Stephen Mumford

Hume thought that if you believed in powers, you believed in necessary connections in nature. He was then able to argue that there were none such because anything could follow anything else. But Hume wrong-footed his opponents. A power does not necessitate its manifestations: rather, it disposes towards them in a way that is less than necessary but more than purely contingent. -/- In this paper a dispositional theory of causation is offered. Causes dispose towards their effects and often produce them. But a set of causes, even though they may succeed in producing an effect, cannot necessitate it since the effect could have been counteracted by some additional power. This would require a separation of our concepts of causal production and causal necessitation. The most conspicuous cases of causation are those where powers accumulate and pass a requisite threshold for an effect to occur. -/- We develop a model for representing powers as constituent vectors within an n-dimensional quality space, where composition of causes appears as vector addition. Even our resultant vector, however, has to be understood as having dispositional force only. This model throws new light on causal modality and cases of prevention, causation by absence and probabilistic causation

What is the new essentialist asking us to accept? Not that there are natural kinds, nor that there are intrinsic causal powers. These things could be accepted without a commitment to essentialism. They are asking us to accept something akin to the Kripke‐Putnam position: a metaphysical theory about kind‐membership in virtue of essential properties. But Salmon has shown that there is no valid argument for the Kripke‐Putnam position: no valid inference that gets us from reference to essence. Why then should we accept essentialism? A remaining reason is Ellis's argument by display: we should buy essentialism because of the benefits it will bring. But are these benefits real? The problem is that the putative benefits of essentialism – that the laws of nature are necessary, that the problem of induction is solved, and so on – look actually to be the assumptions of Ellis's theory. If that is the case, there is no real benefit to be gained from adopting the theory. The argument for essentialism is therefore underdetermined and it remains possible to accept natural kinds into one's ontology without accepting their corresponding essences.

This paper argues that the technical notion of conditional probability, as given by the ratio analysis, is unsuitable for dealing with our pretheoretical and intuitive understanding of both conditionality and probability. This is an ontological account of conditionals that include an irreducible dispositional connection between the antecedent and consequent conditions and where the conditional has to be treated as an indivisible whole rather than compositional. The relevant type of conditionality is found in some well-defined group of conditional statements. As an alternative, therefore, we briefly offer grounds for what we would call an ontological reading: for both conditionality and conditional probability in general. It is not offered as a fully developed theory of conditionality but can be used, we claim, to explain why calculations according to the RATIO scheme does not coincide with our intuitive notion of conditional probability. What it shows us is that for an understanding of the whole range of conditionals we will need what John Heil (2003), in response to Quine (1953), calls an ontological point of view.

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).

Dispositions may be identical to their categorical bases but should we say, with Quine, that all properties are categorical or, with Popper, that all properties are dispositional? Both positions make implicit claims of ontological reduction but if this consists in nothing more than identity then, identity being a symmetrical relation, neither categorical nor dispositional monism is provided. A supervenience relation may be thought decisive, but if the identities are token- token, reduction is ruled out; if the identities are type- type there is no direction of supervenience hence no determination of reduction. It is concluded that both ontologies have been argued inadequately

A theory of laws is developed that takes from E. J. Lowe the claim of natural laws being consistent with certain classes of exceptions. Neither abnormal cases, such as albino ravens, nor miracles falsify covering laws. This suggests that law statements cannot have the form of a universally quantified conditional. Lowe takes it that this is best explained by natural laws having normative force in the same way as moral laws and laws of the land. I argue that there is a non-normative, descriptivist account that also explains the exception cases and which is preferable, given our reservations about normative laws of nature. I also suggest an improved account of miracles within the descriptivist account