Philosophers have found postulating possible worlds to be very useful in a number of areas, including philosophy of language and mind, logic, and metaphysics. Impossible worlds are a natural extension to this use of possible worlds, and can help resolve a number of difficulties thrown up by possible‐worlds frameworks.

Information about the structure of a causal system can come in the form of observational data—random samples of the system's autonomous behavior—or interventional data—samples conditioned on the particular values of one or more variables that have been experimentally manipulated. Here we study people's ability to infer causal structure from both observation and intervention, and to choose informative interventions on the basis of observational data. In three causal inference tasks, participants were to some degree capable of distinguishing between competing causal hypotheses (...) on the basis of purely observational data. Performance improved substantially when participants were allowed to observe the effects of interventions that they performed on the systems. We develop computational models of how people infer causal structure from data and how they plan intervention experiments, based on the representational framework of causal graphical models and the inferential principles of optimal Bayesian decision‐making and maximizing expected information gain. These analyses suggest that people can make rational causal inferences, subject to psychologically reasonable representational assumptions and computationally reasonable processing constraints. (shrink)

Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well (...) as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources. (shrink)

General discussion of grounding, including its formal features, relations to other notions, and applications.

Much of the philosophical literature on causation has focused on the concept of actual causation, sometimes called token causation. In particular, it is this notion of actual causation that many philosophical theories of causation have attempted to capture.2 In this paper, we address the question: what purpose does this concept serve? As we shall see in the next section, one does not need this concept for purposes of prediction or rational deliberation. What then could the purpose be? We will argue (...) that one can gain an important clue here by looking at the ways in which causal judgments are shaped by people‘s understanding of norms. (shrink)

On the now dominant Quinean view, metaphysics is about what there is. Metaphysics so conceived is concerned with such questions as whether properties exist, whether meanings exist, and whether numbers exist. I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. Metaphysics so revived does not bother asking whether properties, meanings, and numbers exist (of course they do!) The question is whether or not they are fundamental.

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector”, a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine’s activation that (...) required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4- year-olds were found. We suggest that children’s causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base-rate of certain events occurring. Fouryear-olds, but not 3-year-olds were able to make this inference. (shrink)

It has recently been suggested that a distinctive metaphysical relation— ‘Grounding’—is ultimately at issue in contexts in which some goings-on are said to hold ‘in virtue of’’, be ‘metaphysically dependent on’, or be ‘nothing over and above’ some others. Grounding is supposed to do good work in illuminating metaphysical dependence. I argue that Grounding is also unsuited to do this work. To start, Grounding alone cannot do this work, for bare claims of Grounding leave open such basic questions as whether (...) Grounded goings-on exist, whether they are reducible to or rather distinct from Grounding goings-on, whether they are efficacious, and so on; but in the absence of answers to such basic questions, we are not in position to assess the associated claim or theses concerning metaphysical dependence. There is no avoiding appeal to the specific metaphysical relations typically at issue in investigations into dependence—for example, type or token identity, functional realization, classical mereological parthood, the set membership relation, the proper subset relation, the determinable/determinate relation, and so on—which are capable of answering these questions. But, I argue, once the specific relations are on the scene, there is no need for Grounding. (shrink)

There is a systematic and suggestive analogy between grounding and causation. In my view, this analogy is no coincidence. Grounding and causation are alike because grounding is a type of causation: metaphysical causation. In this paper I defend the identification of grounding with metaphysical causation, drawing on the causation literature to explore systematic connections between grounding and metaphysical dependence counterfactuals, and I outline a non-reductive counterfactual theory of grounding along interventionist lines.

This paper outlines a non-reductive counterfactual account of grounding along interventionist lines, and uses the account to argue that taking grounding seriously requires ascribing non-trivial truth-conditions to a range of counterpossible counterfactuals. This result allows for a diagnosis of a route to scepticism about grounding, as deriving at least in part from scepticism about non-trivial counterpossible truth and falsity.

Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...) issues in the philosophy of mathematics; in particular it may help platonists respond to a recent challenge by Joseph Melia concerning the force of the Indispensability Argument. (shrink)

Acceptance of Humean Supervenience and thereductive Humean analyses that entail it leadsto a litany of inadequately explained conflictswith our intuitions regarding laws andpossibilities. However, the non-reductiveHumeanism developed here, on which law claimsare understood as normative rather than factstating, can accommodate those intuitions. Rational constraints on such norms provide aset of consistency relations that ground asemantics formulated in terms offactual-normative worlds, solving theFrege-Geach problem of construing unassertedcontexts. This set of factual-normative worldsincludes exactly the intuitive sets ofnomologically possible worlds associated witheach possible (...) set of laws. The extension ofthe semantics to counterfactual and subjunctiveconditionals is sketched. Potential objectionsinvolving subjectivity, mind-dependence, andnon-factuality are discussed. (shrink)

This paper develops an account of metaphysical explanation according to which metaphysical explanations are answers to what-makes-it-the-case-that questions. On this view, metaphysical explanations are not to be considered entirely objective, but are subject to epistemic constraints imposed by the context in which a relevant question is asked. The resultant account of metaphysical explanation is developed independently of any particular views about grounding. Toward the end of the paper an application of the view is proposed that takes metaphysical explanations conceived in (...) this way to characterize reality's structure. According to this proposal, reality's structure is partly constituted by a projection of our explanatory practices onto reality. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine's activation that (...) required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children's causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference. (shrink)

This paper argues that the semantic facts about ‘because’ are best explained via a metaphorical treatment of metaphysical explanation that treats causal explanation as explanation par excellence. Along the way, it defends a commitment to a unified causal sense of ‘because’ and offers a proprietary explanation of grounding skepticism. With the causal metaphor account of metaphysical explanation on the table, an extended discussion of the relationship between conceptual structure and metaphysics ends with a suggestion that the semantic facts about ‘because’ (...) tell against grounding-causation unity. (shrink)

Attempts to elucidate grounding are often made by connecting grounding to metaphysical explanation, but the notion of metaphysical explanation is itself opaque, and has received little attention in the literature. We can appeal to theories of explanation in the philosophy of science to give us a characterization of metaphysical explanation, but this reveals a tension between three theses: that grounding relations are objective and mind-independent; that there are pragmatic elements to metaphysical explanation; and that grounding and metaphysical explanation share a (...) close connection. Holding fixed the mind-independence of grounding, I show that neither horn of the resultant dilemma can be blunted. Consequently, we should reject the assumption that grounding relations are mind-independent. (shrink)

In this paper we provide a psychological explanation for ‘grounding observations’—observations that are thought to provide evidence that there exists a relation of ground. Our explanation does not appeal to the presence of any such relation. Instead, it appeals to certain evolved cognitive mechanisms, along with the traditional modal relations of supervenience, necessitation and entailment. We then consider what, if any, metaphysical conclusions we can draw from the obtaining of such an explanation, and, in particular, if it tells us anything (...) about whether we ought to posit a relation of ground. (shrink)

Many think that sentences about what metaphysically explains what are true iff there exist grounding relations. This suggests that sceptics about grounding should be error theorists about metaphysical explanation. We think there is a better option: a theory of metaphysical explanation which offers truth conditions for claims about what metaphysically explains what that are not couched in terms of grounding relations, but are instead couched in terms of, inter alia, psychological facts. We do not argue that our account is superior (...) to grounding-based accounts. Rather, we offer it to those already ill-disposed towards grounding. (shrink)

We used a new method to assess how people can infer unobserved causal structure from patterns of observed events. Participants were taught to draw causal graphs, and then shown a pattern of associations and interventions on a novel causal system. Given minimal training and no feedback, participants in Experiment 1 used causal graph notation to spontaneously draw structures containing one observed cause, one unobserved common cause, and two unobserved independent causes, depending on the pattern of associations and interventions they saw. (...) We replicated these findings with less‐informative training (Experiments 2 and 3) and a new apparatus (Experiment 3) to show that the pattern of data leads to hidden causal inferences across a range of prior constraints on causal knowledge. (shrink)

Experimental studies suggest that people’s ordinary causal judgments are affected not only by statistical considerations but also by moral considerations. One way to explain these results would be to construct a model according to which people are trying to make a purely statistical judgment but moral considerations somehow distort their intuitions. The present paper offers an alternative perspective. Specifically, the author proposes a model according to which the very same underlying mechanism accounts for the influence of both statistical and moral (...) considerations. On this model, it appears that ordinary causal judgments are quite different from the sorts of judgments one might find in the systematic sciences.Keywords: Causation; Causal cognition; Experimental philosophy; Cognitive science. (shrink)

We propose that children employ specialized cognitive systems that allow them to recover an accurate “causal map” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or “Bayes nets”. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2- to 4-year-old children (...) construct new causal maps and that their learning is consistent with the Bayes net formalism. (shrink)

Do numbers exist? Carnap (1956 [1950]) famously argues that this question can be understood in an “internal” and in an “external” sense, and calls “external” questions “non-cognitive”. Carnap also says that external questions are raised “only by philosophers” (p. 207), which means that, in his view, philosophers raise ”non-cognitive” questions. However, it is not clear how the internal/external distinction and Carnap’s related views about philosophy should be understood. This paper provides a new interpretation. I draw attention to Carnap’s distinction between (...) purely external statements, which are independent from all frameworks, and pragmatic external statements, which concern which framework one should adopt, and argue that the latter express noncognitive mental states. Specifically, I argue that “frameworks” are systems of rules for the assessment of statements, which are utterances of ordinary language sentences. Pragmatic external statements express noncognitive dispositions to follow only certain rules of assessment. For instance, “numbers exist” understood as a pragmatic external statement expresses a noncognitive disposition to use only rules of assessment according to which numbers do exist. Carnap can thereby be understood as proposing a distinctive form of noncognitivism about ontology that is in some respects analogous to norm-expressivism in metaethics. (shrink)

This paper offers a new account of metaphysical explanation. The account is modelled on Kitcher’s unificationist approach to scientific explanation. We begin, in Sect. 2, by briefly introducing the notion of metaphysical explanation and outlining the target of analysis. After that, we introduce a unificationist account of metaphysical explanation before arguing that such an account is capable of capturing four core features of metaphysical explanations: irreflexivity, non-monotonicity, asymmetry and relevance. Since the unificationist theory of metaphysical explanation inherits irreflexivity and non-monotonicity (...) directly from the unificationist theory of scientific explanation that underwrites it, we focus on demonstrating how the account can secure asymmetry and relevance. (shrink)

Ontological expressivism is the view that ontological existence claims express non-cognitive mental states. I develop a version of ontological expressivism that is modeled after Gibbard’s (2003) norm-expressivism. I argue that, when speakers assess whether, say, composite objects exist, they rely on assumptions with regard to what is required for composition to occur. These assumptions guide their assessment, similar to how norms may guide the assessment of normative propositions. Against this backdrop, I argue that “some objects have parts”, uttered in the (...) context of an ontological disagreement, expresses a noncognitive disposition to assess the truth of propositions by using only rules of assessment according to which the proposition that some objects have parts is to be evaluated as true. (shrink)

I survey the philosophical literature on grounding explanation and its connection to metaphysical ground.

Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.