A re-post from 2014.
'Every happening has a cause that produces it.' This proposition means exactly the same as the following: 'It is impossible for our intelligence to think a happening without thinking a cause that produced it.' To show that 'a happening without a cause cannot be thought', we must show that 'the concept of a happening without a cause involves contradiction.' Once this is demonstrated, we will have deduced the principle of cause from the principle of contradiction.
The demonstration is as follows: to say 'What does not exist, acts' is a contradiction. But a happening without a cause means 'What does not exist, acts.' Therefore a happening without a cause is a contradiction. The proofs follow.
As regards the major: to conceive mentally an action (a change) without an ens, is to conceive without conceiving, which is a contradiction. Indeed, the principle of knowledge states: 'The object of thought is ens'; therefore without an ens, we cannot mentally conceive. To conceive an action without conceiving an ens that performs the action, is to conceive without conceiving. Therefore to apply the action to something that does not exist is a contradiction in terms, which was to be proved.
As regards the minor: a happening is an action (a change). If this action has no cause, it is conceived by itself, without belonging to an ens; there is then an action without ens or, which is the same, what does not exist, acts. Thus the minor is proved (cf. 350-352).
Antonio Rosmini, New Essay Concerning the Origin of Ideas, Volume 2, Part III, Chapter 2. To put the argument in another format:
Major: 'Something that does not exist, acts' is a contradiction.
(1) What is conceived is conceived as a being.
(2) An action conceived without being conceived as a being acting, is not conceived as a being.
(3) Therefore, an action conceived without being conceived as a being acting is a contradiction.
Minor: A happening without a cause entails that something that does not exist, acts.
(1) A happening is an action.
(2) An action conceived without a cause is not conceived as a being that acts.
(3) Therefore, a happening conceived without a cause is not conceived as a being that acts.
The section references to 350-352 is from Rosmini's criticism of Kant in Volume 1. There Rosmini argues that 'what happens' conceptually includes the notion of 'cause', and thus the judgment is analytic and not, as Kant would have it, synthetic. As he puts it:
The following, therefore, is the sequence of our conceptions:
1. We conceive coming into existence, a concept which includes that of change.
2. The concept of change contains that of new operation.
3. The concept of new operation contains that of prior existence.
4. The concept of prior existence contains that of cause.
Conclusion: A happening without a cause is a contradiction.