Her Inaugural Lecture as Professor of Philosophy at Cambridge University in 1971 was entitled "Causality and Determination." She explained that we had no empirical grounds for believing in a determinism that is logically necessary or even in the physical determinism that appears to be required by natural laws like Newton's. Anscombe thus properly distinguishes between determinism and determination, which requires only adequate determinism. And she sees that a strict causal, logical, and necessitated determinism (really predeterminism), is an illusion.

The high success of Newton's astronomy was in one way an intellectual disaster: it produced an illusion from which we tend still to suffer. This illusion was created by the circumstance that Newton's mechanics had a good model in the solar system. For this gave the impression that we had here an ideal of scientific explanation; whereas the truth was, it was mere obligingness on the part of the solar system, by having had so peaceful a history in recorded time, to provide such a model. (p.20)

Must a physicist be a 'determinist'? That is, must he believe that the whole universe is a system such that, if its total states at t and t' are thus and so, the laws of nature are such as then to allow only one possibility for its total state at any other time? No.

He did not explain what he meant by being accidental; he must have meant more than not being necessary. He may have meant being uncaused; but, if I am right, not being determined does not imply not being caused. Indeed, I should explain indeterminism as the thesis that not all physical effects are necessitated by their causes. But if we think of Feynman's bomb, we get some idea of what is meant by "accidental". It was random: it 'merely happened' that the radioactive material emitted particles in such a way as to activate the Geiger counter enough to set off the bomb. Certainly the motion of the Geiger counter's needle is caused; and the actual emission is caused too: it occurs because there is this mass of radioactive material here. (I have already indicated that, contrary to the opinion of Hume, there are many different sorts of causality.) But all the same the causation itself is, one could say, mere hap. It is difficult to explain this idea any further. (p.25)

But she goes on to say Broad naively assumed that our actions were therefore randomly caused. Apparently aware that randomness as a cause of action had been criticized since antiquity, she calls Broad naive.

Broad used the idea to argue that indeterminism, if applied to human action, meant that human actions are 'accidental'. Now he had a picture of choices as being determining causes, analogous to determining physical causes, and of choices in their turn being either determined or accidental. To regard a choice as such – i.e. any case of choice – as a predetermining causal event, now appears as a naif mistake in the philosophy of mind, though that is a story I cannot tell here.

It was natural that when physics went indeterministic, some thinkers should have seized on this indeterminism as being just what was wanted for defending the freedom of the will. They received severe criticism on two counts: one, that this 'mere hap' is the very last thing to be invoked as the physical correlate of 'man's ethical behaviour'; the other, that quantum laws predict statistics of events when situations are repeated; interference with these, by the will's determining individual events which the laws of nature leave undetermined, would be as much a violation of natural law as would have been interference which falsified a deterministic mechanical law. (p.25)

Ever since Kant it has been a familiar claim among philosophers, that one can believe in both physical determinism and 'ethical' freedom. The reconciliations have always seemed to me to be either so much gobbledegook, or to make the alleged freedom of action quite unreal. My actions are mostly physical movements; if these physical movements are physically predetermined by processes which I do not control, then my freedom is perfectly illusory. The truth of physical indeterminism is then indispensable if we are to make anything of the claim to freedom. But certainly it is insufficient. The physically undetermined is not thereby 'free'. For freedom at least involves the power of acting according to an idea, and no such thing is ascribed to whatever is the subject (what would be the relevant subject?) of unpredetermination in indeterministic physics. (p.26)

It has taken the inventions of indeterministic physics to shake the rather common dogmatic conviction that determinism is a presupposition or perhaps a conclusion, of scientific knowledge. Not that that conviction has been very much shaken even so. Of course, the belief that the laws of nature are deterministic has been shaken. But I believe it has often been supposed that this makes little difference to the assumption of macroscopic determinism: as if undeterminedness were always encapsulated in systems whose internal workings could be described only by statistical laws, but where the total upshot, and in particular the outward effect, was as near as makes no difference always the same. What difference does it make, after all, that the scintillations, whereby my watch dial is luminous, follow only a statistical law – so long as, the gross manifest effect is sufficiently guaranteed by the statistical law? Feynman's example of the bomb and Geiger counter smashes this conception; but as far as I can judge it takes time for the lesson to be learned. I find deterministic assumptions more common now among people at large, and among philosophers, than when I was an undergraduate. (p.28)