The first step is to argue that the Mentaculus implies a branching tree structure toward the future on the macrolevel, according to which the universe’s macrostate at a time is compatible with many more different macro-evolutions toward the future than macro-evolutions toward the past. Broadly such constraints come in two types: according to the first type of constraint causes do not act where they are not. The challenge, according to the dominant cause argument, is to find a criterion that somehow allows us to distill a small set of causes from the complete goings-on on an initial value surface S. And causal skeptics argue that physical theories themselves cannot provide such a criterion. That is, (a) we need to specify the initial state in the relevant region completely and in whatever detail the laws at issue require; and (b) the relevant region comprising the initial value surface may be quite large. What is important is that nothing less than a complete specification of the state on the initial value surface will allow E to be derived from the laws-the laws are silent on how a system with incompletely specified initial conditions may evolve. 2. Causal notions can, if at all, only be legitimately employed in contexts in which we can isolate a small set of factors of interest as those responsible for the occurrence of an event-the dominant cause or causes-by drawing a distinction between causes and background conditions.

If we assume that a system is governed by deterministic physical laws, then the laws allow us to derive the occurrence of some event E from appropriate initial and boundary conditions. Within the context of an initial value problem, in which the initial state of the balls is given and Newton’s laws are used to calculate the subsequent motion of the balls, the former type of counterfactual is the appropriate one, while the context of a final value problem (which asks us to calculate the balls’ prior motion given their final state) suggests the latter type of counterfactual. But it is not obvious how this verdict is borne out purely by considering Newton’s equations: singling out the forward-looking counterfactual as the correct one seems arbitrary. What, if anything, can single out putatively causal counterfactuals of the form "If the balls’ initial state prior to the collision had been different, their final state after the collision would be different" from putatively anti-causal backtracking counterfactuals of the form "If the balls’ final state were different, their initial state would have to have been different"? In his seminal article (1912), Russell uses similar considerations to argue that the causal law "same cause, same effect" is either trivial or false: if the cause of an event E is taken to include less than a complete specification of all the putatively causal factors relevant to the E’s occurrence, then the law is false, since then the occurrence of E could then still be disrupted by some external influence not captured within the specification of the set of E’s causes.

Within the functional project one could argue in defense of premises 2 and 3 that local causal relations satisfy certain crucial desiderata not satisfied by non-local, putatively causal relations. 4. Causal relations are relations among spatio-temporally localized events, yet fundamental physical laws relate entire global time-slices. Yet, it is often argued that the dynamical laws of the fundamental or established theories of physics are time-symmetric and have the same character in both temporal directions. The laws of classical electrodynamics, the Maxwell-Lorentz equations, imply a wave equation, which is a time-reversal invariant hyperbolic equation of motion and is standardly solved using the Green’s functions formalism. Alternatively, we can take the practices of physical theorizing and model-building as starting points and examine whether we can "engineer" causal concepts that fulfil certain cognitive functions within these contexts. Woodward (2007) takes this approach to the functional project and explores to what extent interventionist causal concepts that play an essential role in how we navigate the world fit with theorizing in physics. As Woodward (2014) emphasizes, it is compatible with causal judgments playing an important cognitive role in some domains that there are limits to the scope of causal thinking and that causal concepts are not universally applicable.

While the neo-Russellian view is compatible with the claim that in some non-fundamental domains and for pragmatic reasons information about the ideal explanatory text may fruitfully be presented in causal terms, the view holds that ideal physical explanations are not causal. In reply to this worry one can argue that interventions into physical systems may be more adequately modeled in term of "soft", non-arrow breaking interventions, as investigated in Eberhardt and Scheines (2007). What the comparative merits of characterizing causal structures in terms of "hard" or "soft" interventions are, is the subject of an ongoing debate. By contrast, Wood and Spekkens show that if we hold on to the Markov condition, then violations of faithfulness have to be a generic feature of quantum causal systems that violate the Bell inequalities. Neo-Machian and neo-Russellian arguments have a common structure. While actual explanations may fall short of providing us with the complete information contained in the ideal explanatory text, they are explanatory, according to the hidden structure strategy, in virtue of providing us with some information about the text.

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