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Possible Mosaic Split theorem (Barseghyan-2015) (view source)
Revision as of 20:29, 6 November 2023
, 20:29, 6 November 2023no edit summary
<blockquote> Consider first the case with one contender theory. Suppose there is a scientific mosaic with its theories and methods and there is also a contender theory which becomes assessed by the currently employed method. If the assessment outcome is conclusive “accept”, the theory necessarily becomes accepted. If the outcome is conclusive “not accept”, the theory remains unaccepted. Both of these cases are quite straightforward. But what will happen if the outcome turns out to be inconclusive, i.e. if the assessment by the current method doesn’t provide a definitive prescription? When the assessment outcome is inconclusive, there are three possible courses of events. First, the new theory can remain unaccepted; in that case the mosaic will maintain its current state. Second, the new theory can also become accepted by the whole community; in that case a regular theory change will take place and the new theory will replace the old one. None of these two scenarios is particularly interesting here. However, there is also the third possible course of events. When the outcome of theory assessment is inconclusive, members of the community are free to choose whichever of the two scenarios – they can accept the theory, but they can equally choose to leave it unaccepted. Naturally, there are no guarantees that all of them will necessarily choose the same course of action. It is quite conceivable that some will opt for accepting the new theory, whereas the rest will prefer to keep the old theory. In other words, when the assessment of a contender theory yields an inconclusive outcome, the mosaic may split in two.[[CiteRef::Barseghyan (2015)|pp. 204-205]]</blockquote>
{{PrintDiagramFile|diagram file=Assessment_outcomes_from_one_contender_resulting_in_mosaic_splitAssessment_Outcomes_from_One_Contender_Theory.jpgpng}}
|Example Type=Hypothetical
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{{Theory Example
|Title=Drug Trial Methods Possible Mosaic Split: Two Contender Theories|Description=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".[[CiteRef::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.[[CiteRef::Barseghyan (2015)|p. 205]]</blockquote> [2 CONTENDER THEORIES IMAGE] <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]] [[CiteRef::Barseghyan (2015)|p. 205]]</blockquote> [Theory Assessment Outcomes and Actual Courses of Events IMAGE] <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: 'Accept'/'inconclusive' (2 combinations): What can happen when the assessment of one theory yields a conclusive “accept”, while the assessment outcome of the other theory is inconclusive? 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]] may take place). 'Not accept'/'inconclusive' (2 combinations): What can happen when the assessment of one theory yields a conclusive “not accept”, while the assessment outcome of the other theory is inconclusive? 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 split is not a consequence of the simultaneous acceptance of two mutually incompatible theories. “Inconclusive”/“inconclusive” (1 combination): Finally, what can happen when the assessment outcomes of both theories are inconclusive? 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 will take place. This meticulous discussion of possible scenarios leads to an important conclusion: a mosaic split is possible in those cases where the assessment outcome of at least one contender theory is inconclusive:</blockquote>|Example Type=Hypothetical}}{{Theory Example|Title=Possible Mosaic Split: Drug Trials
|Description=Suppose we have a method for assessing theories about the efficacy of new pharmaceuticals that says "accept that the pharmaceutical is effective only if a clinically significant result is obtained in a sufficient number of randomized controlled trials." The wording of the method is such that it requires a significant degree of judgement on the part of the community - what constitutes 'clinical significance' and a 'sufficient number' of trials will vary from person to person and by context. This introduces the possibility of mosaic split when it is unclear if two contender theories satisfy this requirement.
