The Zeroth Law (Harder-2015)

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An attempt to answer the question of Mechanism of Compatibility which 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. It is currently accepted by Scientonomy community as the best available theory on the subject.


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 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,”6 he raised two arguments against the Law of Consistency, one logical and one historical.

The 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.

The Historical Argument: There are historical instances in which a scientific community has knowingly accepted a contradiction. One such example is the contradiction in the current mosaic between consequences of Einstein's theories of special and general relativity and quantum mechanics.7 Einstein's 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,8 yet both quantum theory and relativity remain in the mosaic.

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.9 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 The Zeroth Law (Harder-2015):
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 the theory has been suggested:
ModificationCommunityDate SuggestedSummaryVerdictVerdict RationaleDate Assessed
Sciento-2018-0015Scientonomy28 January 2018Accept 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.AcceptedWhile 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".c63 June 2020

Question Answered

The Zeroth Law (Harder-2015) is an attempt to answer 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.

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.10 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.


  1. ^  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. ^  Harder, Rory. (2013) Scientific Mosaics and the Law of Consistency. Unpublished manuscript.
  7. ^  Fine, Aurthur. (2013) The Einstein-Podolsky-Rosen Argument in Quantum Theory. In Zalta (Ed.) (2016). Retrieved from
  8. ^  Einstein, Albert; Podolsky, Boris and Rosen, Nathan. (1935) Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Physical Review 47, 777-780.
  9. ^  Fraser, Patrick and Sarwar, Ameer. (2018) A Compatibility Law and the Classification of Theory Change. Scientonomy 2, 67-82. Retrieved from
  10. ^  Priest, Graham; Tanaka, Koji and Weber, Zachary. (2015) Paraconsistent Logic. In Zalta (Ed.) (2016). Retrieved from