Arnold Koslow

We have seen that Dretske explicitly required that laws related items like F-ness and G-ness, which would normally be understood as a reference to universals. However he also referred to laws as relating physical magnitudes. If all physical magnitudes, including refractive indices in particular, count, according to Dretske, as universals, then it seems to me that universals so understood, are in tremendous abundance, and set no limits for the expressive power of physical theories, beyond those set by the use of ordinary mathematical analysis. We noted in Chap. 10.1007/978-3-030-18846-7_4, there isn’t any problem with those universals used by Dretske, if they are physical magnitudes.

This essay on scientific laws has two parts. (I) Part I, (Chaps. 10.1007/978-3-030-18846-7_2, 10.1007/978-3-030-18846-7_3, 10.1007/978-3-030-18846-7_4, 10.1007/978-3-030-18846-7_5, 10.1007/978-3-030-18846-7_6 and 10.1007/978-3-030-18846-7_7), (Burnishing the Legacy, Laws and explanations.) and Part II (Chaps. 10.1007/978-3-030-18846-7_8, 10.1007/978-3-030-18846-7_9, 10.1007/978-3-030-18846-7_10, 10.1007/978-3-030-18846-7_11 and 10.1007/978-3-030-18846-7_12), Devoted to the explanation of laws by theories: Schematic and non-schematic theories, two kinds of explanation, and the physical modals that each theory provides, and the nomic modals that are associated with laws.

Dretske’s influential account of laws stands in sharp contrast to the classical accounts of Hempel, Nagel, Carnap, and Braithwaite. I will, in the following, refer to these somewhat different accounts as “the standard view”. Dretske’s view has been seen as marking a striking shift away from that view, and the beginning of a series of new non-Humean accounts. His account of laws forcefully declared thatLaws are relations between, properties, quantities, magnitudes, or features that are expressed by certain predicates.The relations in each law are extensional, and can vary from law to law,Laws are singular sentences rather than general, andThe statement of the law All F’s are G will not change it’s truth-value if any co-referential expression replaces “F”, “G”, or both. However the result of that replacement may not be a law. This feature is, he, misleadingly refers to as “the opacity of laws”.With the exception of the first claim, the remaining ones appear to be a wholesale repudiation of the received view about laws. They are not friendly amendments. If true, they cut deeply into the received view. We turn therefore to a detailed consideration of them.

I shall assume for the present that the basic features of Hempel’s Deductive Nomological Model of Explanation are familiar to the reader: a deductive explanation of some fact Ga about a particular object a, requires some other fact Fa, and since it was assumed that Fa would not by itself yield a deduction of Ga, that the deductive connection between the two facts was to be supplied by an additional premise L –a law. So, though the target of their paper was scientific explanation, we want to consider what it tells us about scientific laws.

It might be folly to insist on one overall official characterization of the way scientific and mathematical theories ought to be presented. They are usually presented of course in various ways so that the authors and scholars in a field can find optimal means for communication with others, whether within or outside that field. Nevertheless, if theories were thought of as representations of our knowledge, then one way of looking at the representation of theories is to ask, as Hermann Weyl did (2009) “What is the ultimate purpose of forming theories?”, and he then cited the familiar proposal of Heinrich Hertz (1894):This powerful and compact statement of Hertz, resonated with David Hilbert’s revolutionary proposal for the axiomatic representation of theories. The kind of axiomatization Hilbert advocated was exemplified in his Foundations of Geometry, [1899], and was to become the model for his inquiries into the physical sciences as well as mathematical ones.

Norman Campbell rightly set the task. It is the business of science not only to discover laws, but to explain them. And he added his voice to a philosophical tradition going back to Aristotle, of taking on the task of explaining what laws are, and explaining as well what explanations of laws are. Ever since the renewed interest spurred by seminal paper of Hempel and Oppenheim on scientific explanation, philosophers have been inspired to do better on scientific explanation. But it became painfully clear, from the counter-example offered in their paper, that their account of scientific explanation could not cover the explanation of laws. It is clear that although this is the business of philosophers, it is still unfinished business.

The first volume presents a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic (Aristotle, Avicenna, Buridan, Schröder, MacColl). This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic.

The book has two parts: In the first, after a review of some seminal classical accounts of laws and explanations, a new account is proposed for distinguishing between laws and accidental generalizations. Among the new consequences of this proposal it is proved that any explanation of a contingent generalization shows that the generalization is not accidental. The second part involves physical theories, their modality, and their explanatory power. In particular, it is shown that Each theory has a theoretical implication structure associated with it, such that there are new physical modal operators on these structures and also special modal entities that are in these structures. A special subset of the physical modals, the nomic modals are associated with the laws of theories. The familiar idea that theories always explain laws by deduction of them has to be seriously modified in light of the fact that there are a host of physical theories that we believe are schematic. Nevertheless, we think that there is a kind of non-deductive explanation and generality that they achieve by subsumtion under a schema.

The original motivation of D. Gabbay’s concept of Fibring concerned the combination of logics, and initially it involved the syntactic introduction of modals into formulations of intuitionistic logic in which modals are syntactically absent. We show, using the notion of structural modals that there are many modals of intuitionism, and logics for subjunctive and epistemic conditionals which are not syntactically evident in our best formulations of them. We discuss some cases when the attempt to make them syntactically evident can have undesirable consequences.