Causal Necessity as Logical Necessity
The idea that causation is a kind of logical/conceptual connection has been defended by Kant (1787: A189/B233), Hegel (Hegel & Wallace 1874: 215ff), and McTaggart (1915). At least Kant defends that the connection involves necessity. However, none of them are causal realists, so to refute their arguments is not to refute causal realism. Nothing more needs be said about that.
It is more relevant to note that Elizabeth Anscombe identifies Hobbes as someone who claims that causal necessity is a logical connection, and claims that it was his argument that Hume ‘overthrew’ (Anscombe 1971). Anscombe bases her appraisal of Hobbes on his claim that when a certain total cause is present ‘it cannot be understood but that the effect is produced at the same instant; and if any one of them be wanting, it cannot be understood but that the effect is not produced’ (Hobbes 1656: Ch. X, §3). I think Anscombe is too quick to infer from Hobbes’ use of the phrase ‘cannot be understood’ that the connection is purely logical or conceptual. Hobbes’ epistemology is empiricist, albeit with clear rationalist overtones. In his view, the senses provide us with knowledge about the powers of material objects, and thus knowledge of causes, because powers are causes (Hobbes 1656: Ch. I, §4). From our empirical knowledge of these causes we can rationally calculate the effects they produce, and, vice versa, the causes from the effects. In light of this, I think it would be more charitable to interpret Hobbes as making claims about what can/cannot be thought without violating the nature of the external material world as it is empirically known to us (or assumed). If we find fault with his view, it is with his epistemology and not with his logic.
Someone having read Newton’s Principia in the early 18th century could argue like Hobbes that if Newtonian mechanics is accepted as a true description of the world, then it cannot be understood, on pain of contradicting Newton’s mechanics, but that an object acted upon by an external force will change its state of motion in proportion to the force applied. We then have a valid nomological-deductive argument,
Causal Necessity 85 moving from premises established empirically, leading to a conclusion that therefore is a posteriori. This is a thoroughly realist approach to metaphysical explanation, which has very recently been described by Naomi Thompson (2019). In her view, metaphysical explanations are subject to epistemic constraints imposed by the context in which a question is asked; they are not explanations of what must be the case without regard to any concerns except what can or cannot be conceptualised. This is the kind of natural necessity, and nothing more, that I have hopes of defending, and it seems that this is the kind of necessity that Russell, as well as Mumford & Anjum, is criticising.
Hume may well have had Hobbes’ view in mind, but he cannot be read as overthrowing it merely by showing a flaw in the logic (the logic is valid). He first had to deny Hobbes’ premise that the senses give us knowledge of the nature of external objects, thus turning the question of causation into a mere conceivability issue; one unrestrained by epistemic concerns.
It is noteworthy that Anscombe doesn’t dwell on Mill’s account of causation (1843: Bk. Ill, Ch. V), because he also argues, like Hobbes, that from a total cause an effect follows of necessity. Perhaps she realises that it isn’t easy to portray Mill as a causal realist, since he explicitly claims to ‘make no research into the ultimate or ontological cause of anything’ and said that the causes he concerns himself with ‘are not efficient, but physical causes’ (1843: Bk. Ill, Ch. V, §2). A physical cause, in Mill’s view, is an observable physical state of the world; a physical fact. One may suspect that Mill believes there are real causal connections, in the same way Hume accepts there probably are causal connections as soon as he turns his mind away from philosophy. But that doesn’t make them causal realists, since they positively deny that causal realism is a viable philosophical project. Basically, Mill suspends judgement about the reality of ‘mysterious and powerful ties’ that may or may not connect the physical facts. To be specific: (i) unlike Hume but like Hobbes, Mill believes experience provides knowledge of physical facts, (ii) unlike Hobbes but like Hume, Mill believes experience does not provide knowledge of powers, (iii) unlike Hume, Mill believes (his version of) the law of universal causation can be inductively justified (Mill 1843: Bk. III). Importantly, Mill’s belief in the validity of the law of universal causation is not based on any belief about the nature of substantial connections in nature. That disqualifies him from being a causal realist, and I am happy to concede that Mumford & Anjum’s argument is problematic for Mill.
The bottom line is that none of the thinkers that claim that causation is a logical/conceptual connection are causal realists—at least none of those that appear in the debate—and so arguments professing to show that there is no logical necessity involved do not address causal realism. It is a straw man argument.