An (n, k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n, k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of (...) coherence to characterize strong cutelimination in such systems. We show that the following properties of a canonical system G with arbitrary (n, k)-ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cut-elimination, and (iii) G has a strongly characteristic two-valued generalized non-deterministic matrix. (shrink)

A common way of characterizing Boltzmann’s explanation of thermodynamics in term of statistical mechanics is with reference to three ingredients: the dynamics, the past hypothesis, and the statistical postulate. In this paper I focus on the statistical postulate, and I have three aims. First, I wish to argue that regarding the statistical postulate as a probability postulate may be too strong: a postulate about typicality would be enough. Second, I wish to show that there is no need to postulate anything, (...) for the typicality postulate can be suitably derived from the dynamics. Finally, I discuss how the attempts to give preference to certain stochastic quantum theories (such as the spontaneous collapse theory) over deterministic alternatives on the basis that they do not need the statistical postulate fail. (shrink)

The role of probability is one of the most contested issues in the interpretation of contemporary physics. In this paper, I’ll be reevaluating some widely held assumptions about where and how probabilities arise. Larry Sklar voices the conventional wisdom about probability in classical physics in a piece in the Stanford Online Encyclopedia of Philosophy, when he writes that “Statistical mechanics was the first foundational physical theory in which probabilistic concepts and probabilistic explanation played a fundamental role.” And the conventional wisdom (...) about quantum probabilities is that they are basic, not reducible to the types of probabilities we see in statistical mechanics. In the first section of this paper, I’ll argue that in fact classical physics was steeped in probability long before statistical mechanics came on the scene, specifically, that an objective measure over phase space is an indispensable component of any informative physical theory. In the next section, I’ll argue that this objective measure is the fundamental form of physical probability and that quantum probabilities can be defined in terms of it. In the last, I’ll raise some questions about the metaphysical status of the fundamental measure. (shrink)

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove that such (...) a graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed. (shrink)

An (n, k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n, k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of (...) coherence to characterize strong cutelimination in such systems. We show that the following properties of a canonical system G with arbitrary (n, k)-ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cut-elimination, and (iii) G has a strongly characteristic two-valued generalized non-deterministic matrix. In addition, we define simple calculi, an important subclass of canonical calculi, for which coherence is equivalent to the weaker, standard cut-elimination property. (shrink)

A common way of characterizing Boltzmann’s explanation of thermodynamics in term of statistical mechanics is with reference to three ingredients: the dynamics, the past hypothesis, and the statistical postulate. In this paper I focus on the statistical postulate, and I have three aims. First, I wish to argue that regarding the statistical postulate as a probability postulate may be too strong: a postulate about typicality would be enough. Second, I wish to show that there is no need to postulate anything, (...) for the typicality postulate can be suitably derived from the dynamics. Finally, I discuss how the attempts to give preference to certain stochastic quantum theories (such as the spontaneous collapse theory) over deterministic alternatives on the basis that they do not need the statistical postulate fail. (shrink)

This paper pursues the question, To what extent does the propensity approach to probability contribute to plausible solutions to various anomalies which occur in quantum mechanics? The position I shall defend is that of the three interpretations — the frequency, the subjective, and the propensity — only the third accommodates the possibility, in principle, of providing a realistic interpretation of ontic indeterminism. If these considerations are correct, then they lend support to Popper's contention that the propensity construction tends to remove (...) (at least some of) the mystery from quantum phenomena. (shrink)

This article presents a relational criticism of the "morphogenetic theory" of M. Archer. This theory is founded and representative of the most influential mode of perception of the social universe of the last few decades: co-determinism (structure ↔ agency). Co-determinism's influence can be explained by its integration of modern general presuppositions like freedom, individualism, and the quest for a new social order. By identifying five basic principles of relational sociology, we see that Archer's co-deterministic theory offers a complicated solution (...) to avoid voluntarism and co-determinism, limits the potential of sociological imagination, cannot adequately see the fluidity of social processes, produces a certain reification of social structures and agency, and is based on an inconsistent use of egocentric and relational perspectives. These problems can be avoided if we use a relational approach (actor ↔ actor ⇒ structures) based on the study of complex and empirical trans-actions. (shrink)

Socially Assistive Robots are increasingly conceived as applicable tools to be used in aged care. However, the use carries many negative and positive connotations. Negative connotations come forth out of romanticized views of care practices, disregarding their already established technological nature. Positive connotations are formulated out of techno-deterministic views on SAR use, presenting it as an inevitable and necessary next step in technological development to guarantee aged care. Ethical guidance of SAR use inspired by negative connotations tends to be (...) over-restrictive whereas positive connotations tend to provide over-permissive guidance. To avoid these extremes, we report on the development and content of 21 ethical orientations regarding SAR use in aged care. These orientations resulted from a multi-phased project, which consisted of empirical-ethical research focusing on older adults’ intuitions regarding SAR use and philosophical-ethical research focusing on philosophical-ethical argumentations regarding SAR use. This project led to the Socio-historical contextualization of the ethics of SAR use, in which the ethical impact of SAR use is localized on three interrelated analysis levels: societal, organizational, and individual-relational. The 21 novel orientations regarding SAR use are structured according to these levels and further categorized into foundational and applied orientations. The first category leads to critical reflection on SAR use while the latter category inspires decision-making processes regarding this use. While going beyond the care-romantic and techno-deterministic gaze of SAR use in aged care, the described orientations balance themselves between their over-restrictiveness and over-permissiveness. (shrink)

The notion of (deterministic) chaos is frequently used in an increasing number of scientific (as well as non-scientific) contexts, ranging from mathematics and the physics of dynamical systems to all sorts of complicated time evolutions, e.g., in chemistry, biology, physiology, economy, sociology, and even psychology. Despite (or just because of) these widespread applications, however, there seem to fluctuate around several misunderstandings about the actual impact of deterministic chaos on several problems of philosophical interest, e.g., on matters of prediction (...) and computability, and determinism and the free will. In order to clarify these points a survey of the meaning variance of the concept(s) of deterministic chaos, or the various contexts in which it is applied, is given, and its actual epistemological implications are extracted. In summary, it turns out that the various concepts of deterministic chaos do not constitute a “new science”, or a “revolutionary” change of the “scientific world picture”. Instead, chaos research provides a sort of toolbox of methods which are certainly useful for a more detailed analysis and understanding of such dynamical systems which are, roughly speaking, endowed with the property of exponential sensitivity on initial conditions. Such a property, then, implies merely one, but quantitatively strong type of limitation of long-time computability and predictability, respectively. (shrink)

Gyngell and colleagues consider that the recent Nuffield Council report does not go far enough: heritable genome editing is not just justifiable in a few rare cases; instead, there is a moral imperative to undertake it. We agree that there is a moral argument for this, but in the real world it is mitigated by the fact that it is not usually possible to ensure a better life. We suggest that a moral imperative for HGE can currently only be concluded (...) if one first buys into an overly deterministic view of a genome sequence, and the role of variation within in it, in the aetiology of the disease: most diseases cannot simply be attributed to specific genetic variants that we could edit away. Multiple, poorly understood genetic and environmental factors interact to influence the expression of diseases with a genetic component, even well understood ‘monogenic’ disorders. Population-level genome analyses are now demonstrating that many genetic ’mutations' are much less predictive than previously thought 1. Furthermore, HGE might introduce new risks just as it reduces old ones; or remove protections not yet clearly delineated. (shrink)

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called ( Deterministic Dynamic logic of Agency ) which supports reasoning about actions and joint actions (...) of agents and coalitions, and agentive and coalitional capabilities. In it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess we prove that it embeds Coalition Logic. We then extend with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium. (shrink)

Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg- Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer (...) based on the following insight: we can view Legg-Hutter agents as candidates in an election, whose voters are environments, letting each environment vote (via its rewards) which agent (if either) is more intelligent. This leads to an abstract family of comparators simple enough that we can prove some structural theorems about them. It is an open question whether these structural theorems apply to more practical intelligence measures. (shrink)

There have been two principal paradigms for the formulation of the causal relation--logical implication and functional relationship. In this paper, I present a case for preferring the functional relationship formulation and then discuss how the functional relationship formulation may be implemented in the probabilistic case in a manner analogous to the way others have implemented the logical implication formulation in the probabilistic case. I show how the "local independence" assumption found in many models used in the behavioral and social sciences (...) is a consequence of the functional relation concept of probabilistic causality. I also discuss why causal relations are underdetermined in experience and are to be dealt with pragmatically in a hypothesis-testing framework. (shrink)

We present a logic, $$\mathbf {ELI^r}$$ ELI r, for the discovery of deterministic causal regularities starting from empirical data. Our approach is inspired by Mackie’s theory of causes as INUS-conditions, and implements a more recent adjustment to Mackie’s theory according to which the left-hand side of causal regularities is required to be a minimal disjunction of minimal conjunctions. To derive such regularities from a given set of data, we make use of the adaptive logics framework. Our knowledge of (...) class='Hi'>deterministic causal regularities is, as Mackie noted, most often gappy or elliptical. The adaptive logics framework is well-suited to explicate both the internal and the external dynamics of the discovery of such gappy regularities. After presenting $$\mathbf {ELI^r}$$ ELI r, we first discuss these forms of dynamics in more detail. Next, we consider some criticisms of the INUS-account and show how our approach avoids them, and we compare $$\mathbf {ELI^r}$$ ELI r with the CNA algorithm that was recently proposed by Michael Baumgartner. (shrink)

The classical traditions of Vedānta in India explored the problem of why an omnipotent being like God would permit sentient beings to suffer in His creation. This article explores the solution provided to the problem of suffering by the sixteenth-century philosopher Vyāsatīrtha. Vyāsatīrtha argued that there is a satisfying explanation of why God would permit suffering to both exist and to be unevenly distributed among the individual souls trapped in transmigratory existence. He claims that we can only reconcile the idea (...) of an independent, omnipotent God with the existence of suffering by assuming that God’s treatment of the individual souls is based primarily in their eternal, immutable ethical natures and not purely on their conduct/karma as some earlier philosophers suggested. The article is based on original translations of the passages in the Tātparyacandrikā where Vyāsatīrtha makes these arguments against his Advaita and Viśiṣṭādvaita opponents. (shrink)

In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. (...) Skurt in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed. (shrink)

The equilibrium-point hypothesis (the λ-model) is superior to all other models of single-joint control and provides deep insights into the mechanisms of control of multi-joint movements. Attempts at associating control variables with neurophysiological variables look confusing rather than promising. Probabilistic mechanisms may play an important role in movement generation in redundant systems.

Gabriel Vásquez discusses two deterministic arguments ascribed to John Wyclif. He appeals to the Anselmian solution based on the distinction between two types of necessity: antecedent and subsequent necessity. Unlike the former, the latter necessity does not destroy future event’s contingency, which is required if it is to result from a free choice. The paper discusses the Aristotelian objection according to which a statement describing some contingent future event is either without truth-value, and thus antecedently contingent but not subsequently (...) necessary at present, or it has a truth-value, but then it is not merely subsequently necessary but also antecedently necessary. The Anselmian temporal ontology is such that no absolute present parameter is to be included in the evaluation of modal tensed statements. This recognition disposes of modal notions tied to the absolute temporal qualification of statements and thus undercuts the objection. (shrink)

The main goal of this paper is to provide an abstract framework for constructing proof systems for various many-valued logics. Using the framework it is possible to generate strongly complete proof systems with respect to any finitely valued deterministic and non-deterministic logic. I provide a couple of examples of proof systems for well-known many-valued logics and prove the completeness of proof systems generated by the framework.

Carl Hempel (1965) argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon (1971, 1984, 1990, 1998) and Richard Jeffrey (1969) argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive causal (...) explanation is described and defended. It provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (shrink)

We present a logic, \, for the discovery of deterministic causal regularities starting from empirical data. Our approach is inspired by Mackie’s theory of causes as INUS-conditions, and implements a more recent adjustment to Mackie’s theory according to which the left-hand side of causal regularities is required to be a minimal disjunction of minimal conjunctions. To derive such regularities from a given set of data, we make use of the adaptive logics framework. Our knowledge of deterministic causal regularities (...) is, as Mackie noted, most often gappy or elliptical. The adaptive logics framework is well-suited to explicate both the internal and the external dynamics of the discovery of such gappy regularities. After presenting \, we first discuss these forms of dynamics in more detail. Next, we consider some criticisms of the INUS-account and show how our approach avoids them, and we compare \ with the CNA algorithm that was recently proposed by Michael Baumgartner. (shrink)

Carl Hempel argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon and Richard Jeffrey argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive causal explanation is described and defended. It (...) provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (shrink)

We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations—nowadays more commonly called multiple-conclusion logics—to the setting of non-deterministic matrices (Nmatrices), characterizing the Nmatrix models of an arbitrary logic through a generalization of the standard class operators to the non-deterministic setting. We highlight the main differences that appear in this more general setting, in particular: the possibility to obtain Nmatrix quotients using any compatible equivalence relation (not necessarily a (...) congruence); the problem of determining when strict homomorphisms preserve the logic of a given Nmatrix; the fact that the operations of taking images and preimages cannot be swapped, which determines the exact sequence of operators that generates, from any complete semantics, the class of all Nmatrix models of a logic. Many results, on the other hand, generalize smoothly to the non-deterministic setting: we show for instance that a logic is finitely based if and only if both the class of its Nmatrix models and its complement are closed under ultraproducts. We conclude by mentioning possible developments in adapting the Abstract Algebraic Logic approach to logics induced by Nmatrices and the associated equational reasoning over non-deterministic algebras. (shrink)

Taking hints from the Italian writer and comedian Paolo Villaggio’s works having the unlucky-to-the-utmost accountant Fantozzi as their hero, the essay tackles the issue of the role, and the possible foundations, of the law in the theoretical scenario of a perfectly deterministic world, where everything is determined by pre-set nexuses of cause-and-effect. Fantozzi is condemned by such an inescapable law of causation (Fate) to meet constant failure, in a social context structured along stiff hierarchies which are completely independent from (...) individual merits, where law enforcement always sides with the lucky ones. Within such a context, the law cannot be grounded on rational foundations-thinking, since the only possible rational conclusion is that the law is completely useless. At the same time, the law cannot be considered an outcome of power, since any power different from that of Fate is mere illusion. The essay wonders whether, in such a theoretical setting, there is the possibility of finding an alternative foundation for the law on non-objectifying thinking, starting from imagination and the idea of justice. Is it possible to imagine reliable rules based on imagination? (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part (...) of a larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

Is it possible for God both to create a deterministic world and to act specially, to realize his particular purposes within it? And if there can be such 'particular providence' or 'special divine action' (SDA) in a deterministic world, what form can it take? In this article I consider these questions, exploring a number of different models of SDA and discussing their consistency with the proposition that the world is deterministic; I also consider how the various consequences (...) of each model accord with traditional theistic assumptions about God's action in the world. I argue that, although SDA is possible in a deterministic world, none of the models that have been offered are entirely unproblematic, but accepting any of them commits one to certain consequences that may be found objectionable; thus the potential benefits of each model of SDA must be weighed against the costs of accepting such consequences. (shrink)

It is shown how the temporal-modal system of events TM (axiomatized in Appendix) allows for the avoidance of the logical determinism without the rejection of the principle of bivalence. The point is that the temporal and the modal parts of TM are so inter-related that modalities are in-the-real-world-inherent modalities independently of whether they concern actual or only possible events. Though formulated in a tenseless language, whose interpretation does not require the assumption of tense facts at the basic level of reality, (...) TM implies an objective, observer-independent difference between tenses based only on the way in which modalities are distributed along the time continuum. The conclusion is that the arrow of time is an intra-model characteristic of any model of TM that describes the non-deterministic real world up to a certain point of its history, while the flow of time is an inter-model characteristic of the continuous transition between these models. (shrink)