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There is defensible scientific progress, but it is not well characterized as an uninterrupted accumulation of truths or an inevitable march toward one complete description. Progress can consist in improved empirical discrimination, more accurate and wider-ranging predictions, better scientific explanation, and greater capacity to intervene reliably. Those achievements must be assessed against specified aims and competing accounts, rather than inferred from a theory's being later in time.

The physical content of an improvement matters. A model that fits a fixed data set using arbitrarily many adjustable parameters has not thereby supplied a stronger prediction. Independent tests, specified error bounds and successful application in new conditions distinguish a genuine extension of knowledge from a re-description of familiar results. An apparent failure can itself be progressive when it identifies the boundary of a model's applicability and supports a more reliable successor. More equations or more favourable observations are not enough by themselves.

The relation between Newtonian mechanics and special relativity illustrates a qualified retention of success. With invariant rest mass $m$, relativistic kinetic energy is $(\gamma -1)m{c}^2$. Its low-velocity expansion isThe first term recovers the familiar kinetic-energy expression in a controlled domain; the correction identifies a systematic departure. The successor can preserve successful low-speed calculations while revising the conceptual description of space and time. This demonstrates a relation between models, not that every statement in the earlier framework was true or that the successor is beyond further revision.

Thomas Kuhn's account gives normal science a comparatively clear measure of progress: increasingly effective solution of problems within an accepted scientific paradigm. During revolutionary theory change, the problems, classifications and standards themselves can partly change, and some older achievements may be lost or devalued. His chapter on progress nevertheless emphasizes growing problem-solving capacity; his position is not simply that no improvement occurs. The difficulty is explaining comparison across changes without treating the later community's preferences as automatically decisive.^[ref]

A scientific realist may interpret improved prediction as evidence of a more accurate account of the world. That is a further argument, not the definition of every successful calculation. Larry Laudan's historical objection warns that earlier successful accounts contained central commitments later rejected. Structural realism offers a selective response: ask which interpreted quantitative relations survive, and in which domains, rather than credit the entire old account with approximate truth.^[ref][ref]

The most reasonable conclusion is plural but not indiscriminate. Better error control, wider empirical reach and the identification of previously unknown phenomena provide substantive achievements, although they do not always increase together. Scientific progress is fallible, domain-sensitive improvement in our ability to investigate, predict and explain. A general guarantee of convergence to final truth is stronger than these achievements require, while denying every basis for comparison ignores the controlled relations and independent successes which inquiry can establish.

The no-miracles argument, in its familiar form, principally supports claims about the truth or approximate truth of successful theories. It is not naturally an argument for the bare existence of theoretical entities independently of the correctness of what is said about them. Entity realism can share its interest in scientific success while relying on a different and more local evidential argument.

Hilary Putnam's formulation treats the success of mature science as something requiring explanation. If theories describe relevant features of the world approximately correctly, their predictive and practical achievements become intelligible. If their central claims are far removed from reality, the same success appears surprising. The proposed inference uses abductive reasoning: accept the explanatory account which best makes sense of the achievements. It is not a valid deduction from successful prediction to truth, since a false theory can yield true consequences.^[ref]

The content of the explanandum matters. If the achievement is a quantitatively accurate prediction from equations about charges, fields and interactions, saying merely that electrons exist leaves most of that accuracy unexplained. Their existence is compatible with innumerable false accounts of their behaviour. A realist explanation of this success must therefore retain some trustworthy description of relevant properties or structure, not only an inventory of entities. This need not mean accepting every idealization or every speculative extension of the full theory.

Ian Hacking's intervention-based case for entity realism shifts the emphasis. Once investigators reliably use electrons to produce or investigate other phenomena, the entities are functioning as experimental tools rather than merely appearing in an explanatory story. Their causal powers can be supported across different apparatuses and theoretical descriptions. This provides a way of committing to particular entities while remaining selective about high-level theory. The argument rests on how the entities are manipulated, not simply on the statement that an encompassing theory has been successful.^[ref]

That position has limits too. Identifying the instrument, controlling its effects and distinguishing those effects from alternatives require some theoretical assumptions. Entity realism cannot plausibly mean that an investigator believes literally nothing about the properties or causal roles of an entity. Its more defensible form distinguishes localized, repeatedly usable knowledge from commitment to a complete theoretical picture. One can accept robust causal regularities about an electron source without treating every claim of a fundamental theory as equally established.

The principal challenge to the general no-miracles argument is that history contains successful theories with rejected central posits. The pessimistic induction presses the example of theories of light which retained a mechanical luminiferous aether, or accounts of combustion which included phlogiston. Such cases defeat an unrestricted inference from some success to the truth of every central assertion. A selective realist may ask which parts produced the successful predictions and which relations survived change. That reply must identify those parts with evidence; labelling an entire abandoned theory approximately true without explaining the retained content would merely rename the problem.^[ref][ref]

A constructive empiricist can also agree that theories are successful while treating empirical adequacy, rather than full truth about unobservables, as the appropriate aim of acceptance. The dispute then includes whether explanatory superiority licenses belief in the proposed unobservable account. Calling alternatives miraculous does not settle that epistemic issue by definition.^[ref]

The resulting judgment is selective. The original explanatory form reaches beyond entity existence toward a trustworthy representation of how nature works. It can support entity commitments as part of that representation, but cannot by itself isolate entity realism from all theory realism. Conversely, experimental manipulation can provide particular reasons for entity belief without establishing the whole no-miracles inference. Both arguments are strongest when they specify the achievement, the alternatives and the exact realist commitment being defended.

It is plausible that some claims in current science will be revised, and much stronger to say that every successful part of present science is probably false in every relevant respect. The first is compatible with warranted knowledge. The second needs a substantive argument about the particular claims, their evidence and what “false” means for an approximate or idealized model.

Pessimistic induction points to theories once successful and accepted that were later rejected. Larry Laudan uses historical cases to challenge the inference from predictive success to the truth or successful reference of all theoretical commitments.^[ref] The lesson is especially strong against an indiscriminate realism that treats every productive representation as a literal inventory of nature.

But a historical list is not automatically a representative statistical sample. One must ask which successes were substantial, which theoretical components generated them, what survived and whether current evidence is comparable. The eventual rejection of an entire ontology does not entail that every measurement, mathematical relation or limited-domain prediction associated with it was worthless. Nor does the chance that at least one claim in a large conjunction is false imply a high error probability for each member separately.

Newtonian mechanics illustrates a useful distinction. It is not a universally exact account across all speeds and gravitational regimes, but controlled low-speed and weak-field approximations can remain extremely accurate. That is an empirical and mathematical claim about a domain, not permission to call any false account approximately true. Approximate truth needs interpretable quantities, a specified regime and some account of relevant error. Structural realism similarly needs preserved physical relations rather than merely a shared abstract notation.

The possibility of error therefore matters. It should discipline extrapolation, encourage independent testing and prevent practical success from being turned into unconditional metaphysical certainty. It does not require abandoning the best-supported models within tested domains. An empiricist can retain justified confidence in empirical adequacy, while a selective scientific realist may defend stronger commitments where evidence and intervention support them. Both positions must distinguish fallible confidence from certainty and carefully bounded reliability from unrestricted literal truth.