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<blockquote>Take for instance, Clausius’s attempt to derive Carnot’s theorem, where he drew on two incompatible theories of heat – Carnot’s caloric theory of heat, where heat was considered a fluid, and also Joule’s kinetic theory of heat, where the latter was conceived as a “force” that can be converted into work.[[CiteRef::Meheus (2003)]]. Thus, the existence of incompatible propositions in the context of pursuit is quite obvious. There is good reason to believe that “reasoning from an inconsistent theory usually plays an important heuristic role”[[CiteRef::Meheus(2003)||pp.131]] and that "the use of inconsistent representations of the world as heuristic guideposts to consistent theories is an important part of scientific discovery"[[CiteRef::Smith(1988)||pp.429]].[[CiteRef::Barseghyan (2015)||pp.158]]</blockquote>
|Example Type=Historical
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{{Theory Example
|Title=Inconsistency Tolerance - "The Same Object"
|Description=We find two hypothetical scenarios for ''inconsistency tolerance'' in [[Barseghyan (2015)]]. Here is the first:
 
<blockquote> We seem to be prepared to accept two mutually inconsistent propositions into the mosaic provided that they do not have the same object. More specifically, two propositions seem to be considered compatible by the contemporary community when, by and large, they explain different phenomena, i.e. when they have sufficiently different fragments of reality as their respective objects. When determining the compatibility or incompatibility of any two theories, the community seems to be concerned with whether the theories can be limited to their specific domains. Suppose ''Theory 1'' provides descriptions for phenomena ''A'', ''B'', and ''C'', while ''Theory 2'' provides descriptions for phenomena ''C'', ''D'', and ''E''. Suppose also that the descriptions of phenomenon ''C'' provided by the two theories are inconsistent with each other ... Although the two theories are logically inconsistent, normally this is not an obstacle for the contemporary scientific community. Once the contradiction between the two theories becomes apparent, the community seem to be limiting the applicability of at least one of the two theories by saying that its laws do not apply to phenomenon ''C''. While limiting the domains of applicability of conflicting theories, we may still believe that the laws of both theories should ideally be applicable to phenomenon ''C''. Yet, we understand that currently their laws are not applicable to phenomenon ''C''. In other words, we simply concede that our current knowledge of phenomenon ''C'' is deficient.[[CiteRef::Barseghyan (2015)||pp.158-9]]</blockquote>
 
The most readily apparent example of this phenomenon is the oft-cited conflict between general relativity and quantum physics: "While we admit that ideally singularities within black holes must be subject to the laws of both theories, we also realize that currently the existing theories cannot be consistently applied to these objects, for combining the two theories is not a trivial task. Consequently, we admit that there are many aspects of the behaviour of these objects that we are yet to comprehend. Thus, it is safe to say that nowadays we accept the two theories only with a special “patch” that temporarily limits their applicability".[[CiteRef::Barseghyan (2015)||pp.159]] To Barseghyan, then, "it appears as though the reason why the community considers the two theories compatible despite their mutual inconsistency is that these theories are the best available descriptions of two considerably different domains".[[CiteRef::Barseghyan (2015)||pp.159]]
|Example Type=Hybrid
}}
{{Theory Example
|Title=Inconsistency Tolerance 2
|Description="In the second scenario, we are normally willing to tolerate inconsistencies between an accepted general theory and a singular proposition describing some anomaly. In this scenario, the general proposition and the singular proposition describe the same phenomenon; the latter describes a counterexample for the former. However, the community is tolerant towards this inconsistency for it is understood that anomalies are always possible. No doubt, we are never pleased to find out that a certain accepted empirical theory faces anomalies, but we also understand that no empirical theory is infallible and, therefore, the mere presence of anomalies is no reason for rejecting our accepted empirical theories. We appreciate that both the general theory in question and the singular factual proposition may contain grains of truth. In this sense, we are anomaly-tolerant."
|Example Type=Hybrid
}}
{{Acceptance Record

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