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)

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.

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

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 (...) class='Hi'>necessary and sufficient conditions, adequately interpreted, are converse relations in all cases. (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)

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.

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.

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)

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

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)

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)

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)

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)

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)

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)

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.

Definition: A condition A is said to be sufficient for a condition B, if (and only if) the truth (/existence /occurrence) [as the case may be] of A guarantees (or brings about) the truth (/existence /occurrence) of B.

Philosophical and empirical moral psychologists claim that emotions are both necessary and sufficient for moral judgment. The aim of this paper is to assess the evidence in favor of both claims and to show how a moderate rationalist position about moral judgment can be defended nonetheless. The experimental evidence for both the necessity- and the sufficiency-thesis concerning the connection between emotional reactions and moral judgment is presented. I argue that a rationalist about moral judgment can be happy to (...) accept the necessity-thesis. My argument draws on the idea that emotions play the same role for moral judgment that perceptions play for ordinary judgments about the external world. I develop a rationalist interpretation of the sufficiency-thesis and show that it can successfully account for the available empirical evidence. The general idea is that the rationalist can accept the claim that emotional reactions are sufficient for moral judgment just in case a subject’s emotional reaction towards an action in question causes the judgment in a way that can be reflectively endorsed under conditions of full information and rationality. This idea is spelled out in some detail and it is argued that a moral agent is entitled to her endorsement if the way she arrives at her judgment reliably leads to correct moral beliefs, and that this reliability can be established if the subject’s emotional reaction picks up on the morally relevant aspects of the situation. (shrink)

It would be very desirable to have an account of the relation between mind and world that sustained the integrity of each. In this paper, we will argue that a theory of cognition which is broadly Thomistic can do just that. Many commentators recognize that cognitio is Aquinas’s basic epistemic concept, and that it designates knowledge in the broadest and most basic sense, as distinguished from scientia, or knowledge in the paradigmatic sense. There are several important consequences of this distinction (...) which are relevant to a proper understanding of the way in which a theory of knowledge which is in the Aristotelian-Thomistic tradition approaches the issue of the relation between the mind and the world. First and foremost, knowledge cannot be construed as a univocal concept in the A/t context. There are different senses of knowledge and we should not expect there to be a theory which supplies necessary and sufficient conditions for “S knows that p” that satisfies all the different senses of knowledge. It is perplexing that the contemporary discussion seems to miss this point, for the same sort of systematic ambiguity of the term ‘knowledge’ seems to hold in English. Second, the A/t theory of knowledge is not an epistemological theory in the modern sense, if by “epistemological” we mean one which is clearly demarcated from a metaphysical, psychological, or even semantical theory. The A/t theory is a metaphysics of knowledge. Third, a Thomistic theory of knowledge begins with a theory of cognition which provides the grounds of knowledge across the board, including even that of scientia. (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 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)

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)

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)

In this paper, we motivate, propose and defend the following two conditions as individually sufficient and disjunctively necessary for moral responsibility: PODMA —originally proposed by Coren, Acta Analytica, 33, 145–159,, now cast as sufficient rather than necessary—and the TWC*, which amends versions presented by Young, 961–969, 2016; Philosophia, 45, 1365–1380, 2017). We explain why there is a need for new necessary and sufficient conditions, how these build on and improve existing ideas, particularly (...) in relation to Frankfurt-style counterexamples and the continuing discussion on their effectiveness, and why PODMA and the TWC* are good candidates. Finally, we defend the proposal against anticipated objections in order to clarify why we think these individually sufficient and disjunctively necessary conditions are plausible and able to inform the ongoing debate on the role of alternate possibilities in the ascription of moral responsibility. (shrink)

The Ceci et al. article is consistent with tenure being a necessary condition for controversial research. In the absence of tenure, as in the United Kingdom, professors have been fired and suspended for politically controversial issues. There are a variety of reasons why tenure does not ensure that professors will engage in controversial research, including career interests and the desire to be liked. (Published Online February 8 2007).

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence, a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence, we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of (...) necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We propose a novel formulation of these concepts, and demonstrate its advantages over leading alternatives. We present a sound and complete algorithm for computing explanatory factors with respect to a given context and set of agentive preferences, allowing users to identify necessary and sufficient conditions for desired outcomes at minimal cost. Experiments on real and simulated data confirm our method’s competitive performance against state of the art XAI tools on a diverse array of tasks. (shrink)

We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition formula and a related additive property. Then, we introduce the set of conditional constituents generated by $n$ conditional events and (...) we show that they satisfy the basic properties valid in the case of unconditional events. We obtain a generalized inclusion-exclusion formula, which can be interpreted by introducing a suitable distributive property. Moreover, under logical independence of basic unconditional events, we give two necessary and sufficient coherence conditions. The first condition gives a geometrical characterization for the coherence of prevision assessments on a family F constituted by n conditional events and all possible conjunctions among them. The second condition characterizes the coherence of prevision assessments defined on $F\cup K$, where $K$ is the set of conditional constituents associated with the conditional events in $F$. Then, we give some further theoretical results and we examine some examples and counterexamples. Finally, we make a comparison with other approaches and we illustrate some theoretical aspects and applications. (shrink)

In this paper, we consider two different ways in which modus-ponens type reasoning with conditional obligations may be formalized. We develop necessary and sufficient conditions for the validity of each, and make some philosophical observations about the differences between the minor premises that each formalization requires. All this is done within the context of the Belnap-Perloff stit theory.