Mechanism of Compatibility

Under what conditions can two elements coexist in the same mosaic?

While some theories and methods can coexist in the same mosaic, others seem to be incompatible. So, the task is to understand when two theories (or two methods) can and when they cannot coexist in the same mosaic. For instance, the theories general relativity and quantum physics as it relates to how they explain singularities in black holes are inconsistent, however they remain in the mosaic. On the other hand, inconsistencies between the Aristotelian worldview and Catholic theology means both required modification before they were compatible with each other.1pp. 159-161 What conditions allow for the coexistence of elements, and what conditions require modification or rejection to take place?

In the scientonomic context, this question was first formulated by Hakob Barseghyan and Rory Harder in 2015. The question is currently accepted as a legitimate topic for discussion by Scientonomy community.

In Scientonomy, the accepted answer to the question is:

• If a pair of elements satisfies the compatibility criteria employed at the time, it becomes compatible within the mosaic; if it does not, it is deemed incompatible; and if assessment is inconclusive, the pair can become compatible, incompatible, or its status may be unknown.

Broader History

There are several historical episodes that appear to explicate the mechanism of theory and method incompatibility. For instance, Aristotelian physics appears to contradict some aspects of Catholic scripture in cases, one of which was regarding the status of God’s power. Scripture asserted God as an omnipotent entity, however Aristotelian physics appeared to limit some physical phenomena such as the existence of empty space. The question arose: could God create empty space? In this case, these two elements of the mosaic were inconsistent with eachother and considered incompatible as condemnation came from the church to force natural philosophers to accept the concept of empty space in the name of God’s omnipotence.2 The Aristotelian theory of empty space was removed from the mosaic and replaced with the absolute theological declaration. This seems to show that when incompatibility is discovered, certain theories can push out or force change in others.

The theories of general relativity and quantum physics generally deal with separate aspects of physics, however on the matter of singularities in black holes, they differ.1pp. 159-160 However, this inconsistency is tolerated, and the modern scientific community appears to accept both theories as the best description of what happens in the singularity of a black hole. Potentially, this situation shows that when two theories deal with different domains that are each considered the best possible description for their respective domains, inconsistency in singular propositions is tolerated differ.1p. 160

Another example of incompatibility appears to be between Newtonian physics and Descartes’ physical theories. This appears to be a historical case of two inconsistent theories that both potentially satisfied the vague methods of the time, and illuminates a case of incompatibility that leads to a separation within the scientific community differ.1pp. 212-213

Scientonomic History

The first scientonomic account of compatibility, the zeroth law, was proposed by Rory Harder in 2013. It was meant to address the issues with an earlier formulation by Hakob Barseghyan which rendered inconsistency-toleration in science impossible. By divorcing the notion of compatibility from that of consistency, Harder's formulation made it possible for agents to simultaneously accept mutually inconsistent theories.1p. 153

In 2018, Patrick Fraser and Ameer Sarwar argued that Harder's formulation of the zeroth law is a tautology and that its content can be recovered from the definition of compatibility. They formulated a corollary which preserves this content. They also argued that a new diachronic law of compatibility is needed. The law they proposed spelled out under what conditions a pair of elements became to be considered compatible.3 The law became accepted in 2021.

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 answer to the question, The Zeroth Law (Harder-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
The Zeroth Law (Harder-2015)	At any moment of time, the elements of the scientific mosaic are compatible with each other.	2015
The Law of Compatibility (Fraser-Sarwar-2018)	If a pair of elements satisfies the compatibility criteria employed at the time, it becomes compatible within the mosaic; if it does not, it is deemed incompatible; and if assessment is inconclusive, the pair can become compatible, incompatible, or its status may be unknown.	2018

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Accepted Theories

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

Community	Theory	Accepted From	Accepted Until
Scientonomy	The Zeroth Law (Harder-2015)	1 January 2016	3 June 2020
Scientonomy	The Law of Compatibility (Fraser-Sarwar-2018)	9 October 2021

Suggested Modifications

Here is a list of modifications concerning this topic:

Modification	Community	Date Suggested	Summary	Verdict	Verdict Rationale	Date Assessed
Sciento-2018-0018	Scientonomy	28 December 2018	Accept the new dynamic law of compatibility which specifies how exactly two elements become to be considered compatible or incompatible within a mosaic.	Accepted	It was agreed that the "modification provides a great addition to the current body of scientonomic knowledge"c1 as the law offers "a dynamic account of compatibility"c2 and "allows for a diachronic study of compatibility".c3 The law was praised for its non-tautological nature, since it "forbids a number of logically conceivable scenarios".c4 While finding the law acceptable, one of the commentators raised an important question for future scientonomic research: do we even need a separate law of compatibility? Specifically they asked: "Is assessment for compatibility with other elements of the mosaic really conceptually distinct from the process of assessment for theory acceptance, which is already covered by other scientonomic laws?"c5 On this view, "the issue of the conceptual separability of theory compatibility and theory acceptance, and thus the need for two parallel laws, remains an open question that warrants further investigation".c6	9 October 2021

Current View

In Scientonomy, the accepted answer to the question is The Law of Compatibility (Fraser-Sarwar-2018).

The Law of Compatibility (Fraser-Sarwar-2018) states: "If a pair of elements satisfies the compatibility criteria employed at the time, it becomes compatible within the mosaic; if it does not, it is deemed incompatible; and if assessment is inconclusive, the pair can become compatible, incompatible, or its status may be unknown."

The law of compatibility links the compatibility criteria with various assessment outcomes. If compatibility is defined as the ability of a pair of elements to co-exist in the same mosaic, then the assessment for compatibility is essentially the process by which the epistemic agent decides whether any given pair of elements (i.e. theories, questions, methods) can be simultaneously part of their mosaic. Such an assessment can yield three possible outcomes - satisfied, not satisfied, and inconclusive.3p. 73 Accordingly, the law of compatibility states that if a pair of elements does satisfy the compatibility criteria of the time, then it is deemed as compatible. If, however, an element is taken to be incompatible with the other one, then the pair is deemed as incompatible. Finally, the assessment of compatibility may be inconclusive. In this case, the pair may be deemed compatible, incompatible, or its status may remain unknown. The diagram below summarizes the relation between assessment outcomes and their effects:

Related Topics

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

• Compatibility of Mosaic Elements
• Theory vs. Method Compatibility