Mechanism of Mosaic Split

What happens to a mosaic when two or more similar theories are considered equally acceptable by a scientific community? Under what conditions does a mosaic split occur? What happens to a mosaic when it is transformed into two or more mosaics?

There have been many cases in the history of science when one community, with a single scientific mosaic divided into two or more communities, with different mosaics. These distinct communities would differ regarding at least one of their accepted theories or employed methods. For example, consider the case of the distinct mosaics of French and English natural philosophers in the early part of the 18th century. The former accepted a version of Cartesian theory while the latter accepted a version of Newtonian theory.1p. 203 We can see by various indicators1pp. 113-120 that the dispute between these two communities was not a simple matter of scientific disagreement, like the contemporary dispute between various interpretations of quantum mechanics. In the case of quantum mechanics, even those who advocate alternatives acknowledge that the Copenhagen Interpretation is currently accepted.2 1p. 202 Such contender theories are said to be pursued. What makes the situation in the case of the 18th century French and English communities different is that the two accepted different theories (Cartesian and Newtonian natural philosophies, respectively). In such a case we are justified to regard these as two distinct communities, each bearing its own mosaic. Understanding how and why this sort of situations arise is an important task.

In the scientonomic context, this question was first formulated by Hakob Barseghyan in 2015. 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.

Broader History

Traditionally the topic of why communities of scientists accept different theories has been an enigma for historians and philosophers of science, although the problem has been known about for some time. In the Categories for example, Aristotle grappled with the question of false belief and how false beliefs came to be acquired, and the significance of the question for science and epistemology.3pp. 289-290 Here we are not concerned with judging the truth or falsity of beliefs, but rather with the question of how divergent beliefs arise in epistemic communities.

Pre-Kuhnian philosophers' typical response to divergent community beliefs has largely depended on their views of scientific change more generally. An example of this is the work of Karl Popper. Popper regarded scientific change as being a process of conjectures and refutations, "of boldly proposing theories; of trying our best to show that these are erroneous; and of accepting them tentatively if our critical efforts are unsuccessful".4p. 68 Thus, Popper's approach suggested that any difference in the beliefs of certain communities could be chalked up to differences either in available knowledge (whether a conjecture had been refuted) or a difference in experimental methods (whether the same criteria were being applied in refutations). More generally, differences between philosophers of science during this period in their beliefs about how science changes coloured their views about what factors (or mistakes) present in difference communities were relevant to divergent scientific beliefs. This form of thinking with regards to differences in assessment of scientific theories - if not the exact formulation it takes - was generally held by "positivists" or "logical empiricists" and accepted until the historical turn in the 1960s.5p. 4

It was not until after Thomas Kuhn's publication of his 'Structure of Scientific Revolutions' that the consensus about divergent beliefs was challenged.6 Kuhn's "revolutionary" approach to scientific change radically diverged from his predecessors. On this view science has periods of normal science wherein the prevailing dogmas and core theories (the paradigm) are unquestioned and science proceeds as a process of puzzle solving. This can be interrupted by a crisis in which mounting anomalies cause scientists to question the theoretical foundations of the paradigm.7 Crises may have no impact on normal science or they may result in a revolution; which is what Kuhn calls "the emergence of a new candidate for paradigm and with the ensuing battle over its acceptance".7p. 84 The present question of how divergent beliefs arise within communities fits nicely into this framework - a unified community starts by doing normal science, anomalies emerge within the paradigm, and a revolution occurs which splits the community. Subsequent work by philosophers in the field of scientific change would be coloured by the same kind of analysis of the historical record that shaped Kuhn's view of the subject, including the work done by Imre Lakatos, Paul Feyerabend, and Larry Laudan.5p. 5

One other approach to divergent community beliefs that deserves mention is the approach taken by the social sciences, namely the sociology of scientific knowledge (SSK) advanced principally by David Bloor.8 SSK regards scientific activity as a kind human social activity and as such and area that falls under the purview of the social sciences.9 As such, any divergence in community beliefs is the result of and explainable by sociological factors that contribute to belief formation.

Scientonomic History

This question was proposed by Hakob Barseghyan in 2015 with the publishing of the Laws of Scientific Change.1

Acceptance Record

Here is the complete acceptance record of this question (it includes all the instances when the question was accepted as a legitimate topic for discussion by a community):

Community	Accepted From	Acceptance Indicators	Still Accepted	Accepted Until	Rejection Indicators
Scientonomy	1 January 2016	This is when the community accepted its first answers to this question, the Necessary Mosaic Split theorem (Barseghyan-2015) and the Possible Mosaic Split theorem (Barseghyan-2015), which indicates that the question is itself considered legitimate.	Yes

All Theories

The following theories have attempted to answer this question:

Theory	Formulation	Formulated In
Necessary Mosaic Split theorem (Barseghyan-2015)	When two mutually incompatible theories satisfy the requirements of the current method, the mosaic necessarily splits in two.	2015
Possible Mosaic Split theorem (Barseghyan-2015)	When a theory assessment outcome is inconclusive, a mosaic split is possible.	2015
Split Due to Inconclusiveness theorem (Barseghyan-2015)	When a mosaic split is a result of the acceptance of only one theory, it can only be a result of inconclusive theory assessment.	2015

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Accepted Theories

The following theories have been accepted as answers to this question:

Community	Theory	Accepted From	Accepted Until
Scientonomy	Necessary Mosaic Split theorem (Barseghyan-2015)	1 January 2016
Scientonomy	Possible Mosaic Split theorem (Barseghyan-2015)	1 January 2016
Scientonomy	Split Due to Inconclusiveness theorem (Barseghyan-2015)	1 January 2016

Suggested Modifications

According to our records, there have been no suggested modifications on this topic.

Current View

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).

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.1pp. 204-207

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.1p. 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 century1p. 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.

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.1pp. 208-213

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.

Related Topics

This question is a subquestion of Mechanism of Scientific Change. It has the following sub-topic(s):

• Indicators of Inconclusiveness
• Role of Sociocultural Factors in Mosaic Split

This topic is also related to the following topic(s):

• Mechanism of Theory Acceptance