Sufficient conditions for first-order-based sequent calculi to admit cut elimination by a Schütte–Tait style cut elimination proof are established. The worst case complexity of the cut elimination is analysed. The obtained upper bound is parameterized by a quantity related to the calculus. The conditions are general enough to be satisfied by a wide class of sequent calculi encompassing, among others, some sequent calculi presentations for the first order and the propositional versions of classical and intuitionistic logic, classical and intuitionistic (...) modal logic S4, and classical and intuitionistic linear logic and some of its fragments. Moreover the conditions are such that there is an algorithm for checking if they are satisfied by a sequent calculus. (shrink)

A theory of necessary and sufficient conditions is presented, as well as a theory of necessary and sufficient causes and effects, viewed as a particular case of the former. Ambiguities of the terms 'condition' and 'necessary condition' are explored, and a neutral meaning for 'condition' is favoured. The relation between necessary and sufficient conditions and implicative conditionals (including counterfactuals) is also discussed. Two problems of counterfactual theories of causal explanation are indicated, concerning (i) how (...) to account for causes that are not necessary and (ii) how to interpret the counterfactual from the negation of the effect to the negation of the cause. Application of the theory of necessary and sufficient conditions to Euler’s explanation of the Königsberg bridge problem is discussed. The theory of necessary and sufficient causes and effects is then applied to the flagpole shadow explanation and to two biological explanations, one involving a sufficient but not necessary cause and the other a necessary but not sufficient cause. Causes that are neither sufficient nor necessary are also recognized. Finally, a probabilistic approach to causes that are either not sufficient or not necessary is explored, including its application to examples of such cases. (shrink)

Natural conditions are provided that are sufficient to ensure that causality as defined by approaches that use counterfactual dependence and structural equations will be transitive.

This chapter introduces and discusses the concepts of necessary and sufficient conditions.

In a series of publications E.J. Lowe has advocated an attractive alternative to the orthodox view about conditionals embodied in the Stalnaker-Lewis approach. One alleged advantage of Lowe’s approach over its rival is that it offers the prospect of a simpler conditional logic. Another related advantage is that it appears to treat inference by transitivity more plausibly than does the Stalnaker-Lewis approach. One central goal of this paper is to call into question Lowe’s success in providing an account that is (...) better than the Stalnaker-Lewis account in these respects. As part of this, I develop a Loweian-inspired account of sufficient condition sentences such as ‘Harry’s eating this apple is a sufficient condition for his getting sick’, which is another central goal of the paper. (shrink)

In a series of publications E.J. Lowe has advocated an attractive alternative to the orthodox view about conditionals embodied in the Stalnaker-Lewis approach. One alleged advantage of Lowe’s approach over its rival is that it offers the prospect of a simpler conditional logic. Another related advantage is that it appears to treat inference by transitivity more plausibly than does the Stalnaker-Lewis approach. One central goal of this paper is to call into question Lowe’s success in providing an account that is (...) better than the Stalnaker-Lewis account in these respects. As part of this, I develop a Loweian-inspired account of sufficient condition sentences such as ‘Harry’s eating this apple is a sufficient condition for his getting sick’, which is another central goal of the paper. (shrink)

Let G be a connected graph with minimum degree δ G and vertex-connectivity κ G. The graph G is k -connected if κ G ≥ k, maximally connected if κ G = δ G, and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k -connected, maximally connected, or super-connected in terms of the number of edges, the spectral radius of the (...) graph, and its complement, respectively. Analogous results for triangle-free graphs with given minimum degree to be k -connected, maximally connected, or super-connected are also presented. (shrink)

Hurlburt, K.R., Sufficiency conditions for theories with recursive models, Annals of Pure and Applied Logic 55 305–320. We give conditions under which it is possible to construct recursive models for certain highly non-recursive theories. The main idea is to find an ‘α-friendly family’ of structures corresponding to the given theory and then to construct the desired recursive model by copying appropriate parts of these structures, choosing the part to copy in each structure so as to include important witnesses. All of (...) this is done using the recursive labelling systems designed by C. Ash. An example is given which involves orderings whose elementary first-order theories have degree O. (shrink)

This paper is about two controversial inference-patterns involving counterfactual or subjunctive conditionals. Given a plausible assumption about the truth-conditions of counterfactuals, it is shown that one can't go wrong in applying hypothetical syllogism (i.e., transitivity) so long as the set of worlds relevant for the conclusion is a subset of the sets of worlds relevant for the premises. It is also shown that one can't go wrong in applying antecedent strengthening so long as the set of worlds relevant for the (...) conclusion is a subset of that for the premise. These results are then adapted to Lewis's theory of counterfactuals. (shrink)

We consider the problems arising from using sequences of experiments to discover the causal structure among a set of variables, none of whom are known ahead of time to be an “outcome”. In particular, we present various approaches to resolve conflicts in the experimental results arising from sampling variability in the experiments. We provide a sufficient condition that allows for pooling of data from experiments with different joint distributions over the variables. Satisfaction of the condition allows for (...) an independence test with greater sample size that may resolve some of the conflicts in the experimental results. The pooling condition has its own problems, but should—due to its generality—be informative to techniques for meta-analysis. (shrink)

Claims that necessary and sufficient conditions are not converse relations are discussed, as well as the related claim that If A, then B is not equivalent to A only if B . The analysis of alleged counterexamples has shown, among other things, how necessary and sufficient conditions should be understood, especially in the case of causal conditions, and the importance of distinguishing sufficient-cause conditionals from necessary-cause conditionals. It is concluded that necessary and sufficient conditions, adequately interpreted, (...) are converse relations in all cases. (shrink)

Let an X/Y distinction be a distinction between kinds of properties, such as the distinctions between qualitative and non-qualitative, intrinsic and extrinsic, perfectly natural and less-than-perfectly natural or dispositional and categorical properties. An X/Y distinction is hyperintensional iff there are cointensional properties P and Q, such that P is an X-property, whereas Q is a Y-property. Many accounts of metaphysical distinctions among properties presuppose that such distinctions are non-hyperintensional. In this paper, I call this presupposition into question. I develop a (...) sufficient condition for the hyperintensionality of X/Y distinctions and argue that this condition is satisfied by a number of standard classifications of properties. It follows that non-hyperintensional analyses of distinctions among properties are harder to defend than is often assumed. (shrink)

What role do demand deposits serve in the financial system? The answer to this simple question has great implications in keeping the legal terms of the contract consistent with the demands of the financial system. Demand deposits are a perfect monetary substitute. Since money is only held to hedge against perceived uncertainty in both the timing and magnitude of future expenditures, demand deposits are demanded for the same reason. From this we derive three main conclusions. First, a financial contract similar (...) to a demand deposit cannot substitute for money. Second, full agreement to a financial contract does not create a perfect substitute for money unless it provides money’s two key characteristics: on demand and par value redemption. Finally, the demand for fractional-reserve demand deposits is fostered by an exogenous source and that demand for a good or service is not a sufficient condition to justify its legality or ethicality. (shrink)

A Partial Combinatory Algebra is completable if it can be extended to a total one. In [1] it is asked (question 11, posed by D. Scott, H. Barendregt, and G. Mitschke) if every PCA can be completed. A negative answer to this question was given by Klop in [12, 11]; moreover he provided a sufficient condition for completability of a PCA (M, ·, K, S) in the form of ten axioms (inequalities) on terms of M. We prove that (...) just one of these axiom (the so called Barendregt's axiom) is sufficient to guarantee (a slightly weaker notion of) completability. (shrink)

The results of applying Soft Systems Methodology (SSM) show that the nature of the solution and improvement in the problem situation involves some ambiguity. This is due to SSM’s theoretical inadequacy in extending multiple conceptual models to an agreed-upon human activity system. In fact, one of the most important and controversial issues in soft operations research is to ensure how the solution has been obtained and to secure whether the conditions under which the solution has been obtained were satisfied. This (...) article presents the necessary and sufficient conditions for achieving human activity systems as a solution to one of the widely-used methodologies of soft operations research, i.e. Soft Systems Methodology. Similarly, with the aim of reaching a better understanding of the nature of the solution provided by SSM, the soft solution is compared through an example with that of hard systems methodology. (shrink)

According to the weak version of linguistic relativity, also called the Sapir-Whorf hypothesis, the features of an individual’s native language influence his worldview and perception. We decided to test this hypothesis on the sufficient conditional and the necessary conditional, expressed differently in Chinese and French. In Chinese, connectors for both conditionals exist and are used in everyday life, while there is only a connector for the sufficient conditional in French. A first hypothesis follows from linguistic relativity: for the (...) necessary conditional, better logic performance is expected in Chinese participants rather than French participants. As a second hypothesis, for all participants, we expect performance on the sufficient conditional to be better than on the necessary conditional. Indeed, despite the isomorphism of the two conditionals, they differ in how information is processed for reasoning. We decided to study reasoning under uncertainty as it reflects reality more accurately. To do so, we analyzed the coherence of participants using de Finetti’s theory for deduction under uncertainty. The results of our study show no significant difference in performance between Chinese and French participants, neither on the sufficient conditional nor on the necessary conditional. Thus, our first hypothesis derived from the weak version of linguistic relativity is not confirmed. In contrast, our results confirm the second hypothesis in two out of three inference schemas. (shrink)

Analyzing the process of keeping promise we identify its sequence structure and its phase sequences in time. This allows us to arrive at a time order principle forming according to which obligation performance cannot precede in time its sufficient or necessary conditions performance. We further observe that a given promise must always be taken as an element of a certain system of promises. As a result we review definitions of the terms sufficient condition and necessary condition (...) as no more allowing their mutual defining, or symmetry (conversion). We try to discover the compliance rules concerning the condition – the conditioned vector, the course of events vector and the time vector. We conclude that it indicates an incorrect use if, provided the condition – the conditioned vector complies with the course of events vector, the negative time difference in the descriptive use of sentences involving either the if-then connective or the only if connective is obtained. Only when using sentences for abductive explanation with a dominating epistemic vector the negative difference of time does not indicate erroneous use; however, this is possible only for the term of sufficient condition. We further suggest reviewed definition generalization involving the terms of sufficient condition and necessary condition containing always a parameter element denoting a given modality type, or a particular system of rules, laws, etc. Such definition satisfies Brennan’s requirement of a “general formal scheme” where the notion of sufficient condition and necessary condition symmetry (conversion) does not apply. (shrink)

In this article the standard philosophical method involving intuition-driven conceptual analysis is challenged in a new way. This orthodox approach to philosophy takes analysanda to be the specifications of the content of concepts in the form of sets of necessary and sufficient conditions. Here it is argued that there is no adequate account of what necessary and sufficient conditions are. So, the targets of applications of the standard philosophical method so understood are not sufficiently well understood for this (...) method to be dependable. (shrink)

We define a class of finite partial lattices which admit a notion of rank compatible with embedding constructions, and present a necessary and sufficient condition for the embeddability of a finite ranked partial lattice into the computably enumerable degrees.

We present a necessary and sufficient condition for the embeddability of a principally decomposable finite lattice into the computably enumerable degrees. This improves a previous result which required that, in addition, the lattice be ranked. The same condition is also necessary and sufficient for a finite lattice to be embeddable below every non-zero computably enumerable degree.

Describes the received theory of necessary and sufficient conditions, explains some standard objections to it, and lays out alternative ways of thinking about conditions and conditionals.

Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to have a model completion, extending a characterization provided by Wheeler. For varieties of algebras that have equationally definable principal congruences and the compact intersection property, these conditions yield a more elegant characterization obtained (in a slightly more restricted setting) by Ghilardi and Zawadowski. Moreover, it is shown that under certain further assumptions on congruence lattices, the existence of a model completion (...) implies that the variety has equationally definable principal congruences. This result is then used to provide necessary and sufficient conditions for the existence of a model completion for theories of Hamiltonian varieties of pointed residuated lattices, a broad family of varieties that includes lattice-ordered abelian groups and MV-algebras. Notably, if the theory of a Hamiltonian variety of pointed residuated lattices has a model completion, it must have equationally definable principal congruences. In particular, the theories of lattice-ordered abelian groups and MV-algebras do not have a model completion, as first proved by Glass and Pierce, and Lacava, respectively. Finally, it is shown that certain varieties of pointed residuated lattices generated by their linearly ordered members, including lattice-ordered abelian groups and MV-algebras, can be extended with a binary operation to obtain theories that do have a model completion. (shrink)

We present a necessary and sufficient condition for the embeddability of a finite principally decomposable lattice into the computably enumerable degrees preserving greatest element.

Christopher Boorse’s biostatistical theory of medical disorder claims that biological part-dysfunction (i.e., failure of an internal mechanism to perform its biological function), a factual criterion, is both necessary and sufficient for disorder. Jerome Wakefield’s harmful dysfunction analysis of medical disorder agrees that part-dysfunction is necessary but rejects the sufficiency claim, maintaining that disorder also requires that the part-dysfunction causes harm to the individual, a value criterion. In this paper, I present two considerations against the sufficiency claim. First, I analyze (...) Boorse’s central argument for the sufficiency claim, the “pathologist argument,” which takes pathologists’ intuitions about pathology as determinative of medical disorder and conclude that it begs the question and fails to support the sufficiency claim. Second, I present four counterexamples from the medical literature in which salient part-dysfunctions are considered nondisorders, including healthy disease carriers, HIV-positive status, benign mutations, and situs inversus totalis, thus falsifying the sufficiency claim and supporting the harm criterion. (shrink)

Scoring rules measure the deviation between a forecast, which assigns degrees of confidence to various events, and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is strictly better than the mathematical expectation of any other forecast q by the lights of p. Forecasts need not satisfy the axioms of the probability calculus, but Predd et al. [9] have shown that given a (...) finite sample space and any strictly proper additive and continuous scoring rule, the score for any forecast that does not satisfy the axioms of probability is strictly dominated by the score for some probabilistically consistent forecast. Recently, this result has been extended to non-additive continuous scoring rules. In this paper, a condition weaker than continuity is given that suffices for the result, and the condition is proved to be optimal. (shrink)

In this paper, I defend the claim that the determination conditions for thought must include absences.

I elaborate on Pylyshyn's definition of the cognitive impenetrability (CI) of early vision, and draw on the role of concepts in perceptual processing, which links the problem of the CI or cognitive penetrability (CP) of early vision with the problem of the nonconceptual content (NCC) of perception. I explain, first, the sense in which the content of early vision is CI and I argue that if some content is CI, it is conceptually encapsulated, that is, it is NCC. Then, I (...) examine the definitions of NCC and argue that they lead to the view that the NCC of perception is retrieved in a stage of visual processing that is CI. Thus, the CI of a state and content is a sufficient and necessary condition for the state and its content to be purely NCC, the CI?≡?NCC thesis. Since early vision is CI, the purely NCC of perception is formed in early vision. I defend the CI?≡?NCC thesis by arguing against objections raised against both the sufficient and the necessary part of the thesis. (shrink)

In this paper I argue that many of the core phenomenological insights, including the emphasis on direct perception, are a necessary but not sufficient condition for an adequate account of inter-subjectivity today. I take it that an adequate account of inter-subjectivity must involve substantial interaction with empirical studies, notwithstanding the putative methodological differences between phenomenological description and scientific explanation. As such, I will need to explicate what kind of phenomenology survives, and indeed, thrives, in a milieu that necessitates (...) engagement with the relevant sciences, albeit not necessarily deference to them. -/- There will be two central aims to this paper: 1. to defend the centrality and vitality of phenomenological treatments of inter-subjectivity via a consideration of some remarks in Sartre - which I do think possess a non-trivial unity amongst the various interlocutors - and the manner in which they in fact serve to provide the basis for a better explanation of an array of empirical data than existing inferentialist or mindreading accounts of social cognition (notably Theory Theory, Simulation Theory, and hybrid versions); 2. to offer the methodological resources for renewing phenomenology in a manner that acknowledges ostensibly non-phenomenological moments in theory production - which involve explanation, inference to the best explanation, etc. - but does not abandon phenomenology for all that, allowing it to be simply absorbed into empirical explanation or other forms of philosophical analysis without remainder. (shrink)

The notion of scientific representation plays a central role in current debates on modeling in the sciences. One or maybe the major epistemic virtue of successful models is their capacity to adequately represent specific phenomena or target systems. According to similarity views of scientific representation, models should be similar to their corresponding targets in order to represent them. In this paper, Suárez’s arguments against similarity views of representation will be scrutinized. The upshot is that the intuition that scientific representation involves (...) similarity is not refuted by the arguments. The arguments do not make the case for the strong claim that similarity between vehicles and targets is neither necessary nor sufficient for scientific representation. Especially, one claim that a similarity view wants to uphold, still, is the following thesis: only if a vehicle is similar to a target in relevant respects and to a specific degree of similarity then the vehicle is a scientific representation of that target. (shrink)

In recent years, the fight against money laundering has emerged as a key issue of financial regulation. The Wolfsberg Group is an important multistakeholder agreement establishing corporate responsibility principles against money laundering in a domain where international coordination remains otherwise difficult. The fact that 10 out of the 25 top private banking institutions joined this initiative opens up an interesting puzzle concerning the conditions for the participation of key industry players in the Wolfsberg Group. The article presents a fuzzy-set analysis (...) of seven hypotheses based on firm-level organizational factors, the macro-institutional context, and the regulatory framework. Results from the analysis of these 25 financial institutions show that public ownership of the bank and the existence of a code of conduct are necessary conditions for participation in the Wolfsberg Group, whereas factors related to the type of financial institution, combined with the existence of a black list, are sufficient for explaining participation. (shrink)

In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked (...) domain on a tree if and only if it is the pairwise majority rule and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even. (shrink)

New Caledonian crow populations have developed complex tools that show suggestive evidence of cumulative change. These tool designs, therefore, appear to be the product of cumulative technological culture. We suggest that tool-using NC crows offer highly useful data for current debates over the necessary and sufficient conditions for the emergence of CTC.

In this dissertation, I propose a reductive account of causation. This account may be stated as follows: -/- Causation:c is a cause of e within a possibility horizon H iff a) c is process-connected to e, and b) e security-depends on c within H. -/- More precisely, my suggestion is that there are two kinds of causal relata: instantaneous events (defined in Chapter 4) and possibility horizons (defined in Chapter 5). Causation is a ternary relation between two actual instantaneous events (...) – the cause c and the effect e – and a possibility horizon H. -/- I argue that causation has a dual nature: on the one hand, a cause must be connected to its effect via a genuine process; on the other hand, a cause must make a difference to its effect. The first condition – namely, the condition of process-connection (defined in Chapter 6) – captures the sense in which a cause must be connected to its effect via a genuine process. This condition allows my account to separate causation from mere correlation, distinguish genuine causes from preempted backups, and capture how a cause must be at the right level of detail relative to its effect (Chapter 7). -/- The second condition – namely, the condition of security-dependence (defined in Chapter 8) – captures the sense in which a cause must make a difference to its effect. This condition allows my account to yield intuitively correct verdicts on the counterexamples to the transitivity and intrinsicness of causation, resolve the problem of profligate omissions, accommodate structurally isomorphic but causally different cases, and handle contrastive causal claims (Chapter 9 and 10). -/- Finally, my proposed account of causation logically entails restricted versions of three important principles of causal reasoning concerning the sufficiency of counterfactual dependence for causation, and the transitivity and intrinsicness of causation (Chapter 11). (shrink)