Quantum sidelights on The Material Theory of Induction

John Norton's The Material Theory of Induction bristles with fresh insights and provocative ideas that provide a much needed stimulus to a stodgy if not moribund field. I use quantum mechanics (QM) as a medium for exploring some of these ideas. First, I note that QM offers more predictability than Newtonian mechanics for the Norton dome and other cases where classical determinism falters. But this ability of QM to partially cure the ills of classical determinism depends on facts about the quantum Hamiltonian operator that vary from case to case, providing an illustration of Norton's theme of the importance of contingent facts for inductive reasoning. Second, I agree with Norton that Bayesianism as developed for classical probability theory does not constitute a universal inference machine, and I use QM to explain the sense in which this is so. But at the same time I defend a brand of quantum Bayesianism as providing an illuminating account of how physicists' reasoning about quantum events. Third, I argue that if the probabilities induced by quantum states are regarded as objective chances then there are strong reasons to think that fair infinite lotteries are impossible in a quantum world.     

What are the drivers of induction? Towards a Material Theory+

John Norton's Material Theory of Induction (Norton, 2003, 2005, 2008, forthcoming) has a two-fold, negative and positive, goal. The negative goal is to establish that formal logics of induction fail if they are understood as universally applicable schemas of induction. The positive goal is to establish that it is material facts that enable and justify inductive inferences. I argue in this paper that Norton is more successful with his negative than with his positive ambition. While I do not deny that facts constitute an important type of enabler and justifier of inductions, they are by no means the only type. This paper suggests that there are no less than six other types of background information scientists need and use to fuel and warrant inductions. The discussion of additional enablers and justifiers of inductions will further show there are practically important and intellectually challenging methodological issues Norton's theory prevents us from seeing because it leaves out this or that type of enabler and justifier.     

Epistemic benefits of the material theory of induction

C. D. Broad famously labelled the problem of providing our inductive practices with a proper justification “the scandal of philosophy” (Broad, 1952). Recently, John Norton has provided a dissolution of this problem (2014). According to Norton, inductive inference is grounded in particular facts obtaining within particular domains (J. Norton, 2003b, 2010, 2014). Because the material theory does not involve a universal schema of induction, Norton claims it dissolves the problem of induction (which implies that such universal schemas cannot be justified).In this paper, I critically evaluate Norton's dissolution. In particular, I argue that the problem of induction is an epistemological problem, that Norton's material theory entails an externalist epistemology, and that it is a common feature of such epistemologies that they dissolve the problem of induction. The upshot is that the material theory is not unique in its ability to reap the specifically epistemic benefits of dissolving the problem of induction, and thus that the epistemic advantages of the material theory over extant alternatives in this regard are fewer than it may appear at first sight.     

Norton's material theory of analogy

In his book, The Material Theory of Induction, Norton argues that the quest for a universal formal theory or ‘schema’ for analogical inference should be abandoned. In its place, he offers the “material theory of analogy”: each analogical inference is “powered” by a local fact of analogy rather than by any formal schema. His minimalist model promises a straightforward, fact-based approach to the evaluation and justification of analogical inferences. This paper argues that although the rejection of universal schemas is justified, Norton's positive theory is limited in scope: it works well only for a restricted class of analogical inferences. Both facts and quasi-formal criteria have roles to play in a theory of analogical reasoning.     

The material theory of induction and the epistemology of thought experiments

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn't been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton's fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position.     

How to think about analogical inferences: A reply to Norton

In this paper, I raise some worries with John D. Norton's application of his material theory of induction to the study of analogical inferences. Skeptical that these worries can be properly addressed, I propose a principle to guide the philosophical research on analogical inferences and argue for its usefulness.     

Inference to the best explanation and Norton's material theory of induction

I argue that we should consider Norton's material theory of induction as consisting of two largely independent claims. First, there is the claim that material facts license inductions - a claim which I interpret as a type of contextualism about induction. Second, there is the claim that there are no universal rules of induction. While a good case can be made for the first claim, I believe that Norton's arguments for the second claim are lacking. In particular, I spell out Norton's argument against the claim that all induction may be reduced to inference to the best explanation, and argue that it is not persuasive. Rejecting this part of Norton's theory does not however require us to abandon the first claim that material facts license inductions. In this way, I distinguish the parts of the material theory of induction we should happily accept from the parts about which we should be more skeptical.     

Henry More and the development of absolute time

This paper explores the nature, development and influence of the first English account of absolute time, put forward in the mid-seventeenth century by the ‘Cambridge Platonist’ Henry More. Against claims in the literature that More does not have an account of time, this paper sets out More's evolving account and shows that it reveals the lasting influence of Plotinus. Further, this paper argues that More developed his views on time in response to his adoption of Descartes' vortex cosmology and cosmogony, providing new evidence of More's wider project to absorb Cartesian natural philosophy into his Platonic metaphysics. Finally, this paper argues that More should be added to the list of sources that later English thinkers – including Newton and Samuel Clarke – drew on in constructing their absolute accounts of time.     

Explicating formal epistemology: Carnap's legacy as Jeffrey's radical probabilism

Quine's “naturalized epistemology” presents a challenge to Carnapian explication: why try to rationally reconstruct probabilistic concepts instead of just doing psychology? This paper tracks the historical development of Richard C. Jeffrey who, on the one hand, voiced worries similar to Quine's about Carnapian explication but, on the other hand, claims that his own work in formal epistemology—what he calls “radical probabilism”—is somehow continuous with both Carnap's method of explication and logical empiricism. By examining how Jeffrey's claim could possibly be accurate, the paper suggests that Jeffrey's radical probabilism can be seen as a sort of alternative explication project to Carnap's own inductive logic. In so doing, it deflates both Quine's worries about Carnapian explication and so also, by extension, similar worries about formal epistemology.     

Inductive reasoning in the context of discovery: Analogy as an experimental stratagem in the history and philosophy of science

Building on Norton's “material theory of induction,” this paper shows through careful historical analysis that analogy can act as a methodological principle or stratagem, providing experimentalists with a useful framework to assess data and devise novel experiments. Although this particular case study focuses on late eighteenth and early nineteenth-century experiments on the properties and composition of acids, the results of this investigation may be extended and applied to other research programs. A stage in-between what Steinle calls “exploratory experimentation” and robust theory, I argue that analogy encouraged research to substantiate why the likenesses should outweigh the differences (or vice versa) when evaluating results and designing experiments.     

What conceptual spaces can do for Carnap's late inductive logic

In the last published account of his late inductive logic, the Basic System of Inductive Logic, Rudolf Carnap introduced a new element to the systems of inductive logic, namely the so-called attribute spaces. These geometrical structures model the meanings of the predicates of the object language and have a similar structure as the conceptual spaces employed by cognitive scientists like Peter Gärdenfors. I show how the development of the theory of conceptual spaces helps us to see the addition of attribute spaces as a step forward in explicating the concept of confirmation. I discuss the differences and similarities of the two theories and investigate the possibilities for developing further connections.     

Maxwell's color statistics: From reduction of visible errors to reduction to invisible molecules

This paper presents a cross-disciplinary and multi-disciplinary account of Maxwell's introduction of statistical models of molecules for the composition of gases. The account focuses on Maxwell's deployment of statistical models of data in his contemporaneous color researches as established in Cambridge mathematical physics, especially by Maxwell's seniors and mentors. The paper also argues that the cross-disciplinary, or cross-domain, transfer of resources from the natural and social sciences took place in both directions and relied on the complex intra-disciplinary, or intra-domain, dynamics of Maxwell's researches in natural sciences, in color theory, physical astronomy, electromagnetism and dynamical theory of gases, as well as involving a variety of types of communicating and mediating media, from material objects to concepts, techniques and institutions.     

What induction is (and what it should not be): A concepts-centric perspective on Norton’s radium chloride example

I argue that Norton’s reconstruction of an example inductive inference in Ch.1 of The Material Theory of Induction mischaracterizes scientific induction by treating the ampliation as separable (and separated) from that inherent in conceptualization per se—effectively severing the putative ampliation from its putative warrant. I sketch an alternative analysis in which ampliation and warrant remain closely coupled through a common root in the primary conceptualizations.     

Was Newtonian cosmology really inconsistent?

This paper follows up a debate as to the consistency of Newtonian cosmology. Whereas Malament [(1995). Is Newtonian cosmology really inconsistent? Philosophy of Science 62, 489–510] has shown that Newtonian cosmology is not inconsistent, to date there has been no analysis of Norton's claim [(1995). The force of Newtonian cosmology: Acceleration is relative. Philosophy of Science 62, 511–522.] that Newtonian cosmology was inconsistent prior to certain advances in the 1930s, and in particular prior to Seeliger's seminal paper of Seeliger [(1895). Über das Newton'sche Gravitationsgesetz. Astronomische Nachrichten 137 (3273), 129–136.] In this paper I agree that there are assumptions, Newtonian and cosmological in character, and relevant to the real history of science, which are inconsistent. But there are some important corrections to make to Norton's account. Here I display for the first time the inconsistencies—four in total—in all their detail. Although this extra detail shows there to be several different inconsistencies, it also goes some way towards explaining why they went unnoticed for 200 years.     

Rediscovering Einstein's legacy: How Einstein anticipates Kuhn and Feyerabend on the nature of science

Thomas Kuhn and Paul Feyerabend promote incommensurability as a central component of their conflicting accounts of the nature of science. This paper argues that in so doing, they both develop Albert Einstein's views, albeit in different directions. Einstein describes scientific revolutions as conceptual replacements, not mere revisions, endorsing ‘Kant-on-wheels’ metaphysics in light of ‘world change’. Einstein emphasizes underdetermination of theory by evidence, rational disagreement in theory choice, and the non-neutrality of empirical evidence. Einstein even uses the term ‘incommensurable’ specifically to apply to challenges posed to comparatively evaluating scientific theories in 1949, more than a decade before Kuhn and Feyerabend. This analysis shows how Einstein anticipates substantial components of Kuhn and Feyerabend's views, and suggests that there are strong reasons to suspect that Kuhn and Feyerabend were directly inspired by Einstein's use of the term ‘incommensurable’, as well as his more general methodological and philosophical reflections.     

Debunking material induction

In this paper, we present an explanatory objection to Norton's material theory of induction, as applied to predictive inferences. According to the objection we present, there is an explanatory disconnect between our beliefs about the future and the relevant future facts. We argue that if we recognize such a disconnect, we are no longer rationally entitled to our future beliefs.     

Thomas Clifford Allbutt and Comparative Pathology

This paper reconceptualizes Thomas Clifford Allbutt's contributions to the making of scientific medicine in late nineteenth-century England. Existing literature on Allbutt usually describes his achievements, such as his design of the pocket thermometer and his advocacy of the use of the ophthalmoscope in general medicine, as independent events; and his work on the development of comparative pathology is largely overlooked. In this paper I focus on this latter aspect. I examine Allbutt's books and addresses and claim that Allbutt argued for the centrality of comparative pathology in the advancement of medical knowledge. He held that diseases should be studied as biological phenomena and that medicine should be made a biological science. He also argued that comparative pathology should be based upon the idea of evolution, and its study should embrace other nineteenth-century sciences including neurology, embryology and bacteriology. Allbutt's writings reveal that his endorsement of comparative pathology (1880s to 1920s), his promotion of the use of the ophthalmoscope and the thermometer in clinical medicine (early 1870s), and his support of the hospital unit system (1910s to 1920s) were part of a single programme. All were grounded in his scientific vision of medicine which emphasized a research culture, a stringent nosological attitude and an integration of laboratory sciences and clinical medicine.     

The metaphysics of D-CTCs: On the underlying assumptions of Deutsch׳s quantum solution to the paradoxes of time travel

I argue that Deutsch׳s model for the behavior of systems traveling around closed timelike curves (CTCs) relies implicitly on a substantive metaphysical assumption. Deutsch is employing a version of quantum theory with a significantly supplemented ontology of parallel existent worlds, which differ in kind from the many worlds of the Everett interpretation. Standard Everett does not support the existence of multiple identical copies of the world, which the D-CTC model requires. This has been obscured because he often refers to the branching structure of Everett as a “multiverse”, and describes quantum interference by reference to parallel interacting definite worlds. But he admits that this is only an approximation to Everett. The D-CTC model, however, relies crucially on the existence of a multiverse of parallel interacting worlds. Since his model is supplemented by structures that go significantly beyond quantum theory, and play an ineliminable role in its predictions and explanations, it does not represent a quantum solution to the paradoxes of time travel.