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Philosophers

I'm struggling to reconcile David Hume's critiques of science and religion. On the one hand, he suggests that our application of cause/effect to natural phenomena is problematic since it ammounts to simply equating the present with the past. On the other hand, he warns us against believing in second-hand accounts of miracles since they are interruptions of natural law. Isn't our use of causal reasoning the way we determine the characteristics of natural law? Is this an inconsistency in his argument and, if so, does he address it anywhere?

Good question. You are pointing out an apparent contradiction. Hume seems both to say that we have no good reason to rely on induction (predicting the future based on the past), and yet that we should rely on it when we reject belief in miracles. What Hume says about causal reasoning is that we never have sufficiently good reason to believe present predictions based on past experience. We can only justify induction by appeal to induction itself, but that is arguing in a circle. So we have no good reason to believe that the conclusions of induction are true. Nonetheless we instinctively make and believe the predictions, anyway. We can't help it. So we make a virtue of necessity and rely on these predictions. That is how we come to believe in natural laws. Now comes the part about miracles that are supposed to be violations of these laws. Based on past experience, it is more likely that a report of a miracle is mistaken than it is that the laws were really violated. So if we rely on our instinct to...

Yes, that's a good point. It is true that Hume's practical recommendations are based on inductive claims that he can't ultimately justify. However, he is relying on the natural force of appeals to induction, not their epistemic justifiability. So he is still not relying on the justifiability that he denies.
Philosophers

I want to say Hume was an idealist but this seems controversial. My reasoning goes like this. Hume thinks that all we can know comes from our personal experience (this is uncontroversial Hume was an empiricist). He also thinks that we have no justification for believing in an external world, because all we ever experience are our sense perceptions which, Hume thinks, are wholly mind dependent. So Hume thinks all we can know is mind dependent and we have no justification for believing that there is anything more than this. So for Hume all there is, is mind dependent stuff. This clearly makes Hume an idealist. So my qustion is am I right in saying that Hume was an idealist?

Here is another take on this important and difficult question. The fact that Hume can find no justification for believing in the external world does not prevent him from believing in it. Nature causes us to believe many things we can find no justification for. "We may well ask, What causes induce us to believe in the existence of body? but 'tis vain to ask, Whether there be body or not? That is a point which we must take for granted in all our reasonings" (Treatise 1.4.2.1). Body for Hume is what continues to exist unperceived and is distinct from mind or perception. So he is not an idealist.
Philosophers

I find George Berkley an insightful philosopher in many ways. One puzzle I have is over his view of time as 'the succession of ideas'. Would he contend that our calendar and daily clock times are due to both God's direct imprinting of sensory ideas according to regular natural laws on our minds, and making the structure of human minds similar in their receiving of those perceptions/ideas? (We all receive ideas at the same basic rate). Also, when we dream or people are in a coma, do perceptions somehow continue unabated in our minds?

Berkeley's view of time as the succession of one's ideas is indeed very puzzling. Berkeley seems committed to the claim that there is no common time; there is just time for you and time for me, etc. God does give each of us successions of ideas that can be roughly coordinated, just as you say. For instance, we are able to agree on when the second hand of a clock is successively pointing at different numbers. However, this does not mean that our ideas succeed each other at the same basic rate. My ideas may be flowing much slower than yours, so that watching the second hand is boring for you but not for me. It happens slowly for you, but not for me. A consequence of this subjective account of time is that there is no time for me that I am not having an idea. That does not mean that I am unconscious of some ideas when I am in a deep sleep. It means that there is no time for me when I am in a deep sleep, so no time at which I am lacking a conscious idea. This seems odd, given that my wife might watch me sleep...