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We should be careful not to confuse these concepts In Barseghyan's presentation of ''compatibility'' and ''consistency''. Barseghyan details the distinction between these two conceptsZeroth Law, he explains it thus:<blockquote<"the formal definition of inconsistency is that a set is inconsistent just in case it entails some sentence and its negation, i.e. ''p'' and ''not-p''. The classical logical principle of noncontradiction stipulates that ''p'' and ''not-p'' cannot be true ... In contrast, the notion of compatibility implicit in the zeroth law is much more flexible, for its actual content depends on the criteria of compatibility employed at a given timehas three closely linked aspects. As a resultFirst, the actually employed criteria of compatibility can differ from mosaic to mosaic. While in some mosaics compatibility may be understood in the classical logical sense of consistency, in other mosaics it may be more flexible ... in principle, there can exist such mosaics, where states that two theories that are inconsistent in the classical logical sense are nevertheless mutually compatible and can be simultaneously accepted within in the same mosaiccannot be incompatible with one another. In It also states that at any moment two simultaneously employed methods cannot be incompatible with each other words. Finally, it states that, at any moment of time, a mosaic there can be ''inconsistency-intolerant'' or ''inconsistency-tolerant'' depending on the criteria of compatibility no incompatibility between accepted theories and employed by the scientific community of the timemethods".[[CiteRef::Barseghyan (2015)||pp.154157]]Importantly, the Zeroth Law extends only to theories and methods that are ''accepted'', not merely ''used'' or ''pursued''.</blockquote>
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The Zeroth Law (Harder-2015) (view source)
Revision as of 20:16, 10 February 2023
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|Description=Harder's reformulation of the Zeroth Law states that “at any moment of time, the elements of the mosaic are compatible with each other”. ''Compatibility'' is a broader concept than strict logical ''consistency'', and is determined by the compatibility criteria of each mosaic.
What does it mean that the ''law of compatibility'' also extends to employed ''methods''? This matter receives significant attention in [[Barseghyan (2015)]]. As per Barseghyan, if two disciplines employ different requirements, their methods are not incompatible as they apply to two different disciplines, they merely "appear conflicting".[[CiteRef::Barseghyan (2015)||pp.162]] Even considering methods in the same discipline, two methods that "appear conflicting" are not necessarily incompatible. For instance, these methods may either be complementary ("connected by a logical AND"), providing multiple requirements for new theories, or provide ''alternative'' requirements for new theories ("connected by a logical OR").[[CiteRef::Barseghyan (2015)||pp.162-3]] Thus, Barseghyan asserts that methods are only incompatible "when they state ''exhaustive'' conditions for the acceptance of a theory. Say the first method stipulates that a theory is acceptable if and only if it provides confirmed novel predictions, while the second method requires that in order to become accepted a theory must necessarily solve more problems than the accepted theory. In this case, the two methods are incompatible and, by the ''law of compatibility'', they cannot be simultaneously employed".[[CiteRef::Barseghyan (2015)||pp.163]] Barseghyan also proposes that the only possible conflict between ''methods'' and ''theories'' is an indirect one, given that theories are descriptive propositions, whereas methods are prescriptive and normative. Thus, the method would have to be incompatible with those methods which follow from the theory for the method and theory to be incompatible. We should be careful not to confuse the concepts of ''compatibility'' and ''consistency''. Barseghyan details the distinction between these two concepts:<blockquote>"the formal definition of inconsistency is that a set is inconsistent just in case it entails some sentence and its negation, i.e. ''p'' and ''not-p''. The classical logical principle of noncontradiction stipulates that ''p'' and ''not-p'' cannot be true ... In contrast, the notion of compatibility implicit in the zeroth law is much more flexible, for its actual content depends on the criteria of compatibility employed at a given time. As a result, the actually employed criteria of compatibility can differ from mosaic to mosaic. While in some mosaics compatibility may be understood in the classical logical sense of consistency, in other mosaics it may be more flexible ... in principle, there can exist such mosaics, where two theories that are inconsistent in the classical logical sense are nevertheless mutually compatible and can be simultaneously accepted within the same mosaic. In other words, a mosaic can be ''inconsistency-intolerant'' or ''inconsistency-tolerant'' depending on the criteria of compatibility employed by the scientific community of the time"[[CiteRef::Barseghyan (2015)||pp.154]].</blockquote> The abstract criteria of compatibility have many possible implementations with in a community. These criteria are employed [[method|methods]], and therefore can change over time according to [[The Third Law (Barseghyan-2015)|the law of method employment]]. They dictate the standard that other theories and methods must meet so as to remain compatible with each other. The compatibility criterion of the contemporary scientific mosaic is believed to be along the lines of a non-explosive paraconsistent logic.[[CiteRef::Priest, Tanaka, and Weber (2015)]] This logic allows known contradictions, like the contradiction between signal locality in special relativity and signal non-locality in quantum mechanics to coexist without implying triviality. The compatibility criterion can be understood as a consequence of fallibilism about science. Even a community's best theories are merely truth-like, not strictly true. Our current compatibility criteria appears to be formulated as such. It is very likely that our current compatibility criteria has not always been the one employed. Discovery of the kind of compatibility criteria contained in the current and historical mosaics is an important empirical task for observational scientonomy.
The zeroth law is thus named to emphasize that it applies to the mosaic while viewed from a ''static'' perspective. The other three laws take a ''dynamic'' perspective.[[CiteRef::Barseghyan (2015)||pp.153]].
|Resource=Barseghyan (2015)
|Prehistory=The idea that our beliefs should not contradict each other is one of the oldest in philosophy. It can be traced, at least, to the time of Aristotle (384-322 BCE).[[CiteRef::Carnielli and Marcos (2001)]] In classical logic, it derives from the '''principle of explosion''', which states that a contradiction entails every other sentence. Any system of beliefs that contains a contradiction, since it compels belief in anything and everything, is therefore known as a '''trivialism'''. This deceptively simple premise is implicit in most philosophies of science, and in philosophy overall. For this reason it is rarely stated outright within a philosophical or scientific framework. However, the use of contradictions to reject particular theories is important in frameworks as diverse as Isaac Newton’s Four Rules of Scientific Reasoning (non-contradiction is the fourth)[[CiteRef::Newton (1687)]][[CiteRef::Smith (2009)]] and [[Karl Popper]]’s 'Logic of Scientific Discovery'.[[CiteRef::Popper (1959)]]
"The possibly changeable character of compatibility criteria and the mechanism of their employment has not been properly understood prior to the reformulation of the zeroth law".[[CiteRef::Barseghyan (2015)||pp.157]] For example, Otto Neurath's conception of scientific change relied on mutual agreement,[[CiteRef::Neurath (1973)||pp. 199]] to the extent that "mutual agreement of the elements is basically the only guiding principle of scientific change".[[CiteRef::Barseghyan (2015)||pp.157]] Quine's view is similar,[[CiteRef::Quine and Ullian (1978)]], wherein "we adjust and replace the elements of the so-called web of belief by maintaining the mutual agreement between the elements".[[CiteRef::Barseghyan (2015)||pp.157]] Barseghyan emphasizes that, while "similar views are implicit in a vast majority of conceptions of scientific change," "it has been often tacitly assumed that compatibility of any two elements is decided by the law of noncontradiction of classical logic".[[CiteRef::Barseghyan (2015)||pp.157]] However, by the Zeroth Law, noncontradiction is just one of many possible compatibility criteria a mosaic might have.
|History=''The zeroth law'' was introduced into the [[The Theory of Scientific Change|the theory of scientific change]] (TSC) as ''the law of consistency''. In its initial 2012 formulation the zeroth law stated that “at any moment of time, the elements of a scientific mosaic are consistent with each other”. In 2013 Rory Harder discovered that this formulation could not be correct. In his paper “Scientific Mosaics and the Law of Consistency,”[[CiteRef::Harder (2013)]] he raised two arguments against the Law of Consistency, one logical and one historical.
In 2018, [[Patrick Fraser]] and [[Ameer Sarwar]] suggested that the law has no empirical content as it fails to say much beyond what is implicit in the notion of [[Compatibility|''compatibility'']].[[CiteRef::Fraser and Sarwar (2018)]] Consequently, they suggested that the zeroth law is to be replaced by a definition of ''compatibility'' as well as a [[Compatibility Corollary (Fraser-Sarwar-2018)|compatibility corollary]]. This [[Modification:Sciento-2018-0015|modification]] became accepted in 2020 and the zeroth law became rejected.
}}
{{YouTube Video
Relativity maintains that all signals are local. That is, no signal can travel faster than light. Quantum theory, on the other hand, predicts faster than light influences. This has been known since the 1930's,[[CiteRef::Einstein, Podolsky, and Rosen (1935)]] yet both quantum theory and relativity remain in the mosaic. Yet, despite the existence of this contradiction, the community accepts both theories as the best available descriptions of their respective domains.
|Example Type=Historical
}}
{{Theory Example
|Title=Fallibilist and Infallibilist Communities
|Description=Barseghyan presents the following example of two hypothetical communities to illustrate the notion of ''incompatibility tolerance''.
<blockquote>First, imagine a community that believes that all of their accepted theories are absolutely (demonstratively) true. This ''infallibilist'' community also knows that, according to classical logic, p and not-p cannot be both true. Since, according to this community, all accepted theories are strictly true, the only way the community can avoid triviality is by stipulating that any two accepted theories must be mutually consistent. In other words, by the third law, they end up employing the classical logical law of noncontradiction as their criterion of compatibility.
Now, imagine another community that accepts the position of ''fallibilism''. This community holds that no theory in empirical science can be demonstratively true and, consequently, all accepted empirical theories are merely quasi-true. But if any accepted empirical theory is only quasi-true, it is possible for two accepted empirical theories to be mutually inconsistent. In other words, this community accepts that two contradictory propositions may both contain grains of truth, i.e. to be quasi-true. [[CiteRef::Bueno et al (1998)]]. In order to avoid triviality, this community employs a paraconsistent logic, i.e. a logic where a contradiction does not imply everything. This fallibilist community does not necessarily reject classical logic; it merely realizes that the application of classical logic to quasi-true propositions entails triviality. Thus, the community also realizes that the application of classical principle of noncontradiction to empirical science is problematic, for no empirical theory is strictly true. As a result, by the third law, this community employs criteria of compatibility very different from those employed by the infallibilist community.[[CiteRef::Barseghyan (2015)||pp.154-6]]</blockquote>
|Example Type=Hypothetical
}}
{{Theory Example
|Title=Mutually Incompatible Theory Use
|Description=Barseghyan presents the following example of the possibility for simultaneous use of mutually incompatible theories, even in the same scientific project.
"Circa 1600, astronomers could easily use both Ptolemaic and Copernican astronomical theories to calculate the ephemerides of different planets. Similarly, in order to obtain a useful tool for calculating atomic spectra, Bohr mixed some propositions of classical electrodynamics with a number of quantum hypotheses.[[CiteRef::Smith (1988)]] Finally, when nowadays we build a particle accelerator, we use both classical and quantum physics in our calculations. Thus, sometimes propositions from two or more incompatible theories are mixed in order to obtain something practically useful".[[CiteRef::Barseghyan (2015)||pp.157-8]]
|Example Type=Historical
}}
{{Theory Example
|Title=Mutually Incompatible Theory Pursuit
|Description=Barseghyan presents the following historical examples of the simultaneous pursuit of mutually incompatible theories. Of course, we should note that there is "nothing extraordinary" about this: it is the pursuit of different options that makes scientific change possible!
<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
}}
{{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 - General and singular
|Description=As per Barseghyan, "In the second scenario (of inconsistency tolerance), 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 ... 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".[[CiteRef::Barseghyan (2015)||pp.160]]
|Example Type=Hybrid
}}
{{Theory Example
|Title=Method and Theory Incompatibility
|Description=Barseghyan presents the following example of the indirect incompatibility that can exist between theories and methods:
<blockquote>Say there is an accepted theory which says that better nutrition can improve a patient’s condition. We know from the discussion in the previous section that the conjunction of this proposition with the basic requirement to accept only the best available theories yields a requirement that the factor of improved nutrition must be taken into account when testing a drug’s efficacy.
Now, envision a method which doesn’t take the factor of better nutrition into account and prescribes that a drug’s efficacy should be tested in a straightforward fashion by giving it only to one group of patients. This method will be incompatible with the requirement that the possible impact of improved nutrition must be taken into account. Therefore, indirectly, it will also be incompatible with a theory from which the requirement follows.[[CiteRef::Barseghyan (2015)|p.163-4]]</blockquote>
|Example Type=Hypothetical
}}
{{Acceptance Record
