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.

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.

There are arcane theoretical reasons for thinking that you are not the same person when you wake up. There are also arcane conceptual scenarios that prevent you from being absolutely certain that you are the same person. These considerations are no match for your everyday certainty that it is you, even if they are able to cause short-term anxiety. Your everyday certainty will return, with a faint residue of wonder that we cannot absolutely prove the things we know. That residue is part of the point of doing philosophy. It helps save us from the dogmatic arrogance people are prone to. Your professor was partly joking and partly trying to push you toward this philosophical lesson.

I think you have to compromise. If you only live for today and you make it to the future, you will be worse off in it. However, if you only live for the future but you don't get there, then today is lost. So enjoy some things today that won't ruin your future and defer some gratification today to prepare for a better future, both for yourself and those you care about.

Alternatively, Bertrand Russell uses the problem you raise to critique the Humean account of causation and propose a successor. See Russell's discussion of laws of change in his book The Analysis of Mind .

Some philosophers would say that there are 10 trillion and 1 (at least). After all, you are a person and none of your cells is a person, so you are a distinct thing from each of them, and so an additional thing to all of them. Other philosophers would say that "living thing" is not a count noun because "thing" is not a count noun, and you need to be more specific about what you are counting. Is it persons? Then there is one. Is it cells? Then there are 10 trillion. I am dissatisfied with both these responses. It seems to me that "thing" is as much a count noun as is "item" in a sign for a grocery line that says "Six Items or Less." And it seems to me wrong to think that strictly speaking one should be barred from taking a six-pack through the "Six Items or Less" line because it is seven items: one six-pack plus six cans. Instead, it seems to me that the six-pack just is the six cans (neglecting packaging), not something in addition. The very same portion of reality can be accurately counted two different...

Not everyone who judges is judgmental. To be judgmental is to be prone to condemning people without regard to what can be said on their behalf. If you reserve condemnation for cases in which little can be said for the person and much against, then you are not being judgmental. So, if you have made a good faith effort to discern that your friend condemns people without considering their sides, then you are not being judgmental to point that out. If you have made a good faith effort to find out whether the others are really rapists, child molesters, and cannibals, and you find that they are, then there is little to say on their behalf and you are not being judgmental in condemning them.

For these questions, you would probably be better off asking an older person whose wisdom you respect, than someone with a philosophy degree. However, since they are questions I also have wondered about, I will attempt an answer. The beginnings of love happen when you find that you are not just concerned with what the other person can do for you, but find yourself concerned with their good. When love grows, you find that your concern for their good is equal to and inseparable from your concern for your own. This stretching beyond concern with your own good is one of the main things valuable about marriage. It will more likely happen with someone you admire and who has strengths that complement your weaknesses. Intellectual and social similarities do not seem to me to be as important, even though dissimilarities can be a source of tension sometimes. Which of these men do you feel this loving way about and feels this way about you? One way to tell is to observe if you are kind to each other and willing to...

You might try the first few chapters of Bertrand Russell's The Problems of Philosophy and see if that is relevant to what you have in mind.

You are right that the points in a 4 inch line segment can be put into one-to-one correspondence with the points in a 2 inch line segment. Think of a line swinging through both line segments, the way a door swings through a shorter path nearer its hinge and a longer path further from the hinge. The swinging line matches any point in one with a point in the other. Therefore, they have the same number of points--an infinite number. However, that is not a strike against the claim that the line segments have different lengths. The points are dimensionless, and the length of a line segment is not a function of the number of its dimensionless points. So the 4 inch line segment is still twice the length of the other.