The Zeroth Law (Harder-2015)

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This is an answer to the question Mechanism of Compatibility that states "At any moment of time, the elements of the scientific mosaic are compatible with each other."

The Zeroth Law Harder 2015.png

The Zeroth Law was formulated by Rory Harder in 2015.1 It is also known as the law of compatibility.

Broader History

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).2 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)34 and Karl Popper’s 'Logic of Scientific Discovery'.5

"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".1 For example, Otto Neurath's conception of scientific change relied on mutual agreement,6 to the extent that "mutual agreement of the elements is basically the only guiding principle of scientific change".1 Quine's view is similar,7, wherein "we adjust and replace the elements of the so-called web of belief by maintaining the mutual agreement between the elements".1 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".1 However, by the Zeroth Law, noncontradiction is just one of many possible compatibility criteria a mosaic might have.

Scientonomic History

The zeroth law was introduced into the 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,”8 he raised two arguments against the Law of Consistency, one logical and one historical.

We begin from our logical argument. A scientific community cannot always know all the logical consequences of its theories at the time of their acceptance. Logical consequences of theories often emerge later, in the course of scientific research. Therefore, scientists can never rule out the possibility that their mosaic contains a contradiction. Thus, the presence of contradiction in the consequences of the theory cannot be what determines its presence in a mosaic. As Barseghyan explains:

while ascertaining that no two accepted propositions are mutually inconsistent might be a viable task in a mosaic with only a handful of propositions, the task may prove virtually impossible in a more complex mosaic. In addition, even if the community somehow manages to ascertain logical consistency of all openly accepted propositions, there will still remain a possibility that some of the logical consequences of two accepted theories are mutually inconsistent.1

As we have seen, it is possible that a scientific community may knowingly accept a contradiction, and indeed, there are historical instances of this phenomenon. One such example is the contradiction in the current mosaic between consequences of Einstein's theories of special and general relativity and quantum mechanics. (See Below) 9

Therefore, we cannot stipulate strict non-contradiction in a descriptive scientonomic theory, since at least one historical example contradicts it. Based on these two challenges to the law of consistency, Rory Harder proposed to reformulate the zeroth law as the law of compatibility. This new formulation was accepted by the Scientonomy community.

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.10 Consequently, they suggested that the zeroth law is to be replaced by a definition of compatibility as well as a compatibility corollary. This modification became accepted in 2020 and the zeroth law became rejected.

Acceptance Record

Here is the complete acceptance record of this theory:
CommunityAccepted FromAcceptance IndicatorsStill AcceptedAccepted UntilRejection Indicators
Scientonomy1 January 2016The law became de facto accepted by the community at that time together with the whole theory of scientific change.No3 June 2020The law became rejected as a result of the acceptance of the respective suggested modification.

Suggestions To Reject

These are all the modifications where the rejection of this theory has been suggested:

Modification Community Date Suggested Summary Verdict Verdict Rationale Date Assessed
Sciento-2018-0015 Scientonomy 28 December 2018 Accept the definition of compatibility, as the ability of two elements to coexist in the same mosaic. Also replace the zeroth law with the compatibility corollary. Accepted While the modification induced a few comments on the encyclopedia, it became accepted as a result of discussions that took place mostly offline. It was agreed that the modification "comes to remedy one of the glaring omissions" in the current zeroth which doesn't "say much above and beyond what is already implicit in the notion of compatibility"c1 as it "is lacking in empirical content, and should be replaced with a definition of compatibility".c2 It was also noted that the proposed "definition of compatibility criteria... captures the gist of the concept as it has been used in our community".c3 It was also agreed that "the compatibility corollary follows from this definition".c4 c5 Finally, the community accepted that the definition and the corollary "recover the content of the Zeroth Law".c6 3 June 2020

Question Answered

The Zeroth Law (Harder-2015) is an attempt to theory the following question: Under what conditions can two elements coexist in the same mosaic?

See Mechanism of Compatibility for more details.


The zeroth law explained by Hakob Barseghyan

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.

In Barseghyan's presentation of the Zeroth Law, he explains it thus: "The law of compatibility has three closely linked aspects. First, it states that two theories simultaneously accepted in the same mosaic cannot be incompatible with one another. It also states that at any moment two simultaneously employed methods cannot be incompatible with each other. Finally, it states that, at any moment of time, there can be no incompatibility between accepted theories and employed methods".1 Importantly, the Zeroth Law extends only to theories and methods that are accepted, not merely used or pursued.

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".1 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").1 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".1

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:

"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"1.

The abstract criteria of compatibility have many possible implementations with in a community. These criteria are employed methods, and therefore can change over time according to 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.11 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.1.

The gist of this theory can be illustrated by the following examples.

Inconsistency Tolerance - General and singular

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".1

Fallibilist and Infallibilist Communities

Barseghyan presents the following example of two hypothetical communities to illustrate the notion of incompatibility tolerance.

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. 12. 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.1

Method and Theory Incompatibility

Barseghyan presents the following example of the indirect incompatibility that can exist between theories and methods:

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.1p.163-4

General Relativity and Quantum Physics

Barseghyan writes that "the conflict between general relativity and quantum physics is probably the most famous illustration of this phenomenon," that phenomenon being the knowing acceptance of two contradicting theories by a community. "We normally take general relativity as the best description of the world at the level of massive objects and quantum physics as the best available description of the micro-world. But we also know that, from the classical logical perspective, the two theories contradict each other. The inconsistency of their conjunction becomes apparent when they are applied to objects that are both extremely massive and extremely small (i.e. a singularity inside a black hole)".1 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,13 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.

Mutually Incompatible Theory Pursuit

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!

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.14. 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”15 and that "the use of inconsistent representations of the world as heuristic guideposts to consistent theories is an important part of scientific discovery"16.1

Mutually Incompatible Theory Use

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.17 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".1

Inconsistency Tolerance - "The Same Object"

We find two hypothetical scenarios for inconsistency tolerance in Barseghyan (2015). Here is the first:

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.1

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".1 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".1


No reasons are indicated for this theory.

If a reason supporting this theory is missing, please add it here.

Questions About This Theory

The following higher-order questions concerning this theory have been suggested:

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  1. a b c d e f g h i j k l m n o p q r s t u  Barseghyan, Hakob. (2015) The Laws of Scientific Change. Springer.
  2. ^  Carnielli, Walter and Marcos, Joano. (2001) Ex Contradictione Non Sequitur Quodlibet. Bulletin of Advanced Reasoning and Knowledge 1, 89-109.
  3. ^  Newton, Isaac. (1687) Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). Pepys, London.
  4. ^  Smith, George. (2009) Newton's Philosophiae Naturalis Principia Mathmatica. In Zalta (Ed.) (2016). Retrieved from
  5. ^  Popper, Karl. (1959) The Logic of Scientific Discovery. Hutchinson & Co.
  6. ^ Neurath (1973) 
  7. ^ Quine and Ullian (1978) 
  8. ^  Harder, Rory. (2013) Scientific Mosaics and the Law of Consistency. Unpublished manuscript.
  9. ^  Fine, Aurthur. (2013) The Einstein-Podolsky-Rosen Argument in Quantum Theory. In Zalta (Ed.) (2016). Retrieved from
  10. ^  Fraser, Patrick and Sarwar, Ameer. (2018) A Compatibility Law and the Classification of Theory Change. Scientonomy 2, 67-82. Retrieved from
  11. ^  Priest, Graham; Tanaka, Koji and Weber, Zachary. (2015) Paraconsistent Logic. In Zalta (Ed.) (2016). Retrieved from
  12. ^ Bueno et al (1998) 
  13. ^  Einstein, Albert; Podolsky, Boris and Rosen, Nathan. (1935) Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Physical Review 47, 777-780.
  14. ^ Meheus (2003) 
  15. ^ Meheus(2003) 
  16. ^ Smith(1988) 
  17. ^ Smith (1988)