Indicators of Inconclusiveness
What indicators enable us to identify a historical case of inconclusive theory assessment?
It is possible for a community to accept two theories which are mutually incompatible and not undergo a mosaic split. This question aims to identify which indicators can be used to identify a historical case in which a theory was assessed to be inconclusive, yet accepted nonetheless.
In the scientonomic context, this question was first formulated by Nicholas Overgaard and Paul Patton in 2016. The question is currently accepted as a legitimate topic for discussion by Scientonomy community.
In Scientonomy, the accepted answers to the question can be summarized as follows:
- When two mutually incompatible theories satisfy the requirements of the current method, the mosaic necessarily splits in two. When a theory assessment outcome is inconclusive, a mosaic split is possible. When a mosaic split is a result of the acceptance of only one theory, it can only be a result of inconclusive theory assessment.
|Community||Accepted From||Acceptance Indicators||Still Accepted||Accepted Until||Rejection Indicators|
|Scientonomy||1 April 2016||It was acknowledged as an open question by the Scientonomy Seminar 2016.||Yes|
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In Scientonomy, the accepted answers to the question are Necessary Mosaic Split theorem (Barseghyan-2015), Possible Mosaic Split theorem (Barseghyan-2015) and Split Due to Inconclusiveness theorem (Barseghyan-2015).
Mechanism of Mosaic Split
Necessary Mosaic Split theorem (Barseghyan-2015) states: "When two mutually incompatible theories satisfy the requirements of the current method, the mosaic necessarily splits in two."
Necessary mosaic split is a form of mosaic split that must happen if it is ever the case that two incompatible theories both become accepted under the employed method of the time. Since the theories are incompatible, under the zeroth law, they cannot be accepted into the same mosaic, and a mosaic split must then occur, as a matter of logical necessity.1
As shown in the figure above, the necessary mosaic split theorem follows as a deductive consequence of the second law and the zeroth law. Per the zeroth law, two incompatible elements cannot simultaneously remain in a mosaic, and per the second law any theory that satisfies the method of the time (and the assessment of the theory by the method is not inconclusive) is accepted into the mosaic. This creates the apparently contradictory situation where either of the two theories A) must be accepted because it satisfies the employed method and B) must not be accepted because it in not compatible with another accepted theory.
The necessary mosaic split theorem is thus required to escape the contradiction entailed by the acceptance of two or more incompatible theories. In a situation where this sort of contradiction obtains the mosaic is split and distinct communities are formed each of which bears its own mosaic, and each mosaic will include exactly one of the theories being assessed. By the third law, each mosaic will also have a distinct method that precludes the acceptance of the other contender theory.
Two examples are helpful for demonstrating mosaic split, one formal example and one historical example. Suppose we have some community C' with mosaic M' and that this community assesses two theories, T1 and T2, both of which satisfy M'. Let us further suppose that T1 and T2 both describe the same object and are incompatible with one another. According to the second law both T1 and T2 will be accepted because they both satisfy M', but both cannot simultaneously be accepted by C' due to the zeroth law. The necessary mosaic split theorem says that the result will be a new community C1 which accepts T1 and M1, which precludes their accepting T2. Simultaneously a new community C2 will emerge which accepts T2 and the resulting theory M2, which precludes their accepting T1.
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.1 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 century1 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.
Possible Mosaic Split theorem (Barseghyan-2015) states: "When a theory assessment outcome is inconclusive, a mosaic split is possible."
Possible mosaic split is a form of mosaic split that can happen if it is ever the case that theory assessment reaches an inconclusive result. In this case, a mosaic split can, but need not necessarily, result.1
As pictured, the possible mosaic split theorem follows as a deductive consequence of the second and zeroth laws, given a situation a situation where the assessment of two theories obtains an inconclusive result. This will happen when it is unclear whether or not a theory satisfies the employed method of the community. We can easily imagine such a scenario: 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.
Carrying on the above example, suppose two drugs are being tested for some condition C: drugs A and B. We'll call T1 the theory that A is more effective than B at treating condition C and T2 the theory that B is more effective than A at treating condition C. These two theories are not compatible, and so cannot both be elements of the mosaic according to the zeroth law. Suppose further that both are assessed by the method of the time, meaning that both are subject to double blind trials. In these trials drug A is clearly superior to drug B at inducing clinical remission, but drug B has fewer side effects and is still more effective than a placebo and has had more studies conducted. Even if we accept T1 we may have reason to suspect that T2 better satisfies the method. We can interpret this in two ways: by supposing that our assessment shows that we should accept T1 and that our assessment is inconclusive about T2 or by taking both assessments to be inconclusive. In the first case it is permissible according to the second law to accept T1 and to either accept or reject T2, and in the second case both may be accepted or rejected.
Because any time an assessment outcome is 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.
Split Due to Inconclusiveness theorem (Barseghyan-2015) states: "When a mosaic split is a result of the acceptance of only one theory, it can only be a result of inconclusive theory assessment."
Split due to inconclusiveness can occur when two mutually incompatible theories are accepted simultaneously by the same community.
This question is a subquestion of Mechanism of Mosaic Split.