In this work, the first of a series, we study the nature of informal inconsistency in physics, focusing mainly on the foundations of quantum theory, and appealing to the concept of quasi-truth. We defend a pluralistic view of the philosophy of science, grounded on the existence of inconsistencies and on quasi-truth. Here, we treat only the ‘classical aspects’ of the subject, leaving for a forthcoming paper the ‘non-classical’ part.
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Below we shall distinguish also between axiomatized and formal theories. The former (which can be also called ‘material (or informal) axiomatics’) can be though of as formal in potentia, so we shall remain speaking in terms of the latter.
Sometimes even ideological ideas enter the scenario. The history of science is full of examples of this kind; just remember Lysenko’s genetic. But it is a task for the scientific practice to discipline these situations. Of course, Einstein’s case cannot be compared with these pathological ideological situations.
In the sense that higher-order logic (theory of types) is, in a certain sense, strictly weaker than ZF set theory.
Suppes himself worked always within informal set theory, so he could presuppose the step-theories as given in advance.
DC is not sufficient to prove that there are nonmeasurable subsets of the real numbers.
Another interesting point that deserves investigation and to which we have dedicated some works is related to the concepts of identity, individuality and their relation to sets, for assuming that some quantum objects are entities without individuality (according to a possible interpretation), their collections cannot be sets such as those in ZF; for details, see French and Krause (2006).
A typical example is the value of the dipolar momentum of the electron, experimentally measured as \(1.00115965219 \pm 0.00000000001\) times the combination of constants given by Dirac; see t’Hooft (2001, p. 72).
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da Costa, N.C.A., Krause, D. Physics, inconsistency, and quasi-truth. Synthese 191, 3041–3055 (2014). https://doi.org/10.1007/s11229-014-0472-8
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