At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical structures (...) of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories. (shrink)

The purpose of the paper is to show that by cleaning Classical Logic (CL) from redundancies (irrelevances) and uninformative complexities in the consequence class and from too strong assumptions (of CL) one can avoid most of the paradoxes coming up when CL is applied to empirical sciences including physics. This kind of cleaning of CL has been done successfully by distinguishing two types of theorems of CL by two criteria. One criterion (RC) forbids such theorems in which parts of the (...) consequent (conclusion) can be replaced by arbitrary parts salva validitate of the theorem. The other (RD) reduces the consequences to simplest conjunctive consequence elements. Since the application of RC and RD to CL leads to a logic without the usual closure conditions, an approximation to RC and RD has been constructed by a basic logic with the help of finite (6-valued) matrices. This basic logic called RMQ (relevance, matrix, Quantum Physics) is consistent and decidable. It distinguishes two types of validity (strict validity) and classical or material validity. All theorems of CL (here: classical propositional calculus CPC) are classically or materially valid in RMQ. But those theorems of CPC which obey RC and RD and avoid the difficulties in the application to empirical sciences and to Quantum Physics are separated as strictly valid in RMQ. In the application to empirical sciences in general the proposed logic avoids the well known paradoxes in the area of explanation, confirmation, versimilitude and Deontic Logic. Concerning the application to physics it avoids also the difficulties with distributivity, commensurability and with Bell's inequalities. (shrink)

Inconsistencies in science take several forms. Some occur at the level of substantive claims about the world. Others occur at the level of methodology, and take the form of dilemmas, or cases of conflicting epistemic or cognitive values. In this article, I discuss how methodological dilemmas arise. I then consider how scientists resolve them. There are strong grounds for thinking that emotional judgement plays an important role in resolving methodological dilemmas. Lastly, I discuss whether and under what conditions this reliance (...) on emotional judgement is rationally warranted. I consider two possible mechanisms, based on coherence and induction, able to ensure that scientists’ emotional responses to methodological dilemmas are rationally warranted. (shrink)

Though some influentially critical objections have been raised during the ‘classical’ pre-computational simulation philosophy of science tradition, suggesting a more nuanced methodological category for experiments, it safe to say such critical objections have greatly proliferated in philosophical studies dedicated to the role played by computational simulations in science. For instance, Eric Winsberg suggests that computer simulations are methodologically unique in the development of a theory’s models suggesting new epistemic notions of application. This is also echoed in Jeffrey Ramsey’s notions of (...) “transformation reduction,”—i.e., a notion of reduction of a more highly constructive variety. Computer simulations create a broadly continuous arena spanned by normative and descriptive aspects of theory-articulation, as entailed by the notion of transformation reductions occupying a continuous region demarcated by Ernest Nagel’s logical-explanatory “domain-combining reduction” on the one hand, and Thomas Nickels’ heuristic “domain-preserving reduction,” on the other. I extend Winsberg’s and Ramsey’s points here, by arguing that in the field of computational fluid dynamics as well as in other branches of applied physics, the computer plays a constitutively experimental role—supplanting in many cases the more traditional experimental methods such as flow-visualization, etc. In this case, however CFD algorithms act as substitutes, not supplements when it comes to experimental practices. I bring up the constructive example involving the Clifford-Algebraic algorithms for modeling singular phenomena in CFD by Gerik Scheuermann and Steven Mann & Alyn Rockwood who demonstrate that their algorithms offer greater descriptive and explanatory scope than the standard Navier-Stokes approaches. The mathematical distinction between Navier-Stokes-based and Clifford-Algebraic based CFD has essentially to do with the regularization features exhibited to a far greater extent by the latter, than the former. Hence, CACFD indicate that the utilization of computational techniques can be based on principled reasons, as opposed to merely practical. CACFD hence exhibit a new generative role in the field of fluid mechanics, by offering categories of experimental evidence that are optimally descriptive and explanatory—i.e., pace Batterman can be both ontologically and epistemically fundamental. (shrink)

This article proposes a basic logic for application in physics dispensing with the Principle of Excluded Middle. It is based on the article “Matrix Based Logics for Application in Physics (RMQ) which appeared 2009. In his article with Stachow on the Principle of Excluded Middle in Quantum Logic (QL), Peter Mittelstaedt showed that for some suitable QLs, including their own, the Principle of Excluded Middle can be added without any harm for QL; where ‘without any harm for QL’ means that (...) the basic desiderata and the basic results (theorems) of those QLs remain satised in the sense that they avoid the well known difficulties with commensurability and distributivity.In the following article I want to show that the basic desiderata and results (theorems) of RMQ (of avoiding the well-known difficulties with commensurability, distributivity, fusion and Bell’s inequalities) remain satised if by introducing a strong negation (or strong negation and disjunction) the resulting weak intuitionist system RMQI dispenses with the Principle of Excluded Middle; it becomes either invalid or not strictly valid. (shrink)