Mechanism of Error Rejection

When epistemic agent discover that a theory was accepted erroneously, they often reject the theory; the theory rejection theorem suggests that those propositions are replaced by something. What are they replaced by?

Errors are ubiquitous in scientific practice: scientists often come to realize that the acceptance of a certain theory was erroneous. This applies to both general theories and singular propositions describing the results of experiments and observations. The theory rejection theorem suggests that when these erroneously accepted theories become rejected they are still replaced by some other theory or theories. The question is: what are these erroneously accepted theories replaced by? For example, astronomical databases trivially reject inaccurate data points from their databases. Are these data points replaced by anything? More generally, how are instances of scientific error handled in science?

In the scientonomic context, this question was first formulated by Maxim Mirkin and Sinan Karamehmetoglu in 2018. 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:

• The handling of instances of scientific error is consistent with the theory rejection theorem; it involves a replacement of an erroneously accepted theory either with a first- or second-order proposition.
• A theory becomes rejected only when other theories that are incompatible with the theory become accepted.

Scientonomic History

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	8 March 2018	It was asked in the seminar and upon uniform agreement we accepted it as an open question.	Yes

All Theories

The following theories have attempted to answer this question:

Theory	Formulation	Formulated In
Error Rejection by Replacement (Machado-Marques-Patton-2021)	The handling of instances of scientific error is consistent with the theory rejection theorem; it involves a replacement of an erroneously accepted theory either with a first- or second-order proposition.	2021

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Accepted Theories

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

Community	Theory	Accepted From	Accepted Until
Scientonomy	Error Rejection by Replacement (Machado-Marques-Patton-2021)	8 October 2021

Suggested Modifications

Here is a list of modifications concerning this topic:

Modification	Community	Date Suggested	Summary	Verdict	Verdict Rationale	Date Assessed
Sciento-2021-0004	Scientonomy	1 August 2021	Accept that the handling of scientific error, as defined by Machado-Marques and Patton, is compatible with the theory rejection theorem.	Accepted	The commentators agreed that "the historical cases of scientific error identified and treated by Machado-Marques and Patton effectively demonstrate the compatibility of instances of scientific error with the theory rejection theorem".c1 c2 c3 It was agreed that the rejection of a theory that was accepted erroneously can be "a result of the acceptance of other theories incompatible with it - be these some first- or second-order theories".c4 c5 c6 One commentator expressed a common opinion when saying that "the authors are able to put to rest concerns about the handling of scientific error potentially contravening the theory rejection theorem".c7	8 October 2021

Current View

In Scientonomy, the accepted answers to the question are Error Rejection by Replacement (Machado-Marques-Patton-2021) and Theory Rejection theorem (Barseghyan-2015).

Error Rejection by Replacement (Machado-Marques-Patton-2021) states: "The handling of instances of scientific error is consistent with the theory rejection theorem; it involves a replacement of an erroneously accepted theory either with a first- or second-order proposition."

The analysis of several several instances of scientific error by Machado-Marques and Patton suggest that the handling of these instances by scientists is in accord with the theory rejection theorem. Handling of error involves, according to this view, not only a rejection of some of the propositions that are considered to be accepted erroneously but also an acceptance of some new propositions. In some cases, an erroneously accepted first-order proposition is replaced by another first-order proposition incompatible with it. In other cases, an erroneously accepted first-order proposition is replaced by a second-order proposition stating the lack of sufficient reason for accepting the first-order proposition. According to this view, the handling of erroneously accepted theories involves their replacement with other theories; the handling of scientific error is therefore in full accord with the theory rejection theorem.

Mechanism of Theory Rejection

Theory Rejection theorem (Barseghyan-2015) states: "A theory becomes rejected only when other theories that are incompatible with the theory become accepted."

According to the theory rejection theorem, a theory becomes rejected only when other theories that are incompatible with the theory become accepted.

Implicit in the theorem is the idea that each theory is assessed on an "individual basis by its compatibility with the propositions of the newly accepted theory".1p. 168 If it turns out that a previously accepted theory is compatible with the newly accepted theory, it remain in the agent's mosaic.

Barseghyan notes that, although we normally expect a theory to be replaced by another theory in the same "field" of inquiry, this is not necessarily the case. For example, he writes, "HSC knows several cases where an accepted theory became rejected simply because it wasn’t compatible with new accepted theories of some other fields".1p. 171

Barseghyan summarizes the theory rejection theorem as such:

In short, when the axioms of a theory are replaced by another theory, some of the theorems may nevertheless manage to stay in the mosaic, provided that they are compatible with the newly accepted theory. This is essentially what the theory rejection theorem tells us. Thus, if someday our currently accepted general relativity gets replaced by some new theory, the theories that followed from general relativity, such as the theory of black holes, may nevertheless manage to remain in the mosaic. 1p. 171

Related Topics

This question is a subquestion of Mechanism of Theory Rejection.