Hierarchy of Theories
Is there a hierarchy of theories that determines hierarchical authority delegation, hierarchical anomaly-tolerance, compatibility criteria or theory acceptance criteria?
Relations between theories evidently exist within mosaics. However, whether these relations are simply pure historical coincidence, the results of communal or sociological behaviours, or patterns emerging from the way science changes (the laws of scientific change) is unknown. The trans-historical prevalence of hierarchical structures surrounding theories suggests that these structures may not just be recurring accidents and thus not a topic reserved exclusively for observational scientonomy, but one also for theoretical scientonomy.
Whether or not these hierarchical structures can be explained theoretically within the theory of scientific change is yet to be attempted. However, it does seem that such hierarchical structures exist and that it can be integrated into the TSC. This could, for example, add another aspect or dimension to the scientific mosaic, making it no longer a simple set of theories, but perhaps an ordering (hierarchy) of theories.
But now, what suggests this could be expressible in theoretical terms, and not only by historical references to certain methods? Although just a hunch, it does seem that certain theories have in of themselves properties of dependence upon other theories. For example, the field of inquiry of a theory (its scope) may be a subset of the scope of another theory, e.g., the scope of agricultural science is a subset of the scope of biology. From these dependencies a hierarchy of theory dependence may emerge. Another reoccurring theme is that certain communities hold certain theories more dearly than others, i.e. the theories seem to be `accepted strongly'. This makes the hierarchy of theories perhaps an attempt to organize theories by their 'strength of acceptance'. These hierarchies may then have predictable consequences of authority delegation, anomaly-tolerance, compatibility criteria and acceptance criteria.
Some cases resembling such hierarchies will now be considered along with their purported effects:
Hierarchies of theories may determine authority delegation. Authority delegation may occur on the grounds that a field of science's scope does not involve a topic of inquiry, so that field may authority delegate to another field of science whose scope does include that topic. This happens very often. A geologist could ask why a diamond is so hard, but they would most likely delegate the answer to a chemist. A chemist on the other hand may ask why a nickel crystal creates a certain electron diffraction pattern, but the answer would most likely be delegated to a physicist. A biologist may ask how do blood, oxygen and salt lead to muscle contraction, but a (biological) chemist will provide the answer. Anyone may ask why the sky is blue and a nearby physicist will be happy to answer. As can be seen, if there is a dependence between theories and their scopes, a hierarchy of authority delegation may appear.
A hierarchy of theories may correspond to a hierarchy of anomaly-tolerance. Theories that are the most depended on are typically far more anomaly-tolerant than those which are less depended on. Lakatos and Quine provide many examples in their works (see the Prehistory section of this page for two of these examples). Physical laws (e.g. Newton's laws, Maxwell's equations) are very anomaly tolerant as they are heavily depended on and anomalies of the physical laws are typically redirected as either anomalies in less depended-on theories such as those of measurement apparatus, initial conditions, etc. Thus, it does seem that anomaly-tolerance (at least a certain type of anomaly) increases as theories are increasingly depended on.
A hierarchy of theories may determine acceptance and compatibility criteria. When a contending theory is unaccepted and fails to enter the mosaic, sometimes it is due to the theory's conflicting nature with an already accepted theory. Often, a theory takes priority over another and denies its annexation into the mosaic. Take for example Copernican theory that goes against Aristotelian physics and Scripture by postulating that the Earth moves and is not at the centre of the universe. It is clear that despite Copernican theory being more accurate (and more 'elegant' by removing the equant of Ptolemaic theory), it remained unaccepted. However, the theory was used for astronomic tables. One might say from this example that conformity with Aristotelian physics and Scripture was part of the acceptance and compatibility criteria of the time. Scripture and Aristotelian physics perhaps found themselves 'high up' in the hierarchy of theory dependence. This sort of scenario is also more common in contemporary science. No biological theory would become accepted if it proposed an impossible chemical reaction, no chemical theory would be accepted if it violated physical conservation laws, no physical theory would be accepted if it had logical/mathematical contradictions within. Acceptance and compatibility criteria do seem to stem from the hierarchical relations between theories.
All in all, the existence of such a hierarchical structure seems plausible in our theory, historically observable and having many predictable (and significant) repercussions.
In the scientonomic context, this question was first formulated by Abdullah Sarwar and Kye Palider in 2018. The question is currently accepted as a legitimate topic for discussion by Scientonomy community.
Lakatos's The Methodology of Scientific Research Programmes proposes a scientific methodology that involves a hierarchical-structure of theories which definitely determines anomaly-tolerance and even some methods. In his methodology, Lakatos describes science as historically (and perhaps necessarily) having a hard core and a protective belt. This hard core is a set of beliefs that stand as pillars of a Lakatos's research programmes, they are the most important beliefs that are incredibly difficult to refute. They owe their sturdiness to the protective belt, a set of auxiliary hypotheses that is susceptible to change and refutation. Lakatos notes that modus tollens refutations towards the hard core are typically redirected towards the protective belt, and auxiliary hypotheses are created in order to tackle the refutation. For example, Newton's law of gravitation can be considered as part of the hard core and when observations are made that contradict this law, auxiliary hypotheses like atmospheric refraction being unaccounted for are created. Even more than that, the research programme also had a method of problem solving, or heuristic as Lakatos called it, that served to protect the hard core and bulked up requirements of alternative theories and refutations. So, it does seem that Lakatos had a hierarchy of theories between his hard core and protective belt, and this hierarchy did determine anomaly-intolerance and even methods. Lakatos also made numerous historical references to back up these ideas.
Quine also had similar ideas in his The Web of Belief. Quine spoke of a refutation of certain beliefs in reality involving a family of beliefs. In that regard, if a contradictory observation is made, one cannot immediately by modus tollens refute a specific belief or the hypothesis at hand, as the culprit may be a member of the larger family of beliefs. This is a result of the Duhem-Quine thesis. Following this contradictory observation, of the family of beliefs, the beliefs in the periphery of our web of knowledge are the first to be questioned. For example, if measurements contradicting Boyle's law are made, typically the measurement apparatus and initial conditions are questioned rather than refuting Boyle's law which finds itself closer to the centre of our web of beliefs. Thus, it does seem that Quine also had ideas of a hierarchy between theories that determines anomaly-tolerance, and his view did have historical grounding.
Originally, this question was posed in reference to a hierarchy of theory priority that determines methods of theory acceptance and compatibility criteria within a mosaic. However, in the second rendition of this question, the scope of a hierarchy existing between theories has been extended to methods of anomaly-tolerance and methods of hierarchical authority delegation.
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This question is a subquestion of Ontology of Scientific Change.
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