Francis Bacon's classification of recurrent intellectual distortions associated with human tendencies, individual dispositions, language and received systems. It forms part of his programme for correcting inquiry.[ref]
A hypothesis is a proposed claim whose consequences can be investigated through observations, experiments or a specified analysis. A useful scientific hypothesis identifies what would be observed under stated conditions, so evidence can change how strongly it is supported.
For example, suppose a particular component is hypothesized to obey Ohm's law over a specified operating range. Holding its temperature approximately fixed and varying the applied voltage predicts a straight-line relation between voltage and electric current. The measured departures, together with measurement uncertainty, determine how well that claim describes the component. The experiment tests the stated range and conditions.
A statistical hypothesis instead specifies a claim about a probability distribution or its parameters. It can help assess the measurements, while the physical interpretation also depends on the instrument and the mathematical model.
A scientific law expresses a regular relationship among observable quantities, together with a domain in which that relationship is applicable. It can supply quantitative predictions that connect an experiment with a mathematical model.
For example, Boyle's law describes the approximately constant product of pressure and volume for a fixed amount of gas at fixed temperature. The ideal gas law combines this relation with the dependence on temperature and amount of substance. Measurements at different conditions examine the limits of the approximation, while kinetic theory provides a microscopic account of why the relation emerges.
The usefulness of a scientific law rests on both its predictive success and its stated conditions. A compact equation such as becomes experimentally meaningful when its quantities, measurement procedure and range of applicability are specified.
A rule constraining the admissible interpretations of predicates in a stated formal language. A sentence can then count as analytic relative to the chosen rules if it holds in every admitted interpretation. This precise relative notion does not itself establish an unrevisable division of all natural-language statements.[ref]
An evidential situation in which rival scientific accounts remain compatible with the relevant evidence. Agreement with the observations so far is weaker than empirical equivalence across all possible observations in a stated domain.
A substantial reorganization of scientific concepts, accepted problems or methods. This generic notion is distinct from the particular early modern historical episode called the Scientific Revolution.
In Thomas Kuhn's account, research conducted within an accepted framework of exemplary achievements, problems and methods.[ref]
The Structure of Scientific Revolutions by Thomas Kuhn. Introduction
A deliberately arranged intervention or comparison used to investigate a claim. A useful experiment specifies the conditions changed, the outcome observed and the alternative explanations the comparison can discriminate.
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]
Structural Realism: The Best of Both Worlds? by John Worrall. discussion of the Fresnel–Maxwell transition
Two scientific accounts are empirically equivalent relative to a stated domain when they give the same observable consequences there. Agreement on the observations so far is weaker than agreement on every possible observation.
For Newtonian mechanics with forces depending only on relative positions, a common Galilean transformation leaves relative positions and accelerations unchanged. Internal mechanical observations therefore cannot discriminate rival choices of a wholly uncoupled privileged uniform rest state. The qualification concerns uniform motion; it does not imply that rotation or acceleration is unobservable, or that special relativity makes identical predictions.
Evidence supports a scientific hypothesis without necessarily proving it. Distinguish increasing its credibility from showing it highly credible in absolute terms; a low prior probability can rise substantially while remaining low.
Inference beyond what the premises deductively entail, often from observed cases to unobserved cases. This is distinct from mathematical induction.
The challenge of justifying inductive reasoning without either assuming the reliability being justified or demanding a deduction from premises that do not entail the conclusion.[ref]
An Enquiry Concerning Human Understanding by David Hume. section IV, part II
Nelson Goodman's challenge to explain why some predicates, rather than all predicates fitting the examined cases, are legitimate candidates for projection. It concerns projectibility, not a demonstration that every conceivable continuation is equally credible.[ref]
Fact, Fiction, and Forecast by Nelson Goodman. Chapter III, section 4
The eligibility of a predicate or generalization for extending an inference beyond examined cases. Agreement with positive instances alone does not establish projectibility: grue and green can fit the same past examples while supporting incompatible predictions.
In Nelson Goodman's account, the standing a predicate acquires through a history of actual projections. It concerns the use of the predicate in inference, rather than merely the number of past objects satisfying it. Entrenchment is revisable and is not a proof of future reliability.[ref]
For a fixed cutoff , let mean examined before . Nelson Goodman's predicate is . An already examined green object remains grue after without a colour change. The conflicting projection concerns objects not examined before .
From and , infer only . A failed prediction therefore does not logically isolate failure of the target from failure of auxiliary hypotheses . Independent calibration and varied experiments can discriminate packages; the logical ambiguity does not imply that every package is equally supported.[ref]
The Aim and Structure of Physical Theory by Pierre Duhem. part II, chapter VI, section 2
An assumption used with a target scientific hypothesis to obtain a prediction, for example an apparatus calibration or an initial condition. Independent evidence for an auxiliary hypothesis helps distinguish a failure of the target from a failure of the test setup.
Evidence confirms relative to background when it increases its conditional probability. With and positive evidence probability, Bayes' theorem givesIndeed, writing , and gives the posterior probability ; comparison with reduces to . Thus scientific confirmation depends on the alternatives and background, not just on a statement's logical form.
Fix ravens and nonblack objects in a finite population. Under , all ravens are black; under , exactly one is nonblack. The total numbers are held fixed under both hypotheses, so the classification of one nonraven also changes between hypotheses. This is a deliberately specified model for Bayesian confirmation, not a universal rule about how bird observations supply evidence.
A uniform draw among nonblack objects returns a nonraven with probabilities under and under . A uniform draw among ravens returns a black object with probabilities and . The respective likelihood ratios for over are therefore and . When , the former is closer to one, so supplies less support under these assumptions.
With equal prior probabilities, Bayes' theorem gives posterior probabilities and . More generally, with prior probability for , replace the two expressions by and . Previously known information or a different sampling protocol requires different likelihoods; selecting an object already known to be a nonraven need not supply new evidence.
Already accepted evidence can support a newly considered theory even though conditioning again on a fact of probability one produces no increase in its posterior probability. Distinguish new learning, retrospective support and discovering a previously unrecognized theory–evidence connection.[ref]
“All ravens are black” is logically equivalent to “all nonblack things are nonravens”. An unrestricted rule that positive instances confirm universal generalizations would make a white shoe confirm the first statement. A Bayesian confirmation account instead conditions on background knowledge and the sampling procedure.[ref]
Some physical relations permit deduction in both directions while supporting different explanatory roles. Pole height and solar angle can explain a shadow length even though the height can also be inferred from that length. An evidential inference need not have the same direction as the causal explanation.
An approach to scientific explanation that subsumes a phenomenon under general laws and specified circumstances. Its deductive form is the deductive-nomological model; statistical forms permit probabilistic support rather than entailment.
A form of scientific explanation using statistical laws and high conditional probability, relative to appropriate available information. A low-probability event can nevertheless have a mechanistic explanation, so high probability is not an uncontested necessary condition for explanation.
An explanation derives an event description from laws and circumstances, with valid deduction, essential use of a law, empirical content and true premises. These requirements do not by themselves settle explanatory direction or eliminate irrelevant additions.[ref]
Distinguish a criterion of empirical meaningfulness from a methodological demand for verification, and conclusive verification from fallible scientific confirmation.
A hypothesis is falsifiable if some possible empirical outcomes conflict with it under specified testing assumptions. Falsifiability does not mean that an anomalous reading identifies which member of a theoretical package is false, or that a falsifiable statement is well supported.
A methodology emphasizing conjectures exposed to demanding attempts at refutation. Falsifiability is a property of claims under testing assumptions; falsificationism is a view about scientific practice.
An intersubjectively testable report of an observable occurrence in specified circumstances, capable of participating in a test or attempted falsification. In Karl Popper's account, accepting a basic statement is provisional and may be reopened by further testing.[ref]
The Logic of Scientific Discovery by Karl Popper. Sections 28–30
Karl Popper's appraisal of a conjecture's survival of demanding tests relative to accepted basic statements. It is a retrospective methodological assessment, distinct from a proof of truth or an inductive probability of truth.[ref]
The Logic of Scientific Discovery by Karl Popper. Sections 82–84
The dependence of scientific observation, description or interpretation on background concepts and assumptions. Dependence on some theory is weaker than dependence on the truth of the particular theory being tested.
Acceptance of a scientific theory involves belief in its empirical adequacy and practical commitment to its use, without requiring belief in its full truth about unobservables. This concerns epistemic attitudes, whereas the distinction between a constructive theory and a principle theory concerns explanatory organization.[ref]
Constructive Empiricism Now by Bas van Fraassen. section III
A theory is empirically adequate when it correctly represents the observable phenomena, including those not yet observed. Agreement with the data already collected is therefore insufficient to establish empirical adequacy.
A classification whose usefulness in prediction and explanation is grounded in relevant natural structure, rather than solely in a convenient label. Exact membership conditions can help identify a natural kind but do not alone demonstrate its explanatory significance.
An account of some natural kinds in terms of traits whose association is sustained by causal processes, without requiring every member to possess every trait. For species, shared descent, gene flow and developmental processes can sustain relevant similarities. Whether a cluster supports reliable inference is an empirical issue.[ref]
A family of positions taking scientific theories to make literal claims about a mind-independent world, with warranted belief extending to at least some unobservable aspects. The extent of that commitment and the meaning of approximate truth require specification.
In an account of perception, distinguish an object's physical constitution from its powers to produce experiences in perceivers. The distinction between primary qualities and secondary qualities does not by itself prove an external world or imply that dispositions are unreal.[ref]
An Essay Concerning Human Understanding by John Locke. book II, chapter VIII, sections 8–15 and 23–26
In John Locke's account, a body's power to produce an experience such as a colour or taste through its physical constitution. Distinguish that power from the experience itself.
In John Locke's account, a quality such as extension, solidity, shape, number or motion, attributed to bodies independently of whether they are perceived. This historical list should not be treated as an unrevisable inventory of fundamental physical properties.
In John Locke's terminology, a body's exclusion of another body from the space it occupies. This is not the material-science notion of hardness: John Locke treats water as solid in this sense while distinguishing its yielding response from a diamond's resistance.[ref]
An Essay Concerning Human Understanding by John Locke. Book II, chapter IV, especially section 4: barryfvaughan.org/text/philtext/locke/bk2/4.html
Scientific reproducibility concerns whether the basis of a scientific result can be reconstructed and checked. It requires enough information about the measurement, data handling and reasoning to distinguish repeating a procedure from merely obtaining a similar-looking answer.
Terminology varies between fields. The 2019 National Academies report distinguishes computational reproducibility, using the same data and computational procedure, from scientific replication, which collects new data to address the same scientific question. These test different links in the argument. Repeating a calculation can expose a software or transcription error; new observations can test whether the finding persists beyond the original sample.[ref]
Reproducibility and Replicability in Science by National Academies of Sciences, Engineering, and Medicine. Summary, pp. 6–9: Definitions, Reproducibility and the distinction from new-data replication
Consider an original toy measurement of three lengths, , and units. Recomputing their arithmetic mean as checks the recorded calculation. Measuring three new objects tests a different question: whether the estimated mean describes further observations, allowing for measurement uncertainty and sampling variation. Neither exercise alone establishes that the instrument was correctly calibrated.
Testing a scientific finding with newly collected data or an independently conducted study. Terminology varies, so the operational meaning should be stated.
Computational reproducibility means obtaining consistent results from the same input data, computational procedure and stated conditions. A reproducible analysis identifies the actual inputs and their data provenance, the software versions, parameters and relevant environment. Exact bitwise agreement is stronger than agreement within a justified numerical tolerance.[ref]
For example, changing the order of a floating point sum can change its last few digits through rounding error. A useful check states the acceptable absolute error or relative error before comparing results. Successfully rerunning the same code also reruns any undetected mistake in it, so consistency is evidence about the computational process rather than a proof that the physical model is correct.
The recorded origins and transformations of data, including references, versions, preprocessing and identifiers.
The stronger claim that higher-level explanations can or should be replaced by explanations in terms of more basic components and their interactions.
A claim about what entities and processes are made of, distinguished from a claim that every useful explanation must be expressed at the microscopic level.
A role of a biological feature, interpreted either through its contribution to a current system or through its evolutionary history. A claim about function does not imply foresight in evolution.
A higher-level relationship or function can be implemented by different underlying physical mechanisms.
The capacity of a field to frame and test useful explanations at its own level of description, consistently with the physical realization of its objects.
The view that living systems are physically realized and do not require a separate nonphysical substance. This does not by itself settle which level of description provides the best scientific explanation.
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