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Possible Mosaic Split theorem (Barseghyan-2015) (view source)
Revision as of 21:45, 10 November 2023
, 21:45, 10 November 2023no edit summary
|Formulated Year=2015
|Formulation File=Possible-mosaic-split-box-only.jpg
|Description=Possible [[Scientific Mosaic|mosaic]] split is a form of mosaic split that can happen if it is ever the case that [[Theory|theory]] assessment reaches an inconclusive result. In this case, a mosaic split can, but need not necessarily, result.[[CiteRef::Barseghyan (2015)|pp. 208-213]]That is, "the sufficient condition for this second variety of mosaic split is an element of inconclusiveness in the assessment outcome of at least one of the contender theories".[[CiteRef::Barseghyan (2015)|p. 208]] Barseghyan notes that, "if there have been any actual cases of inconclusive theory assessment, they can be detected only indirectly".[[CiteRef::Barseghyan (2015)|p. 208]] Therefore: <blockquote>One way of detecting an inconclusive theory assessment is through studying a particular instance of mosaic split. Unlike inconclusiveness, mosaic split is something that is readily detectable. As long as the historical record of a time period is available, it is normally possible to tell whether there was one united mosaic or whether there were several different mosaics. For instance, we are quite confident that in the 17th and 18th centuries there were many differences between the British and French mosaics.[[CiteRef::Barseghyan (2015)|p. 208]] </blockquote> Thus, the historical examples of mosaic split below also serve as points of detection for historical instances of inconclusive theory assessment.
|Resource=Barseghyan (2015)
|Prehistory=Like the broader topic of the [[Mechanism of Mosaic Split]] the matter of possible mosaic split has classically been regarded as a case of divergent belief systems in communities, with the caveat that the divergence in the community is contingent, not necessary. As such pre-scientonomic approaches are those that are considerate of situations in which community beliefs ''may'' diverge but will not do so necessarily.
Because any time an assessment outcome is [[Outcome Inconclusive|inconclusive]] we may either accept or reject the theory being assessed we always face the possibility that one subsection of the community will reject the theory and another subsection will accept it. In these cases the two communities now bear distinct mosaics and a mosaic split has occurred. However it is important to note that the ambiguity inherent in inconclusive assessments means that it is never entailed that there will be competing subsections of the community. A community may, in the face of an inconclusive assessment, collectively agree to accept or reject the theory being assessed. Thus, in cases with an inconclusive assessment mosaic split is possible but never necessarily entailed by the circumstances.
|Example Type=Hybrid
}}
{{Theory Example
|Title=Possible Mosaic Split: Acceptance of the Cartesian natural philosophy in Cambridge circa 1680.
|Description=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.[[CiteRef::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:
{{PrintDiagramFile|diagram file=Draft_Timeline_1680_Mosaics.png}}
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.[[CiteRef::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''.[[CiteRef::Barseghyan (2015)|pp. 212-213]]</blockquote>
|Example Type=Historical
}}
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