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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.

There are serious philosophical reasons to resist inferring the literal truth of every successful theoretical description. Those reasons support a selective and revisable attitude; they do not establish that none of the unobservable entities investigated by science exists.

Pessimistic induction starts from successful earlier theories whose central ontological claims were later rejected. Their history challenges an unrestricted inference from predictive success to truth. For example, successful descriptions of light transmission were once combined with an account involving a mechanical luminiferous aether. Continued use of some mathematical relations does not show that the proposed medium was real. The force of the objection depends on which part of a theory produced its successful predictions, not on collecting a list of old mistakes.^[ref]

Scientific underdetermination supplies a different challenge. Agreement with available data can leave rival accounts open. If they are empirically equivalent throughout a specified domain, another experiment restricted to that domain cannot discriminate them. This limits what those data establish. It does not show that every actual theoretical disagreement is permanently undecidable, or that equally compatible models must receive equal confidence given all relevant background evidence.

The realist reply emphasizes convergence across independent ways of detecting and manipulating a putative entity. An electron is not supported by one formula alone: accounts of its electric charge, scattering and response to fields connect different apparatuses and phenomena. Such success can be a reason to infer a common physical cause. The no-miracles argument expresses that explanatory motivation, but its force is abductive rather than deductive. It must not assume that only a literally true total theory could produce any success.

Several qualified positions remain defensible. Entity realism places particular weight on robust experimental use of entities without endorsing every theoretical account of them. Structural realism emphasizes specified relations retained across theory change. Neither label removes the need to identify what experimental interventions establish or which interpreted structure survives. Preserving an equation's shape alone is insufficient if the meanings and tested domains have changed.^[ref]

Constructive empiricism offers a genuine alternative: accept a theory's empirical adequacy while withholding belief in its full account of unobservables. The realist must explain why stronger belief is warranted, rather than accuse this stance of denying ordinary laboratory success.

A defensible realism therefore concerns particular well-supported claims, mechanisms and relations, with explicit domains and error allowances. It recognizes historical revision without treating every surviving term as equally secure. Neither universal literal realism nor universal scepticism about entities follows from scientific success or its historical failures.

Theory change defeats an inference from scientific success to final, unrestricted truth. It does not show that successive theories make no progress in accuracy, explanation or warranted knowledge. Calling two theories false says too little about how their claims compare.

The strongest pessimistic argument is historical: theories once regarded as successful and well supported have later lost central commitments. If successful predecessors could misidentify what exists, the success of a present theory cannot by itself guarantee its full ontology. Larry Laudan uses the historical record to challenge a simple connection between success, reference and approximate truth.^[ref] The challenge is serious for scientific realism, particularly when it treats an entire accepted framework as a single package of warranted beliefs.

But the slogan conflates several claims: that an unrestricted theory contains a false assertion, that every one of its assertions is false, and that its successes were accidental. The first does not entail either of the others. A theory can be wrong outside its proper domain while accurately representing relationships within it. Establishing that domain is itself a scientific achievement.

The velocity-addition formula makes the difference precise. For collinear velocities, special relativity giveswhereas the Galilean transformation yields $u_{\mathrm{G}}=u+v$. Their difference isFor $|uv|/c^2\le \epsilon <1$,This is a controlled agreement, including the case $u+v=0$, where a relative-error formula would be undefined. At $u=v=0.6c$, the classical value $1.2c$ differs dramatically from $15c/17\simeq 0.882c$. At small velocities the same comparison explains why ordinary classical calculations work so well. The relativistic rule and its low-speed relation to the classical rule appear in Albert Einstein's treatment of velocity composition.^[ref]

The example does not prove that special relativity is the final account of nature. It shows that a successor can explain an earlier theory's restricted success and predict when it fails. One obtains a stronger account of the evidence than either blanket rejection of the older theory or unqualified belief in it. The surviving mathematical relation also need not preserve the older interpretation of absolute time.

Structural realism develops this possibility by locating continuity in interpreted relations rather than every proposed entity. John Worrall uses continuity between Augustin Fresnel's optics and later electromagnetism to motivate such a response.^[ref] Its attraction is discrimination: some tested structure can survive an ontological change. Its difficulty is specifying which structure deserves belief before the next change, rather than selecting the survivors afterwards. An equation without a physical interpretation and domain is too weak a candidate.

An empiricist can accept the improvement in prediction and systematic representation while withholding belief about unobservables. That shows that progress does not logically require scientific realism. The realist can reply that independent tests, novel successful predictions and quantitatively explained limiting relations support cautious belief beyond the immediately observed. Neither side should treat historical examples as a deductive proof of its complete position.

The original claim is therefore defensible only in a thin sense: successive unrestricted theories may each contain falsehoods. Used to deny progress, it is misleading. Theories can become more accurate, discriminate more possibilities and explain why earlier approximations succeeded. Theory change should make scientific confidence selective and revisable, rather than erase the distinction between a useful approximation and an arbitrary mistake.

Scientific change is a serious threat to indiscriminate scientific realism, but not a deductive refutation of every realist position. A defensible realism must identify which claims deserve belief, at what precision and within which domain, rather than merely promise that mature theories are “approximately true”.

Scientific realism includes the claim that a mind-independent world exists and the stronger epistemic claim that scientific inquiry gives warranted knowledge of at least some unobservable aspects of it. Theory replacement directly challenges the latter inference, not the bare existence of an external world. Disagreement between successive descriptions does not imply that neither describes anything real.

The historical objection is nevertheless substantial. A theory can make successful predictions while its central interpretation is later rejected. The luminiferous aether illustrates the risk of identifying successful wave optics with the literal truth of a particular mechanical medium. If earlier scientists had impressive evidence and still endorsed dispensable theoretical entities, why suppose that comparable evidence now guarantees our own entire interpretation? Laudan presses this challenge against the connection between success, reference and approximate truth.^[ref]

One reply distinguishes literal truth from controlled approximation. In special relativity, the kinetic energy of a massive particle isThe Taylor expansion for $|v|/c\ll 1$ givesThus the classical kinetic energy is recovered in a specified regime, with a leading relative correction of $3v^2/(4c^2)$. It would be wrong to conclude that Newtonian mechanics is globally true, or that all its physical concepts survive unchanged. It would be equally wrong to infer that its low-speed predictions were accidental. The survival of a quantitatively controlled relation is a more discriminating claim than survival of every piece of ontology.

John Worrall's structural realism makes preservation of mathematical relations central, using the transition from Augustin Fresnel's optics to electromagnetism as a key example.^[ref] This explains why a theory might retain a real achievement while abandoning its proposed mechanism. However, structure cannot mean just any equations with some empirical fit: the realist must identify the relevant physical interpretation, domain and counterfactual content. Otherwise the view risks saying little beyond empirical adequacy.

A related selective response commits to elements that carry a theory's tested successes, while treating speculative additions more cautiously. Its strongest evidence is convergence across independent experiments, robustness under changes in modelling assumptions, and success on predictions not used to tune the theory. For example, support for a stable electron electric charge need not amount to belief in every current claim about the ultimate nature of an electron. But selectivity must be defensible before a later replacement occurs; choosing surviving components only in hindsight cannot vindicate past realist confidence.

The anti-realist can still explain scientific success by demanding empirical fit and retaining successful models, without inferring truth about unobservables. That response blocks any simple argument that realism is logically compulsory. Conversely, pointing to historical failures does not establish that every presently supported claim will fail. Such an inference would need a justified comparison class, a measure of success and an account of how testing has changed.

The appropriate conclusion is discriminating fallibilism. Changes threaten claims of finality and blanket trust in a theory's full ontology. They can also reveal stable, independently tested relations and improve our understanding of their limits. Scientific realism survives as a qualified position only if it makes those distinctions explicit and remains willing to revise the very commitments it currently regards as best supported.

A form of scientific realism emphasizing warranted knowledge of physical relations or structure despite changes in proposed underlying entities. An account must specify which interpreted relations survive and in which domains, rather than merely point to recurring notation.^[ref]