In this paper, completed only months before his death, the author studies a number of concepts of importance for the analysis of intentional action. Four themes in particular are discussed: the intentionality of action, the practical syllogism, what the author terms the practical causality of practical thinking, and the proximate cause of action. (K. S.).

We respond to Jack Vromen’s critique of our discussion of the missing micro-foundations of work on routines and capabilities in economics and management research. Contrary to Vromen, we argue that inter-level relations can be causal, and that inter-level causal relations may also obtain between routines and actions and interactions; there are no macro-level causal mechanisms; and on certain readings of the notion of routines and capabilities, these may be macro causes.

An important function of scientific diagrams is to identify causal relationships. This commonly relies on contrasts that highlight the effects of specific difference-makers. However, causal contrast diagrams are not an obvious and easy to recognize category because they appear in many guises. In this paper, four case studies are presented to examine how causal contrast diagrams appear in a wide range of scientific reports, from experimental to observational and even purely theoretical studies. It is (...) shown that causal contrasts can be expressed in starkly different formats, including photographs of complexly visualized macromolecules as well as line graphs, bar graphs, or plots of state spaces. Despite surface differences, however, there is a measure of conceptual unity among such diagrams. In empirical studies they generally serve not only to infer and communicate specific causal claims, but also as evidence for them. The key data of some studies is given nowhere except in the diagrams. Many diagrams show multiple causal contrasts in order to demonstrate both that an effect exists and that the effect is specific -- that is, to narrowly circumscribe the phenomenon to be explained. In a large range of scientific reports, causal contrast diagrams reflect the core epistemic claims of the researchers. (shrink)

Previous research on the use of diagrams for argumentation instruction has highlighted, but not conclusively demonstrated, their potential benefits. We examine the relative benefits of using diagrams and diagramming tools to teach causal reasoning about public policy. Sixty-three Carnegie Mellon University students were asked to analyze short policy texts using either: 1) text only, 2) text and a pre-made, correct diagram representing the causal claims in the text, or 3) text and a diagramming tool with which (...) to construct their own causal diagram. After a pretest and training, we tested student performance on a new policy text and found that students given a correct diagram significantly outperformed the other groups. Finally, we compared learning by testing students on a third policy problem in which we removed all diagram or tool aids and found that students who constructed their own diagrams learned the most. We describe these results and interpret them in a way that foreshadows work we now plan for a cognitive-tutor on causal diagram construction. (shrink)

We respond to Jack Vromen’s (this issue) critique of our discussion of the missing micro-foundations of work on routines and capabilities in economics and management research. Contrary to Vromen, we argue that (1) inter-level relations can be causal, and that inter-level causal relations may also obtain between routines and actions and interactions; (2) there are no macro-level causal mechanisms; and (3) on certain readings of the notion of routines and capabilities, these may be macro causes.

Can humans get arbitrarily capable reinforcement learning agents to do their bidding? Or will sufficiently capable RL agents always find ways to bypass their intended objectives by shortcutting their reward signal? This question impacts how far RL can be scaled, and whether alternative paradigms must be developed in order to build safe artificial general intelligence. In this paper, we study when an RL agent has an instrumental goal to tamper with its reward process, and describe design principles that prevent instrumental (...) goals for two different types of reward tampering. Combined, the design principles can prevent reward tampering from being an instrumental goal. The analysis benefits from causal influence diagrams to provide intuitive yet precise formalizations. (shrink)

THE ART OF CAUSAL CONJECTURE Glenn Shafer Table of Contents Chapter 1. Introduction........................................................................................ ...........1 1.1. Probability Trees..........................................................................................3 1.2. Many Observers, Many Stances, Many Natures..........................................8 1.3. Causal Relations as Relations in Nature’s Tree...........................................9 1.4. Evidence............................................................................................ ...........13 1.5. Measuring the Average Effect of a Cause....................................................17 1.6. Causal Diagrams..........................................................................................20 1.7. Humean Events............................................................................................23 1.8. Three Levels of Causal Language................................................................27 1.9. An Outline of the Book................................................................................27 Chapter 2. Event Trees............................................................................................... .....31 2.1. Situations and Events...................................................................................32 2.2. The Ordering of Situations and Moivrean Events.......................................35 2.3. (...) Cuts................................................................................................ ..............39 2.4. Humean Events............................................................................................43 2.5. Moivrean Variables......................................................................................49 2.6. Humean Variables........................................................................................53 2.7. Event Trees for Stochastic Processes...........................................................54 2.8. Timing in Event Trees.................................................................................56 2.9. Intersecting Event Trees...............................................................................60 2.10. Notes on the Literature...............................................................................61 Chapter 3. Probability Trees...........................................................................................63 3.1. Some Types of Probability Trees.................................................................64 ii 3.2. Axioms for the Probabilities of Moivrean Events.......................................68 3.3. Zero Probabilities....................................................................................... ..70 3.4. A Sample-Space Analysis of the Event-Tree Axioms.................................72 3.5. Probabilities and Expected Values for Variables.........................................74 3.6. Martingales......................................................................................... .........79 3.7. The Expectation of a Variable in a Cut........................................................83 3.8. Conditional Expected Value and Conditional Expectation.........................87 Chapter 4. The Meaning of Probability...........................................................................91 4.1. The Interpretation of Expected Value..........................................................92 4.2. The Interpretation of Expectation................................................................95 4.3. The Long Run..............................................................................................98 4.4. Changes in Belief.........................................................................................101 4.5. The Empirical Validation of Probability......................................................106 4.6. The Diversity of Uses of Probability...........................................................108 4.7. Notes on the Literature.................................................................................110 Chapter 5. Independent Events.......................................................................................113 5.1. Independence........................................................................................ .......114 5.2. Weak Independence.....................................................................................118 5.3. The Principle of the Common Cause...........................................................121 5.4. Conditional Independence............................................................................128 5.5. Notes on the Literature.................................................................................133 Chapter 6. Events Tracking Events.................................................................................135 6.1. Tracking............................................................................................ ...........137 6.2. Tracking and Conditional Independence.....................................................142 6.3. Stochastic Subsequence...............................................................................143 6.4. Singular Diagrams for Stochastic Subsequence...........................................147 6.5. Conjunctive and Interactive Forks...............................................................149 Chapter 7. Events as Signs of Events..............................................................................153 iii 7.1. Sign................................................................................................ ..............154 7.2. Weak Sign................................................................................................ ....159 7.3. The Ethics of Causal Talk............................................................................160 7.4. Screening Off...............................................................................................16 2 Chapter 8. Independent Variables...................................................................................167 8.1. Unconditional Independence........................................................................170 8.2. Conditional Independence............................................................................175 8.3. Independence for Partitions.........................................................................177 8.4. Independence for Families of Variables......................................................182 8.5. Individual Properties of the Independence Relations...................................186 Chapter 9. Variables Tracking Variables........................................................................189 9.1. Tracking and Conditional Independence: A Summary...............................190 9.2. Strong Tracking............................................................................................ 192 9.3. Strong Tracking and Conditional Independence..........................................198 9.4. Stochastic Subsequence...............................................................................201 9.5. Functional Dependence................................................................................203 9.6. Tracking in Mean.........................................................................................204 9.7. Linear Tracking............................................................................................ 207 9.8. Tracking by Partitions..................................................................................210 9.9. Tracking by Families of Variables...............................................................212 Chapter 10. Variables as Signs of Variables...................................................................215 10.1. Sign................................................................................................ ............219 10.2. Linear Sign................................................................................................ .222 10.3. Scored Sign................................................................................................ 225 10.4. Families of Variables.................................................................................227 Chapter 11. AnTheory of Event Trees.............................................................229 11.1. Event Trees as Sets of Sets........................................................................230 11.2. Event Trees as Partially Ordered Sets........................................................232 iv 11.3. Regular Event Trees...................................................................................240 11.4. The Resolution of Moivrean Variables......................................................244 11.5. Humean Events and Variables...................................................................246 Chapter 12. Martingale Trees..........................................................................................247 12.1. Examples of Decision Trees......................................................................249 12.2. The Meaning of Probability in a Decision Tree.........................................253 12.3. Martingales......................................................................................... .......257 12.4. The Structure of Martingale Trees.............................................................261 12.5. Probability and Causality...........................................................................265 12.6. Lower and Upper Probability.....................................................................269 12.7. The Law of Large Numbers.......................................................................272 12.8. Notes on the Literature...............................................................................274 Chapter 13. Refining............................................................................................ ...........275 13.1. Examples of Refinement............................................................................277 13.2. A Constructive Definition of Finite Refinement.......................................281 13.3. Axioms for Refinement..............................................................................282 13.4. Lifting Moivrean Events and Variables.....................................................288 13.5. Refining Martingale Trees.........................................................................288 13.6. Grounding........................................................................................... .......294 Chapter 14. Principles of Causal Conjecture..................................................................299 14.1. The Diversity of Causal Explanation.........................................................302 14.2. The Mean Effect of the Happening of a Moivrean Event..........................305 14.3. The Effect of a Humean Variable..............................................................311 14.4. Attribution and Generality.........................................................................316 14.5. The Statistical Measurement of the Effect of a Cause...............................319 14.6. Measurement by Experiment.....................................................................320 14.7. Using Our Knowledge of How Things Work............................................322 v 14.8. Sampling Error...........................................................................................329 14.9. The Sampling Frame..................................................................................329 14.10. Notes on the Literature.............................................................................330 Chapter 15. Causal Models.............................................................................................3 31 15.1. The Causal Interpretation of Statistical Prediction....................................333 15.2. Generalizing to a Family of Exogenous Variables....................................337 15.3 Some Joint Causal Diagrams......................................................................339 15.4. Causal Path Diagrams................................................................................342 15.5. Causal Relevance Diagrams.......................................................................346 15.6. The Meaning of Latent Variables..............................................................352 15.7. Notes on the Literature...............................................................................357 Chapter 16. Representing Probability Trees...................................................................359 16.1. Three Graphical Representations...............................................................361 16.2. Skeletal Simplifications.............................................................................368 16.3. Martingale Trees in Type Theory...............................................................371 Appendix A. Huygens’s Probability Trees.....................................................................379 Huygens’s Manuscript in Translation..................................................................380 Appendix B. Some Elements of Graph Theory..............................................................385 B1. Undirected Graphs........................................................................................385 B2. Directed Graphs............................................................................................38 6 Appendix C. Some Elements of Order Theory...............................................................393 C1. Partial and Quasi Orderings.........................................................................393 C2. Singular and Joint Diagrams for Binary Relations.......................................394 C3. Lattices............................................................................................ .............395 C4. The Lattice of Partitions of a Set..................................................................396 Appendix D. The Sample-Space Framework for Probability.........................................399 D1. Probability Measures....................................................................................399 D2. Variables........................................................................................... ...........400 vi D3. Families of Variables...................................................................................401 D4. Expected Value............................................................................................402 D5. The Law of Large Numbers.........................................................................405 D6. Conditional Probability................................................................................406 D7. Conditional Expected Value........................................................................407 Appendix E. Prediction in Probability Spaces................................................................409 E1. Conditional Distribution...............................................................................411 E2. Regression on a Single Variable...................................................................412 E3. Regression on a Partition or a Family of Variables......................................415 E4. Linear Regression on a Single Variable.......................................................418 E5. Linear Regression on a Family of Variables................................................422 Appendix F. Sample-Space Concepts of Independence.................................................425 F1. Overview............................................................................................ ...........426 F2. Independence Proper.....................................................................................432 F3. Unpredictability in Mean..............................................................................434 F4. Simple Uncorrelatedness..............................................................................437 F5. Mixed Uncorrelatedness...............................................................................438 F6. Partial Uncorrelatedness...............................................................................440 F7. Independence for Partitions..........................................................................442 F8. Independence for Families of Variables.......................................................445 F9. The Basic Role of Uncorrelatedness.............................................................448 F10. Dawid’s Axioms.........................................................................................449 Appendix G. Prediction Diagrams..................................................................................453 G1. Path Diagrams..............................................................................................454 G2. Generalized Path Diagrams..........................................................................462 G3. Relevance Diagrams.....................................................................................466 G4. Bubbled Relevance Diagrams......................................................................475 Appendix H. Abstract Stochastic Processes...................................................................479 vii H1. Probability Conditionals and Probability Distributions...............................477 H2. Abstract Stochastic Processes......................................................................479 H3. Embedding Variables and Processes in a Sample Space.............................480 References.......................................................................................... ..............................491. (shrink)

Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, (...) such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams. This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a ancestral graph. We present two main results. The first result extends Pearl 's celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (shrink)

Causal reasoning and game-theoretic reasoning are fundamental topics in artificial intelligence, among many other disciplines: this paper is concerned with their intersection. Despite their importance, a formal framework that supports both these forms of reasoning has, until now, been lacking. We offer a solution in the form of (structural) causal games, which can be seen as extending Pearl's causal hierarchy to the game-theoretic domain, or as extending Koller and Milch's multi-agent influence diagrams to the causal (...) domain. We then consider three key questions: i) How can the (causal) dependencies in games - either between variables, or between strategies - be modelled in a uniform, principled manner? ii) How may causal queries be computed in causal games, and what assumptions does this require? iii) How do causal games compare to existing formalisms? To address question i), we introduce mechanised games, which encode dependencies between agents' decision rules and the distributions governing the game. In response to question ii), we present definitions of predictions, interventions, and counterfactuals, and discuss the assumptions required for each. Regarding question iii), we describe correspondences between causal games and other formalisms, and explain how causal games can be used to answer queries that other causal or game-theoretic models do not support. Finally, we highlight possible applications of causal games, aided by an extensive open-source Python library. (shrink)

Scientists use a variety of modes of representation in their work, but philosophers have studied mainly sentences expressing propositions. I ask whether diagrams are mere conveniences in expressing propositions or whether they are a distinct, ineliminable mode of representation in scientific texts. The case of path analysis, a statistical method for quantitatively assessing the relative degree of causal determination of variation as expressed in a causal path diagram, is discussed. Path analysis presents a worst case for arguments (...) against eliminability since path diagrams are usually presumed to be mathematically or logically “equivalent” in an important sense to sets of linear path equations. I argue that path diagrams are strongly generative, i.e., that they add analytical power to path analysis beyond what is supplied by linear equations, and therefore that they are ineliminable in a strong scientific sense. (shrink)

The Effect: An Introduction to Research Design and Causality is about research design, specifically concerning research that uses observational data to make a causal inference. It is separated into two halves, each with different approaches to that subject. The first half goes through the concepts of causality, with very little in the way of estimation. It introduces the concept of identification thoroughly and clearly and discusses it as a process of trying to isolate variation that has a causal (...) interpretation. Subjects include heavy emphasis on data-generating processes and causal diagrams. Concepts are demonstrated with a heavy emphasis on graphical intuition and the question of what we do to data. When we "add a control variable" what does that actually do? (shrink)

Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error” or “disturbance” terms), and an associated path diagram corresponding to the causal relations among variables specified by the structural equations and the correlations among the error terms. It is often thought that the path diagram (...) is nothing more than a heuristic device for illustrating the assumptions of the model. However, in this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling. (shrink)

It has become common to find diagrams and flow-charts used in our organizations to illustrate the nature of processes, what is involved and how it happens, or to show how parts of the organization interrelate to each other and work together. Such diagrams are used as they are thought to help visualization and simplify things in order to represent the essence of a particular situation, the core features. In this paper, using a social semiotic approach, we show that (...) we need to develop a much more critical sense of how these diagrams and flowcharts can easily abstract, conceal and substitute actual causalities, work roles and relationships. We demonstrate this using the example of a series of interrelated flows-charts used to implement a new system of target-based learning in preschool/kindergartens in Sweden – a system which works highly in favor of a rapidly privatizing education sector. Here, the flow charts shape how school processes and learning are presented to devalue the former system and value the new. (shrink)

That diagrams are analog, i.e., homomorphic, representations of some kind, and sentential representations are not, is a generally held intuition. In this paper, we develop a formal framework in which the claim can be stated and examined, and certain puzzles resolved. We start by asking how physical things can represent information in some target domain. We lay a basis for investigating possible homomorphisms by modeling both the physical medium and the target domain as sets of variables, each with a (...) constraint structure. When a homomorphism exists, the causality of the physical medium can provide a “free ride,” automatically determining the information that is needed to solve a problem. The modeling technique enables us to show how in sentential representations the structure of the 2-D space is used non-homomorphically to define tokens, and to provide a minimal homomorphism with respect to the ordering of the arguments for n-ary functions, predicates, and operators, but otherwise there is no homomorphism with the target domain. Our treatment also characterizes diagrams as a type of a more general class of physical representations in which physical causality plays a role in providing the information needed to solve a problem. (shrink)

In a series of joint papers, Teppo Felin and Nicolai J. Foss recently launched a microfoundations project in the field of strategic management. Felin and Foss observe that extant explanations in strategic management are predominantly collectivist or macro. Routines and organizational capabilities, which are supposed to be properties of firms, loom large in the field of strategic management. Routines figure as explanantia in explanations of firm behavior and firm performance, for example. Felin and Foss plead for a replacement of such (...) macro-explanations by micro-explanations. Such a replacement is needed, Felin and Foss argue, because macro-explanations are necessarily incomplete: they miss out on crucial links in the causal chain that connect macro phenomena with each other. I argue that this argument is flawed. It is based on a doubtful if not outright incorrect understanding and use of Coleman’s diagram. In a sense to be explained below, only if Coleman’s diagram is squared it can accurately account for the relations between individual action and interaction, routines and firm behavior and firm performance. Once Coleman’s diagram is squared, one can see why and how macro-explanations need not miss out on any link in the causal chains that connect macro phenomena. Micro-analyses are still needed, not to highlight and specify causal links that macro-explanations miss out on, but to check whether the many properties that are ascribed to routines in macro-explanations of firm behavior are warranted. (shrink)

Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for assessing causal compatibility is in the presence of partial information; i.e. when some of the variables are hidden/latent. This paper introduces the possible (...) worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called a possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency. (shrink)

Abell, Felin and Foss argue that "macro-explanations" in strategic management, explanations in which organizational routines figure prominently and in which both the explanandum and explanans are at the macro-level, are necessarily incomplete. They take a diagram (which has the form of a trapezoid) from Coleman, Foundations of Social Theory, The Belknap Press of Harvard University Press, Cambridge (Mass.)/London, (1990) to task to show that causal chains connecting two macro-phenomena always involve "macro-to-micro" and "micro-tomacro" links, links that macro-explanations allegedly fail (...) to recognize. Their plea for micro-foundations in strategic management is meant to shed light on these "missing links". The paper argues that while there are good reasons for providing micro-foundations, Abell, Felin and Foss's causal incompleteness argument is not one of them. Their argument does not sufficiently distinguish between causal and constitutive relations. Once these relations are carefully distinguished, it follows that Coleman's diagram has to be squared. This in turn allows us to see that macroexplanations need not be incomplete. (shrink)

Structural Causal Modeling (SCM) is an approach to causal inference closely associated with Judea Pearl and given an accessible instroduction in [Pearl, J., & Mackenzie, D. (2018). The book of why: The new science of cause and effect. Basic Books]. It is highly popular outside of economics, but has seen relatively little application within it. This paper briefly introduces the main concepts of SCM through the lens of whether applied economists are likely to find marginal benefit in these (...) methods beyond standard economic approaches to causal inference. The most promising areas are those where SCM's causal diagrams alone offer significant value: covariate selection, the development of placebo tests, causal discovery, and identification in complex models. (shrink)

In QED, an external electromagnetic field can be accounted for non-perturbatively by replacing the causal propagators used in Feynman diagram calculations with Green’s functions for the Dirac equation under the external field. If the external field destabilises the vacuum, then it is a difficult problem to determine which Green’s function is appropriate, and multiple approaches have been developed in the literature whose equivalence, in many cases, is not clear. In this paper, we demonstrate for a broad class of external (...) fields that includes all that act for a finite time, that four Green’s functions used in the literature are equivalent: Schwinger’s “proper-time” propagator; the “causal propagator” used in the “Bogoliubov transformation” method based on the canonical quantization of the field operator; and two defined using analytic continuation from complexified parameters. To do so, we formulate Schwinger’s “proper-time quantum mechanics" as a Schrödinger wave mechanics, and use this to re-derive Schwinger’s expression for the propagator as a statement relating solutions of the inhomogeneous Dirac equation to those of the inhomogeneous “proper-time Dirac equation”. This is done by constructing direct integral spectral decompositions of the Hamiltonians of both equations, and deriving a form for solutions of the inhomogeneous Dirac equation in terms of these decompositions. We then show that all four propagators return solutions of the inhomogeneous Dirac equation that satisfy the same boundary condition, which under a physically reasonable assumption is sufficient to specify the solution uniquely. (shrink)

This work addresses and resolved Kant's first antinomy, and brings metaphysics in line with advances in he science of big bang cosmology, introduces a new philosophical argument for the existence of a Supreme Being, and is presented in three versions, with the first version quoting Kant's most relevant remarks with regard to what he calls a science of metaphysics, and an abbreviated version without any quotes, as well as a one page abstract diagram of the argument.

Invasion ecology addresses the spread of species outside of their native ranges. A central aim of this field is to find mechanistic explanations for why species are able to establish and spread in an area in which they did not evolve. Usually it remains unclear, however, what exactly is meant by ‘mechanistic explanation’ or ‘mechanism’. The paper argues that the field can benefit from the philosophical discussion of what a mechanism is. Based on conceptions of mechanisms as processes in concrete (...) systems, causal mechanisms can be defined as one type of mechanism, representing recurring networks of causal relationships. With the example of a well-known hypothesized mechanism in invasion ecology, namely enemy release, the paper demonstrates how such causal mechanisms can be depicted as causal network diagrams. This approach could facilitate the development of step-by-step explanations, enhance clear argumentation and allow for more precise linkage of empirical tests to theory. Challenges to assessing the empirical relevance of hypothesized mechanisms are discussed, and suggestions are made concerning how the proposed approach could help in overcoming some of them. (shrink)

This paper examines racial discrimination and algorithmic bias in predictive policing algorithms (PPAs), an emerging technology designed to predict threats and suggest solutions in law enforcement. We first describe what discrimination is in a case study of Chicago’s PPA. We then explain their causes with Broadbent’s contrastive model of causation and causal diagrams. Based on the cognitive science literature, we also explain why fairness is not an objective truth discoverable in laboratories but has context-sensitive social meanings that need (...) to be negotiated through democratic processes. With the above analysis, we next predict why some recommendations given in the bias reduction literature are not as effective as expected. Unlike the cliché highlighting equal participation for all stakeholders in predictive policing, we emphasize power structures to avoid hermeneutical lacunae. Finally, we aim to control PPA discrimination by proposing a governance solution—a framework of a social safety net. (shrink)

Causal models of agents have been used to analyse the safety aspects of machine learning systems. But identifying agents is non-trivial -- often the causal model is just assumed by the modeler without much justification -- and modelling failures can lead to mistakes in the safety analysis. This paper proposes the first formal causal definition of agents -- roughly that agents are systems that would adapt their policy if their actions influenced the world in a different way. (...) From this we derive the first causal discovery algorithm for discovering agents from empirical data, and give algorithms for translating between causal models and game-theoretic influence diagrams. We demonstrate our approach by resolving some previous confusions caused by incorrect causal modelling of agents. (shrink)

Data-driven algorithms are currently deployed in several fields, leading to a rapid increase in the importance algorithms have in decision-making processes. Over the last years, several instances of discrimination by algorithms were observed. A new branch of research emerged to examine the concept of “algorithmic fairness.” No consensus currently exists on a single operationalization of fairness, although causal-based definitions are arguably more aligned with the human conception of fairness. The aim of this article is to investigate the degree of (...) this alignment in a case study inspired by a recent ruling of an Italian court on the reputational-ranking algorithm used by a food delivery platform. I relied on the documentation of the legal dispute to discuss the applicability, intuitiveness and appropriateness of causal models in evaluating fairness, with a specific focus on a causal-based fairness definition called “counterfactual fairness.” I first describe the details of the dispute and the arguments presented to the court, as well as the court’s final decision, to establish the context of the case study. Then, I translate the dispute into a formal simplified problem using a causal diagram, which represents the main aspects of the data generation process in the case study. I identify the criteria used by the court in ruling that the algorithm was unfair and compare them with the counterfactual fairness definition. The definition of counterfactual fairness was found to be well aligned with the human conception of fairness in this case study, using the court order rationale as a gold standard. (shrink)

This innovative text is psychologically informed, both in its diagnosis of inferential errors, and in teaching students how to watch out for and work around their natural intellectual blind spots. It also incorporates insights from epistemology and philosophy of science that are indispensable for learning how to evaluate premises. The result is a hands-on primer for real world critical thinking. The authors bring a fresh approach to the traditional challenges of a critical thinking course: effectively explaining the nature of validity, (...) assessing deductive arguments, reconstructing, identifying and diagramming arguments, and causal and probabilistic inference. Additionally, they discuss in detail, important, frequently neglected topics, including testimony, including the evaluation of news and other information sources, the nature and credibility of science, rhetoric, and dialectical argumentation. The treatment of probability uses frequency trees and a frequency approach more generally, and argument reconstruction is taught using argument maps; these methods have been shown to improve students’ reasoning and argument evaluation. (shrink)

A standard way of representing causation is with neuron diagrams. This has become popular since the influential work of David Lewis. But it should not be assumed that such representations are metaphysically neutral and amenable to any theory of causation. On the contrary, this way of representing causation already makes several Humean assumptions about what causation is, and which suit Lewis’s programme of Humean Supervenience. An alternative of a vector diagram is better suited for a powers ontology. Causation should (...) be understood as connecting property types and tokens where there are dispositions towards some properties rather than others. Such a model illustrates how an effect is typically polygenous: caused by many powers acting with each other, and sometimes against each other. It models causation as a tendency towards an effect which can be counteracted. The model can represent cases of causal complexity, interference, over-determination and causation of absence (equilibrium). (shrink)

The Theory of Important Criteria is used to argue that the age?old problem of the compatibility of free will and determinism turns on the question of the importance of causal indeterminacy of choice as a criterion of being able to do otherwise. One's answer to this question depends in turn on one's evaluation of certain moral issues and of the force and significance of certain similes, analogies and diagrams in terms of which one can ?depict? a deterministic universe. (...) It is further argued that the problem of free will and determinism is not a pseudo?problem, but a genuine problem that is hard to solve because of the depth and complexity of the evaluative issues on which it hangs. (shrink)

This paper investigates the relationship between Stakeholder Engagement (SE) and Corporate Social Responsibility (CSR), approaching CSR as a complex system made up of components and interactions. Adopting a System Thinking approach to analyze CSR in a stakeholders-company network, explorative research is conducted through three stages: (1) a critical literature review aimed to identify the components of the CSR system model, (2) the development of the dataset and of the Causal Loop Diagram (CLD) model, (3) the analysis of the CSR (...) behavior in light of the ‘system archetypes’ underpinning the system. The analysis reveals both the structure and the dynamics of CSR and explain its behavior in light of the stakeholder engagement network variables. Findings from this research underscore the existence of six feedback loops, which characterize the relation CSR-SE. The ‘company-stakeholder fit’ acts as a growth engine for the stakeholder engagement network, however other balancing dynamics (e.g., detriment of business objectives) require a tradeoff between Social and Business orientation. This paper contributes to a more profound understanding of the relation between CSR and stakeholder engagement, showing in particular the link between CSR and SE under the assumption of stakeholder-company network. The insights provided serve as a guide for managers and policymakers to navigate the complex dynamics of SE to inform effective strategies of CSR based on network structural actions. (shrink)

Most of us create and use a panoply of non-sentential representations throughout our ordinary lives: we regularly use maps to navigate, charts to keep track of complex patterns of data, and diagrams to visualize logical and causal relations among states of affairs. But philosophers typically pay little attention to such representations, focusing almost exclusively on language instead. In particular, when theorizing about the mind, many philosophers assume that there is a very tight mapping between language and thought. Some (...) analyze utterances as the outer vocalizations of inner thoughts (e.g. Grice 1957, Devitt 2005), while others treat thought as a form of inner speech (e.g. Sellars 1956/1997, Carruthers 2002). But even philosophers who take no stand on the relative priority of language and thought still tend to individuate mental states in terms of the sentences we use to ascribe them. Indeed, Dummett (1993) claims that it is constitutive of analytic philosophy that it approaches the mind by way of language. In many ways, this linguistic model is salutary. Our thoughts are often intimately intertwined with their linguistic expression, and public language does provide a comparatively tractable proxy for, and a window into, the messier realm of thought. However, an exclusive focus on thought as it is expressed in language threatens to leave other sorts of thought unexplained, or even to blind us to their possibility. In particular, many cognitive ethologists and psychologists find it useful to talk about humans, chimpanzees, birds, rats, and even bees as employing cognitive maps. We need to make sense of this way of talking about minds as well as more familiar sentential descriptions. In what follows, I investigate the theoretical and practical possibility of non-sentential thought. Ultimately, I am most interested in the contours of distinctively human thought: what forms does human thought take, and how do those different forms interact? How does human thought compare with that of other animals? In this essay, however, I focus on a narrower and more basic theoretical question: could thought occur in maps? Many philosophers are convinced that in some important sense, thought per se must be language-like.. (shrink)

Creationists who object to evolution in the science curriculum of public schools often cite Jonathan Well’s book Icons of Evolution in their support (Wells 2000). In the third chapter of his book Wells claims that neither paleontological nor molecular evidence supports the thesis that the history of life is an evolutionary process of descent from preexisting ancestors. We argue that Wells inappropriately relies upon ambiguities inherent in the term ‘Darwinian’ and the phrase ‘Darwin’s theory’. Furthermore, he does not accurately distinguish (...) between the overwhelming evidence that supports the thesis of common descent and controversies that pertain to causal mechanisms such as natural selection. We also argue that Wells’ attempts to undermine the evidence in support of common descent are flawed and his characterization of the relevant data is misleading. In particular, his assessment of the ‘Cambrian explosion’ does not do justice to the fossil record. Nor do his selective references to debate about molecular and paleontological phylogenies constitute a case against common descent. We conclude that the fossil and molecular evidence is more than sufficient to warrant science educators to present common descent as a well-established scientific fact. We also argue that diagrams depicting the ‘tree of life’ can be pedagogically useful as simplified representations of the history of life. (shrink)

Imagine yourself sitting on your front porch, sipping your morning coffee and admiring the scene before you. You see trees, houses, people, automobiles; you see a cat running across the road, and a bee buzzing among the flowers. You see that the flowers are yellow, and blowing in the wind. You see that the people are moving about, many of them on bicycles. You see that the houses are painted different colors, mostly earth tones, and most are one-story but a (...) few are two-story. It is a beautiful morning. Thus the world interfaces with your mind through your senses. There is a strong intuition that we are not disconnected from the world. We and the other things we see around us are part of a continuous whole, and we have direct access to them through vision, touch, etc. However, the philosophical tradition tries to drive a wedge between us and the world by insisting that the information we get from perception is the result of inference from indirect evidence that is about how things look and feel to us. The philosophical problem of perception is then to explain what justifies these inferences. We will focus on visual perception. Figure one presents a crude diagram of the cognitive system of an agent capable of forming beliefs on the basis of visual perception. Cognition begins with the stimulation of the rods and cones on the retina. From that physical input, some kind of visual processing produces an introspectible visual image. In response to the production of the visual image, the cognizer forms beliefs about his or her surroundings. Some beliefs the perceptual beliefs are formed as direct responses to the visual input, and other beliefs are inferred from the perceptual beliefs. The perceptual beliefs are, at the very least, caused or causally influenced by having the image. This is signified by the dashed arrow marked with a large question mark. We will refer to this as the mystery link. Figure one makes it apparent that in order to fully understand how knowledge is based on perception, we need three different theories.. (shrink)

This paper builds upon ethnomethodological and social constructivist studies of representation in the natural sciences to examine sociological theory, a field that is much closer to home. An analysis of diagrams and related illustrations in theory texts shows that labels, geometric boundaries, vectors, and symmetries often are used to convey a sense of orderly flows of causal influences in a homogeneous field. These graphic elements make up what I call a "rhetorical mathematics" that conveys an impression of rationality. (...) Although theory pictures rarely show much beyond what a text already says in its writing, they simulate a hermeneutic passage from written ideas to an independent representational or mathematical space. The paper discusses two modes of textual disruption of the rhetorical mathematics of theory pictures: parody and deconstruction. Parody makes ironic use of graphic devices in order to expose the rationalistic associations that come with the territory. Deconstruction displaces (and, if taken far enough, dissolves entirely) the Flatland of pictorial rationality. These negative maneuvers raise the possibility of using figural space for alternative modes of sociological inquiry. (shrink)

We argue that current discussions of criteria for actual causation are ill-posed in several respects. (1) The methodology of current discussions is by induction from intuitions about an infinitesimal fraction of the possible examples and counterexamples; (2) cases with larger numbers of causes generate novel puzzles; (3) "neuron" and causal Bayes net diagrams are, as deployed in discussions of actual causation, almost always ambiguous; (4) actual causation is (intuitively) relative to an initial system state since state changes are (...) relevant, but most current accounts ignore state changes through time; (5) more generally, there is no reason to think that philosophical judgements about these sorts of cases are normative; but (6) there is a dearth of relevant psychological research that bears on whether various philosophical accounts are descriptive. Our skepticism is not directed towards the possibility of a correct account of actual causation; rather, we argue that standard methods will not lead to such an account. A different approach is required. (shrink)

We argue that current discussions of criteria for actual causation are ill-posed in several respects. (1) The methodology of current discussions is by induction from intuitions about an infinitesimal fraction of the possible examples and counterexamples; (2) cases with larger numbers of causes generate novel puzzles; (3) “neuron” and causal Bayes net diagrams are, as deployed in discussions of actual causation, almost always ambiguous; (4) actual causation is (intuitively) relative to an initial system state since state changes are (...) relevant, but most current accounts ignore state changes through time; (5) more generally, there is no reason to think that philosophical judgements about these sorts of cases are normative; but (6) there is a dearth of relevant psychological research that bears on whether various philosophical accounts are descriptive. Our skepticism is not directed towards the possibility of a correct account of actual causation; rather, we argue that standard methods will not lead to such an account. A different approach is required. Once upon a time a hungry wanderer came into a village. He filled an iron cauldron with water, built a fire under it, and dropped a stone into the water. “I do like a tasty stone soup” he announced. Soon a villager added a cabbage to the pot, another added some salt and others added potatoes, onions, carrots, mushrooms, and so on, until there was a meal for all. (shrink)

Mental and physical causes do not competedthe presence of one does not exclude the efficacy of the other. This point is obvious from the perspective of an interventionist theory of causation, but only when this theory gets its proper due. Doubts about the interventionist justification for concluding that there is both physical and mental causation, we have argued, rest on misunderstandings of interventionism. When looking to interventions to reveal causal structures, care must be taken to consider the right variable (...) sets. Jaegwon Kim’s diagram is the wrong starting point for interventionist causal reasoning because it includes variables that are related by non-causal relations in addition to causal relations. When it comes to understanding exclusion, less is more. (shrink)

The history of biological systematics documents a continuing tension between classifications in terms of nested hierarchies congruent with branching diagrams (the ‘Tree of Life’) versus reticulated relations. The recognition of conflicting character distribution led to the dissolution of the scala naturae into reticulated systems, which were then transformed into phylogenetic trees by the addition of a vertical axis. The cladistic revolution in systematics resulted in a representation of phylogeny as a strictly bifurcating pattern (cladogram). Due to the ubiquity of (...) character conflict—at the genetic or morphological level, or at any level in between—some characters will necessarily have to be discarded ( qua noise) in favor of others in support of a strictly bifurcating phylogenetic tree. Pattern analysts will seek maximal congruence in the distribution of characters (ultimately of any kind) relative to a branching tree-topology; process explainers will call such tree-topologies into question by reference to incompatible evolutionary processes. Pattern analysts will argue that process explanations must not be brought to bear on pattern reconstruction; process explainers will insist that the reconstructed pattern requires a process explanation to become scientifically relevant, i.e., relevant to evolutionary theory. The core question driving the current debate about the adequacy of the ‘Tree of Life’ metaphor seems to be whether the systematic dichotomization of the living world is an adequate representation of the complex evolutionary history of global biodiversity. In ‘Questioning the Tree of Life’, it seems beneficial to draw at least four conceptual distinctions: pattern reconstruction versus process explanation as different epistemological approaches to the study of phylogeny; open versus closed systems as expressions of different kinds of population (species) structures; phylogenetic trees versus cladograms as representations of evolutionary processes versus patterns of relationships; and genes versus species as expressions of different levels of causal integration and evolutionary transformation. (shrink)

This paper presents a case study of the South African operation of a logistics company, operating in a context of short-termism and under-performance. Frustration with managing in this context, and concern that this environment might erode the customer value proposition, prompted an exploration of the question: “How can the business prioritise its investment in intangibles to support sustainable growth in an environment of short-termism and sub-par business performance?” The study followed an inductive grounded theory approach and began with an exploration (...) of the system of short-termism as it was being experienced by the management team. This evolved in an iterative process to include an exploration of the customer value proposition, the organisation’s capabilities and the system of investment in intangibles. Data were collected over a period of 6 months, across a series of four stages as the management team grappled with the short-term financial objectives imposed on them. The data categories were used to develop 214 propositions across all stages. Through the four stages, four artefacts were developed from the propositions a causal loop diagram of the system of short-termism; a documented value proposition; an assessment of the health of the business’ capitals; and a multi-year intangibles investment programme. The findings indicate that a focus on investment in intangible assets can play a vital role in stimulating sustainable value creation in an environment of historically poor returns on investment and pressure for short-term financial results. It is suggested that investment in intangibles can be introduced as a multi-year capabilities investment plan. The study succeeded in getting investment in intangibles approved and the implication is that long-term decision-making can co-exist in an environment of short-termism and low growth. (shrink)

One way of assessing the philosophical literature on causation is to consider views on the nature of the causal relation. Early theorists were 'monists', taking there to be one causal relation. More recent theorists, however, have turned to pluralism, which holds that the causal relation is only accurately captured by two (or more) relations. I argue that one way of being a pluralist – the way which takes there to be exactly two types of causation – is (...) self defeating, if it promises to handle intuitions about all causal situations. I illustrate the point via neuron diagrams. (shrink)

Materialism, epiphenomenalism, dualism, idealism, and dual-aspect theories may all be represented by an appealing abstract mathematical device called a commutative diagram. Properties of the components of such diagrams characterize and, to some extent, even parameterize these systems and attendant metaphysical concepts (such as causal closure and supervenience) in a unified framework; process thought is of particular interest in this connection. In many cases we can even exemplify the theories typified by these diagrams in explicit graphical models. All (...) of this tends to clarify the relationships among key philosophical positions and to sharpen our sense of the effective domain and principal limitations of each. Systematic variation of these abstract diagrams may even suggest cogent metaphysical systems yet to be examined. (shrink)

Much contemporary biology consists of identifying the molecular components that associate to perform biological functions, then discovering how these functions are controlled. The concept of control is key to biological understanding, at least of the physiological kind; identifying regulators of processes underpins ideas of causality and allows complicated, multicomponent systems to be summarized in relatively simple diagrams and models. Unfortunately, as this article demonstrates by drawing on published articles, there is a growing tendency for authors to claim that a (...) molecule is a ‘regulator’ of something on evidence that cannot support the conclusion. In particular, gene knockout experiments, which can demonstrate only that a molecule is necessary for a process, are all too frequently being misinterpreted as revealing regulation. This logical error threatens to blur the important distinction between regulation and mere necessity and therefore to weaken one of our strongest tools for comprehending how organisms work. (shrink)

In Posterior Analytics 1.13, Aristotle introduced a distinction between two kinds of demonstrations: of the fact (quia), and of the reasoned fact (propter quid). Both demonstrations take a syllogistic form, in which the middle term links either two facts (in the case of quia demonstrations) or a proximate cause and a fact (in the case of propter quid demonstrations). While Aristotle stated that all the terms of one demonstration must be taken from within the same subject matter, he admitted some (...) exceptions in which the fact and the reasoned fact are instantiated by terms from different sciences, as when mathematics provides the reason and another science the empirical fact. This was the methodological foundation of the “mixed sciences”, a subject of varying interpretations in the thirteenth century. Roger Bacon (C. 1220–1292), adhering to Robert Grosseteste’s (C. 1168–1563) commentary on Posterior Analytics, presented a unique interpretation of this exception. He replaced propositional demonstrations with geometrical considerations and diagrams, thus producing geometrical arguments for theorems in natural philosophy. I focus on Bacon’s propter quid arguments, as applied in three case studies: (1) the heat caused by a body moving to its natural place; (2) the motion of the scale; (3) and the contraction of water. Based on an analysis of these demonstrations, I argue that Bacon’s interpretation of propter quid demonstration reflects his application of a scientific methodology that imbues geometrical objects with causal power over material bodies. (shrink)

The Half-Causation Method is a metaphysical-epistemic model for developing industrialised technological inventions. It consists of five phases of reasoning through which methodological success is achieved. The Method is named after its first phase, which consists of a methodological idealisation of the causal process, by pinpointing half of a possible causal relation while ignoring everything else. Following this, the Method prescribes how the reasoning should proceed, which ultimately constructs a complete and novel causal process. Each phase terminates with (...) an epistemic justification which the inventor (or inventors) can share with other knowers and have them deliberated and scrutinised. As such, the entire process of developing industrialised technological inventions, including the early stages which are traditionally regarded as mysterious can be understood as a sequence of epistemic justifications. In this paper, the Half-Causation Method is presented as a detailed practical prescription for future projects which aim to develop industrialised technological inventions. Throughout the paper two case studies from the recent history of technology are used as exemplars, namely: the invention of the microwave oven and the invention of the centrifugal vacuum cleaner. First, a definition of the ‘technological invention’ is proposed. Following that, the prescription is presented as fifteen methodological instructions: three instructions that repeat at each phase. The prescription is supplemented by a set-theoretic diagram. Although this is a philosophy paper, it is spoken directly to the scientists and engineers who aim to direct part of their research towards the development of inventions. (shrink)

The Half-Causation Method is a metaphysical-epistemic model for developing industrialised technological inventions. It consists of five phases of reasoning through which methodological success is achieved. The Method is named after its first phase, which consists of a methodological idealisation of the causal process, by pinpointing half of a possible causal relation while ignoring everything else. Following this, the Method prescribes how the reasoning should proceed, which ultimately constructs a complete and novel causal process. Each phase terminates with (...) an epistemic justification which the inventor can share with other knowers and have them deliberated and scrutinised. As such, the entire process of developing industrialised technological inventions, including the early stages which are traditionally regarded as mysterious can be understood as a sequence of epistemic justifications. In this paper, the Half-Causation Method is presented as a detailed practical prescription for future projects which aim to develop industrialised technological inventions. Throughout the paper two case studies from the recent history of technology are used as exemplars, namely: the invention of the microwave oven and the invention of the centrifugal vacuum cleaner. First, a definition of the ‘technological invention’ is proposed. Following that, the prescription is presented as fifteen methodological instructions: three instructions that repeat at each phase. The prescription is supplemented by a set-theoretic diagram. Although this is a philosophy paper, it is spoken directly to the scientists and engineers who aim to direct part of their research towards the development of inventions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:119. HUME'S CONDITIONS FOR' CAUSATION: FURTHER TO GRAY AND IMLAY As part of his second proof of the existence of God, Descartes in Meditations III argues a causal premise derived from the nature of time. He argues it follows from the nature of time "that, in order to be conserved in each moment in which it endures, a substance has need of the same power and action as (...) would be necessary to produce and create it anew, supposing it did not yet exist; so that the light of nature shows us clearly that the distinction between creation and conservation is solely a distinction of reason." The nature of time to which he refers allows only a finite divisibility into durationless moments, each of which is entirely independent of every other. In the ultimate analysis, nothing true of one moment is deducible from what is true of any other, even what happens to be eternally true. The doctrine of the creation of the eternal verities is of a piece with this conception of time, and following with it from the conception of the divinity as sheer omnipotence, points to Hume's view that experience is the only guide to the world. It would seem to be Descartes' view, that nothing at a given time can stand in the necessary relation it must have to be a cause of something at another time; or, only something outside time can be a cause, for whose operation things in time can serve as but occasions. To what extent this dialectic in fact led to later occasionalist views is an historical question we need not consider. My only suggestion here concerns Hume's réponse to the occasionalists. With all but psychological necessity eliminated from his analysis of causation, Hume effectively argues the familiar case that occasional causes are the only causes by arguing the finite divisibility of time. In the literature only Laporte has held that for Descartes time is infinitely divisible and in this sense continuous. The separability of the parts of time, he 120. thought, suffice for their independence and contingency. But if time is continuous, its parts are inseparable; as Gueroult correctly observes, by discontinuity is meant con2 tingence, independence and separability. In addition, if a moment had duration, light would not be propagated instant aneously, thus according to Descartes upsetting his entire 3 physics. Gueroult maintains, rather, that Descartes' view of time is determined by his view of motion. Whatever the historical and logical priorities, there clearly is a connection between the above and what Bergson called the cinematographic conception of motion as a succession of static objects. It is a conception that precludes events as such. Motion occurs only in time, never at the moment, and occurs as a result of the re-creation of matter with regularly differing spatial relations. Due to metaphysical consideration expressed in theological terms, especially with reference to the immutability and simplicity of divine ways, this recreation of matter is constrained in certain ways, some of which we pick out as conditions for what was later called occasional causation. Put very simply, only what is constantly conjoined can stand in this relation; and that there should be instances of constant conjunction follows from the metaphysical considerations. With Hume's elimination of these metaphysical considerations, the status of the conditions, which he takes over as conditions for causation simpliciter, becomes problematic. But a recent challenge to Hume's program is still more problematic. The contention is that there is a case in which Hume's conditions necessary fo constant conjunction cannot all be satisfied. Even worse, i is a case in which his analysis ought to be conspicuously successful, viz. collision, which Hume like Descartes con4 ceives in cinematographic terms. The aim of this paper is to show that Hume's analysis stands against the challenge. Consider the following diagram which illustrates the positions (A3, A_...) of two balls (x,y) at successive moments (t_, t.,...)· 121. A3 A2 A1 A B -B1 B2 B3 fc0 T T T ©© © G®©T©T h fc3 fc4 fc5 H Robert Gray's thesis is that in at least one case of causation, collision which results in... (shrink)