Reasoning in Biological Discoveries brings together a series of essays, which focus on one of the most heavily debated topics of scientific discovery. Collected together and richly illustrated, Darden's essays represent a groundbreaking foray into one of the major problems facing scientists and philosophers of science. Divided into three sections, the essays focus on broad themes, notably historical and philosophical issues at play in discussions of biological mechanism; and the problem of developing and refining reasoning strategies, including interfield (...) relations and anomaly resolution. Darden summarizes the philosophy of discovery and elaborates on the role that mechanisms play in biological discovery. Throughout the book, she uses historical case studies to extract advisory reasoning strategies for discovery. Examples in genetics, molecular biology, biochemistry, immunology, neuroscience and evolutionary biology reveal the process of discovery in action. (shrink)

This invited article is a response to the paper “Quantum Misuse in Psychic Literature,” by Jack A. Mroczkowski and Alexis P. Malozemoff, published in this issue of the Journal of Near-Death Studies. Whereas I sympathize with Mroczkowski’s and Malozemoff’s cause and goals, and I recognize the problem they attempted to tackle, I argue that their criticisms often overshot the mark and end up adding to the confusion. I address nine specific technical points that Mroczkowski and Malozemoff accused popular writers in (...) the fields of health care and parapsychology of misunderstanding and misrepresenting. I argue that, by and large—and contrary to Mroczkowski’s and Malozemoff’s claims—the statements made by these writers are often reasonable and generally consistent with the current state of play in foundations of quantum mechanics. (shrink)

Throughout his life J. J. Thomson was committed to a mechanical interpretation of nature. This work proceeded in several stages. Early in his career he attempted a Lagrangian formulation of mechanics. But due to certain epistemological difficulties with this approach, he began exploring various analogies and models, particularly those involving vortex motion. After his discovery of the electron in 1897, he commenced a synthesis of the electron with his previous physical conceptions. The result was a hypothesis of the ether (...) as being composed of particles even smaller than electrons. (shrink)

I show why old and new claims on the role of counterfactual reasoning for the EPR argument and Bell’s theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, after emphasizing the role of incompleteness arguments that Einstein developed before the EPR paper, I critically review more recent claims that equate the use (...) of counterfactual reasoning with the assumption of a strong form of realism and argue that such claims are untenable. (shrink)

Introduction to a special issue of Philosophia Mathematica on the mechanization of reasoning. Authors include: M. Detlefsen, D. Mundici, S. Shanker, S. Shapiro, W. Sieg and C. Wright.

: In this commentary on Sinhababu’s Humean Nature I will explore three lines of inquiry. The first asks about the explanatory power of the Desire-Belief Theory of Reasoning, by way of wondering about how desires and beliefs combine with one another. The second question continues along these lines, asking about the further conditions Sinhababu places on reasoning and whether a theory of reasoning can be normatively neutral. The third points out the need for more clarity in his (...) account of intention by contrasting it with practical reasoning. Keywords: Desire; Belief; Humean Psychology; Intention; Practical Reasoning Meccanica e psicologia del ragionamento pratico Riassunto: In questo commento su Humean Nature di Neil Sinhababu intendo esplorare tre linee di indagine. La prima si interroga sul potere esplicativo della Desire-Belief Theory of Reasoning, indagando come desideri e credenze si combinano reciprocamente. La seconda prosegue su questa strada, interrogando le ulteriori condizioni che Sinhababu pone sul ragionamento e chiedendomi se una teoria del ragionamento possa essere normativamente neutrale. La terza individua il bisogno di maggiore chiarezza nella sua descrizione dell’intenzione, mostrandone le differenze rispetto al ragionamento pratico. Parole chiave: Desiderio; Credenza; Psicologia humeana; Intenzione; Ragionamento pratico. (shrink)

ArgumentTalk of “reason” and “rationality” has been perennial in the philosophy and sciences of the European, Latin tradition since antiquity. But the use of these terms in the early-modern period has left especial marks on the specialties and disciplines that emerged as components of “science” in the modern world. By examining discussions by seventeenth-century philosophers, including natural philosophers such as Descartes, Pascal, and Hobbes, the practical meanings of, specifically, inferential reasoning can be seen as reducing, for most, to intellectual (...) processes deriving from foundations that required intuitional insight that was owing to God. Mechanical reasoning, or artificial intelligence, was a contradiction in terms for such as Pascal, whose views of his own arithmetical machine illustrate the issue well. Hobbes’ analysis of reason, however, replaced the ineffable authority of God with the authority of the civil power, to reveal the social reality of “reason” as nothing other than authorized judgment. (shrink)

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section of (...) the research project _Logical Systems and Algorithms for Automatic Testing of Reasoning,_ 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE ) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration. (shrink)

Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers, even of those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that commonly called "Eulerian circles," has met with any general acceptance. A variety of others indeed have been proposed by ingenious and celebrated logicians, several of which would (...) claim notice in a historical treatment of the subject; but they mostly do not seem to me to differ in any essential respect from that of Euler. They rest upon the same leading principle, and are subject all alike to the same restrictions and defects. We must therefore cast about for some new scheme of diagrammatic representation which shall be competent to indicate imperfect knowledge on our part; for this will at once enable us to appeal to it step by step in the process of working out our conclusions. I have never seen any hint at such a scheme, though the want seems so evident that one would suppose that something of the kind must have been proposed before. (shrink)

I show why old and new claims on the role of counterfactual reasoning for the EPR argument and Bell’s theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, after emphasizing the role of incompleteness arguments that Einstein developed before the EPR paper, I critically review more recent claims that equate the use (...) of counterfactual reasoning with the assumption of a strong form of realism and argue that such claims are untenable. (shrink)

ABSTRACTNegative emotions typically have an adverse effect on reasoning, especially analytic or logical reasoning. This effect can be explained using an attentional framework in which emotion detracts limited-capacity cognitive resources which are required for reasoning. Another possibility is that the effect of emotion on reasoning is mediated by arousal, as previous research has shown that physiological arousal can be associated with decreased reasoning performance. In this research, we used a dual-task paradigm combining a syllogistic (...) class='Hi'>reasoning task and a time production task. Prospective timing allows to disentangle the effects of attention and arousal: time productions should lengthen if emotion takes up cognitive resources that are therefore not available for timing, whereas time productions should shorten if emotional reasoning results from increased arousal. Results from two experiments confirm the adverse impact of emotion on logical reasoning performance. Reasoning about emotional contents led t... (shrink)

in O’Rourke, F. (ed.), Human Destinies (Notre Dame Press, forthcoming).

Even though the evidence‐based medicine movement (EBM) labels mechanisms a low quality form of evidence, consideration of the mechanisms on which medicine relies, and the distinct roles that mechanisms might play in clinical practice, offers a number of insights into EBM itself. In this paper, I examine the connections between EBM and mechanisms from several angles. I diagnose what went wrong in two examples where mechanistic reasoning failed to generate accurate predictions for how a dysfunctional mechanism would respond to (...) intervention. I then use these examples to explain why we should expect this kind of mechanistic reasoning to fail in systematic ways, by situating these failures in terms of evolved complexity of the causal system(s) in question. I argue that there is still a different role in which mechanisms continue to figure as evidence in EBM: namely, in guiding the application of population‐level recommendations to individual patients. Thus, even though the evidence‐based movement rejects one role in which mechanistic reasoning serves as evidence, there are other evidentiary roles for mechanistic reasoning. This renders plausible the claims of some critics of evidencebased medicine who point to the ineliminable role of clinical experience. Clearly specifying the ways in which mechanisms and mechanistic reasoning can be involved in clinical practice frames the discussion about EBM and clinical experience in more fruitful terms. (shrink)

A key question for cognitive theories of reasoning is whether logical reasoning is inherently a sentential linguistic process or a process requiring spatial manipulation and search. We addressed this question in an event-related fMRI study of syllogistic reasoning, using sentences with and without semantic content. Our findings indicate involvement of two dissociable networks in deductive reasoning. During content-based reasoning a left hemisphere temporal system was recruited. By contrast, a formally identical reasoning task, which lacked (...) semantic content, activated a parietal system. The two systems share common components in bilateral basal ganglia nuclei, right cerebellum, bilateral fusiform gyri, and left prefrontal cortex. We conclude that syllogistic reasoning is implemented in two distinct systems whose engagement is primarily a function of the presence or absence of semantic content. Furthermore, when a logical argument results in a belief–logic conflict, the nature of the reasoning process is changed by recruitment of the right prefrontal cortex. (shrink)

The principle of sufficient reason asserts that anything that happens does so for a reason: no definite state of affairs can come into being unless there is a sufficient reason why that particular thing should happen. This principle is usually attributed to Leibniz, although the first recorded Western philosopher to use it was Anaximander of Miletus. The demand that nature be rational, in the sense that it be compatible with the principle of sufficient reason, conflicts with a basic feature of (...) contemporary orthodox physical theory, namely the notion that nature’s response to the probing action of an observer is determined by pure chance, and hence on the basis of absolutely no reason at all. This appeal to pure chance can be deemed to have no rational fundamental place in reason-based Western science. It is argued here, on the basis of other basic principles of quantum physics, that in a world that conforms to the principle of sufficient reason, the usual quantum statistical rules will naturally emerge at the pragmatic level, in cases where the reason behind nature’s choice of response is unknown, but that the usual statistics can become biased when the reason for the choice is empirically identifiable. It is explained here that if the statistical laws of quantum mechanics were to be biased in this way then the basically forward-in-time unfolding of empirical reality described by orthodox quantum mechanics would generate the appearances of backward-time-effects of the kind that have been reported in the scientific literature. (shrink)

In talking about the compatibility of quantum observables, discussions often center on the question of whether the corresponding operators commute—even though commutativity is a coarse-grained notion that largely fails to capture the salient “nonclassical” features of quantum theory. Often, too, such discussions involve the issue of whether the operators in question satisfy a Heisenberg-like inequality, of the form ΔA·ΔB≥r>0—even though such inequalities are specific to unbounded operators and (for this and other reasons) are typically not a useful way to discuss (...) joint uncertainty in quantum mechanics. In the present paper we emphasize a simpler dichotomy, in which operator pairs (A, B) are classified according to whether or not states can be found with arbitrarily small dispersions in both A and B. If A and B cannot be made arbitrarily dispersionless simultaneously, then we call A and B an uncertainty pair. Otherwise, we call A and B a certainty pair. An interesting feature of uncertainty pairs in particular is that they are stable, in the sense that if A and B form an uncertainty pair, then slight enough perturbations of A and B must also form an uncertainty pair. This stability, obvious in the finite-dimensional case, follows in general from an operator inequality derived herein. A consequence of this inequality is that perturbed position and momentum operators X+δX and P+δP cannot share an eigenvector unless |δX|·|δP|≥ℏ/2. (Here vertical bars denote the operator norm.) This, despite the fact that (as we show) arbitrarily slight perturbations of X and P can fail to satisfy a Heisenberg inequality—a fact which raises interesting measurement issues in its own right. (shrink)

I criticize the widely-defended view that the quantum measurement problem is an example of underdetermination of theory by evidence: more specifically, the view that the unmodified, unitary quantum formalism (interpreted following Everett) is empirically indistinguishable from Bohmian Mechanics and from dynamical-collapse theories like the GRW or CSL theories. I argue that there as yet no empirically successful generalization of either theory to interacting quantum field theory and so the apparent underdetermination is broken by a very large class of quantum experiments (...) that require field theory somewhere in their description. The class of quantum experiments reproducible by either is much smaller than is commonly recognized and excludes many of the most iconic successes of quantum mechanics, including the quantitative account of Rayleigh scattering that explains the color of the sky. I respond to various arguments to the contrary in the recent literature. (shrink)

Mechanical Choices details the intimate connection that exists between morality and law: the morality we use to blame others for their misdeeds and the criminal law that punishes them for these misdeeds. This book shows how both law and morality presuppose the accuracy of common sense, a centuries-old psychology that defines people as rational agents who make honorable choices and act for just reasons. It then shows how neuroscience is commonly taken to challenge these fundamental psychological assumptions.

While the importance of mechanisms in determining causality in medicine is currently the subject of active debate, the role of mechanistic reasoning in clinical practice has received far less attention. In this paper we look at this question in the context of the treatment of a particular individual, and argue that evidence of mechanisms is indeed key to various aspects of clinical practice, including assessing population-level research reports, diagnostic as well as therapeutic decision making, and the assessment of treatment (...) effects. We use the pulmonary condition bronchiectasis as a source of examples of the importance of mechanistic reasoning to clinical practice. (shrink)

: In this article we shall deal with the construction and defense of subjective identity as a topic at the intersection of psychology and anthropology. In this perspective, defense mechanisms are seen as falling along a spectrum that stretches from the individual to the collective level. The individual mind is the sphere of the intrapsychic defenses and the interpersonal maneuvers to which each of us appeals, in the relationship with other people and with one’s own environment, to defend one’s own (...) self-describability and, indissolubly, the solidity of one’s own self-conscious being. At a social and collective level, on the other hand, the individual self-protective structures are supported by cultural interventions that organize and intersubjectively “domesticate” our subjectivity and our feeling of being-there. Keywords: Autobiographical Reasoning; Defense Mechanisms; Grief; Narrative Identity; Ontological Insecurity Meccanismi di difesa: dall’individuale al collettivo Riassunto: L’articolo si occupa di costruzione e difesa dell’identità soggettiva come tema all’intersezione di psicologia e antropologia. In questa prospettiva, i meccanismi di difesa si dispongono lungo uno spettro che dal livello individuale conduce a quello collettivo. La mente individuale è la sfera delle difese intrapsichiche e delle manovre interpersonali a cui ognuno di noi fa ricorso, nella relazione con gli altri e col proprio ambiente, per difendere la propria autodescrivibilità e, inscindibilmente, la solidità del proprio essere autocosciente. Al livello sociale e collettivo, invece, le strutture autoprotettive dell’individuo sono sorrette da interventi culturali che organizzano e “addomesticano” intersoggettivamente la nostra soggettività e il nostro sentirci esistere. Parole chiave: Ragionamento autobiografico; Meccanismi di difesa; Cordoglio; Identità narrativa; Insicurezza ontologica. (shrink)

In this paper, I investigate the study of causal mechanisms in the social sciences. I argue that unless one adopts a clear notion of causation, such as Woodward's manipulability theory of causation, one does not find evidence for causal claims. I show that adopting Woodward’s theory entails that a researcher must take into account both the observable implications of the mechanisms, and possible interventions on those mechanisms. In a backlash against the pervasiveness of statistical methods, in the last decade or (...) so social scientists have become more focused on finding the causal mechanisms behind observed correlations. To provide evidence for such causal claims, researchers often rely on process-tracing, a method which involves contrasting the observable implications of several alternative mechanisms. Although process-tracing has gained prominence as a technique, researchers do not share a fundamental framework of what causation is. I will show what process-tracers’ reasoning would look like if they were to commit to Woodward’s manipulability theory. This theory tells us that any successful explanation of an effect must refer to causal factors that could be manipulated to change the phenomenon under study. Specifically, a variable X is a cause of another variable Y if there exists some ‘intervention variable’ I. I is an intervention variable if we can use I to change X, which will then in turn change Y without any interference of other variables linked to Y. In other words, using I we will be able to ascertain that it was X that made the change in Y happen. I will argue that if a process-tracing researcher were to adopt the manipulability notion of causation, she would not only have to find observable implications of the alternative mechanisms under study, but also information regarding an intervention variable for each link of the causal chain. (shrink)

This paper offers an account of what it is for a physical system to be a computing mechanism—a system that performs computations. A computing mechanism is a mechanism whose function is to generate output strings from input strings and (possibly) internal states, in accordance with a general rule that applies to all relevant strings and depends on the input strings and (possibly) internal states for its application. This account is motivated by reasons endogenous to the philosophy of computing, namely, doing (...) justice to the practices of computer scientists and computability theorists. It is also an application of recent literature on mechanisms, because it assimilates computational explanation to mechanistic explanation. The account can be used to individuate computing mechanisms and the functions they compute and to taxonomize computing mechanisms based on their computing power. (shrink)

Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very notion (...) of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science. (shrink)

As much as assumptions about mechanisms and mechanistic explanation have deeply affected psychology, they have received disproportionately little analysis in philosophy. After a historical survey of the influences of mechanistic approaches to explanation of psychological phenomena, we specify the nature of mechanisms and mechanistic explanation. Contrary to some treatments of mechanistic explanation, we maintain that explanation is an epistemic activity that involves representing and reasoning about mechanisms. We discuss the manner in which mechanistic approaches serve to bridge levels rather (...) than reduce them, as well as the different ways in which mechanisms are discovered. Finally, we offer a more detailed example of an important psychological phenomenon for which mechanistic explanation has provided the main source of scientific understanding. (shrink)

Can findings from psychology and cognitive neuroscience about the neural mechanisms involved in decision-making can tell us anything useful about the commonly-understood mental phenomenon of making voluntary choices? Two philosophical objections are considered. First, that the neural data is subpersonal, and so cannot enter into illuminating explanations of personal level phenomena like voluntary action. Secondly, that mental properties are multiply realized in the brain in such a way as to make them insusceptible to neuroscientific study. The paper argues that both (...) objections would be weakened by the discovery of empirical generalisations connecting subpersonal properties with the personal level. It gives three case studies that furnish evidence to that effect. It argues that the existence of such interrelations are consistent with a plausible construal of the personal-subpersonal distinction. Furthermore, there is no reason to suppose that the notion subpersonal representation relied on in cognitive neuroscience illicitly imports personal-level phenomena like consciousness or normativity, or is otherwise explanatorily problematic. (shrink)

In a paper that recently appeared in this journal, we proposed a model that aims at providing a comprehensive account of our ability to intelligently use tools, bridging sensorimotor and reasoning-based explanations of this ability. Central to our model is the notion of generalized motor programs for tool use, which we defined as a synthesis between classic motor programs, as described in the scientific literature, and Peircean habits. In his commentary, Osiurak proposes a critique of the notion of generalized (...) motor program, and suggests that the limitations of our model can be solved by integrating it with the view that motor programs are generated by a previous mechanical reasoning, independent from sensorimotor knowledge. Here we reply that while on the one hand our reference to Peircean habits gets over the temptation to consider motor programs as fixed internal entities, it also rejects the view, endorsed by Osiurak, that intelligent practice is a mixture of antecedent abstract reasoning and subsequent motor execution. (shrink)

Philosophers of social science have emphasized mechanistic approaches to causal inquiry for some time now, showing why focusing on the mechanisms behind correlations is preferable to focusing on correlations alone (cf. Johnson 2006, Little 1991, Reiss 2007, 2009, Steel 2004, see also King, Keohane, and Verba 1994 for an example of purely correlational research). In Process Tracing: from Metaphor to Analytic Tool, political scientists Andrew Bennett and Jeffrey Checkel present a concrete method for finding evidence of causal mechanisms, process tracing. (...) Process tracers give evidence for causal relations in terms of the observable implications of the underlying causal mechanisms through which a putative cause affects some effect of interest. Such observable implications often take the form of a chain of events, or process, which connects cause and effect. Though Process Tracing contains applications of mechanistic reasoning unfamiliar to philosophers, and as such will be of interest to those working in the mechanist tradition, Bennett and Checkel’s own discussion of the philosophical foundations of process tracing is limited. The reader will have to delve deep into the volume’s contributed chapters for links between the literature on causation and this new method. (shrink)

Some proponents of mechanistic explanation downplay the significance of how-possibly explanations. We argue that developing accounts of mechanisms that could explain a phenomenon is an important aspect of scientific reasoning, one that involves imagination. Although appeals to imagination may seem to obscure the process of reasoning, we illustrate how, by examining diagrams we can gain insights into the construction of mechanistic explanations.

The capacity to generate recursive sequences is a marker of rich, algorithmic cognition, and perhaps unique to humans. Yet, the precise processes driving recursive sequence generation remain mysterious. We investigated three potential cognitive mechanisms underlying recursive pattern processing: hierarchical reasoning, ordinal reasoning, and associative chaining. We developed a Bayesian mixture model to quantify the extent to which these three cognitive mechanisms contribute to adult humans’ performance in a sequence generation task. We further tested whether recursive rule discovery depends (...) upon relational information, either perceptual or semantic. We found that the presence of relational information facilitates hierarchical reasoning and drives the generation of recursive sequences across novel depths of center embedding. In the absence of relational information, the use of ordinal reasoning predominates. Our results suggest that hierarchical reasoning is an important cognitive mechanism underlying recursive pattern processing and can be deployed across embedding depths and relational domains. (shrink)

With In Search of Mechanisms, Carl F. Craver and Lindley Darden offer both a descriptive and an instructional account of how biologists discover mechanisms. Drawing on examples from across the life sciences and through the centuries, Craver and Darden compile an impressive toolbox of strategies that biologists have used and will use again to reveal the mechanisms that produce, underlie, or maintain the phenomena characteristic of living things. They discuss the questions that figure in the search for mechanisms, characterizing the (...) experimental, observational, and conceptual considerations used to answer them, all the while providing examples from the history of biology to highlight the kinds of evidence and reasoning strategies employed to assess mechanisms. At a deeper level, Craver and Darden pose a systematic view of what biology is, of how biology makes progress, of how biological discoveries are and might be made, and of why knowledge of biological mechanisms is important for the future of the human species. (shrink)

In this paper I offer an analysis of causation based upon a theory of mechanisms-complex systems whose internal parts interact to produce a system's external behavior. I argue that all but the fundamental laws of physics can be explained by reference to mechanisms. Mechanisms provide an epistemologically unproblematic way to explain the necessity which is often taken to distinguish laws from other generalizations. This account of necessity leads to a theory of causation according to which events are causally related when (...) there is a mechanism that connects them. I present reasons why the lack of an account of fundamental physical causation does not undermine the mechanical account. (shrink)

I argue that difference-making should be a crucial element for evaluating the quality of evidence for mechanisms, especially with respect to the robustness of mechanisms, and that it should take central stage when it comes to the general role played by mechanisms in establishing causal claims in medicine. The difference- making of mechanisms should provide additional compelling reasons to accept the gist of Russo-Williamson thesis and include mechanisms in the protocols for Evidence- Based Medicine, as the EBM+ research group has (...) been advocating. (shrink)

I argue that Bohmian mechanics cannot reasonably be claimed to be a deterministic theory. If one assumes the “quantum equilibrium distribution” provided by the wave function of the universe, Bohmian mechanics requires an external random oracle in order to describe the algorithmic randomness properties of typical outcome sequences of long runs of repeated identical experiments. This oracle lies beyond the scope of Bohmian mechanics, including the impossibility of explaining the randomness property in question from “random” initial conditions. Thus the advantages (...) of Bohmian mechanics over other interpretations of quantum mechanics, if any, must lie at an ontological level, and in its potential to derive the quantum equilibrium distribution and hence the Born rule. (shrink)

A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of interest for two primary reasons. Firstly, NCQs arise prominently in semi-classical approximation schemes. Their formal study may yield improved approximation techniques in the near-classical regime. More importantly for the purposes of this note, it may be possible for NCQs to reproduce quantum results over experimentally tested regimes while (...) having a well defined classical limit, and hence are viable alternative theories. We illustrate an NCQ by considering an explicit class of NCQ mechanics. Here this class will be arrived at via a natural generalization of classical mechanics formulated in terms of a probability density functional. (shrink)