Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual (A ∨ B) > C at a causal model M (...) as a weighted average of the probability of C in those submodels that truthmake A∨ B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined. (shrink)

This paper brings together Thompson's naive action explanation with interventionist modeling of causal structure to show how they work together to produce causal models that go beyond current modeling capabilities, when applied to specifically selected systems. By deploying well-justified assumptions about rationalization, we can strengthen existing causal modeling techniques' inferential power in cases where we take ourselves to be modeling causal systems that also involve actions. The internal connection between means and end (...) exhibited in naive action explanation has a modal strength like that of distinctively mathematical explanation, rather than that of causal explanation. Because it is stronger than causation, it can be treated as if it were merely causal in a causal model without thereby overextending the justification it can provide for inferences. This chapter introduces and demonstrate the usage of the Rationalization condition in causal modeling, where it is apt for the system(s) being modeled, and to provide the basics for incorporating R variables into systems of variables and R arrows into DAGs. Use of the Rationalization condition supplements causal analysis with action analysis where it is apt. (shrink)

An important question for the causal modeling approach is how to integrate non‐causal dependence relations such as asymmetric supervenience into the approach. The most prominent proposal to that effect (due to Gebharter) is to treat those dependence relationships as formally analogous to causal relationships. We argue that this proposal neglects some crucial differences between causal and non‐causal dependencies, and that in the context of causal modeling non‐causal dependence relationships should be represented (...) as mutual dependence relationships. We develop a new kind of model – “hybrid models” ‐ based on this suggestion, and formulate a set of axioms for those models. Our formalism has important implications for Kim's exclusion problem: whereas Gebharter's framework vindicates Kim's causal exclusion objection against nonreductive physicalism, our framework has no such implication, and can help non‐reductive physicalists vindicate the efficacy of high‐level properties. A further benefit of our formalism is that it yields a natural and plausible way of thinking about interventions in multi‐level contexts. (shrink)

Causal modeling methods such as path analysis, used in the social and natural sciences, are also highly relevant to philosophical problems of probabilistic causation and statistical explanation. We show how these methods can be effectively used (1) to improve and extend Salmon's S-R basis for statistical explanation, and (2) to repair Cartwright's resolution of Simpson's paradox, clarifying the relationship between statistical and causal claims.

Recent philosophical studies of probabilistic causation and statistical explanation have opened up the possibility of unifying philosophical approaches with causal modeling as practiced in the social and biological sciences. This unification rests upon the statistical tools employed, the principle of common cause, the irreducibility of causation to statistics, and the idea of causal process as a suitable framework for understanding causal relationships. These four areas of contact are discussed with emphasis on the relevant aspects of (...) class='Hi'>causal modeling. (shrink)

Brandon claims that to explain adaptation one must specify fitnesses in each selective environment and specify the distribution of individuals across selective environments. Glymour claims, using an example of the adaptive evolution of costly plasticity in a symmetric environment, that there are some predictive or explanatory tasks for which Brandon’s claim is limited. In this paper, I provide necessary conditions for carrying out Brandon’s task, produce a new version of the argument for his claim, and show that Glymour’s reasons for (...) making his claim are problematic. I provide a few interpretations of Glymour’s argument but ultimately raise worries for what I take to be the key premises. (shrink)

I highlight a metaphysical concern that stands in the way of more widespread adoption of causal modeling techniques such as causal Bayes nets. Researchers in some fields may resist adoption due to concerns that they don't 'really' understand what they are saying about a system when they apply such techniques. Students in these fields are repeated exhorted to be cautious about application of statistical techniques to their data without a clear understanding of the conditions required for those (...) techniques to yield genuine insight into the data. They are acutely aware that anyone can chuck some data into a software package and get what looks like an answer, even though these tests may not be well-defined for the data on which they can apparently be run. This is thus a healthy skepticism for uptake of causal modeling methods, which points directly to the need for a metaphysical understanding of causation in order to successfully use the modeling methods. Without a clear understanding of what the methods are committing to, including what it means to say that there exists a causal relationship, researchers have limited ability to identify potentially bad output, or to independently verify results. (shrink)

Recent studies on probabilistic causation and statistical explanation (Cartwright 1979; Salmon 1984), I believe, have opened up the possibility of a genuine unification between philosophical approaches and causal modeling (CM) in the social, behavioral and biological sciences (Wright 1934; Blalock 1964; Asher 1976). This unification rests on the statistical tools employed, the principle of common cause, the irreducibility of causation to probability or statistics, and the idea of causal process as a suitable framework for understanding causal (...) relationships. The aim of this paper is to draw attention to these four areas of contact by focusing on the relevant aspects of CM.Causal analysis in the social sciences is based on two fundamental notions: model and method. A causal model is an idealized picture of the causal relationships in the world. Method, on the other hand, refers to certain statistical techniques that are used to evaluate and test a causal model using data which consist of joint observations on the model variables. (shrink)

Causal models provide a framework for precisely representing complex causal structures, where specific models can be used to efficiently predict, infer, and explain the world. At the same time, we often do not know the full causal structure a priori and so must learn it from data using a causal model search algorithm. This chapter provides a general overview of causal models and their uses, with a particular focus on causal graphical models (the most (...) commonly used causal modeling framework) and methods for learning such models from observational and experimental data. The chapter concludes with two examples of productive causal search and modeling in experimental philosophy. (shrink)

Drawing substantive conclusions from linear causal models that perform acceptably on statistical tests is unreasonable if it is not known how alternatives fare on these same tests. We describe a computer program, TETRAD, that helps to search rapidly for plausible alternatives to a given causal structure. The program is based on principles from statistics, graph theory, philosophy of science, and artificial intelligence. We describe these principles, discuss how TETRAD employs them, and argue that these principles make TETRAD an (...) effective tool. Finally, we illustrate TETRAD's effectiveness by applying it to a multiple indicator model of Political and Industrial development. A pilot version of the TETRAD program is described in this paper. The current version is described in our forthcoming Discovering Causal Structure: Artificial Intelligence for Statistical Modeling. (shrink)

This paper examines the adequacy of causal graph theory as a tool for modeling biological phenomena and formalizing biological explanations. I point out that the causal graph approach reaches it limits when it comes to modeling biological phenomena that involve complex spatial and structural relations. Using a case study from molecular biology, DNA-binding and -recognition of proteins, I argue that causal graph models fail to adequately represent and explain causal phenomena in this field. The (...) inadequacy of these models is due to their failure to include relevant spatial and structural information in a way that does not render the model non-explanatory, unmanageable, or inconsistent with basic assumptions of causal graph theory. (shrink)

Some cases show that counterfactual conditionals (‘counterfactuals’ for short) are inherently ambiguous, equivocating between forward-tracking and backtracking counterfactu- als. Elsewhere, I have proposed a causal modeling semantics, which takes this phenomenon to be generated by two kinds of causal manipulations. (Lee 2015; Lee 2016) In an important paper (Hiddleston 2005), Eric Hiddleston offers a different causal modeling semantics, which he claims to be able to explain away the inherent ambiguity of counterfactuals. In this paper, I (...) discuss these two semantic treatments and argue that my (bifurcated) semantics is theoretically more promising than Hiddleston’s (unified) semantics. (shrink)

Philosophers have long analyzed the truth-condition of counterfactual conditionals in terms of the possible-worlds semantics advanced by Lewis [13] and Stalnaker [23]. In this paper, I argue that, from the perspective of philosophical semantics, the causal modeling semantics proposed by Pearl [17] and others (e.g., Briggs [3]) is more plausible than the Lewis-Stalnaker possible-worlds semantics. I offer two reasons. First, the possible-worlds semantics has suffered from a specific type of counterexamples. While the causal modeling semantics can (...) handle such examples with ease, the only way for the possible-worlds semantics to do so seems to cost it its distinctive status as a philosophical semantics. Second, the causal modeling semantics, but not the possible-worlds semantics, has the resources enough for accounting for both forward-tracking and backtracking counterfactual conditionals. (shrink)

We construct a causal-modeling semantics for both indicative and counterfactual conditionals. As regards counterfactuals, we adopt the orthodox view that a counterfactual conditional is true in a causal model M just in case its consequent is true in the submodel M∗, generated by intervening in M, in which its antecedent is true. We supplement the orthodox semantics by introducing a new manipulation called extrapolation. We argue that an indicative conditional is true in a causal model M (...) just in case its con- sequent is true in certain submodels M∗, generated by extrapolating M, in which its antecedent is true. We show that the proposed semantics can account for some important minimal pairs nicely and naturally. We also prove a theorem showing under what conditions intervention and extrapolation will yield the same result, and thus explain how counterfactual and indicative conditionals would behave in a causal-modeling semantics. (shrink)

Mechanist philosophers have examined several strategies scientists use for discovering causal mechanisms in neuroscience. Findings about the anatomical organization of the brain play a central role in several such strategies. Little attention has been paid, however, to the use of network analysis and causal modeling techniques for mechanism discovery. In particular, mechanist philosophers have not explored whether and how these strategies incorporate information about the anatomical organization of the brain. This paper clarifies these issues in the light (...) of the distinction between structural, functional and effective connectivity. Specifically, we examine two quantitative strategies currently used for causal discovery from functional neuroimaging data: dynamic causal modeling and probabilistic graphical modeling. We show that dynamic causal modeling uses findings about the brain’s anatomical organization to improve the statistical estimation of parameters in an already specified causal model of the target brain mechanism. Probabilistic graphical modeling, in contrast, makes no appeal to the brain’s anatomical organization, but lays bare the conditions under which correlational data suffice to license reliable inferences about the causal organization of a target brain mechanism. The question of whether findings about the anatomical organization of the brain can and should constrain the inference of causal networks remains open, but we show how the tools supplied by graphical modeling methods help to address it. (shrink)

Recording of neural activity during grasping actions in macaques showed that grasp-related sensorimotor transformations are accomplished in a circuit constituted by the anterior part of the intraparietal sulcus (AIP), the ventral (F5) and the dorsal (F2) region of the premotor area. In humans, neuroimaging studies have revealed the existence of a similar circuit, involving the putative homolog of macaque areas AIP, F5, and F2. These studies have mainly considered grasping movements performed with the right dominant hand and only a few (...) studies have measured brain activity associated with a movement performed with the left non-dominant hand. As a consequence of this gap, how the brain controls for grasping movement performed with the dominant and the non-dominant hand still represents an open question. A functional magnetic resonance imaging (fMRI) experiment has been conducted, and effective connectivity (dynamic causal modeling, DCM) was used to assess how connectivity among grasping-related areas is modulated by hand (i.e., left and right) during the execution of grasping movements toward a small object requiring precision grasping. Results underlined boosted inter-hemispheric couplings between dorsal premotor cortices during the execution of movements performed with the left rather than the right dominant hand. More specifically, they suggest that the dorsal premotor cortices may play a fundamental role in monitoring the configuration of fingers when grasping movements are performed by either the right and the left hand. This role becomes particularly evident when the hand less-skilled (i.e., the left hand) to perform such action is utilized. The results are discussed in light of recent theories put forward to explain how parieto-frontal connectivity is modulated by the execution of prehensile movements. (shrink)

Understanding the neural basis of schizophrenia (SZ) is important for shedding light on the neurobiological mechanisms underlying this mental disorder. Structural and functional alterations in the anterior cingulate cortex (ACC), dorsolateral prefrontal cortex (DLPFC), hippocampus, and medial prefrontal cortex (MPFC) have been implicated in the neurobiology of SZ. However, the effective connectivity among them in SZ remains unclear. The current study investigated how neuronal pathways involving these regions were affected in first-episode SZ using functional magnetic resonance imaging (fMRI). Forty-nine patients (...) with a first-episode of psychosis and diagnosis of SZ—according to the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision—were studied. Fifty healthy controls (HCs) were included for comparison. All subjects underwent resting state fMRI. We used spectral dynamic causal modeling (DCM) to estimate directed connections among the bilateral ACC, DLPFC, hippocampus, and MPFC. We characterized the differences using Bayesian parameter averaging (BPA) in addition to classical inference (t-test). In addition to common effective connectivity in these two groups, HCs displayed widespread significant connections predominantly involved in ACC not detected in SZ patients, but SZ showed few connections. Based on BPA results, SZ patients exhibited anterior cingulate cortico-prefrontal-hippocampal hyperconnectivity, as well as ACC-related and hippocampal-dorsolateral prefrontal-medial prefrontal hypoconnectivity. In summary, spectral DCM revealed the pattern of effective connectivity involving ACC in patients with first-episode SZ. This study provides a potential link between SZ and dysfunction of ACC, creating an ideal situation to associate mechanisms behind SZ with aberrant connectivity among these cognition and emotion-related regions. (shrink)

This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering on rules (...) which is syntactically derived from the knowledge base. This ordering accounts for rule interactions, respects specificity considerations and facilitates the construction of coherent states of beliefs. Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries. Imprecise observations are incorporated using qualitative versions of Jeffrey's rule and Bayesian updating, with the result that coherent belief revision is embodied naturally and tractably. Finally, causal rules are interpreted as imposing Markovian conditions that further constrain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal projections, explanations, actions and change. (shrink)

Aging is accompanied by stereotyped changes in functional brain activations, for example a cortical shift in activity patterns from posterior to anterior regions is one hallmark revealed by functional magnetic resonance imaging (fMRI) of aging cognition. Whether these neuronal effects of aging could potentially contribute to an amelioration of or resistance to the cognitive symptoms associated with psychopathology remains to be explored. We used a visual illusion paradigm to address whether aging affects the cortical control of perceptual beliefs and biases. (...) Our aim was to understand the effective connectivity associated with volitional control of ambiguous visual stimuli and to test whether greater top-down control of early visual networks emerged with advancing age. Using a bias training paradigm for ambiguous images we found that older participants (n = 16) resisted experimenter-induced visual bias compared to a younger cohort (n = 14) and that this resistance was associated with greater activity in prefrontal and temporal cortices. By applying Dynamic Causal Models for fMRI we uncovered a selective recruitment of top-down connections from the middle temporal to Lingual gyrus (LIN) by the older cohort during the perceptual switch decision following bias training. In contrast, our younger cohort did not exhibit any consistent connectivity effects but instead showed a loss of driving inputs to orbitofrontal sources following training. These findings suggest that perceptual beliefs are more readily controlled by top-down strategies in older adults and introduce age-dependent neural mechanisms that may be important for understanding aberrant belief states associated with psychopathology. (shrink)

In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics. We will argue that—leaving aside instrumentalism which restricts the physical meaning of QM to the algorithmic prediction of measurement outcomes—the many interpretations which can be found in the literature can be distinguished through the way they model the measurement process, either in terms of the efficient cause or in terms of the final cause. (...) We will discuss and analyze why both, ‘final cause’ and ‘efficient cause’ models, face severe difficulties to solve the measurement problem. In contradistinction to these schemes we will present a new model based on the immanent cause which, we will argue, provides an intuitive understanding of the measurement process in QM. (shrink)

The Lotka–Volterra predator-prey-model is a widely known example of model-based science. Here we reexamine Vito Volterra’s and Umberto D’Ancona’s original publications on the model, and in particular their methodological reflections. On this basis we develop several ideas pertaining to the philosophical debate on the scientific practice of modeling. First, we show that Volterra and D’Ancona chose modeling because the problem in hand could not be approached by more direct methods such as causal inference. This suggests a philosophically (...) insightful motivation for choosing the strategy of modeling. Second, we show that the development of the model follows a trajectory from a “how possibly” to a “how actually” model. We discuss how and to what extent Volterra and D’Ancona were able to advance their model along that trajectory. It turns out they were unable to establish that their model was fully applicable to any system. Third, we consider another instance of model-based science: Darwin’s model of the origin and distribution of coral atolls in the Pacific Ocean. Darwin argued more successfully that his model faithfully represents the causal structure of the target system, and hence that it is a “how actually” model. (shrink)

I argue for the causal character of modeling in data-intensive science, contrary to widespread claims that big data is only concerned with the search for correlations. After discussing the concept of data-intensive science and introducing two examples as illustration, several algorithms are examined. It is shown how they are able to identify causal relevance on the basis of eliminative induction and a related difference-making account of causation. I then situate data-intensive modeling within a broader framework of (...) an epistemology of scientific knowledge. In particular, it is shown to lack a pronounced hierarchical, nested structure. The significance of the transition to such “horizontal” modeling is underlined by the concurrent emergence of novel inductive methodology in statistics such as non-parametric statistics. Data-intensive modeling is well equipped to deal with various aspects of causal complexity arising especially in the higher level and applied sciences. (shrink)

Clark Glymour, Richard Scheines, Peter Spirtes and Kevin Kelly. Discovering Causal Structure: Artifical Intelligence, Philosophy of Science and Statistical Modeling.

Throughout the Covid-19 pandemic, people have been eager to learn what factors, and especially what public health policies, cause infection rates to wax and wane. But figuring out conclusively what causes what is difficult in complex systems with nonlinear dynamics, such as pandemics. We review some of the challenges that scientists have faced in answering quantitative causal questions during the Covid-19 pandemic, and suggest that these challenges are a reason to augment the moral dimension of conversations about causal (...) inference. We take a lesson from Martha Nussbaum—who cautions us not to think we have just one question on our hands when we have at least two—and apply it to modeling for causal inference in the context of cost-benefit analysis. (shrink)

Mechanisms play an important role in many sciences when it comes to questions concerning explanation, prediction, and control. Answering such questions in a quantitative way requires a formal represention of mechanisms. Gebharter (2014) suggests to represent mechanisms by means of one or more causal arrows of an acyclic causal net. In this paper we show how this approach can be extended in such a way that it can also be fruitfully applied to mechanisms featuring causal feedback.

Contemporary action theory is generally concerned with giving theories of action ontology. In this paper, we make the novel proposal that the standard view in action theory—the Causal Theory of Action—should be recast as a “model”, akin to the models constructed and investigated by scientists. Such models often consist in fictional, hypothetical, or idealized structures, which are used to represent a target system indirectly via some resemblance relation. We argue that recasting the Causal Theory as a model can (...) not only accomplish the goals of causal theorists, but also give the theory greater flexibility in responding to common objections. (shrink)

This paper explores some issues concerning how we should think about interventions (in the sense of unconfounded manipulations) of "upper-level" variables in contexts in which these supervene on but are not identical with lower-level realizers. It is argued that we should reject the demand that interventions on upper-level variables must leave their lower-level realizers unchanged– a requirement that within an interventionist framework would imply that upper-level variables are causally inert. Instead an intervention on an upper-level variable at the same time (...) changes its lower-level realizer in a way that is consistent with the change in the upper- level variable. The lower-level realizer should not be regarded as a potential "confounder" of upper-level causal relations, as in "exclusionist" arguments. Several proposals for making this precise are considered and several pro-exclusionist arguments are criticized. (shrink)

The paper investigates the question as to which features of hypotheses make them explanatory. Given the intuitive appeal of causal explanations, one might suspect that explanatoriness is deeply connected with causation. I argue in detail that this is wrong by showing that none of the dominant analyses of causation are suited for general accounts of explanatoriness. In the second part, I provide the outlines of an account of explanatoriness that connects it with scientific understanding, which in turn is argued (...) to be analyzable as the cognitive realization of scientific models. (shrink)

Estimating the effect of a randomized treatment and the effect that is transmitted through a mediator is often complicated by treatment noncompliance. In literature, an instrumental variable (IV)-based method has been developed to study causal mediation effects in the presence of treatment noncompliance. Existing studies based on the IV-based method focus on identifying the mediated portion of the intention-to-treat effect, which relies on several identification assumptions. However, little attention has been given to assessing the sensitivity of the identification assumptions (...) or mitigating the impact of violating these assumptions. This study proposes a two-stage joint modeling method for conducting causal mediation analysis in the presence of treatment noncompliance, in which modeling assumptions can be employed to decrease the sensitivity to violation of some identification assumptions. The use of a joint modeling method is also conducive to conducting sensitivity analyses to the violation of identification assumptions. We demonstrate our approach using the Jobs II data, in which the effect of job training on job seekers’ mental health is examined. (shrink)

Since the introduction of mathematical population genetics, its machinery has shaped our fundamental understanding of natural selection. Selection is taken to occur when differential fitnesses produce differential rates of reproductive success, where fitnesses are understood as parameters in a population genetics model. To understand selection is to understand what these parameter values measure and how differences in them lead to frequency changes. I argue that this traditional view is mistaken. The descriptions of natural selection rendered by population genetics models are (...) in general neither predictive nor explanatory and introduce avoidable conceptual confusions. I conclude that a correct understanding of natural selection requires explicitly causal models of reproductive success. *Received May 2006; revised December 2006. †To contact the author, please write to: Department of Philosophy, Kansas State University, 201 Dickens Hall, Manhattan, KS 66506; e‐mail: [email protected] . (shrink)

This monograph looks at causal nets from a philosophical point of view. The author shows that one can build a general philosophical theory of causation on the basis of the causal nets framework that can be fruitfully used to shed new light on philosophical issues. Coverage includes both a theoretical as well as application-oriented approach to the subject. The author first counters David Hume’s challenge about whether causation is something ontologically real. The idea behind this is that good (...) metaphysical concepts should behave analogously to good theoretical concepts in scientific theories. In the process, the author offers support for the theory of causal nets as indeed being a correct theory of causation. Next, the book offers an application-oriented approach to the subject. The author shows that causal nets can investigate philosophical issues related to causation. He does this by means of two exemplary applications. The first consists of an evaluation of Jim Woodward’s interventionist theory of causation. The second offers a contribution to the new mechanist debate. Introductory chapters outline all the formal basics required. This helps make the book useful for those who are not familiar with causal nets, but interested in causation or in tools for the investigation of philosophical issues related to causation. (shrink)

Within the causal modeling literature, debates about the Causal Faithfulness Condition have concerned whether it is probable that the parameters in causal models will have values such that distinct causal paths will cancel. As the parameters in a model are fixed by the probability distribution over its variables, it is initially puzzling what it means to assign probabilities to these parameters. I propose that to assign a probability to a parameter in a model is to (...) treat that parameter as a function of a variable in an augmented model. By combining this proposal with widely adopted principles regarding which variables must be included in a model, I argue that the various proposed counterexamples to CFC involving coordinated parameters are not genuine counterexamples. I then consider the cases in which CFC fails due not to coordination, but by coincidence, and propose explanatory and predictive bases for ruling out such coincidences without presuming that they are improbable. The aim of the proposed defenses is not to show that CFC never fails, but rather to argue that its use in a particular context may be defended using general modeling assumptions rather than by relying on claims about how often it fails. (shrink)

Experimental modeling in biology involves the use of living organisms (not necessarily so-called "model organisms") in order to model or simulate biological processes. I argue here that experimental modeling is a bona fide form of scientific modeling that plays an epistemic role that is distinct from that of ordinary biological experiments. What distinguishes them from ordinary experiments is that they use what I call "in vivo representations" where one kind of causal process is used to stand (...) in for a physically different kind of process. I discuss the advantages of this approach in the context of evolutionary biology. (shrink)

Social scientists report difficulties in drawing out testable predictions from the literature on intersectionality theory. We alleviate that difficulty by showing that some characteristic claims of the intersectionality literature can be interpreted causally. The formalism of graphical causal modeling allows claims about the causal effects of occupying intersecting identity categories to be clearly represented and submitted to empirical testing. After outlining this causal interpretation of intersectional theory, we address some concerns that have been expressed in the (...) literature claiming that membership in demographic categories can have causal effects. (shrink)

Modeling mechanisms is central to the biological sciences – for purposes of explanation, prediction, extrapolation, and manipulation. A closer look at the philosophical literature reveals that mechanisms are predominantly modeled in a purely qualitative way. That is, mechanistic models are conceived of as representing how certain entities and activities are spatially and temporally organized so that they bring about the behavior of the mechanism in question. Although this adequately characterizes how mechanisms are represented in biology textbooks, contemporary biological research (...) practice shows the need for quantitative, probabilistic models of mechanisms, too. In this paper we argue that the formal framework of causal graph theory is well-suited to provide us with models of biological mechanisms that incorporate quantitative and probabilistic information. On the ba-sis of an example from contemporary biological practice, namely feedback regulation of fatty acid biosynthesis in Brassica napus, we show that causal graph theoretical models can account for feedback as well as for the multi-level character of mechanisms. However, we do not claim that causal graph theoretical representations of mechanisms are advantageous in all respects and should replace common qualitative models. Rather, we endorse the more balanced view that causal graph theoretical models of mechanisms are useful for some purposes, while being insufficient for others. (shrink)