The Zeroth Law (Harder-2015)
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 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.
|Community||Accepted From||Acceptance Indicators||Still Accepted||Accepted Until||Rejection Indicators|
|Scientonomy||1 January 2016||The law became de facto accepted by the community at that time together with the whole theory of scientific change.||Yes|
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.
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.9 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.
- Barseghyan, Hakob. (2015) The Laws of Scientific Change. Springer.
- Carnielli, Walter and Marcos, Joano. (2001) Ex Contradictione Non Sequitur Quodlibet. Bulletin of Advanced Reasoning and Knowledge 1, 89-109.
- Newton, Isaac. (1687) Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). Pepys, London.
- Smith, George. (2009) Newton's Philosophiae Naturalis Principia Mathmatica. In Zalta (Ed.) (2016). Retrieved from http://plato.stanford.edu/archives/spr2009/entries/newton-principia/.
- Popper, Karl. (1959) The Logic of Scientific Discovery. Routledge.
- Harder, Rory. (2013) Scientific Mosaics and the Law of Consistency. Unpublished manuscript.
- Fine, Aurthur. (2013) The Einstein-Podolsky-Rosen Argument in Quantum Theory. In Zalta (Ed.) (2016). Retrieved from http://plato.stanford.edu/archives/win2014/entries/qt-epr/.
- Einstein, Albert; Podolsky, Boris and Rosen, Nathan. (1935) Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Physical Review 47, 777-780.
- Priest, Graham; Tanaka, Koji and Weber, Zachary. (2015) Paraconsistent Logic. In Zalta (Ed.) (2016). Retrieved from http://plato.stanford.edu/archives/spr2015/entries/logic-paraconsistent/.