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Local Epistemic Action Is a Subtype of Epistemic Action (Allen-2023) + (Allen argues that many types of epistemic actions are local (e.g. simulating, modeling, experimenting).[[CITE_Allen (2023)|p. 79]])
Local Action Availability (Allen-2023) + (Allen explains that to say that a local epistemic action is available to an epistemic agent amounts to saying that the agent employs the norm that such an action is permissible/desirable/obligatory/etc.[[CITE_Allen (2023)|p. 79]])
Global Epistemic Action Is a Subtype of Epistemic Action (Allen-2023) + (Allen makes a case that epistemic actions can be global or local.[[CITE_Allen (2023)]])
Global Epistemic Action Exists + (Allen makes a case that there is such a thing as a global epistemic action, (e.g. ''accepting a theory'').[[CITE_Allen (2023)|p. 79]])
Global Epistemic Action (Allen-2023) + (Allen makes a case that while many types o … Allen makes a case that while many types of epistemic actions are local, i.e. available to only ''some'' agents at ''some'' periods, there are also global epistemic actions. According to Allen, "taking a stance of acceptance (i.e., accepting) seems to be a global action, as without this epistemic action no process of scientific change seems possible". [[CITE_Allen (2023)|p. 79]][[CITE_Allen (2023)|p. 79]])
Local Epistemic Action Exists + (Allen points out that many epistemic actions are local (e.g. actions of simulating, experimenting, or modelling).[[CITE_Allen (2023)|p. 79]])
Local Action Availability theorem (Allen-2023) Reason1 + (Allen shows that the theorem is a deductive consequence of the ''law of norm employment'' and the definition of ''local action availability''. [[File:Local Action Availability theorem Deduction (Allen-2023).png|662px|center||]])
Local Epistemic Action (Allen-2023) + (Allen suggests that local actions are the … Allen suggests that local actions are the ones that are not universally available but are specific to a time period and/or an agent. For example "such epistemic actions as simulating, experimenting, or modelling seem to be local actions since they need not necessarily be part of the repertoire of epistemic actions of all conceivable epistemic agents; such local actions emerge at a certain time and become available to some but not all epistemic agents".[[CITE_Allen (2023)|p. 79]][[CITE_Allen (2023)|p. 79]])
Local Action Availability theorem (Allen-2023) + (Allen's theorem is based on the definition … Allen's theorem is based on the definition of ''local action availability'' that states that "the availability of local epistemic action ''A'' to an agent amounts to the employment of the norm that says “Epistemic action ''A'' is permissible/obligatory/desirable/etc.”".[[CITE_Allen (2023)|p. 79]] Thus, from the law of norm employment, one can argue that:[[CITE_Allen (2023)|p. 81]] <blockquote>For an action ''A'' to become available to an agent, the agent must employ at least one norm and accept one theory from which the norm “Action ''A'' is permissible/desirable” deductively follows.</blockquote>Thus, it follows from the law of norm employment that a local epistemic action becomes available to an agent only when its permissibility/desirability is derivable from a non-empty subset of other elements of the agent’s mosaic.-empty subset of other elements of the agent’s mosaic.)
Response to the Argument from Nothing Permanent (Barseghyan-2015) + (Although both the theories and methods of … Although both the theories and methods of science have changed over history and differ across disciplines, the nothing permanent thesis is denied. Instead, the fixed and stable features of science can take the form of dynamics or laws that govern changes in science through a piecemeal approach. A theory of scientific change is possible by positing laws that describe transitions in science and its constituent elements.Although it is generally accepted that there seems to be no static transhistorical properties of science, this does not deny the possibility of laws governing the process of scientific change in a piecemeal fashion. Theories have, of course, proven themselves to be changeable. Methods of practicing and theory appraising have also proven to be changeable. The aims, goals and philosophies behind what science ought to be have also clearly changed. However, although a case can be made for these static properties of science to be non-permanent, perhaps the fundamental mechanism governing how these properties change can be permanent. Hence, the absence of static properties in science fails to show the impossibility of a general theory of scientific change.There is the possibility of a mechanism of scientific change that governs the changes in theories, methods and other elements of science.[[File:Fixed and changing methods.jpg|center|600px]][[File:Fixed and changing methods.jpg|center|600px]])
Epistemic Agent (Patton-2019) + (An ''epistemic agent'' acts in relation to … An ''epistemic agent'' acts in relation to [[Epistemic Element|epistemic elements]] such as theories, questions, and methods. The actions of an epistemic agent amount to taking [[Epistemic Stance|epistemic stances]] towards these elements, such as accepting or pursuing a theory, accepting a question, or employing a method. The stances of an epistemic agent must be ''intentional''. To be so, they must satisfy the following conditions: # the agent must have a semantic understanding of the propositions that constitute the epistemic element in question and of its available alternatives; and # the agent must be able to choose from among the available alternatives with reason, and for the purpose of acquiring knowledge.[[CITE_Patton (2019)]][[CITE_Patton (2019)]])
Tool Reliance (Patton-2019) + (An [[Epistemic Agent|epistemic agent]] … An [[Epistemic Agent|epistemic agent]] is said to rely on an [[Epistemic Tool|epistemic tool]] ''iff'' there is a procedure through which the tool can provide an acceptable source of knowledge for answering some [[Question|question]] under the employed [[Method|method]] of that agent. Note that tool reliance, like [[Authority Delegation|authority delegation]], is reducible to the theories and methods of an agent.e to the theories and methods of an agent.)
The Second Law (Barseghyan-2015) + (Another example from ''The Laws of Scienti … Another example from ''The Laws of Scientific Change'':<blockquote>Suppose we study the history of the transition from the Aristotelian-medieval natural philosophy to that of Descartes in France and that of Newton in Britain circa 1700. It follows from ''the second law'' that both theories managed to satisfy the actual expectations of the respective scientific communities, for otherwise they wouldn’t have become accepted.[[CITE_Barseghyan (2015)|p. 130]]</blockquote>CITE_Barseghyan (2015)|p. 130]]</blockquote>)
Dynamic Substantive Methods theorem (Barseghyan-2015) + (Another example is the transition from the … Another example is the transition from the Aristotelian-Medieval Method to the Hypothetico-Deductive Method. While in the former it was assumed that there was an essential difference between natural and artificial, and that therefore the results of experiments, being artificial, were not to be trusted when trying to grasp the essence of things, in both the Cartesian and Newtonian worldviews such a distinction was not assumed and therefore experiments could be as reliable as observations when trying to understand the world. Once the theories changed (from the natural/artificial distinction to no such distinction) the methods changed too (from no-experiments to the experimental method).o-experiments to the experimental method).)
Theory Rejection theorem (Barseghyan-2015) + (Another example of the theory rejection th … Another example of the theory rejection theorem, specifically explaining that theories may not only be rejected because of the acceptance of new theories in their respective theories, is the case of ''natural astrology'' presented in [[Barseghyan (2015)]].<blockquote>The exile of astrology from the mosaic is yet another example. It is well known that astrology was once a respected scientific discipline and its theories were part of the mosaic. Of course, not all of the astrology was accepted; it was the so-called ''natural astrology'' – the theory of celestial influences on physical phenomena of the terrestrial region – that was part of the Aristotelian-medieval mosaic. ... Although, for now, we cannot reconstruct all the details or even the approximate decade when the exile of natural astrology took place, one thing is clear: when the once-accepted theory of natural astrology became rejected, it wasn’t replaced by another theory of natural astrology.[[CITE_Barseghyan (2015)|p. 172]]</blockquote>_Barseghyan (2015)|p. 172]]</blockquote>)
Theory Rejection theorem (Barseghyan-Pandey-2023) + (Another example of the theory rejection th … Another example of the theory rejection theorem, specifically explaining that theories may not only be rejected because of the acceptance of new theories in their respective theories, is the case of ''natural astrology'' presented in [[Barseghyan (2015)]].<blockquote>The exile of astrology from the mosaic is yet another example. It is well known that astrology was once a respected scientific discipline and its theories were part of the mosaic. Of course, not all of the astrology was accepted; it was the so-called ''natural astrology'' – the theory of celestial influences on physical phenomena of the terrestrial region – that was part of the Aristotelian-medieval mosaic. ... Although, for now, we cannot reconstruct all the details or even the approximate decade when the exile of natural astrology took place, one thing is clear: when the once-accepted theory of natural astrology became rejected, it wasn’t replaced by another theory of natural astrology.[[CITE_Barseghyan (2015)|p. 172]]</blockquote>_Barseghyan (2015)|p. 172]]</blockquote>)
Method (Barseghyan-2015) + (Any ''method'' is essentially a set of cri … Any ''method'' is essentially a set of criteria which can become [[Employed Method|employed]] in theory evaluation. Different methods may have different Methods can be very general and apply to theories of a variety of types (e.g. ''the hypothetico-deductive method''), or very specific (e.g. ''the double-blind trial method'' of drug testing). [[CITE_Barseghyan (2015)|pp. 4-5]]Methods of theory evaluation should be differentiated from ''research techniques'', which are used in theory construction and data gathering.[[CITE_Barseghyan (2015)|p. 5]][[CITE_Barseghyan (2015)|p. 5]])
Scope of Scientonomy - All Scales (Barseghyan-2015) + (Any change in a mosaic is within the scope … Any change in a mosaic is within the scope of scientonomy. Scientonomy should explain not only ''major'' transitions in the mosaic such as those from the Aristotelian-Medieval set of theories to those of Descartes and his followers, but also relatively ''minor'' transitions, such as a transition from "the Solar system has 7 planets" to "the Solar system has 8 planets".The question of actual taxonomy of scales is to be settled by an actual scientonomic theory. A scientonomic theory may distinguish between between grand and minor changes, revolutions and normal-science changes, or hard core and auxiliary changes; in any case, it ought to provide explanations at changes at all levels.ide explanations at changes at all levels.)
The Third Law (Barseghyan-2015) + (As Barseghyan explains, ''the double-blind … As Barseghyan explains, ''the double-blind trial method'' "is based on our belief that by performing a double-blind trial we forestall the chance of unaccounted effects, placebo effect, and experimenter’s bias".[[CITE_Barseghyan (2015)|p. 141]] The propositions that this premise is based on in turn derive from theories that are acecpted; for example, "our belief that a trial with two similar groups minimizes the chance of unaccounted effects follows from our knowledge about statistical regularities, i.e. from our belief that two statistically similar groups can be expected to behave similarly ''ceteris paribus''".[[CITE_Barseghyan (2015)|p. 142]] Similarly, our knowledge of physiology and psychology lead to our understanding that we can void the placebo effect with fake pills.[[CITE_Barseghyan (2015)|p. 142]] Our knowledge of psychology allows us to understand that researchers can bias patients from their own knowledge of which group is which.[[CITE_Barseghyan (2015)|p. 142]] Clearly, these premises, although trivial, are currently accepted within our scientific mosaic.[[CITE_Barseghyan (2015)|p. 142]] Hence, the ''double-blind trial method'', although an ''implementation'' of abstract requirements, is still based on our currently accepted theories. This is true in all scenarios of ''implementation''.[[CITE_Barseghyan (2015)|p. 142]]Thus, methods follow deductively from elements of the mosaic whether they follow strictly from theories and methods or implement abstract requirements. This is an important similarity between the two scenarios for method employment.n the two scenarios for method employment.)
Synchronism of Method Rejection theorem (Barseghyan-2015) + (As Barseghyan notes, it can be tempting to … As Barseghyan notes, it can be tempting to say that the ''double blind trial method'' replaced ''the blind trial method''. But this is not a correct explication of the method dynamics at play. Barseghyan provides a more detailed explanation in this historical example that helps to explain the ''synchronism of method rejection theorem''. He begins:<blockquote>To be sure, ''the blind trial method'' was replaced in the mosaic, but not by ''the double-blind trial method''. Rather, it was replaced by the abstract requirement that when assessing a drug’s efficacy one must take into account the possible experimenter’s bias. The employment of ''the double-blind trial method ''was due to the fact that it specified this abstract requirement. Its employment ''per se'' had nothing to do with the rejection of the blind trial method.[[CITE_Barseghyan(2015)|p. 178]]</blockquote>He continues his explanation with a closer look at the ''blind trial method'':<blockquote>Recall ''the blind trial method'' which required that a drug’s efficacy is to be shown in a trial with two groups of patients, where the active group is given the real pill, while the control group is given a placebo. Implicit in ''the blind trial method'' was a clause that it is ok if the researchers know which group is which. This clause was based on the tacit assumption that the researchers’ knowledge cannot affect the patients and, thus, cannot void the results of the trial. Although this assumption was hardly ever expressed, it is safe to say that it was taken for granted – we would allow the researchers to know which group of patients is which until we learned about the phenomenon of experimenter’s bias... Once we learned about the possibility of experimenter’s bias, the blind trial method became instantly rejected. More precisely, the acceptance of the ''experimenter’s bias thesis'' immediately resulted in the abstract requirement that, when assessing a drug’s efficacy, one must take the possibility of the experimenter’s bias into account. Consequently, two elements of the mosaic became rejected: the blind trial method and the tacit assumption that the experimenters’ knowledge doesn’t affect the patients and cannot void the results of trials... Now, ''the experimenter’s bias thesis'' yielded the new abstract requirement to take into account the possible experimenter’s bias. This requirement, in turn, replaced the blind trial method with which it was incompatible (by the method rejection theorem).[[CITE_Barseghyan (2015)|p. 178-80]] </blockquote>Therefore, Barseghyan concludes, "the double-blind trial method had nothing to do with the rejection of the blind trial method. By the time the double-blind trial method became employed, the blind trial method had already been rejected. So even if we had never devised the double-blind trial method, the blind trial method would have been rejected all the same".[[CITE_Barseghyan (2015)|p. 180]] In summary, "the rejection of the blind trial method took place synchronously with the rejection of the theory on which it was based".[[CITE_Barseghyan (2015)|p. 180]] Hence, this is a historical example of the ''synchronism of method rejection theorem''.180]] Hence, this is a historical example of the ''synchronism of method rejection theorem''.)
Pursuit as Distinct from Acceptance (Barseghyan-2015) + (As a distinct epistemic stance, [[Theory Pursuit|theory pursuit]] is not reducible to [[Theory Acceptance|acceptance]].)
Method Hierarchy Exists + (As argued by [[Mathew Mercuri|Mercuri]] … As argued by [[Mathew Mercuri|Mercuri]] and [[Hakob Barseghyan|Barseghyan]], it is often the case that "criteria employed by the same epistemic agent constitute a certain preference hierarchy",[[CITE_Mercuri and Barseghyan (2019)|p. 45]] illustrated among other things by the fact that "practitioners in different fields customarily speak of more or less reliable evidence".[[CITE_Mercuri and Barseghyan (2019)|p. 46]] For example, when the community of art historians attempts to establish the authenticity of a certain work of art, they often accept the position of the expert they find most reliable; if, for whatever reason, this expert doesn't have a position on the authenticity of that work of art, the community refers to their second-best expert, and so on.[[CITE_Loiselle (2017)]] Another example of method hierarchies comes from the field of clinical epidemiology that features "a variety of different requirements – from more stringent to more lenient".[[CITE_Mercuri and Barseghyan (2019)|p. 58]] Thus, when the requirements of the randomized controlled trial method are met, the results of the study become accepted. If however, when no studies meet these requirements, clinical epidemiologists often accept the results of studies that satisfy less stringent requirements. Mercuri and Barseghyan discuss a number of such cases in their [[Mercuri and Barseghyan (2019)|''Method Hierarchies in Clinical Epidemiology'']].[[CITE_Mercuri and Barseghyan (2019)]]CITE_Mercuri and Barseghyan (2019)]])
The First Law for Theories (Barseghyan-2015) + (As is noted in the description above, acce … As is noted in the description above, accepted theories may simply be replaced by their negation. Barseghyan (2015) uses a hypothetical example to explain this possibility: <blockquote>Suppose a scientific community accepts that a certain drug is therapeutically efficient in alleviating a certain condition. In principle, this proposition can be replaced by its own negation, i.e. the proposition that the drug is not efficient in alleviating the condition. HSC shows many examples of this sort. Recall, for instance, the medieval and early modern belief that bloodletting is efficient in restoring the proper balance of humors in the body and, thus, restoring health. When this belief was rejected it was simply replaced by its negation.[[CITE_Barseghyan (2015)|p. 122]]</blockquote>[[CITE_Barseghyan (2015)|p. 122]]</blockquote>)
The Zeroth Law (Harder-2015) + (As per Barseghyan, "In the second scenario … As per Barseghyan, "In the second scenario (of inconsistency tolerance), we are normally willing to tolerate inconsistencies between an accepted general theory and a singular proposition describing some anomaly. In this scenario, the general proposition and the singular proposition describe the same phenomenon; the latter describes a counterexample for the former. However, the community is tolerant towards this inconsistency for it is understood that anomalies are always possible ... We appreciate that both the general theory in question and the singular factual proposition may contain grains of truth. In this sense, we are anomaly-tolerant".[[CITE_Barseghyan (2015)||pp.160]][[CITE_Barseghyan (2015)||pp.160]])
Theory (Barseghyan-2015) + (At any moment of the history of science, t … At any moment of the history of science, there are certain ''theories'' that the scientific community of the time accepts as the best available descriptions of their respective domains. According to the original definition of the term suggested in [[Barseghyan (2015)|''The Laws of Scientific Change'']], the class of ''theory'' includes only those propositions which attempt to describe a certain object under study. A theory may refer to any set of propositions that attempt to describe something. Theories may be empirical (e.g. theories in natural or social science) or formal (e.g. logic, mathematics). Theories may be of different levels of complexity and elaboration, for they may consist of hundreds of systematically linked propositions, or of a few loosely connected propositions. They may or may not be axiomatized, formalized, or mathematized. It encompasses all proposition which attempt to tell us how things were, are or will be, i.e. substantive propositions of empirical and formal sciences. The definition excludes [[Normative Theory|normative propositions]], such as those of methodology, ethics, or aesthetics.[[CITE_Barseghyan (2015)|pp. 3-5]] Examples of theories satisfying the definition include the theory that the Earth is round, Newton's laws of universal gravitation, The phlogiston theory of combustion, quantum mechanics, Einstein's theory of relativity, and the theory of evolution.f relativity, and the theory of evolution.)

Authority Delegation (Overgaard-Loiselle-2016) + (Authority delegation explained by Gregory Rupik)

The First Law for Theories (Barseghyan-2015) + (Barseghyan (2015) contends that "the attit … Barseghyan (2015) contends that "the attitude of the community towards anomalies is historically changeable and non-uniform across different fields of science."[[CITE_Barseghyan (2015)|p.124]] Both anomaly-intolerant and anomaly-tolerant attitudes can prevail in different communities. Firstly, consider the ""historical"" example put forth by Barseghyan (2015):<blockquote>Consider the famous four color theorem currently accepted in mathematics which states that no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Suppose for the sake of argument that a map were found such that required no less than five colors to color. Question: how would mathematicians react to this anomaly? Yes, they would check, double-check, and triple-check the anomaly, but once it were established that the anomaly is genuine and it is not a hoax, the proof of the four color theorem would be revoked and the theorem itself would be rejected. Importantly it could be rejected without being replaced by any other general proposition. Its only replacement in the mosaic would be the singular proposition stating the anomaly itself. This anomaly-intolerance is a feature of our contemporary formal science.278 Thus, we have to accept that anomaly-tolerance is not a universal feature of science.[[CITE_Barseghyan (2015)|p.125]]</blockquote>Additionally, Barseghyan (2015) extends this example into a brief ''theoretical'' discussion. That is:<blockquote>The first law for theories doesn’t impose any limitations as to what sort of propositions can in principle replace the accepted propositions; it merely says that there is always some replacement. This replacement can be as simple as a straightforward negation of the accepted proposition, or a full-fledged general theory, or a singular proposition describing some anomaly. The actual attitude of the community may be different at different time periods and in different fields of science.[[CITE_Barseghyan (2015)|p.125]]</blockquote>CITE_Barseghyan (2015)|p.125]]</blockquote>)
Possible Mosaic Split theorem (Barseghyan-2015) + (Barseghyan (2015) contrasts the replacemen … Barseghyan (2015) contrasts the replacement of the Aristotelian-Medieval method with the Newtonian method in Britain and the Cartesian method in France -- a broad case which might seem like an instance of mosaic split, but is not -- with a more specific historical example of potential mosaic split. He outlines that specific historical example, ''the acceptance of the Cartesian natural philosophy in Cambridge circa 1680'', as follows:<blockquote>Let us begin with the available historical data. Prior to the 1680s, the Aristotelian-medieval natural philosophy was taught in schools across Europe, with alternative theories included into the curricula only sporadically. If my understanding is correct, the first university where the Cartesian natural philosophy was accepted and taught on a regular basis was Cambridge. Although the theory had been sporadically taught since the 1660s, it began to be taught systematically only circa 1680.379 Thus, it is not surprising that when one Cambridge professor Isaac Newton was writing his magnum opus, the main target of his criticism was Descartes’s theory, not that of Aristotle. According to the historical data, during the last two decades of the 17th century, Cambridge remained the only university where the Cartesian theory was generally accepted. The situation changed circa 1700, when the Cartesian natural philosophy together with its respective modifications by Huygens, Malebranche and others became accepted in France, Holland and Sweden. As for Oxford, it never accepted the Cartesian theory but switched directly to the Newtonian theory circa 1690. In Cambridge, the transition from the Cartesian natural philosophy to that of Newton took place in the 1700s. Most likely, the universities of the Dutch Republic (Leiden and Utrecht) were the first on the Continent to accept the Newtonian theory by 1720. In France and Sweden, the Newtonian theory replaced the Cartesian natural philosophy circa 1740.386 The picture wouldn’t be complete if we didn’t mention the important theological differences: Catholic theology was accepted in Paris; Anglican theology was accepted in Oxford and Cambridge; in Holland and Sweden the accepted theology was that of Protestantism.[[CITE_Barseghyan (2015)|pp. 211-212]]</blockquote>A draft timeline of the situation, including theological differences, at the end of the 17th century has been constructed by Barseghyan:[[File:Draft_Timeline_1680_Mosaics.png|1216px|center||]] Barseghyan (2015) continues as follows:<blockquote> Although the diagram hardly scratches the surface of the colorful 17-18th century landscape, it points to ''at least two possible candidates of mosaic split''. Apparently, there seem to have been a split in the Anglican mosaic of Britain circa 1680, when the Cartesian natural philosophy became accepted in Cambridge, and also probably in the Protestant mosaic sometime by 1720, when the Newtonian theory became accepted in Holland.[[CITE_Barseghyan (2015)|pp. 212]]</blockquote>Barseghyan (2015) more closely examines the first potential case: the acceptance of Cartesian natural philosophy in Cambridge:<blockquote> If my reading is correct, then this was a typical case of mosaic split: after the acceptance of the Cartesian theory, the mosaic of Cambridge became different from the Aristotelian-Anglican mosaic of other British universities. Note that this mosaic split was caused by the acceptance of only one new theory. Therefore, it could only be a result of an inconclusive theory assessment. At this point, we can only hypothesize as to why exactly the outcome of the assessment of the Cartesian theory was inconclusive. My historical hypothesis is that it had to do with the inconclusiveness of the Aristotelian-medieval method employed at the time, i.e. with the vagueness of the implicit expectations of the community of the time. It is easily seen that the then-employed Aristotelian-medieval method allowed for two distinct scenarios of theory assessment. On the one hand, if a proposition was meant as a theorem, it was only expected to show that it did in fact follow from other accepted propositions. That much would be sufficient for a new theorem to become accepted. This part of the method is straightforward – no ambiguity here. If, on the other hand, a proposition was not meant as a theorem – if it was supposed to be a separate axiom – then it was expected to be intuitively true. But what does it mean to be intuitively true? Nowadays we seem to realize that no proposition can be intuitively true (unless of course it is a tautology) and that intuition, even when “schooled by experience”, is not the best advisor in theory assessment.66 Therefore, a theory could merely appear intuitively true to the community of the time. This was the actual expectation of the scientific community in the 17th century – the appearance of intuitive truth. One indication of this is the fact that both Descartes and Newton understood the vital necessity of presenting their systems in the axiomatic-deductive form. They also made all possible efforts to show that their axioms – the starting points of their deductions – were beyond any reasonable doubt. They both realized that if their theories are ever to be accepted, their axioms must appear clear to anyone who is knowledgeable enough to understand them. But this is exactly what was expected by the scientific community of the time. Yet, the requirement of intuitive truth is extremely vague: what appears intuitively true to me need not necessarily appear intuitively true to others. I think this can explain why the mosaic split of the 1680s took place. The axioms of the Cartesian natural philosophy were meant as self-evident intuitively true propositions. But as with any “intuitive truth”, scientists could easily disagree as to whether the axioms were indeed intuitively true. As a result, the outcome of the assessment of the Cartesian theory was “inconclusive”. In that situation, a mosaic split was one of the possible courses of events (by the possible mosaic split theorem). Of course the mosaic split wasn’t inevitable – it was merely one of the possibilities which actualized. This Aristotelian “bring before me intuitive true propositions” requirement was so vague that theory assessment could easily yield an “inconclusive” outcome and, consequently, result in a mosaic split. It is not surprising, therefore, that the British mosaic did actually split in the 1680s when the Cartesian natural philosophy was accepted only in Cambridge. This was an instance of ''possible mosaic split''.[[CITE_Barseghyan (2015)|pp. 212-213]]</blockquote>/blockquote>)
Static Procedural Methods theorem (Barseghyan-2015) Reason1 + (Barseghyan (2015) deduces the Static Proce … Barseghyan (2015) deduces the Static Procedural Methods theorem as follows and with the following justification:[[CITE_Barseghyan (2015)|pp. 224-225]]<blockquote>By the method rejection theorem, a method is rejected only when other methods that are incompatible with the method in question become employed. Thus, a replacement of a procedural method by another method would be possible if the two were incompatible with each other. However, it can be shown that a procedural method can never be incompatible with any other method, procedural or substantive. Consider first the case of a procedural method being replaced by another procedural method. By definition, procedural methods don’t presuppose anything contingent: they can only presuppose necessary truths. But two necessary truths cannot be incompatible, since necessary truths (by definition) hold in all possible worlds. Therefore, two methods based exclusively on necessary truths cannot be incompatible either; i.e. any two procedural methods are always compatible. Consequently, by the method rejection theorem, one procedural method cannot replace another procedural method. Consider a new necessarily true mathematical proposition that has been proven to follow from other necessary true mathematical propositions. By the second law, this new theorem becomes accepted into the mosaic. The acceptance of this theorem can lead to the invention and employment of a new procedural method based on this new theorem. Yet, this new method can never be incompatible with other employed procedural methods, just as the newly proven theorem can never be incompatible with those theorems which were proven earlier (of course, insofar as all of these theorems are necessary truths). Thus, the only question that remains to be answered here is whether a procedural method can be replaced by a substantive method? Again, the answer is “no”. Substantive methods presuppose some contingent propositions about the world, while procedural methods presuppose merely necessary truths. But a necessary truth is compatible with any other truth (contingent or necessary). Therefore, no newly accepted theory can be incompatible with an accepted necessary truth. In particular, if we take the principles of pure mathematics to be necessarily true, then it follows that no empirical theory (i.e. physical, chemical, biological, psychological, sociological etc.) can be incompatible with the principles of mathematics. Consequently, a new substantive method can never be incompatible with procedural methods. Take the above-discussed abstract deductive acceptance method based on the definition of deductive inference: if a proposition is deductively inferred from other accepted propositions, it is to be accepted. It is safe to say that no substantive method can be incompatible with this requirement, for to do so would mean to be incompatible with the definition of deductive inference, which is inconceivable. Thus, a procedural method can be replaced neither by substantive nor by procedural methods.This brings us to the conclusion that all procedural methods are in principle static.</blockquote>Here is the deduction:[[File:Static-procedural-methods.jpg|607px|center||]]:Static-procedural-methods.jpg|607px|center||]])
Mosaic Split (Barseghyan-2015) + (Barseghyan (2015) illustrates the distinct … Barseghyan (2015) illustrates the distinction here succinctly:<blockquote>Two physicists or even two groups of physicists may disagree on one topic or another. Yet, as long as they take the same theories as accepted ones, there is a regular scientific disagreement. Suppose, for instance, there are two groups of quantum physicists which subscribe to two different quantum theories – say, the so-called Many Worlds theory and GRW theory respectively. Suppose also that the two groups understand that the currently accepted theory is the orthodox quantum mechanics. Consequently, in their university lectures both groups present the orthodox theory as the currently accepted one. Here we have a typical example of scientific disagreement. The members of the two groups may even tell their students that they personally believe there is a better theory available. But as long as they stress that their personal favourite theory is not the currently accepted one, we deal with an instance of regular scientific disagreement.[[CITE_Barseghyan (2015)|p.202-3]]</blockquote>Barseghyan also provides a more historically grounded example in the context of the physics community:<blockquote>Imagine a group of physicists circa 1918 who considered general relativity as the best available description of its domain. This view was in disagreement with the position of the vast majority of scientists who believed in the then-accepted version of the Newtonian theory. Yet there was no mosaic split, since both the Newtonians and Einsteinians clearly realised which theory was accepted and which theory was merely a contender. Take Eddington, for instance, who was in that small group of early adherents of general relativity. He had no illusions regarding the status of general relativity, for he knew perfectly well that it wasn’t the accepted theory.[[CITE_Barseghyan (2015)|p.203]]<blockquote>TE_Barseghyan (2015)|p.203]]<blockquote>)
Contextual Appraisal theorem (Barseghyan-2015) + (Barseghyan (2015) provides another rich il … Barseghyan (2015) provides another rich illustration for the Contextual Appraisal theorem with "the famous Eucharist episode which took place in the second half of the 17th century," which is a subtler important piece of the already difficult scientonomic case of the 18th-century transition from Cartesian to Newtonian natural philosophy.[[CITE_Barseghyan (2015)|p. 190]] Barseghyan describes the episode as follows:<blockquote>This episode has been often portrayed as a clear illustration of how religion affects science. In particular, the episode has been presented as though the acceptance of Cartesianism in Paris was delayed due to the role played by the Catholic Church. It is a historical fact that Descartes’s natural philosophy was harshly criticized by the Church. In 1663, his works were even placed on the Index of Prohibited Books and in 1671 his conception was officially banned from schools. Thus, at first sight, it may appear as though the acceptance of the Cartesian science in Paris was indeed hindered by religion. Yet, upon closer scrutiny, it becomes obvious that this interpretation is too superficial. When Descartes constructed his natural philosophy, it soon turned out that it had a very troubling consequence: it wasn’t readily reconcilable with the doctrine of transubstantiation accepted by the Aristotelian-Catholic scientific community of Paris. The idea of transubstantiation was proposed by Thomas Aquinas in his Summa Theologiae as an explanation of one of the Christian dogmas – namely, that of the Real Presence which states that, in the Eucharist, Christ is really present under the appearances of the bread and wine (i.e. literally, rather than metaphorically or symbolically). In his explanation of Real Presence, Aquinas employed Aristotelian concepts of substance and accident. In particular, he stated that in the Eucharist the consecration of bread and wine effects the change of the whole substance of the bread into the substance of Christ’s body and of the whole substance of the wine into the substance of his blood. Thus, what happens in the Eucharist is transubstantiation – a transition from one substance to another. As for the accidents of the bread and wine such as their taste, color, smell etc., Aquinas held that they remain intact, for transubstantiation doesn’t affect them. The doctrine of transubstantiation soon became the accepted Catholic explanation of the Real Presence. The problem was that Descartes’s theory of matter didn’t provide any mechanism similar to that stated in the doctrine of transubstantiation. To be more precise, it followed from Descartes’s original theory that transubstantiation was impossible. Recall that, according to Descartes, the only principal attribute of matter is extension: to be a material object amounts to occupying some space. It follows from this basic axiom that accidents such as smell, color, or taste are effects produced upon our senses by the configuration and motion of material particles. In other words, we simply cannot perceive the accidents of bread and wine unless there is bread and wine in front of us. What makes bread what it is, what constitutes its substance (to use Aristotle’s terms) is a specific combination of material particles; and the same goes for wine. Thus, when the substance of bread changes into the substance of Christ’s body, in the Cartesian theory, it means that some combination of particles which constitutes the bread changes into another combination of particles which constitutes Christ’s body. The key point here is that, in Descartes’s theory, it is impossible for Christ’s body to have the appearance of bread, since the appearance is merely an effect produced by that specific combination of particles upon our senses; Christ’s body and blood simply cannot produce the accidents of bread and wine. Obviously, on this point, Descartes’s theory was in conflict with the doctrine of transubstantiation. This conflict became the focal point of criticism of Descartes’s theory. To a 21st-century reader used to a clear-cut distinction between science and religion this may seem a purely religious matter. Yet, in the second half of the 17th century, this was precisely a scientific concern. The crucial point is that back then theology wasn’t separate from other scientific disciplines: the scientific mosaic of the time included many theological propositions such as “God exists”, “God is omnipotent”, or “God created the world”. These propositions where part of the mosaic just as any other accepted proposition. If we could visit 17th-century Paris, we would see that the dogma of Real Presence and the doctrine of transubstantiation weren’t something foreign to the scientific mosaic of the time – they were accepted parts of it alongside such propositions as “the Earth is spherical”, “there are four terrestrial elements”, “there are four bodily fluids” and so on. Thus, Descartes’s theory was in conflict not with some “irrelevant religious views” but with a key element of the scientific mosaic of the time, the doctrine of transubstantiation. More precisely, the problem was that back then no theory was allowed to be in conflict with the accepted theological propositions. This latter requirement was part of the method of the time. The requirement strictly followed from the then-accepted belief that theological propositions are infallible.Yet, eventually, the Cartesian natural philosophy did become accepted in Paris. If the laws of scientific change are correct, it could become accepted only with a special patch that would reconcile it with the doctrine of transubstantiation. It is not clear as to what exactly this patch was. To be sure, there is vast literature on different Cartesian solutions of the problem: the solutions proposed by Descartes, Desgabets, and Arnauld are all well known.359 However, I have failed to find a single historical narrative revealing which of these patches became accepted in the mosaic alongside the Cartesian natural philosophy circa 1700.360 Based on the available data, I can only hypothesize that the accepted patch was the one proposed by Arnauld in 1671. According to Arnauld’s solution, the Cartesian natural philosophy concerns only the natural course of events. However, since God is omnipotent, he is able to alter the natural course of events. Thus, he can turn bread and wine into the body and blood of Christ even if that is not something that can be expected naturally. Moreover, since our capacity of reason is limited, God can do things that are beyond our reason. Therefore, it is possible for Christ to be really present under the accidents of the bread and wine without our being able to comprehend the mechanism of that presence.361 One reason why I think that this could be the accepted patch is that a similar solution was also proposed by both Régis and Malebranche.362 The latter basically held that what happens in the Eucharist is a miracle and is not to be explicated in philosophical terms. In this context, the position of Malebranche is especially important for, at the time, his Recherche de la Vérité was among the main Cartesian texts studied at the University of Paris.363 Again, I cannot be sure that the accepted patch was exactly that of Arnauld and Malebranche; only closer scrutiny of the curriculum of Paris University in 1700-1740 as well as other relevant sources can settle this issue. Yet, the laws of scientific change tell us that there should be one patch or another – the Cartesian natural philosophy couldn’t have been accepted without one. In short, initially the Cartesian theory didn’t satisfy the requirements implicit in the mosaic of the time, namely it was in conflict with one of those propositions which were not supposed to be denied. Thus, the acceptance of Descartes’s theory was hindered not because “dogmatic clergy” didn’t like it on some mysterious religious grounds, but because initially it didn’t satisfy the requirements of the time. This point will become clear if we turn our attention to the scientific mosaic of Cambridge of the same time period. Circa 1660, the mosaics of Paris and Cambridge were similar in many respects. For one, they both included all the elements of the Aristotelian-medieval natural philosophy. In addition, they shared the basic Christian dogmas, such as the dogma of Real Presence. Yet, they were different in one important respect: whereas the mosaic of Paris included the propositions of Catholic theology, the mosaic of Cambridge included the propositions of Anglican theology. Namely, the Cambridge mosaic didn’t include the doctrine of transubstantiation. In that mosaic, the Cartesian theory was only incompatible with the Aristotelian-medieval natural philosophy which it aimed to replace.This difference proved crucial. Whereas reconciling the Cartesian natural philosophy with the doctrine of transubstantiation was a challenging task, reconciling it with the dogma of Real Presence wasn’t difficult. One such reconciliation was suggested by Descartes himself and was developed by Desgabets. The idea was that the bread becomes the body of Christ by virtue of being united with the soul of Christ, while the material particles of the bread remain intact. For the Catholic, this solution was unacceptable, for it denied the doctrine of transubstantiation and, therefore, was a heresy. Yet, for the Anglican, this solution could be acceptable, since the doctrine of transubstantiation wasn’t part of the Anglican mosaic. Thus, whereas the Catholic was faced with a seemingly insurmountable problem of reconciling the Cartesian natural philosophy with the doctrine of transubstantiation, the Anglican didn’t have that problem. This explains why the whole Eucharist case was almost exclusively a Catholic affair. This episode illustrates the main point of the contextual appraisal theorem: a theory is assessed only in the context of a specific mosaic and the outcome of the assessment depends on the state of the mosaic of the time.[[CITE_Barseghyan (2015)|p. 190-196]]</blockquote>)
The First Law for Theories (Barseghyan-2015) + (Barseghyan (2015) provides further example … Barseghyan (2015) provides further examples of anomaly-tolerance that precede Newtonian theory:<blockquote>Take the Aristotelian-medieval natural philosophy accepted up until the late 17th century. Tycho’s Nova of 1572 and Kepler’s Nova of 1604 seemed to be suggesting that, contrary to the view implicit in the Aristotelian-medieval mosaic, there is, after all, generation and corruption in the celestial region. In addition, after Galileo’s observations of the lunar mountains in 1609, it appeared that celestial bodies are not perfectly spherical in contrast to the view of the Aristotelian-medieval natural philosophy. Moreover, observations of Jupiter’s moons (1609) and the phases of Venus (1611) appeared to be indicating that planets are much more similar to the Earth than to the Sun in that they too have the capacity for reflecting the sunlight. All these observational results were nothing but anomalies for the accepted theory which led to many attempts to reconcile new observational data with the accepted Aristotelian-medieval natural philosophy. What is important is that the theory was not rejected; it remained accepted throughout Europe for another ninety years and was overthrown only by the end of the 17th century.[[CITE_Barseghyan (2015)|p.123-4]]</blockquote>arseghyan (2015)|p.123-4]]</blockquote>)
Synchronism of Method Rejection theorem (Barseghyan-2015) + (Barseghyan answers this question using the … Barseghyan answers this question using the following historical example:<blockquote>Once we understood that the unaided human eye is incapable of obtaining data about extremely minute objects (such as cells or molecules), we were led to an employment of the abstract requirement that the counted number of cells is acceptable only if it is acquired with an “aided” eye. This abstract requirement has many different implementations such as ''the counting chamber method'', ''the plating method'', ''the flow cytometry method'', and ''the spectrophotometry method''. What is interesting from our perspective is that these different implementations are compatible with each other – they are not mutually exclusive. In fact, a researcher can pick any one of these methods, for these different concrete methods are connected with a logical OR. Thus, the number of cells is acceptable if it is counted by means of a counting chamber, or a flow cytometer, or a spectrophotometer. The measured value is acceptable provided that it satisfies the requirements of at least one of these methods ... To generalize the point, different implementations of the same abstract method cannot possibly be in conflict with each other, for any concrete method is a logical consequence of some conjunction of the abstract method and one or another accepted theory (by ''the third law'').[[CITE_Barseghyan(2015)|p. 175-6]]</blockquote>_Barseghyan(2015)|p. 175-6]]</blockquote>)
The Second Law (Barseghyan-2015) Reason1 + (Barseghyan argued that the second law dire … Barseghyan argued that the second law directly follows from the [[Employed Method (Barseghyan-2015)|the definition of employed method]]. According to him, "since employed method is defined as a set of implicit criteria actually employed in theory assessment, it is obvious that any theory that aims to become accepted must meet these requirements".[[CITE_Barseghyan (2015)|p. 129]] Thus, he argues, the second law is a mere explication of what is implicit in the definition of ''employed method''. in the definition of ''employed method''.)
Theory Rejection theorem (Barseghyan-2015) + (Barseghyan considers the case of ''plenism … Barseghyan considers the case of ''plenism,'' "the view that there can be no empty space (i.e. no space absolutely devoid of matter)", as a key historical illustration of the '''Theory Rejection theorem''' in [[Barseghyan (2015)]]. <blockquote> Within the system of the Aristotelian-medieval natural philosophy, ''plenism'' was one of many theorems. Yet, when the Aristotelian natural philosophy was replaced by that of Descartes, ''plenism'' remained in the mosaic, for it was a theorem in the Cartesian system too. To appreciate this we have to consider the Aristotelian-medieval law of violent motion, which states that an object moves only if the applied force is greater than the resistance of the medium. In that case, according to the law, the velocity will be proportional to the force and inversely proportional to resistance. Otherwise the object won’t move; its velocity will be zero ... Taken as an axiom, this law has many interesting consequences. It follows from this law, that if there were no resistance the velocity of the object would be infinite. But this is absurd since nothing can move infinitely fast (for that would mean being at two places simultaneously). Therefore, there should always be some resistance, i.e. something that fills up the medium. Thus, we arrive at the conception of plenism ...There weren’t many elements of the Aristotelian-medieval mosaic that maintained their state within the Cartesian mosaic. The conception of plenism was among the few that survived through the transition. In the Cartesian system, plenism followed directly from the assumption that extension is the attribute of matter and that no attribute can exist independently from the substance in which it inheres ...In short, when the axioms of a theory are replaced by another theory, some of the theorems may nevertheless manage to stay in the mosaic, provided that they are compatible with the newly accepted theory. This is essentially what the theory rejection theorem tells us. Thus, if someday our currently accepted general relativity gets replaced by some new theory, the theories that followed from general relativity, such as the theory of black holes, may nevertheless manage to remain in the mosaic.[[CITE_Barseghyan (2015)|p. 168-170]] </blockquote>TE_Barseghyan (2015)|p. 168-170]] </blockquote>)
Theory Rejection theorem (Barseghyan-Pandey-2023) + (Barseghyan considers the case of ''plenism … Barseghyan considers the case of ''plenism,'' "the view that there can be no empty space (i.e. no space absolutely devoid of matter)", as a key historical illustration of the '''Theory Rejection theorem''' in [[Barseghyan (2015)]]. <blockquote> Within the system of the Aristotelian-medieval natural philosophy, ''plenism'' was one of many theorems. Yet, when the Aristotelian natural philosophy was replaced by that of Descartes, ''plenism'' remained in the mosaic, for it was a theorem in the Cartesian system too. To appreciate this we have to consider the Aristotelian-medieval law of violent motion, which states that an object moves only if the applied force is greater than the resistance of the medium. In that case, according to the law, the velocity will be proportional to the force and inversely proportional to resistance. Otherwise the object won’t move; its velocity will be zero ... Taken as an axiom, this law has many interesting consequences. It follows from this law, that if there were no resistance the velocity of the object would be infinite. But this is absurd since nothing can move infinitely fast (for that would mean being at two places simultaneously). Therefore, there should always be some resistance, i.e. something that fills up the medium. Thus, we arrive at the conception of plenism ...There weren’t many elements of the Aristotelian-medieval mosaic that maintained their state within the Cartesian mosaic. The conception of plenism was among the few that survived through the transition. In the Cartesian system, plenism followed directly from the assumption that extension is the attribute of matter and that no attribute can exist independently from the substance in which it inheres ...In short, when the axioms of a theory are replaced by another theory, some of the theorems may nevertheless manage to stay in the mosaic, provided that they are compatible with the newly accepted theory. This is essentially what the theory rejection theorem tells us. Thus, if someday our currently accepted general relativity gets replaced by some new theory, the theories that followed from general relativity, such as the theory of black holes, may nevertheless manage to remain in the mosaic.[[CITE_Barseghyan (2015)|p. 168-170]] </blockquote>TE_Barseghyan (2015)|p. 168-170]] </blockquote>)
Possible Mosaic Split theorem (Barseghyan-2015) + (Barseghyan continues providing examples of … Barseghyan continues providing examples of possible mosaic split, noting that an analysis of the case in which there are two contender theories and not just one is "more illustrative".[[CITE_Barseghyan (2015)|p. 205]]<blockquote>The case with two contender theories is more illustrative. When two contender theories undergo assessment by the current method, each assessment can have three possible outcomes. Therefore, there are nine possible combinations of assessment outcomes overall and, in five of these nine combinations, there is an element of inconclusiveness.[[CITE_Barseghyan (2015)|p. 205]]</blockquote>[[File:Two_Contender_Theories_Possible_Assessment_Outcomes.png|509px|center||]]<blockquote>The actual course of events in the first four combinations is relatively straightforward. If the assessment of one theory yields a conclusive “accept” while the assessment of the other yields a conclusive “not accept”, then, by the second law, the former becomes accepted while the latter remains unaccepted. When the assessments of both theories yield conclusive “not accept”, then both remain unaccepted and the mosaic maintains its current state. Finally, when the assessment yields “accept” for both theories, then both theories become accepted and a mosaic split takes place, as we know from the [[Necessary Mosaic Split theorem (Barseghyan-2015)]] [[CITE_Barseghyan (2015)|p. 205]]</blockquote>[[File:Theory_Assessment_Outcomes_and_Actual_Courses_of_Events.png|581px|center||]]<blockquote>As we can see, in each of these four cases, there is only one necessary course of events. In other words, when the assessment outcomes of both theories are conclusive, the actual course of events is strictly determined by the assessment outcomes. This is not the case with the other five combinations of assessment outcomes. Let us consider them in turn.[[CITE_Barseghyan (2015)|p. 206]]</blockquote> ''Accept/inconclusive'': What can happen when the assessment of one theory yields a conclusive “accept”, while the assessment outcome of the other theory is inconclusive? <blockquote>In such a scenario, the former theory must necessarily become accepted, while the latter may or may not become accepted. Therefore, only two courses of events are possible in this case: it is possible that only the former theory will become accepted and it is also possible that both theories will become simultaneously accepted (i.e. a [[Mosaic Split|mosaic split]] may take place).[[CITE_Barseghyan (2015)|p. 206]]</blockquote>''Not accept/inconclusive'': What can happen when the assessment of one theory yields a conclusive “not accept”, while the assessment outcome of the other theory is inconclusive? <blockquote>In such an instance, it is impossible for the former theory to become accepted, while the latter may or may not become accepted. Thus, it is possible that both theories will remain unaccepted as well as it is possible that only the latter theory will become accepted. Finally, the [[mosaic split]] is also among the possibilities, since it is conceivable that one part of the community may opt for accepting the latter theory while the other part may prefer to maintain the current state of the mosaic. Disregard for a moment the former theory: it cannot become accepted, since its assessment yields a conclusive “not accept”. With the former theory out of the picture, we are left with the latter theory – the one with an inconclusive assessment outcome. Thus, this case becomes similar to the above-discussed case with only one contender theory: we have a contender with an inconclusive assessment outcome and, consequently, a mosaic split may take place provided that one part of the community decides to opt for the theory while the other part prefers to stick to the existing mosaic. Note that, in this case, a [[Mosaic Split|split]] is not a consequence of the simultaneous acceptance of two mutually incompatible theories.[[CITE_Barseghyan (2015)|pp. 206-207]]</blockquote>''Inconclusive/inconclusive'': Finally, what can happen when the assessment outcomes of both theories are inconclusive? <blockquote>In such a scenario, both theories may or may not become accepted. Thus, it is possible that none of the theories will become accepted, just as it is possible that only one of the two will become accepted. It is also possible that both theories will become simultaneously accepted and, consequently, a [[Mosaic Split|mosaic split]] will take place.[[CITE_Barseghyan (2015)|p. 207]]</blockquote> Therefore, Barseghyan concludes through this meticulous example that "a mosaic split is possible in those cases where the assessment outcome of at least one contender theory is inconclusive".[[CITE_Barseghyan (2015)|p. 207]][[File:Five_Cases_of_Possible_Mosaic_Split.png|589px|center||]]Mosaic_Split.png|589px|center||]])
Dogmatism No Theory Change theorem (Barseghyan-2015) + (Barseghyan emphasizes that with the [[Dogmatism No Theory Change theorem]] … Barseghyan emphasizes that with the [[Dogmatism No Theory Change theorem]], "we can easily distinguish between genuinely dogmatic communities and communities which only ''appear'' dogmatic".[[CITE_Barseghyan (2015)|p. 166]]. He presents the following example:<blockquote>It was once believed that the medieval scientific community with its Aristotelian mosaic was a dogmatic community, for it (allegedly) held on to its theories at all costs and disregarded all new theories. Yet, upon closer scrutiny it becomes obvious that the Aristotelian-medieval community was anything but dogmatic. Had the medieval community indeed taken a genuinely dogmatic stance, no scientific change would have been possible in their mosaic. But it is a historical fact that the Aristotelian-medieval mosaic was gradually changing especially in the 16th and 17th centuries; towards the end of the 17th century many of its key elements were replaced by new elements. Finally, by circa 1700 the Aristotelian-medieval system of theories was replaced with those Descartes and Newton. This would have been impossible had the theories of the mosaic been actually taken as revealing the final truth. Thus, the Aristotelian-medieval community was not dogmatic. For some real examples of dogmatic communities think of those communities which, having started with some dogmas, fanatically held on to those dogmas and never considered their modification possible.[[CITE_Barseghyan (2015)|p. 166-7]]</blockquote>[[CITE_Barseghyan (2015)|p. 166-7]]</blockquote>)
Synchronism of Method Rejection theorem (Barseghyan-2015) Reason1 + (Barseghyan explains the deduction:[[CITE_Barseghyan (2015)|pp. 177-178]] … Barseghyan explains the deduction:[[CITE_Barseghyan (2015)|pp. 177-178]]<blockquote>By the ''method rejection theorem'', a method is rejected only when other methods incompatible with the method become employed. Thus, we must find out when exactly two methods can be in conflict. In order to find that out, we must refer to the ''third law'' which stipulates that an employed method is a deductive consequence of accepted theories and other methods. Logic tells us that when a new employed method is incompatible with an old method, it is also necessarily incompatible with some of the theories from which the old method follows. Therefore, an old method can be rejected only when some of the theories from which it follows are also rejected.</blockquote>[[File:Synchronism-of-method-rejection.jpg|607px|center||]][[File:Synchronism-of-method-rejection.jpg|607px|center||]])
Necessary Mosaic Split theorem (Barseghyan-2015) + (Barseghyan illustrates the necessary mosai … Barseghyan illustrates the necessary mosaic split theorem with the example of the French and English physics communities circa 1730, at which time the French accepted the Cartesian physics and the English accepted the Newtonian physics.[[CITE_Barseghyan (2015)|p. 203]] These communities would both initially accepted the Aristotelian-medieval physics due to their mutual acceptance of the Aristotelian-medieval mosaic until the start of the eighteenth century[[CITE_Barseghyan (2015)|p. 210]] but clearly had different mosaics within a few decades. According to the second law both the Cartesian and Newtonian physics must have satisfied the methods of the Aristotelian-medieval mosaic in order to have been accepted, but since both shared the same object and posited radically different ontologies they were incompatible with one another and could not both be accepted, per the second law. The necessary result was that the unified Aristotelian-medieval community split and the resulting French and English communities emerged, each with a distinct mosaic.ties emerged, each with a distinct mosaic.)
Split Due to Inconclusiveness theorem (Barseghyan-2015) Reason1 + (Barseghyan notes that, "when a mosaic spli … Barseghyan notes that, "when a mosaic split is a result of the acceptance of two new theories, it may or may not be a result of inconclusiveness".[[CITE_Barseghyan (2015)|p. 209]][[File:Mosaic Split Resulting From Two Mutually Incompatible Theories May Not Be A Result of Inconclusive Theory Assessment.png|578px|center||]]"Thus," he concludes, "if we are to detect any instances of inconclusive theory assessment, we must refer to the case of a mosaic split that takes place with only one new theory becoming accepted by one part of the community with the other part sticking to the old theory. This scenario is covered by the possible mosaic split theorem. We can conclude that when a mosaic split takes place with only one new theory involved, this can only indicate that the outcome of the assessment of that theory was inconclusive."[[CITE_Barseghyan (2015)|pp. 209-210]]This is the deduction of the Split Due to Inconclusiveness Theorem.the Split Due to Inconclusiveness Theorem.)
Subtypes of Epistemic Element + (Barseghyan present the the redrafted ontology)
Theory Rejection theorem (Barseghyan-2015) Reason2 + (Barseghyan presented the initial deduction … Barseghyan presented the initial deduction (2015) of the theorem:[[CITE_Barseghyan (2015)|p. 167]]<blockquote> By the first law for theories, we know that an accepted theory can become rejected only when it is replaced in the mosaic by some other theory. But the law of compatibility doesn’t specify under what conditions this replacement takes place. For that we have to refer to the zeroth law, which states that at any moment of time the elements of the mosaic are mutually compatible. Suppose that a new theory meets the requirements of the time and becomes accepted into the mosaic. Question: what happens to the other theories of the mosaic? While some of the accepted theories may preserve their position in the mosaic, other theories may be rejected. The fate of an old accepted theory depends on whether it is compatible with the newly accepted theory. If it is compatible with the new accepted theory, it remains in the mosaic; the acceptance of the new theory doesn’t affect that old theory in any way. This is normally the case when the new theory comes as an addition to the theories that are already in the mosaic. For instance, when the new theory happens to be the first accepted theory of its domain, i.e. when there is a new field of science that has never had any accepted theories before). Yet, if an old theory is incompatible with the new one, the old theory becomes rejected, for otherwise the mosaic would contain mutually incompatible elements, which is forbidden by the law of compatibility. Therefore, there is only one scenario when a theory can no longer remain in the mosaic, i.e. when other theories which are incompatible with that theory become accepted.</blockquote>[[File:Theory-rejection-theorem.jpg|607px|center||]]le:Theory-rejection-theorem.jpg|607px|center||]])
Asynchronism of Method Employment theorem (Barseghyan-2015) + (Barseghyan presents a historical example s … Barseghyan presents a historical example showing that scientific change is not necessarily a ''synchronous'' process. <blockquote> When it comes to acquiring data about such minute objects as molecules or living cells, the unaided human eye is virtually useless. This proposition yields, among other things, an abstract requirement that, when counting the number of cells, the resulting value is acceptable only if it is obtained with an “aided” eye. This abstract requirement has been implemented in a variety of different ways. First, there is the counting chamber method where the cells are placed in a counting chamber – a microscope slide with a special sink – and the number of cells is counted manually under a microscope. There is also the plating method where the cells are distributed on a plate with a growth medium and each cell gives rise to a single colony. The number of cells is then deduced from the number of colonies. In addition, there is the flow cytometry method where the cells are hit by a laser beam one by one and the number of cells is counted by means of detecting the light reflected by the cells. Finally, there is the spectrophotometry method where the number of cells is obtained by means of measuring the turbidity in a spectrophotometer.[[CITE_Barseghyan (2015)|pp. 151-152]]</blockquote>These are three different implementations of the ''same'' abstract requirement, which were, importantly, all devised and employed at different times.ortantly, all devised and employed at different times.)
Contextual Appraisal theorem (Barseghyan-2015) Reason1 + (Barseghyan presents the following descript … Barseghyan presents the following description of the deduction of the ''contextual appraisal theorem'':<blockquote> By the second law, in actual theory assessment a contender theory is assessed by the method employed at the time ... In addition, it follows from the first law for theories that a theory is assessed only if it attempts to enter into the mosaic; once in the mosaic, the theory no longer needs any further appraisal. In this sense, the accepted theory and the contender theory are never on equal footing, for it is up to the contender theory to show that it deserves to become accepted. In order to replace the accepted theory in the mosaic, the contender theory must be declared superior by the current method; to be “as good as” the accepted theory is not sufficient.</blockquote>[[File:Contextual-appraisal.jpg|607px|center||]]le:Contextual-appraisal.jpg|607px|center||]])
The Zeroth Law (Harder-2015) + (Barseghyan presents the following example … Barseghyan presents the following example of two hypothetical communities to illustrate the notion of ''incompatibility tolerance''.<blockquote>First, imagine a community that believes that all of their accepted theories are absolutely (demonstratively) true. This ''infallibilist'' community also knows that, according to classical logic, p and not-p cannot be both true. Since, according to this community, all accepted theories are strictly true, the only way the community can avoid triviality is by stipulating that any two accepted theories must be mutually consistent. In other words, by the third law, they end up employing the classical logical law of noncontradiction as their criterion of compatibility.Now, imagine another community that accepts the position of ''fallibilism''. This community holds that no theory in empirical science can be demonstratively true and, consequently, all accepted empirical theories are merely quasi-true. But if any accepted empirical theory is only quasi-true, it is possible for two accepted empirical theories to be mutually inconsistent. In other words, this community accepts that two contradictory propositions may both contain grains of truth, i.e. to be quasi-true. [[CITE_Bueno et al (1998)]]. In order to avoid triviality, this community employs a paraconsistent logic, i.e. a logic where a contradiction does not imply everything. This fallibilist community does not necessarily reject classical logic; it merely realizes that the application of classical logic to quasi-true propositions entails triviality. Thus, the community also realizes that the application of classical principle of noncontradiction to empirical science is problematic, for no empirical theory is strictly true. As a result, by the third law, this community employs criteria of compatibility very different from those employed by the infallibilist community.[[CITE_Barseghyan (2015)||pp.154-6]]</blockquote>[[CITE_Barseghyan (2015)||pp.154-6]]</blockquote>)
The Zeroth Law (Harder-2015) + (Barseghyan presents the following example … Barseghyan presents the following example of the possibility for simultaneous use of mutually incompatible theories, even in the same scientific project. "Circa 1600, astronomers could easily use both Ptolemaic and Copernican astronomical theories to calculate the ephemerides of different planets. Similarly, in order to obtain a useful tool for calculating atomic spectra, Bohr mixed some propositions of classical electrodynamics with a number of quantum hypotheses.[[CITE_Smith (1988)]] Finally, when nowadays we build a particle accelerator, we use both classical and quantum physics in our calculations. Thus, sometimes propositions from two or more incompatible theories are mixed in order to obtain something practically useful".[[CITE_Barseghyan (2015)||pp.157-8]][[CITE_Barseghyan (2015)||pp.157-8]])
The Zeroth Law (Harder-2015) + (Barseghyan presents the following example … Barseghyan presents the following example of the indirect incompatibility that can exist between theories and methods:<blockquote>Say there is an accepted theory which says that better nutrition can improve a patient’s condition. We know from the discussion in the previous section that the conjunction of this proposition with the basic requirement to accept only the best available theories yields a requirement that the factor of improved nutrition must be taken into account when testing a drug’s efficacy.Now, envision a method which doesn’t take the factor of better nutrition into account and prescribes that a drug’s efficacy should be tested in a straightforward fashion by giving it only to one group of patients. This method will be incompatible with the requirement that the possible impact of improved nutrition must be taken into account. Therefore, indirectly, it will also be incompatible with a theory from which the requirement follows.[[CITE_Barseghyan (2015)|p.163-4]]</blockquote>arseghyan (2015)|p.163-4]]</blockquote>)
The Zeroth Law (Harder-2015) + (Barseghyan presents the following historic … Barseghyan presents the following historical examples of the simultaneous pursuit of mutually incompatible theories. Of course, we should note that there is "nothing extraordinary" about this: it is the pursuit of different options that makes scientific change possible!<blockquote>Take for instance, Clausius’s attempt to derive Carnot’s theorem, where he drew on two incompatible theories of heat – Carnot’s caloric theory of heat, where heat was considered a fluid, and also Joule’s kinetic theory of heat, where the latter was conceived as a “force” that can be converted into work.[[CITE_Meheus (2003)]]. Thus, the existence of incompatible propositions in the context of pursuit is quite obvious. There is good reason to believe that “reasoning from an inconsistent theory usually plays an important heuristic role”[[CITE_Meheus(2003)||pp.131]] and that "the use of inconsistent representations of the world as heuristic guideposts to consistent theories is an important part of scientific discovery"[[CITE_Smith(1988)||pp.429]].[[CITE_Barseghyan (2015)||pp.158]]</blockquote>(2015)||pp.158]]</blockquote>)
Compatibility Criteria (Barseghyan-2015) + (Barseghyan presents the following hypothet … Barseghyan presents the following hypothetical-historical example when compatibility criteria are introduced in [[Barseghyan (2015)]].<blockquote>It can be argued that our contemporary criteria of compatibility have not always been employed. Consider the case of the reconciliation of the Aristotelian natural philosophy and metaphysics with Catholic theology. As soon as most works of Aristotle and its Muslim commentators were translated into Latin (circa 1200), it became obvious that some propositions of Aristotle’s original system were inconsistent with several dogmas of the then-accepted Catholic theology. Take, for instance, the Aristotelian conceptions of determinism, the eternity of the cosmos, and the mortality of the individual soul. Evidently, these conceptions were in direct conflict with the accepted Catholic doctrines of God’s omnipotence and free will, of creation, and of the immortality of the individual human soul.[[CITE_Lindberg (2007)|p. 228–253]]. Moreover, some of the passages of Scripture, when taken literally, appeared to be in conflict with the propositions of the Aristotelian natural philosophy. In particular, Scripture seemed to imply that the Earth is flat (e.g. Daniel 4:10-11; Mathew 4:8; Revelation 7:1), which was in conflict with the Aristotelian view that the Earth is spherical. It is no surprise, therefore, that many of the propositions of the Aristotelian natural philosophy were condemned on several occasions during the 13th century.[[CITE_Lindberg (2007)|p.226-249]]. To resolve the conflict, Albert the Great, Thomas Aquinas and others modified both the Aristotelian natural philosophy and the biblical descriptions of natural phenomena to make them consistent with each other. On the one hand, they stipulated that the laws of the Aristotelian natural philosophy describe the natural course of events only insofar as they do not limit God’s omnipotence, for God can violate any laws if he so desires. Similarly, they modified Aristotle’s determinism by adding that the future of the cosmos is determined by its present only insofar as it is not affected by free will or divine miracles. Similar modifications were introduced to many other Aristotelian propositions. On the other hand, it was also made clear that biblical descriptions of cosmological and physical phenomena are not to be taken literally, for Scripture often employs a simple language in order to be accessible to common folk. Thus, where possible, literal interpretations of Scripture were supposed to be replaced by interpretations based on the Aristotelian natural philosophy.[[CITE_Grant (2004)|p.220-224, 245]] Importantly, it is only after this reconciliation that the modified Aristotelian-medieval natural philosophy became accepted by the community.[[CITE_Lindberg (2007)|p.250-1]]This and similar examples seem to be suggesting that the compatibility criteria employed by the medieval scientific community were quite different from those employed nowadays. While apparently we are inconsistency-tolerant (at least when dealing with theories in empirical science), the medieval scientific community was inconsistency-intolerant in the sense that they wouldn’t tolerate any open inconsistencies in the mosaic.[[CITE_Barseghyan (2015)|p.160-161]]</blockquote>ghyan (2015)|p.160-161]]</blockquote>)
The Zeroth Law (Harder-2015) + (Barseghyan writes that "the conflict betwe … Barseghyan writes that "the conflict between general relativity and quantum physics is probably the most famous illustration of this phenomenon," that phenomenon being the knowing acceptance of two contradicting theories by a community. "We normally take general relativity as the best description of the world at the level of massive objects and quantum physics as the best available description of the micro-world. But we also know that, from the classical logical perspective, the two theories contradict each other. The inconsistency of their conjunction becomes apparent when they are applied to objects that are both extremely massive and extremely small (i.e. a singularity inside a black hole)".[[CITE_Barseghyan (2015)||pp.154]]Relativity maintains that all signals are local. That is, no signal can travel faster than light. Quantum theory, on the other hand, predicts faster than light influences. This has been known since the 1930's,[[CITE_Einstein, Podolsky, and Rosen (1935)]] yet both quantum theory and relativity remain in the mosaic. Yet, despite the existence of this contradiction, the community accepts both theories as the best available descriptions of their respective domains. descriptions of their respective domains.)

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