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The Zeroth Law (Harder-2015) (view source)
Revision as of 19:12, 10 February 2023
, 19:12, 10 February 2023no edit summary
<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.
