Has there ever been shown to be an effect without a cause? Is it even possible for there to be an effect without a cause? If this is not possible, does that prove determinism is true, at least what I believe is called "Hard Determinism?" And even if you can't prove that there can never be an effect without a cause, isn't probability justification enough to make any belief other than determinism ridiculous?

It's not clear what it would mean (or what it would take) to show that there was an effect without a cause (unless we just define an effect as something that is caused, in which case there'd be nothing to show). We certainly have not shown (proven) that every event has a cause in the sense that we have not, and could not, pick out the causes of every event that has ever happened. Rather, we tend to assume that all events have causes, except perhaps those people who assume that free choices are uncaused or who assume that there is a first event that was not caused by any prior event. It's an assumption that tends to work for us--that is, it helps us explain things in science and our everyday life--and it is an assumption that does not have any clear counterexamples (but again, it's not clear what a counterexample would look like). So, as you suggest, this thesis of Universal Causation (UC) might be the most justifiable.

However, one might think that a possible counterexample involves the events described by quantum physics, since it looks like those events are indeterministic: given the exact same prior conditions (or causes) and the same laws of physics, more than one effect might occur. For instance, the electron shot at a barrier might go one way or another and nothing explains (or causes?) which way it goes. However, a better way to describe indeterministic events is that they are probabilistically caused. Quantum physics does not entail randomness--rather it describes objective probabilities between events. So, one can say that the set of events that leads to the electron's hitting the barrier causes it to end up in position 1 (with 50% probability) and causes it to end up in position 2 (with 50% probability). Wherever it ends up, it was caused to end up there by prior effects.

OK, all this is just to set up the take-home message which is that the thesis of UC (Universal Causation), which says that every event--or at least every event after the first event--has a cause, does not entail the thesis of determinism. Determinism is the thesis that: Necessarily, given the same prior events and laws of nature, the same later events occur. UC is consistent with indeterministic causation and hence with the falsity of determinism. So, even if we answer your first two questions 'no', that does not mean we have to answer your third question 'yes'.

Finally, "Hard Determinism" is the thesis in the free will debate that says (a) determinism is incompatible with free will, (b) determinism is true, and therefore (c) free will does not exist. Lots of philosophers (like me) are compatibilists who reject (a) (if interested, see my prior responses to questions in the Freedom category). And most philosophers reject (b) since they accept that the dominant interpretation of quantum physics is indeterministic. But many still think determinism, if true, would rule out free will and do so for reasons that make Universal Causation just as threatening, so indeterminism doesn't help. (Basically, they think that our decisions, like everything else are caused by prior events, ultimately by events over which we have no control, so we do not have ultimate control over our decisions, and they think such ultimate control is required for free will--again, I see no reason to think free will requires such unattainable powers!). These philosophers sometimes call themselves "Hard Incompatibilists" (or Skeptics about free will), and they are the descendants of the Hard Determinists.

This is complicated stuff and I've tried to keep it brief. But I hope this helps!

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