Online research in philosophy

As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. (...) In this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided. (shrink)

Fixed-rate versions of rule-consequentialism and rule-utilitarianism evaluate rules in terms of the expected net value of one particular level of social acceptance, but one far enough below 100% social acceptance to make salient the complexities created by partial compliance. Variable-rate versions of rule-consequentialism and rule-utilitarianism instead evaluate rules in terms of their expected net value at all different levels of social acceptance. Brad Hooker has advocated a fixed-rate version. Michael Ridge has argued that the variable-rate version is better. (...) The debate continues here. Of particular interest is the difference between the implications of Hooker's and Ridge's rules about doing good for others. (shrink)

Philosophical discussions of prioritarianism, the view that we ought to give priority to those who are worse off, have hitherto been almost exclusively focused on cases involving a fixed population. The aim of this paper is to extend the discussion of prioritarianism to encompass also variable populations. I argue that prioritarianism, in its simplest formulation, is not tenable in this area. However, I also propose several revised formulations that, so I argue, show more promise.

NPs with intensional relative clauses such as 'the impact of the book John needs to write' pose a significant challenge for trope theory (the theory of particularized properties), since they seem to refer to tropes that lack an actual bearer. This paper proposes a novel semantic analysis of such NPs on the basis of the notion of a variable object. The analysis avoids a range of difficulties that an alternative analysis based on the notion of an individual concept would (...) face. (shrink)

Wittgenstein presents in the Tractatus a variable purporting to capture the general form of proposition. One understanding of what Wittgenstein is doing there, an understanding in line with the ‘new’ reading of his work championed by Diamond, Conant and others, sees it as a deflationary or even an implosive move—a move by which a concept sometimes put by philosophers to distinctively metaphysical use is replaced, in a perspicuous notation, by an innocent device of generalization, thereby dispersing the clouds (...) of philosophy that formerly surrounded the concept. By asking how Wittgenstein supposed his variable to work, and what work he imagined it was fit for, the paper questions the adequacy of that understanding. (shrink)

Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view in (...) linguistics is that reflexive and personal pronouns are free variables that get bound by an antecedent through some coindexing mechanism. In variable free semantics the same task is performed by some combinator that identifies two arguments of the function it operates on (a duplicator). This combinator may be built into the lexical semantics of the pronoun, into that of the antecedent, or it may be a free-floating operation applicable to predicates or larger chunks of texts, i.e. a typeshifter. This note is concerned with the case of cross-sentential anaphora. It adopts Hepple’s and Jacobson’s interpretation of pronouns as identity maps and asks how this can be extended to the cross-sentential case, assuming the dynamic semantic view of anaphora. It first outlines the possibility of interpreting indefinites that antecede non-ccommanded pronouns as existential quantifiers enriched with a duplicator. Then it argues that it is preferable to use the duplicator as a type-shifter that applies “on the fly”. The proposal has consequences for two central ingredients of the classical dynamic semantic treatment: it does away with abstraction over assignments and with treating indefinites as inherently existentially quantified. However, cross-sentential anaphora remains a matter of binding, and the idea of propositions as context change potentials is retained. (shrink)

Where there is a fixed population (i.e., who exists does not depend on what choice an agent makes), the deontic version of anonymous Paretian egalitarianism holds that an option is just if and only if (1) it is anonymously Pareto optimal (i.e., no feasible alternative has a permutation that is Pareto superior), and (2) it is no less equal than any other anonymously Pareto optimal option. We shall develop and discuss a version of this approach for the variable population (...) case (i.e., where who exists does depend on what choice an agent makes). More specifically, we shall develop and discuss it in the context of a person-affecting framework—in which an option is just if and only if it wrongs no one according to certain plausible conditions on wronging. (shrink)

This paper provides an account of the experimental conditions required for establishing whether correlating or causally relevant factors are constitutive components of a mechanism connecting input (start) and output (finish) conditions. I argue that two-variable experiments, where both the initial conditions and a component postulated by the mechanism are simultaneously manipulated on an independent basis, are usually required in order to differentiate between correlating or causally relevant factors and constitutively relevant ones. Based on a typical research project molecular biology, (...) a flowchart model detailing typical stages in the formulation and testing of hypotheses about mechanistic components is also developed. (shrink)

There is a solution to the antinomy of the variable that does not call for semantic relationism. I argue that if we carefully distinguish between variable types and variable tokens or occurrences, and if we take the number of variable types involved properly into account, then coordination among variable tokens or occurrences is reducible to an intrinsic semantic feature of those tokens or occurrences. The fact that two tokens or occurrences of the same variable (...) type contained in the same sentence or context assume the same value at a time derives from an intrinsic semantic feature of a token or occurrence, namely from being a token or occurrence of a type whose tokens or occurrences must assume the same value at a time if contained in the same sentence or context. (shrink)

E. C. Tolman's 'purposive behaviorism' is commonly interpreted as an attempt to operationalize a cognitivist theory of learning by the use of the 'Intervening Variable' (IV). Tolman would thus be a counterinstance to an otherwise reliable correlation of cognitivism with realism, and S-R behaviorism with operationalism. A study of Tolman's epistemological background, with a careful reading of his methodological writings, shows the common interpretation to be false. Tolman was a cognitivist and a realist. His 'IV' has been systematically misinterpreted (...) by both behaviorists and antibehaviorists. For this reason, Tolman's alliance with modern cognitivism and his influence on its development have been underestimated. (shrink)

I show that for any quantum dynamics and any choice of observables as hidden variables an adequate hidden variable theory always exists. I argue that hidden variable theories have no more problems in reconciling non-locality with relativity than no-hidden-variable theories.

Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. (...) This is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields realvalued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense. (shrink)

The basic idea of rule-utilitarianism is that right action should be defined in terms of what would be required by rules which would maximize either actual or expected utility if those rules gained general acceptance, or perhaps general compliance. Rule-utilitarians face a dilemma. They must characterize 'general acceptance' either as 100% acceptance, or as something less. On the first horn of the dilemma, rule-utilitarianism in vulnerable to the charge of utopianism; on the second, it is open to the charge of (...) arbitrariness and lack of philosophical depth. I press this objection, and develop and defend an alternative version of rule-utilitarianism which can evade the dilemma. I call this new version 'variable-rate rule-utilitarianism'. (shrink)

Why do societies collapse? We use an individual-based evolutionary model to show that, in environmental conditions dominated by low-frequency variation (“red noise”), extirpation may be an outcome of the evolution of cultural capacity. Previous analytical models predicted an equilibrium between individual learners and social learners, or a contingent strategy in which individuals learn socially or individually depending on the circumstances. However, in red noise environments, whose main signature is that variation is concentrated in relatively large, relatively rare excursions, individual learning (...) may be selected from the population. If the social learning system comes to lack sufficient individual learning or cognitively costly adaptive biases, behavior ceases tracking environmental variation. Then, when the environment does change, fitness declines and the population may collapse or even be extirpated. The modeled scenario broadly fits some human population collapses and might also explain nonhuman extirpations. Varying model parameters showed that the fixation of social learning is less likely when individual learning is less costly, when the environment is less red or more variable, with larger population sizes, and when learning is not conformist or is from parents rather than from the general population. Once social learning is fixed, extirpation is likely except when social learning is biased towards successful models. Thus, the risk of population collapse may be reduced by promoting individual learning and innovation over cultural conformity, or by preferential selection of relatively fit individuals as models for social learning. © 2009 Elsevier Inc. All rights reserved. (shrink)

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.

We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded (...) variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we consider generalizations for non-linear systems. Keywords: latent variable models, causality, graphical models.. (shrink)

Where there is a fixed population (i.e., who exists does not depend on what choice an agent makes), the deontic version of anonymous Paretian egalitarianism holds that an option is just if and only if (1) it is anonymously Pareto optimal (i.e., no feasible alternative has a permutation that is Pareto superior), and (2) it is no less equal than any other anonymously Pareto optimal option. We shall develop and discuss a version of this approach for the variable population (...) case (i.e., where who exists does depend on what choice an agent makes). More specifically, we shall develop and discuss it in the context of a person-affecting framework—in which an option is just if and only if it wrongs no one according to certain plausible conditions on wronging. (shrink)

The sum, difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propositions and conditional events as three-valued indicator functions that are undefined when their condition is false. Extended operations of and, or, (...) not and conditioning are then defined on these conditional events with variable conditions. The probabilities of the disjunction (or) and of the conjunction (and) of two conditionals are expressed in terms of the conditional probabilities of the component conditionals. In a special case, these are shown to be weighted averages of the component conditional probabilities where the weights are the relative probabilities of the various conditions. Next, conditional random variables are defined to be random variables X whose domain has been restricted by a condition on a second random variable Y. The extended sum, difference, product and conditioning operations on functions are then applied to these conditional random variables. The expectation of a random variable and the conditional expectation of a conditional random variable are recounted. Theorem 1 generalizes the standard result that the conditional expectation of the sum of two conditional random variables with disjoint and exhaustive conditions is a weighted sum of the conditional expectations of the component conditional random variables. Because of the extended operations, the theorem is true for arbitrary conditions. Theorem 2 gives a formula for the expectation of the product of two conditional random variables. After the definition of independence of two random variables is extended to accommodate the extended operations, it is applied to the formula of Theorem 2 to simplify the expectation of a product of conditional random variables. Two examples end the paper. The first concerns a work force of n workers of different output levels and work shifts. The second example involves two radars with overlapping surveillance regions and different detection error rates. One radar's error rate is assumed to be sensitive to fog and the other radar's error rate is assumed to be sensitive to air traffic density. The combined error rate over the combined surveillance region given heavy fog and moderate air traffic is computed. (shrink)

The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.

From 1905–1908 onward, Russell thought that his new ‘substitutional theory’ provided him with the right framework to resolve the set-theoretic paradoxes. Even if he did not finally retain this resolution, the substitutional strategy was instrumental in the development of his thought. The aim of this paper is not historical, however. It is to show that Russell's substitutional insight can shed new light on current issues in philosophy of mathematics. After having briefly expounded Russell's key notion of a ‘structured variable’, (...) I connect it to two ongoing discussions: the Caesar problem, and absolute generality. (shrink)

Theabstract variable binding calculus (VB-calculus) provides a formal frame-work encompassing such diverse variable-binding phenomena as lambda abstraction, Riemann integration, existential and universal quantification (in both classical and nonclassical logic), and various notions of generalized quantification that have been studied in abstract model theory. All axioms of the VB-calculus are in the form of equations, but like the lambda calculus it is not a true equational theory since substitution of terms for variables is restricted. A similar problem with the (...) standard formalism of the first-order predicate logic led to the development of the theory of cylindric and polyadic Boolean algebras. We take the same course here and introduce the variety of polyadic VB-algebras as a pure equational form of the VB-calculus. In one of the main results of the paper we show that every locally finite polyadic VB-algebra of infinite dimension is isomorphic to a functional polyadic VB-algebra that is obtained from a model of the VB-calculus by a natural coordinatization process. This theorem is a generalization of the functional representation theorem for polyadic Boolean algebras given by P. Halmos. As an application of this theorem we present a strong completeness theorem for the VB-calculus. More precisely, we prove that, for every VB-theory T that is obtained by adjoining new equations to the axioms of the VB-calculus, there exists a model D such that T s=t iff D s=t. This result specializes to a completeness theorem for a number of familiar systems that can be formalized as VB-calculi. For example, the lambda calculus, the classical first-order predicate calculus, the theory of the generalized quantifierexists uncountably many and a fragment of Riemann integration. (shrink)

The statistical evidence for the detrimental effect of exposure to low levels of lead on the cognitive capacities of children has been debated for several decades. In this paper I describe how two techniques from artificial intelligence and statistics help make the statistical evidence for the accepted epidemiological conclusion seem decisive. The first is a variable-selection routine in TETRAD III for finding causes, and the second a Bayesian estimation of the parameter reflecting the causal influence of Actual Lead Exposure, (...) a latent variable, on the measured IQ score of middle class suburban children. (shrink)

Bell's proof purports to show that any hidden variable theory satisfying a physically reasonable locality condition is characterized by an inequality which is inconsistent with the quantum statistics. It is shown that Bell's inequality actually characterizes a feature of hidden variable theories which is much weaker than locality in the sense considered physically motivated. We consider an example of non-local hidden variable theory which reproduces the quantum statistics (and hence violates Bell's inequality). A simple extension of (...) the theory, which preserves the non-local character, alters the statistics in such a way that Bell's inequality is satisfied. (shrink)

A recent analysis by de Barros and Suppes of experimentally realizable GHZ correlations supports the conclusion that these correlations cannot be explained by introducing local hidden variables. We show, nevertheless, that their analysis does not exclude local hidden variable models in which the inefficiency in the experiment is an effect not only of random errors in the detector equipment, but is also the manifestation of a pre-set, hidden property of the particles ("prism models"). Indeed, we present an explicit prism (...) model for the GHZ scenario; that is, a local hidden variable model entirely compatible with recent GHZ experiments. (shrink)

In this paper we study the logic of relational and partial variable sets, seen as a generalization of set-valued presheaves, allowing transition functions to be arbitrary relations or arbitrary partial functions. We find that such a logic is the usual intuitionistic and co-intuitionistic first order logic without Beck and Frobenius conditions relative to quantifiers along arbitrary terms. The important case of partial variable sets is axiomatizable by means of the substitutivity schema for equality. Furthermore, completeness, incompleteness and independence (...) results are obtained for different kinds of Beck and Frobenius conditions. (shrink)

The satisfiability problem for the two-variable fragment of first-order logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations. It is shown that FO 2 over ordered, respectively wellordered, domains or in the presence of one well-founded relation, is decidable for satisfiability as well as for finite satisfiability. Actually the complexity of these decision problems is (...) essentially the same as for plain unconstrained FO 2 , namely non-deterministic exponential time. In contrast FO 2 becomes undecidable for satisfiability and for finite satisfiability, if a sufficiently large number of predicates are required to be interpreted as orderings, wellorderings, or as arbitrary wellfounded relations. This undecidability result also entails the undecidability of the natural common extension of FO 2 and computation tree logic CTL. (shrink)

The basic idea of rule-utilitarianism is that right action should be defined in terms of what would be required by rules which would maximize either actual or expected utility if those rules gained general acceptance, or perhaps general compliance. Rule-utilitarians face a dilemma. They must characterize 'general acceptance' either as 100% acceptance, or as something less. On the first horn of the dilemma, rule-utilitarianism in vulnerable to the charge of utopianism; on the second, it is open to the charge of (...) arbitrariness and lack of philosophical depth. I press this objection, and develop and defend an alternative version of rule-utilitarianism which can evade the dilemma. I call this new version 'variable-rate rule-utilitarianism'. (shrink)

Many private business relationships are increasingly characterized by claims that certain actions should not be permitted since particular right claims are involved. Such claims should be taken seriously, but are they always ethically legitimate? This paper analyzes one context, the use of age as a rating variable in the pricing of automobile insurance, where such claims are made. By identifying, evaluating and assessing the relevant basis for the differentiation, actuarial equity, it is concluded that there is an ethical basis (...) for such a practice. The analysis also provides an equivalent means for considering other such analogous claims where actuarial equity is involved. (shrink)

In this paper some parts of the model theory for logics based on generalised Kripke semantics are developed. Löwenheim-Skolem theorems and some applications of ultraproduct constructions for generalised Kripke models with variable universe are investigated using similar theorems of the model theory for classical logic. The results are generalizations of the theorems of [4].

Model RB is a model of random constraint satisfaction problems, which exhibits exact satisfiability phase transition and many hard instances, both experimentally and theoretically. Benchmarks based on Model RB have been successfully used by various international algorithm competitions and many research papers. In a previous work, Xu and Li defined two notions called i-constraint assignment tuple and flawed i-constraint assignment tuple to show an exponential resolution complexity of Model RB. These two notions are similar to some kind of consistency in (...) constraint satisfaction problems, but seem different from all kinds of consistency so far known in literatures. In this paper, we explicitly define this kind of consistency, called variable-centered consistency, and show an upper bound on a parameter in Model RB, such that up to this bound the typical instances of Model RB are variable-centered consistent. (shrink)

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no‐go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non‐contextual way. In contrast to an earlier (...) theorem (Breuer 2002) this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy. (shrink)

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non-contextual way. In contrast to an earlier (...) theorem [Breuer, Phys. Rev. Lett. 88(2002), 240402] this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy. (shrink)

A constructive proof is given which shows that every nonrecursive r.e. many-one degree is represented by the family of decision problems for partial implicational propositional calculi whose well-formed formulas contain at most two distinct variable symbols.

A three-variable biochemical prototype involving two enzymes with autocatalytic regulation proposed by Decroly and Goldbeter (1987) is analyzed using a topological approach. A two-branched manifold, a so-called template, is thus identified. For certain control parameter values, this template is a horseshoe template with a global torsion of two half-turns. This implies that the bifurcation diagram can be described using the usual sequences associated with a unimodal map with a differentiable maximum as well as exemplified by the logistic map. Moreover, (...) a type-I intermittency associated with a saddle-node bifurcation is exhibited. The dynamics from a single time series are also investigated to determine whether it is possible to investigate the dynamics of this biochemical model from the measure of a single concentration. (shrink)

Controlled languages are regimented fragments of natural languagedesigned to make the processing of natural language more efficient andreliable. This paper defines a controlled language, E2V, whose principalgrammatical resources include determiners, relative clauses, reflexivesand pronouns. We provide a formal syntax and semantics for E2V, in whichanaphoric ambiguities are resolved in a linguistically natural way. Weshow that the expressive power of E2V is equal to that of thetwo-variable fragment of first-order logic. It follows that the problemof determining the satisfiability of a (...) set of E2V sentences is NEXPTIMEcomplete. We show that E2V can be extended in various ways withoutcompromising these complexity results; however, relaxing our policy onanaphora resolution renders the satisfiability problem for E2Vundecidable. Finally, we argue that our results have a bearing on thebroader philosophical issue of the relationship between natural andformal languages. (shrink)

The satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly.

We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded (...) variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we consider generalizations for non-linear systems. Keywords: latent variable models, causality, graphical models.. (shrink)

The tableau substitution rule in free variable tableau reasoning is destructive, for in general, T has consequences that T0 lacks. We show how this destructive feature can be eliminated in favour of a set-up that replaces tableau substitution with the generation and incremental merge of variable constraints on tableau branches. The approach diifers from other constraint based techniques in tableau reasoning in that we constrain tableau branches rather than clauses, and use disunification constraints rather than unification constraints. We (...) prove soundness and completeness, with the completeness proof based on a new way to generate models from open tableaux. (shrink)

If all differences in behavior are explainable in terms of universal values pursued under variable constraints, then much ethical theorizing is pointless. A strong presumption in favor of universal values can be established by showing that differences in behavior that were previously thought to be explainable only in terms of differences in values, can in fact be explained in terms of differences in constraints. Eleven such cases are briefly discussed, including cases of differences among racial, religious and other groups (...) in crime, culinary practices and the acceptance of innovation. (shrink)

The paper deals with the meaning of the word ‘variable’ as used by various authors in various disciplines. In the first part of his article the author explains the synonyms used for this word such as indefinite numbers, mappings or concepts. He further discusses the meaning of variables and unknowns as applied in modern logic and traditional mathematics. In economic models the variable is inseparably linked to the economic quantity by which it is characterized and interpreted. Distinctions are (...) made between endogenous and exogenous variables and between a variable and its time path. (shrink)

In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, except four of them, are not strongly complete. We considerably improve this result by showing that all the intermediate logics axiomatizable by formulas in one variable, except eight of them, are not strongly ω-complete. Thus, a definitive classification of such logics with respect to the notions of canonicity, strong completeness, ω-canonicity and strong ω-completeness is given.

We study the notion of H-dimension and the formally stronger k-variable property, as considered by Gabbay, Immerman and Kozen. We exhibit a class of flows of time that has H-dimension 3, and admits a finite expressively complete set of onedimensional temporal connectives, but does not have the k-variable property for any finite k.

In this paper we find an algebraic equivalent of the Hallden property in modal logics, namely, we prove that the Hallden-completeness in any normal modal logic is equivalent to the so-called super-embedding property of a suitable class of modal algebras. The joint embedding property of a class of algebras is equivalent to the Pseudo-Relevance Property. We consider connections of the above-mentioned properties with interpolation and amalgamation. Also an algebraic equivalent of of the principle of variable separation in superintuitionistic logics (...) will be found. (shrink)

In this paper we study proof procedures for some variants of first-order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We define both ground and free variable tableau methods, parametric with respect to the variants of the considered logics. The treatment of each variant is equally simple and is based on the annotation of functional symbols by natural numbers, conveying some semantical information on the worlds (...) where they are meant to be interpreted.This paper is an extended version of a previous work where full proofs were not included. Proofs are in some points rather tricky and may help in understanding the reasons for some details in basic definitions. (shrink)

One of the main theorems of the paper states the following. Let R-K-M be finite extensions of a rational one variable function field R over a finite field of constants. Let S be a finite set of valuations of K. Then the ring of elements of K having no poles outside S has a Diophantine definition over its integral closure in M.

This paper gives an extended presentation of the treatment of variable-binding operators adumbrated in earlier works. Illustrative examples include elementary languages with quantifiers and lambda-equipped categorial languages. Some remarks are also offered to illustrate the philosophical import of the resulting picture. Particularly, a certain conception of logic emerges from the account: the view that logics are true theories in the model-theoretic sense, i.e. the result of selecting a certain class of models as the only "admissible" interpretation structures (for a (...) given language). (shrink)

It is common in attempts to extend the theory of evolution to culture to generalize from the causal basis of biological evolution, so that evolutionary theory becomes the theory of copying processes. Generalizing from the formal dynamics of evolution allows greater leeway in what kinds of things cultural entities can be, if they are to evolve. By understanding the phenomenon of cultural transmission in terms of coordinated phenotypic variability, we can have a theory of cultural evolution which allows us to (...) avoid the various difficulties with the elaboration of informational entities such as the cultural replicator, or meme. Such an account is a boon to the project of evolutionary epistemology since it confirms the presumption in favor of the general adaptiveness of culture, illuminating rather than obscuring the inherent intimacy of our relationship to (e.g.) our ideas. (shrink)

A Bayesian network consists of two distinct parts: a directed acyclic graph (DAG or belief-network structure) and a set of parameters for the DAG. The DAG in a Bayesian network can be used to represent both causal hypotheses and sets of probability distributions. Under the causal interpretation, a DAG represents the causal relations in a given population with a set of vertices V when there is an edge from A to B if and only if A is a direct cause (...) of B relative to V. (We adopt the convention that sets of variables are capitalized and boldfaced, and individual variables are capitalized and italicized.) Under the statistical interpretation a DAG G can be taken to represent a set of all distributions all of which share a set of conditional independence relations that are entailed by satisfying a local directed Markov property (defined below). (shrink)

We are used to the idea that computers operate on numbers, yet another kind of data is equally important: the syntax of formal languages, with variables, binding, and alpha-equivalence. The original application of nominal techniques, and the one with greatest prominence in this paper, is to reasoning on formal syntax with variables and binding. Variables can be modelled in many ways: for instance as numbers (since we usually take countably many of them); as links (since they may `point' to a (...) binding site in the term, where they are bound); or as functions (since they often, though not always, represent `an unknown'). None of these models is perfect. In every case for the models above, problems arise when trying to use them as a basis for a fully formal mechanical treatment of formal language. The problems are practical—but their underlying cause may be mathematical. The issue is not whether formal syntax exists, since clearly it does, so much as what kind of mathematical structure it is. To illustrate this point by a parody, logical derivations can be modelled using a Gödel encoding (i.e., injected into the natural numbers). It would be false to conclude from this that proof-theory is a branch of number theory and can be understood in terms of, say, Peano's axioms. Similarly, as it turns out, it is false to conclude from the fact that variables can be encoded e.g., as numbers, that the theory of syntax-with-binding can be understood in terms of the theory of syntax-without-binding, plus the theory of numbers (or, taking this to a logical extreme, purely in terms of the theory of numbers). It cannot; something else is going on. What that something else is, has not yet been fully understood. In nominal techniques, variables are an instance of names, and names are data. We model names using urelemente with properties that, pleasingly enough, turn out to have been investigated by Fraenkel and Mostowski in the first half of the 20th century for a completely different purpose than modelling formal language. What makes this model really interesting is that it gives names distinctive properties which can be related to useful logic and programming principles for formal syntax. Since the initial publications, advances in the mathematics and presentation have been introduced piecemeal in the literature. This paper provides in a single accessible document an updated development of the foundations of nominal techniques. This gives the reader easy access to updated results and new proofs which they would otherwise have to search across two or more papers to find, and full proofs that in other publications may have been elided. We also include some new material not appearing elsewhere. (shrink)

Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from onto A if for all states E(A) the composite state ° L E() can be obtained as an (...) average over states in E() that have smaller entropic uncertainty than the entropic uncertainty of . It is shown that if L is a Jordan homomorphism then (, E()) is not an entropic hidden theory of (A, E(A)) via L. (shrink)

Researchers routinely face the problem of inferring causal relationships from large amounts of data, sometimes involving hundreds of variables. Often, it is the causal relationships between "latent" (unmeasured) variables that are of primary interest. The problem is how causal relationships between unmeasured variables can be inferred from measured data. For example, naval manpower researchers have been asked to infer the causal relations among psychological traits such as job satisfaction and job challenge from a data base in which neither trait is (...) measured directly, but in which answers to interview questions are plausibly associated with each trait. By combining background knowledge with an algorithm that searches for causal structure among the unobserved variables, we have created a tool that can reliably extract useful causal information about latent variables from large data bases. In what follows we describe the class of causal models to which our.. (shrink)

We identify the computational complexity of the satisfiability problem for FO 2 , the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO 2 has the finite-model property, which means that if an FO 2 -sentence is satisfiable, then it has a finite (...) model. Moreover, Mortimer showed that every satisfiable FO 2 -sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO 2 -sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO 2 is NEXPTIME-complete. (shrink)

Linear structural equation models with latent (unmeasured) variables are used widely in sociology, psychometrics, and political science. When such models have a unidimensional..

Few problems in the philosophy of evolutionary biology are more widely disseminated and discussed than the charge of Darwinian evolution being a tautology. The history is long and complex, and the issues are many, and despite the problem routinely being dismissed as an introductory-level issue, based on misunderstandings of evolution, it seems that few agree on what exactly these misunderstandings consist of. In this paper, I will try to comprehensively review the history and the issues. Then, I will try to (...) present the following “solution”, or, one might say, “dissolution”, of the problem, and consider the wider implications of formal, or schematic, explanations in science: yes, the principle of natural selection is a tautology, and so what? It is a promissory note for actual, physical, explanations in particular cases, and is none the worse for that. This is not a new argument, of course, but it does point up the importance of formal schematic models in science. (shrink)

The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all (...) relevant reasons. (shrink)

It is argued that there is no agreed definition of disease. Purely biological definitions are inadequate and combined biological and social definitions are not yet satisfactory. One approach has been to say that what doctors treat is disease. We are uncomfortable with that because we feel it releases people from obligations on a basis of convenience. In practice the weight given to the idea of disease varies according to what it will imply about obligations and privileges. It is suggested that (...) what doctors treat can be accepted as disease provided that we recognize that the significance of disease must vary with circumstances. Those circumstances include the agreement, more or less, of all persons affected when someone is considered to be a patient. The individual must also be competent and not constrained except by his own biological or psychological characteristics. Keywords: disease, patient-physician relationship, obligation CiteULike Connotea Del.icio.us What's this? (shrink)

In the last several decades, a confluence of work in the social sciences, philosophy, statistics, and computer science has developed a theory of causal inference using directed graphs. This theory typically rests either explicitly or implicitly on two major assumptions.

We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. We show (...) that the notions of Zλ- and lexλ-entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, Zλ-entailment is weaker than lexλ-entailment, and both Zλ- and lexλ-entailment are proper generalizations of their classical counterparts. (shrink)

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. A difference between the confirmation lent to a hypothesis by one evidence set and the confirmation lent to that hypothesis by another evidence set is robustly tracked by a difference in focused correlations of those evidence sets on that hypothesis, provided that all the individual pieces of evidence are equally, positively relevant to that hypothesis. (...) However, that result depends on a very strong equal relevance condition on individual pieces of evidence. In this essay, we prove tracking results for focused correlation analogous to Wheeler and Scheines’s results but for cases involving unequal relevance. Our result is robust as well, and we retain conditions for bidirectional tracking between incremental confirmation measures and focused correlation. (shrink)

We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.

Rule-utilitarianism, in spite of its considerable attractions, is a theory in need of a plausible and precise formulation. The basic idea behind rule-utilitarianism is that right action should be defined in terms of what would be required by rules which would maximise either actual or expected utility if those rules gained general acceptance or (on some versions of the theory) general compliance. Rule-utilitarians differ over whether acceptance or compliance is the key notion (see Hooker 2000: 75-80) and also over whether (...) the theory should be couched in terms of actual or expected utility. I shall here officially remain neutral on these difficult questions, as the main arguments here go through equally well on either interpretation, assuming that both versions of the theory are otherwise defensible, anyway (see below). However, partly for ease of exposition and partly because I consider it to be the more plausible view, I shall frame my discussion in terms of acceptance and expected utility. (shrink)

Dept. of Philosophy Center for Biomedical Center for Biomedical Dept. of Philosophy Carnegie Mellon Univ.

Many philosophers have called for elimination of racial taxonomies in biomedical contexts, basing their arguments on one of two claims: that the use of racial terminology is unjust, and that the use of racial terminology in scientific contexts is inappropriate because race is scientifically meaningless. I argue that each of these claims is flawed, because justice sometimes demands the use of racial terminology, and because the utility of race in biomedical contexts makes it scientifically meaningful. I suggest a third argument (...) that eliminativists might utilize: in spite of its usefulness, we should forego racialized medicine because given our long history of racism, any use of race will tend to crowd out other relevant factors. So, instead of continuing to use race as a convenient proxy for unknown “x-factors,” we ought to forego race and insist that researchers name the x-factors. The result will be better science, both morally and epistemically. (shrink)

The reduction of the lambda calculus to the theory of combinators in [Sch¨ onfinkel, 1924] applies to positive implicational logic, i.e. to the typed lambda calculus, where the types are built up from atomic types by means of the operation A −→ B, to show that the lambda operator can be eliminated in favor of combinators K and S of each type A −→ (B −→ A) and (A −→ (B −→ C)) −→ ((A −→ B) −→ (A −→ C)), (...) respectively.1 I will extend that result to the case in which the types are built up by means of the general function type ∀x : A.B(x) as well as the disjoint union type ∃x : A.B(x)– essentially to the theory of [Howard, 1980]. To extend the treatment of −→ to ∀ we shall need a generalized form of the combinators K and S, and to deal with ∃ we will need to introduce a new form of the combinator S.. (shrink)

One of the most startling, and hence theoretically challenging, properties of wh-movement in Sluicing is that it can move wh-phrases out of islands, an important observation which goes back to Ross (1969). Equally challenging is the fact that similar wh-movement out of VP Ellipsis sites remains for the most part illicit. Briefly put, it seems that for a wide range of cases, deletion of an IP containing an island voids the effect of that island for wh-movement, while deletion of a (...) VP containing an island does not. This chapter investigates one aspect of this puzzling dichotomy with respect to island repair, and attempts to show that an interesting and partly novel range of data follow if island deviancies come about due to illicit traces of intermediate movement, working in tandem with a constraint on ellipsis operative in structures that host wh-movement. I will argue that a wide range of islands are indeed active at PF, but not in the way that this claim has usually been understood thus far. Instead of the island node itself being responsible for the degradation in acceptability, I will show that the data support the idea that it is the traces of wh-movement outside the island itself which trigger a PF-crash. I begin with some relevant Background on Sluicing, given in section 6.1, before taking up the Sluicing data in section 6.2 and the VP Ellipsis facts in section 6.3. (shrink)

This paper draws upon a recently completed research study of the responses of accountants and HR professionals to actual issues at work that had posed them ethical qualms. The study sought to get beyond ethical reasoning about hypothetical scenarios and to address issues of actual behaviour, focusing upon the interviewees explanations of these behaviours. In general terms there was an observable difference between the attitudes and behaviours of accountants and HR professions, but not in the simple, stereotypical sense. The concerns (...) expressed by the interviewees when calculating their chosen courses of action in a given situation, reflected grave concerns for their current and future employment prospects, if they were to raise their concerns, either within their employing organisation, or beyond. The problems of whistleblowers are well documented, but at a time when corporate governance issues occupy the attention of financial markets and corporate boards around the world, and national governments are introducing new laws to ostensibly provide enhanced protection for whistleblowers, the evidence of this study is that moral agency remains at best an aspiration, and at worst a chimera. (shrink)