical validity does not show that the added fact helps explain it. Conversely, many accepted explanations are statistical or mechanistic rather than deductions from exceptionless universal laws. Extending the account to the inductive-statistical model helps, but a high conditional probability does not by itself establish causal relevance.

The covering-law model is thus a useful account of one important explanatory structure, not a complete criterion of scientific explanation. A stronger account must consider which assumptions make a difference, what mechanism operates and why the explanatory direction is appropriate. The model's virtues survive when it is treated as a component of explanation rather than an exhaustive definition.

Let $R(x)$ mean that $x$ is a raven and $B(x)$ that it is black. The hypothesisis logically equivalent to $\forall x[\neg B(x)\Rightarrow \neg R(x)]$. If the observed paper is both nonblack and a nonraven, it is a positive instance of the second formulation. Combining an unrestricted positive-instance rule with preservation of scientific confirmation under logical equivalence produces the raven paradox.^[ref]

Whether the observation actually supplies evidence depends on what was already known and how the object was selected. In Bayesian confirmation, with background $K$, support means $P(H\mid E,K)>P(H\mid K)$. If the observer already knows the selected item is a nonraven and its colour is conditionally independent of $H$, then $P(E\mid H,K)=P(E\mid \neg H,K)$: the likelihood ratio is one and there is no confirmation. If all of $E$ was already known, learning it again also gives no update.

Under a different sampling scheme, the same classification can provide slight support. In the finite-population model of raven confirmation, fix $r$ ravens and $M$ nonblack objects. Compare no nonblack raven with exactly one. Sampling uniformly among the nonblack objects gives a nonraven with probabilities $1$ and $1-1/M$, hence likelihood ratio $(1-1/M{)}^{-1}>1$. If $M$ is large this is tiny evidence, not a proof. This example establishes possibility under explicit assumptions, not that every white-paper observation has that evidential role.

The appropriate answer is therefore conditional: mere logical instantiation does not settle the support supplied by observing this paper. State the background and sampling procedure. A familiar paper deliberately selected as a known nonraven normally supplies no new evidence about raven colour; a specified alternative sampling model may yield a small positive update.