Contrary to popular belief, I argue that Leibniz is not hopelessly confused about motion: Leibniz is indeed both a relativist and an absolutist about motion, as suggested by the textual evidence, but, appearances to the contrary, this is not a problem; Leibniz’s infamous doctrine of the equivalence of hypotheses is well-supported and well-integrated within Leibniz’s physical theory; Leibniz’s assertion that the simplest hypothesis of several equivalent hypotheses can be held to be true can be explicated in such (...) a way that it makes good sense; the mere Galilean invariance of Leibniz’s conservation law does not compromise Leibniz’s relativism about motion; and Leibniz has a straightforward response to Newton’s challenge that the observable effects of the inertial forces of rotational motions empirically distinguish absolute from relative motions. (shrink)

Leibniz’s conception of the relativity of motion has been discussed at length for a very long time. This paper doesn’t aim to give a full solution to this question, but to contribute to the debate by clarifying how the principle of relativity is introduced, justified and used in the “Dynamica”. Four different principles are identified : one purely geometrical, and three (meta) physical principles, which express God’s wisdom : a principle of equivalence of hypotheses linked to the action/reaction (...) principle, a Galilean principle of relativity and a general principle which apply not only to rectilinear motions but also to circular ones. I argue that to appreciate the coherence of Leibniz’ approach, we should distinguish these principles more sharply than he himself did and pay more attention to their status : are they consequences of the definition of motion, consequences of the physical laws or necessary conditions for any physical theory? (shrink)

We characterize elementary equivalences and inclusions between von Neumann regular real closed rings in terms of their boolean algebras of idempotents, and prove that their theories are always decidable. We then show that, under some hypotheses, the map sending an L-structure R to the L-structure of definable functions from R n to R preserves elementary inclusions and equivalences and gives a structure with a decidable theory whenever R is decidable. We briefly consider structures of definable functions satisfying an extra (...) condition such as continuity. (shrink)

In the introduction to his famous book, La Science et l’hypothèse, Poincaré remarks on the necessary role and legitimacy of hypotheses. He establishes a triple classification of hypotheses, dividing them into verifiable, useful, and apparent. However, in chapter 9, entitled ‘Les hypothèses en physique’, he gives a slightly different triadic classification: natural hypotheses, indifferent hypotheses, and real generalizations. The origin of this second classification is a lecture given at the International Congress of Physics, Paris, 1900. What (...) are the similarities and differences between these two classifications? My main purpose is to provide a possible equivalence between the two classifications in order to clarify the role of hypotheses in Poincaré’s epistemology of natural science. The discussion will be based on the two fundamental texts mentioned above and on the contrast between Poincaré’s use of the notion of hypothesis and that of some of his contemporaries. (shrink)

Two logics L1 and L2 are negatively equivalent if for any set of formulas X and any negated formula ¬, ¬ can be deduced from the set of hypotheses X in L1 if and only if it can be done in L2. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.

According to Nicod's criterion of confirmation, a hypothesis of the form ‘All P are Q’ is confirmed by its positive instances, i.e. by entities that are P and Q. It is well known, however, that the criterion gives origin to counterintuitive results. For example, it sanctions the confirmation of ‘All nonblacks are nonravens’ by a nonblack nonraven. Since this hypothesis is logically equivalent to ‘All ravens are black,’ it follows that the criterion indirectly sanctions the counterintuitive confirmation of ‘All ravens (...) are black’ by a non black nonraven, e.g. by a white shoe. (shrink)

The underdetermination of theory by evidence must be distinguished from holism. The latter is a doctrine about the testing of scientific hypotheses; the former is a thesis about empirically adequate logically incompatible global theories or "systems of the world". The distinction is crucial for an adequate assessment of the underdetermination thesis. The paper shows how some treatments of underdetermination are vitiated by failure to observe this distinction, and identifies some necessary conditions for the existence of multiple empirically equivalent global (...) theories. We consider how empiricists should respond to the possibility of such systems of the world. (shrink)

I consider the error-statistical account as both a theory of evidence and as a theory of inference. I seek to show how inferences regarding the truth of hypotheses can be upheld by avoiding a certain kind of alternative hypothesis problem. In addition to the testing of assumptions behind the experimental model, I discuss the role of judgments of implausibility. A benefit of my analysis is that it reveals a continuity in the application of error-statistical assessment to low-level empirical (...) class='Hi'>hypotheses and highly general theoretical principles. This last point is illustrated with a brief sketch of the issues involved in the parametric framework analysis of tests of physical theories such as General Relativity and of fundamental physical principles such as the Einstein Equivalence Principle. (shrink)

Pursuant to criticism, this paper revisits the relation between the theses of empirical equivalence and evidential underdetermination. I argue against some antirealist strategies for fixing the empirical commitments of underdetermined theories.

Jarrett Leplin in A Novel Defense of Scientific Realism (1997) argues that if the thesis of empirical equivalence is cogent, then the thesis of underdetermination cannot even get off the ground. Part of Leplin's argument rests on the claim that auxiliary hypotheses can be independently confirmed, thus enabling us to determine the epistemic worth of a theory. This, in turn, helps in determining about what we should be realists. Leplin's claims are demonstrated to be problematic. Leplin wants, inconsistently, (...) to use only those auxiliary hypotheses which dovetail with confirmed theories. Finally, a detail of Leplin's argument is found wanting. (shrink)

Although children learn more when teachers gesture, it is not clear how gesture supports learning. Here, we sought to investigate the nature of the memory processes that underlie the observed benefits of gesture on lasting learning. We hypothesized that instruction with gesture might create memory representations that are particularly resistant to interference. We investigated this possibility in a classroom study with 402 second‐ and third‐grade children. Participants received classroom‐level instruction in mathematical equivalence using videos with or without accompanying gesture. (...) After instruction, children solved problems that were either visually similar to the problems that were taught, and consistent with an operational interpretation of the equal sign (interference), or visually distinct from equivalence problems and without an equal sign (control) in order to assess the role of gesture in resisting interference after learning. Gesture facilitated learning, but the effects of gesture and interference varied depending on type of problem being solved and the strategies that children used to solve problems prior to instruction. Some children benefitted from gesture, while others did not. These findings have implications for understanding the mechanisms underlying the beneficial effect of gesture on mathematical learning, revealing that gesture does not work via a general mechanism like enhancing attention or engagement that would apply to children with all forms of prior knowledge. (shrink)

A Bayesian measure of evidence for precise hypotheses is presented. The intention is to give a Bayesian alternative to significance tests or, equivalently, to p-values. In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the “Highest Posterior Density Region” that is “tangent” to the set that defines the null hypothesis. Our measure of evidence is the complement of the credibility of the “tangent” region.

This essay develops a interpretation of Leibniz’ theory of motion that strives to integrate his metaphysics of force with his doctrine of the equivalence of hypotheses, but which also supports a realist, as opposed to a fully idealist, interpretation of his natural philosophy. Overall, the modern approaches to Leibniz’ physics that rely on a fixed spacetime backdrop, classical mechanical constructions, or absolute speed, will be revealed as deficient, whereas a more adequate interpretation will be advanced that draws inspiration (...) from an invariantist conception of reality and recent non-classical theories of physics. (shrink)

We suggest that human culture exhibits key Darwinian evolutionary properties, and argue that the structure of a science of cultural evolution should share fundamental features with the structure of the science of biological evolution. This latter claim is tested by outlining the methods and approaches employed by the principal subdisciplines of evolutionary biology and assessing whether there is an existing or potential corresponding approach to the study of cultural evolution. Existing approaches within anthropology and archaeology demonstrate a good match with (...) the macroevolutionary methods of systematics, paleobiology, and biogeography, whereas mathematical models derived from population genetics have been successfully developed to study cultural microevolution. Much potential exists for experimental simulations and field studies of cultural microevolution, where there are opportunities to borrow further methods and hypotheses from biology. Potential also exists for the cultural equivalent of molecular genetics in “social cognitive neuroscience,” although many fundamental issues have yet to be resolved. It is argued that studying culture within a unifying evolutionary framework has the potential to integrate a number of separate disciplines within the social sciences. (shrink)

One of the most difficult and interesting problems of rational decision is the choice among possible diverging paths in theory construction and among competing scientific theories—i.e., systems of accurate testable hypotheses. This task involves many beliefs—some warranted and others not as warranted—and marks decisive crossroads. Suffice to recall the current conflict between the general theory of relativity and alternative theories of gravitation that account for the same empirical evidence, the rivalry among different interpretations of quantum mechanics, and the variety (...) of cosmological theories. They all account for the same observed facts although they may predict different kinds of as yet unknown facts; they are consequently, up to now, empirically equivalent theories even though they are conceptually different and may even involve different philosophical views—i.e., they are conceptually inequivalent. (shrink)

What, if anything, is wrong with conspiracy theories? A conspiracy refers to a group of people acting in secret to achieve some nefarious goal. But given that the pages of history are full of such plots, why are CTs regarded with suspicion? Just like with the traditional demarcation problem, philosophers disagree about where to draw the line between legitimate hypotheses about conspiracies and unfounded ‘conspiracy theories’. Some believe that there is no such demarcation line to be drawn, that each (...) CT should be evaluated on its own merits, and that the bad reputation of CTs is wholly undeserved. In this paper, I intend to rescue the intuition that there is indeed something prima facie suspicious about CTs. First, I demarcate legitimate theorizing about real-life conspiracies from “mere conspiracy theories”. Along the way, my analysis will clarify some epistemological issues surrounding falsifiability, asymmetries between causes and effects, and hypotheses involving intentional agents. Because of their extreme resilience to external criticism and counterevidence, I argue, CTs are the epistemological equivalent of a ‘black hole’, in which unwary truth-seekers are drawn, never to escape again. But this strong attraction of CTs comes at a steep price: their theoretical parameters are essentially arbitrary, making them vulnerable to internal disruption. In essence, because it is so easy to construct a novel CT, it is equally easy to construct many ones about the same historical event. And that is what justifies our suspicion of CTs. (shrink)

The existence of superstition and religious beliefs in most, if not all, human societies is puzzling for behavioral ecology. These phenomena bring about various fitness costs ranging from burial objects to celibacy, and these costs are not outweighed by any obvious benefits. In an attempt to resolve this problem, we present a verbal model describing how humans and other organisms learn from the observation of coincidence (associative learning). As in statistical analysis, learning organisms need rules to distinguish between real patterns (...) and randomness. These rules, which we argue are equivalent to setting the level of α for rejection of the null hypothesis in statistics, are governed by risk management as well as by comparison to previous experiences. Risk management means that the cost of a possible type I error (superstition) has to be traded off against the cost of a possible type II error (ignorance). This trade-off implies that the occurrence of superstitious beliefs is an inevitable consequence of an organism’s ability to learn from observation of coincidence. Comparison with previous experiences (as in Bayesian statistics) improves the chances of making the right decision. While this Bayesian approach is found in most learning organisms, humans have evolved a unique ability to judge from experiences whether a candidate subject has the power to mechanistically cause the observed effect. Such “strong” causal thinking evolved because it allowed humans to understand and manipulate their environment. Strong causal thinking, however, involves the generation of hypotheses about underlying mechanisms (i.e., beliefs). Assuming that natural selection has favored individuals that learn quicker and more successfully than others owing to (1) active search to detect patterns and (2) the desire to explain these patterns mechanistically, we suggest that superstition has evolved as a by-product of the first, and that belief has evolved as a by-product of the second. (shrink)

This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further developing these (...) ideas. That project was still incomplete when Blok died. In fact, there is no indication that he had prepared a draft of the paper, and we do not know what new material he intended to include. I am therefore not in a position to complete the project as he had envisioned it. So, I have settled for the more limited objective of presenting the material from the three lectures, leaving to others the task of adapting the techniques used there to more general situations. (shrink)

Have Sober and Wilson salvaged a sophisticated and sound perspective for group selection from the rhetorical overkill of the selfish-gene’s-eye gang, or have they merely reinvented Hamilton’s and Maynard Smith’s alternative to group selection models, models that can do justice to all the observed and even imagined phenomena of cooperation in the biosphere? One of the main lessons I have learned in thinking about the issues raised by Unto Others over the last two years is that they are, at least (...) for me, mind-twistingly elusive and slippery. The appeal of the competing metaphors is such that there is unwitting sleight of hand in every direction, as the perspectives shift back and forth. One stern admonition might then be: eschew the metaphors, stick to the math! The problem is that the math doesn’t distinguish between the perspectives Sober and Wilson champion and those they oppose. By their own account, the mathematical models are equivalent in what they can predict—and hence equivalent in what they can, in one important sense, explain. But that is not the end of it: “When one theory achieves an insight by virtue of its perspective, the same insight can usually be explained in retrospect by the other theories. As long as the relationships among the theories are clearly understood, this kind of pluralism is a healthy part of science.”. Good point. Patrick Suppes used to delight in challenging cognitive psychologists to point to any “cognitive” phenomenon that he couldn’t model, retrospectively, in strict behaviorist terms. The wise response was to deflect the challenge. His behaviorist models were parasitic: they would never have been devised—the phenomena in question were all but invisible to the behaviorists—without the inspiration of the cognitive model they translated into behaviorese. And what Sober and Wilson say here echoes what one of their chief opponents, Richard Dawkins, had already claimed for his perspective: “The extended phenotype may not constitute a testable hypothesis in itself, but it so far changes the way we see animals and plants that it may cause us to think of testable hypotheses that we would otherwise never have dreamed of.” So what’s all the fuss about? If each side is just saying “Here’s a good way of thinking of things, a prolific generator of hypotheses to test!” they could both be right, with their different perspectives having rather different utilities in different circumstances. (shrink)

In recent years, the principle of equivalence has been accepted in many countries as the standard against which healthcare provision for prisoners should be measured. There are several ways in which this principle can be interpreted, but current policy in the UK and elsewhere seems to focus on the measurement and achievement of equivalence in the process of healthcare provision. We argue that it is not appropriate to apply this interpretation to all aspects of prisoner healthcare, as it (...) does not necessarily address the challenges inherent to the prisoner population and prison setting. Consequently equivalence of health outcomes should also be considered alongside processes in the interests of providing healthcare in prison that is equivalent to that outside prison. (shrink)

We hypothesize that in modern societies the striving for high positions in the hierarchy of organizations is equivalent to the striving for status and power in historical and traditional societies. Analyzing a sample of 4,491 US men and 5,326 US women, we find that holding a supervisory position or being in charge of hiring and firing is positively associated with offspring count in men but not in women. The positive effect in men is attributable mainly to the higher proportion of (...) childlessness among men in non-supervisory positions and those without the power to hire and fire. This effect is in accordance with the positive relationship between other status indicators and reproductive success found in men from traditional, historical, and modern societies. In women, we further find a curvilinear relationship between income percentile and offspring number by analyzing US census data, indicating that women may strive for resources associated with advancement rather than for status per se. (shrink)

Dijkstra and Scholten have proposed a formalization of classical predicate logic on a novel deductive system as an alternative to Hilbert's style of proof and Gentzen's deductive systems. In this context we call it CED (Calculus of Equational Deduction). This deductive method promotes logical equivalence over implication and shows that there are easy ways to prove predicate formulas without the introduction of hypotheses or metamathematical tools such as the deduction theorem. Moreover, syntactic considerations (in Dijkstra's words, "letting the (...) symbols do the work") have led to the "calculational style," an impressive array of techniques for elegant proof constructions. In this paper, we formalize intuitionistic predicate logic according to CED with similar success. In this system (I-CED), we prove Leibniz's principle for intuitionistic logic and also prove that any (intuitionistic) valid formula of predicate logic can be proved in I-CED. (shrink)

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCAσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathsf {ZFCA}_{\sigma }$$\end{document} with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.

Dijkstra and Scholten have proposed a formalization of classical predicate logic on a novel deductive system as an alternative to Hilbert's style of proof and Gentzen's deductive systems. In this context we call it CED . This deductive method promotes logical equivalence over implication and shows that there are easy ways to prove predicate formulas without the introduction of hypotheses or metamathematical tools such as the deduction theorem. Moreover, syntactic considerations have led to the "calculational style," an impressive (...) array of techniques for elegant proof constructions. In this paper, we formalize intuitionistic predicate logic according to CED with similar success. In this system , we prove Leibniz's principle for intuitionistic logic and also prove that any valid formula of predicate logic can be proved in I-CED. (shrink)

The history of biochemistry and molecular biology is replete with examples of erroneous theories that persisted for considerable lengths of time before they were rejected. This paper examines patterns of dissolution of three such erroneous hypotheses: The idea that nucleic acids are tetrads of the four nucleobases (‘the tetranucleotide hypothesis’); the notion that proteins are collinear with their encoding genes in all branches of life; and the hypothesis that proteins are synthesized by reverse action of proteolytic enzymes. Analysis of (...) these cases indicates that amassed contradictory empirical findings did not prompt critical experimental testing of the prevailing theories nor did they elicit alternative hypotheses. Rather, the incorrect models collapsed when experiments that were not purposely designed to test their validity exposed new facts. (shrink)

We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. This leads to a natural equivalence notion for gaps about which we answer questions by constructing many simultaneous gaps. The first result is proved in ZFC while new combinatorial hypotheses generalizing ♣ are introduced to prove the second result. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory. Additionally, the notion of (...) an incollapsible gap is introduced and the existence of such a gap is shown to be independent of ZFC. (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the (...) cases of k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

The main result of this paper is the equivalence of several definition schemas of bar recursion occurring in the literature on functionals of finite type. We present the theory of functionals of finite type, in [T] denoted byqf-WE-HA ω, which is necessary for giving the equivalence proofs. Moreover we prove two results on this theory that cannot be found in the literature, namely the deduction theorem and a derivation of Spector's rule of extensionality from [S]: ifP→T 1=T 2 (...) and Q[X∶≡T1], then P→Q[X∶≡ T2], from the at first sight weaker rule obtained by omitting “P→”. (shrink)

The introduction of statistical models represented by directed acyclic graphs (DAGs) has proved fruitful in the construction of expert systems, in allowing efficient updating algorithms that take advantage of conditional independence relations (Pearl, 1988, Lauritzen et al. 1993), and in inferring causal structure from conditional independence relations (Spirtes and Glymour, 1991, Spirtes, Glymour and Scheines, 1993, Pearl and Verma, 1991, Cooper, 1992). As a framework for representing the combination of causal and statistical hypotheses, DAG models have shed light on (...) a number of issues in statistics ranging from Simpson’s Paradox to experimental design (Spirtes, Glymour and Scheines, 1993). The relations of DAGs with statistical constraints, and the equivalence and distinguishability properties of DAG models, are now well understood, and their characterization and computation involves three properties connecting graphical structure and probability distributions: (i) a local directed Markov property, (ii) a global directed Markov property, (iii) and factorizations of joint densities according to the structure of a graph (Lauritizen, et al., 1990). (shrink)

Normative systems have been advocated as an effective tool to regulate interaction in multi-agent systems. The use of deontic operators and the ability to represent defeasible information are known to be two fundamental ingredients to represent and reason about normative systems. In this paper, after introducing a framework that combines standard deontic logic and non-monotonic logic programming, deontic logic programs (DLP), we tackle the fundamental problem of equivalence between normative systems using a deontic extension of David Pearce’s Equilibrium Logic (...) and its monotonic basis, the logic of Here-and-There. We also show how deontic logic programs can be used to represent and reason about normative systems, and establish a strong connection with input-output logic. (shrink)

We discuss several axiomatizations of set theory in first order predicate calculus with epsilon and a constant symbol W, starting with the simple system K(W) which has a strong equivalence with ZF without Foundation. The other systems correspond to various extensions of ZF by certain large cardinal hypotheses. These axiomatizations are unusually simple and uncluttered, and are highly suggestive of underlying philosophical principles that generate higher set theory.

In a seminal paper, Aumann (1987, Econometrica 55, 1–18) showed how the choices of rational players could be analyzed in a unified state space framework. His innovation was to include the choices of the players in the description of the states, thus abolishing Savage’s (1954, The Foundations of Statistics. Wiley, New York) distinction between acts and consequences. But this simplification comes at a price: Aumann’s notion of Bayes rationality does not allow players to evaluate what would happen were they to (...) deviate from their actual choices. We show how the addition of a causal structure to the framework enables us to analyze such counterfactual statements, and use it to introduce a notion of causal rationality. Under a plausible causal independence condition, the two notions are shown to be equivalent. If we are prepared to accept this condition we can dispense with the causal apparatus and retain Aumann’s original framework. (shrink)

Research on sleep loss and vigilance both focus on declines in cognitive performance, but theoretical accounts have developed largely in parallel in these two areas. In addition, computational instantiations of theoretical accounts are rare. The current work uses computational modeling to explore whether the same mechanisms can account for the effects of both sleep loss and time on task on performance. A classic task used in the sleep deprivation literature, the Psychomotor Vigilance Test, was extended from the typical 10-min duration (...) to 35 min, to make the task similar in duration to traditional vigilance tasks. A computational cognitive model demonstrated that the effects of time on task in the PVT were equivalent to those observed with sleep loss. Subsequently, the same mechanisms were applied to a more traditional vigilance task—the Mackworth Clock Task—providing a good fit to existing data. This supports the hypothesis that these different types of fatigue may produce functionally equivalent declines in performance. (shrink)

The author considers James’ (1910) essay The Moral Equivalent of War and applies some of its ideas to another pressing problem of our times, which for short is called greed, but can be described more precisely as the working out of the possessive market society under the conditions of neoliberalism and great technological power. James considered that pacifists had the best arguments, but failed to persuade mainstream society. The same can be said today of the critics of neoliberalism. There is (...) need for radical change away from an unjust and dysfunctional economic system, but mainstream society is unwilling to try new ideas. The present author adapts James’ idea and considers benign and malign forms of greed. What we all desire, more than huge monetary assets, is self-respect and social respect. There are already many rewards that are not primarily monetary. In a radically different culture, which rejected the principles of unlimited accumulation and almost unlimited convertibility, benign rewards would motivate constructive activity. The moral equivalents of greed briefly discussed here are—Honours and prizes for merit (administered justly); Celebrity (important in society); Luck (gambling, with certain constraints, could be benign); Power (rewarding in itself, so large monetary gain need not go with it); Services (people making important contributions to society could concentrate their commitment); Temporary custody of public treasures (a privilege prized by some). The essay ends by linking James’ idea, the Faustian bargain myth, and the necessity of hope. (shrink)

This article presents a weak system of intuitionistic second-order arithmetic, WKV, a subsystem of the one in S.C. Kleene, R.E. Vesley [The Foundations of Intuitionistic Mathematics: Especially in Relation to Recursive Functions, North-Holland Publishing Company, Amsterdam, 1965]. It is then shown that some statements of real analysis, like a version of the Heine–Borel Theorem, and some statements of logic, e.g. compactness of classical proposition calculus, are equivalent to the Fan Theorem in this system.

Several extensions of Gödel's system TT with new forms of recursion have been designed for the purpose of giving a computational interpretation to classical analysis. One can organise many of these extensions into two groups: those based on bar recursion , which include Spector's original bar recursion, modified bar recursion and the more recent products of selections functions, or those based on open recursion which in particular include the symmetric Berardi–Bezem–Coquand functional. We relate these two groups by showing that both (...) open recursion and the BBC functional are primitive recursively equivalent to a variant of modified bar recursion. Our results, in combination with existing research, essentially complete the classification up to primitive recursive equivalence of those extensions of system TT used to give a direct computational interpretation to choice principles. (shrink)

Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, (...) Glymour and Halvorson. (shrink)

The ArgumentThis paper applies the approach developed by the congnitive sciences to a classical field of social anthropology—i.e., the analysis of represetations and behaviors relative to misfortune in “traditional” societies.The initial argument is that the conceptual division and the modes of description and explanation of anthropology suffer from serious weaknesses: these concepts cannot serve to understand empirical phenomena ; they rely on a confused and erroneous conception of the different domains involved and the causalities between them; and they use simplistic (...) hypotheses about the existence and causal status of the entities that usually form the ultima ratio of anthropological reasoning. These entities would directly “cause” other individual representations or behaviors. This simplification also affects the analysis of states of belief in these entities, to which individuals would supposedly “adhere”.I argue here that the cognitivist approach, within a “methodological individualism” framework, provides a more adequate description of phenomena observed in the field. This enables the various levels and domains to be more finely defined. The analysis of “typical” utterances and inferences in a “tranditional” society, the Senufo of the Ivory Coast, is here used to clarify these anthropological problems. Two levels can be distinguished: a priori representations, which are underdetermined, enabling them to occur within valid inferences; perception and/or action, which obeys different cognitive constraints. The existential status of unobservable entities appearing in causal inferences is not equivalent depending on whether they are determined as antecedent or consequent.This paper suggests a theory of interpretive processes and beliefs having flexible references, because they are incomplete and domain-specific. It allows a comparison with facts observed in Western societies. It is also in contrast to the ordinary conception of religious states of belief — i.e., these states would be purely psychological, states of “adherence,” collective, autonomous, obligatory, part of a systemized set of knowledge; collective notions would here logically precede individual representations. (shrink)

It is argued that neither the "theory-informity" of observations nor the Quine-Duhem thesis pose any in principle threat to the objectivity of theory evaluation. The employment of exploratory theories does not generate incommensurability, but on the contrary is responsible for the mensurability and commensurability of explanatory theories, since exploratory theories enable scientists to make observations which are critical in the evaluation of explanatory theories. The employment of exploratory theories and other auxiliary hypotheses does not enable a theory to always (...) accommodate recalcitrant observations to preserve evidential equivalence with a rival theory. Explanatory theories become rapidly degenerating if exploratory theories or other auxiliary hypotheses which inform the original confirmation base are modified to accommodate recalcitrant observations. (shrink)