The version of Occam's Razor quoted above seems to support solipsism, the view that only one's conscious experience exists, over a view which also admits the reality of the external world. After all, solipsism is committed to fewer entities than the latter view, which also countenances the existence of stars, atoms, and rollercoasters.

I'll interpret the quote that explicates Occam's Razor as holding that the following is a priori: if we have two theories, X and Y, and Y says that fewer kinds of things exist than X does, then Y is more likely to be true, on some given some body of evidence, than X. This principle does indeed indicate that we should take solipsism to be more likely to be true than realism about the external world. The problem is that the principle isn't quite right.

As it stands, the above principle says that the theory on which nothing exists is more likely to be true than any other theory, given our current evidence. No matter what you take our current evidence to be, even if you restrict our evidence to conscious experience, the theory on which nothing exists is almost certainly false. For if there were nothing, there would be no conscious experience. So, given our evidence, the theory on which nothing exists is less likely to be true than either solipsism or realism about the external world, contradicting the above version of Occam's Razor.

This is why Occam's Razor often has a clause specifying that all other theoretical virtues, aside from ontological parsimony, must be equal in order for Y to be more likely than X. By "theoretical virtues" I just mean whatever features theories can have that increase their likelihood of being true, such as explanatory power. If we were to add such a clause to the version of Occam's Razor I formulated above, it should no longer be obvious whether it supports solipsism over realism about the external world. The reason is that if realism explains more of our evidence than solipsism or explains the evidence better, this new principle will say that realism may be more likely to be true despite its positing more kinds of entities.

I leave it up to you to determine whether realism about the external world in fact has more theoretical virtues like explanatory power than solipsism does.

As you've described the case, there's something the inventor could do that would save lives. There's also a dispute about how to analyze the notion of a cause. Some would say (your friend apparently is in this camp) that absences—in the case, not doing something—can't be causes. Others disagree and provide accounts that allow absences to be causal. This is an abstract and complicated issue, but how much difference will it make to how we judge the inventor?

Suppose I'm in a war zone and happen to know that there's an IED in a certain spot. I see someone running on a path that will take him over the IED and almost certainly leave him dead. Let's assume I even know who it is and know that in all relevant respects, he's an innocent. As it happens, I'm behind a barrier, but I could easily warn him. I don't. He runs over the IED and dies in the blast.

Is there something I could have done that would have saved him? We've already said yes. Would it have come at any significant cost? We can stipulate for purposes of this example that the answer is no. Should I have warned him? I'd say yes; I'd hope your friend would too. Was my silence a cause (note: I didn't say the cause) of his death? Why, exactly, does it matter beyond what we've already said?

Change the story a bit. Before he gets to the IED, the running man yells to me: "Is it safe ahead?" I lie and say yes. Was my lie a cause of his death? Maybe there's less dispute about that in this example. In any case, there's likely to be more agreement that the lie is even worse than saying nothing. But unless using the word "cause" is just a way of talking about culpability, it's not clear how much difference worrying about the fine points of causation makes.

We can imagine other variations. We might think that even though the lie would make me even more culpable, I'd still be less culpable than if I'd shot him. There are interesting and tricky questions here about responsibility. And for those whose tastes run to analytic metaphysics, there are interesting and tricky background questions about the best way to analyze causation. But my hunch is that in the case of the inventor and in the case of the IED, trying to sort out the metaphysics of causation is likely to be less useful than starting with what everyone can agree on and worrying about the question of responsibility in the morally weighted sense. In the case you and your friend are arguing about, everyone can agree that it's in the inventor's power to save lives. I'd hope we'd also agree that it's wrong of him not to. We can also agree that there are even worse things he could do—like helping to spread the disease among the very people he's chosen to keep the cure away from. But once we have all of these sorts of details on the table, it's not clear what's added by taking sides on whether or not to use the word "cause."

Great questions and concerns. For most philosophical theists (those who affirm the existence of God) "good" and "evil" need to be used with the same sense / meaning in terms of humans and God. For you to be compassionate and God to be compassionate and to be called 'good' presumably we mean praise-worthy / desirable / it is better that there is such compassion rather than not. But value judgements are often contextual depending on those involved. For those in the Abrahamic faiths (Judaism, Christianity, and Islam), God is understood to be the creator and sustainer of the cosmos, who is revealed in human history through prophets and (for Christians) in the incarnation. As such, God is not to be assessed as we would assess a human bi-stander. So, for you and I to not prevent a murder when we could do so is blameworthy. Does it follow that if God has created and sustained a cosmos in which there is murder, then God is blameworthy? Maybe, but so many factors enter into this. One has to do with what is called the Free Will Defense, and the appeal to Greater Goods. Check out the entry Philosophy of Religion on the free online Stanford Encyclopedia of Philosophy. Most theists believe that when something is evil (murder of innocent persons) this is contrary to the will and nature of God, a misuse of power, a destroying of something sacred. It is (as you might explore in the free will defense) never justified (right or ultimately good) from the standpoint of the Abrahamic faiths. Nonetheless, most philosophers in this tradition contend that an all good God may allow some evils in order to ultimately redeem both victims and victimizers. I have worked up such a view in two books you might check out: Contemporary Philosophical Theology co-authored with Chad Meister and What is Philosophy of Religion? Your concerns and questions are excellent and I hope you might find one of these sources helpful.

The reason you feel you don't understand the claim is because it's nonsense.

I know that there are three pillows on the bed behind me, but no science was committed in finding that out. I just turned around, looked and counted. I know that I had dinner with friends yesterday. No scienceing there either. I just remember. I know that one of our neighbors recently quit a committee he'd been a member of. Once again, no science; someone in a position to know told me. In fact, it's safe to say that by far most of what we know we know without anyone doing science.

Of course people doing science make observations, consult their memories and get information from other people. But so does everyone, and most of us are not scientists and don't do science. The fact that X has important things in common with Y doesn't make X a Y.

According to the internet, the sun rose at 6:02 this morning in Washington. I was awake and when I got around to opening the blinds I could see that the sky was blue. The sheets on the bed are blue too, though not the same blue. They're a few years old and I like the way they feel when I touch them.

But the sun doesn't rise, does it? Although centuries ago, people thought it did, they were just wrong. And there isn't really a sky—no dome or roof or thing of any sort. There are sheets, but they're made of atoms, which aren't colored, nor are collections of them.

And touching the sheets; don't get me started on that.

Except…

If someone says the sky is blue, they've said nothing false, nothing wrong. Same goes for telling you the color of their sheets; likewise for telling you they touched them. People may be mistaken about what being a blue sheet amounts to, or a blue sky, or about what's going on under the covers, so to speak, when we touch a sheet, or anything else. But that doesn't make the ordinary things they say false.

Of course, if someone says that the sun doesn't rise, or that there isn't really a sky, or that it isn't really blue, nor are anybody's sheets, or that you can't really touch your sheets, we know what they mean, or we can be brought to know. Given what they mean, they aren't wrong though they are pedants. But the sun did rise this morning and the sky is blue. Sheets can be blue, and some of them feel lovely to the touch. There's no contradiction here and no paradox. We can use words in more than one way and we don't need to be scientists to say true things with ordinary words used in ordinary ways.

One reason it doesn't sound right to me is that I don't know what could be meant by a "deductive statement." I know what a deductive argument is, but it always contains more than one token statement. Did the site say, instead, "every declarative statement" (i.e., every declarative sentence)?

In any case, consider the statement "There are no colorless red cars." It's a declarative statement. Does it regard the real world? Arguably, yes: it's at least partly about cars. But knowing its truth doesn't require induction -- it's analytically true. On the other hand, maybe despite appearances it's not a statement even partly about cars but only about the logic of the concepts red and color. We'd need an agreed-on criterion of "aboutness" in order to decide.

I can't think of any ordinary sense of "opposite" that allows for the existence of opposite shapes (i.e., closed plane figures). But you and your friends could invent a technical sense of "opposite" that allows for opposite shapes. Maybe the opposite of a shape is the mirror image of the shape along the vertical axis, or along the horizontal axis, or along some oblique axis, provided that opposite shapes never look the same. On that definition, a circle wouldn't have an opposite shape, but a triangle could. In any case, there's nothing to disagree about until you have a suitably precise definition of "opposite shape," which again I think you'll have to stipulate, because ordinary language doesn't supply one.

Not if they really are necessary truths. By definition, any necessary truth couldn't possibly have been false.

It takes some care to state propositions in such a way that they really are necessarily true. For instance, Red is a color asserts the existence of something -- red, or redness -- that arguably doesn't exist in every possible world. If there are possible worlds in which nothing physical ever exists, then nothing is red or (arguably) even could be red in such worlds, making it unclear whether there is a color red in such worlds. By contrast, the necessarily true proposition Whatever is red is colored doesn't assert the existence of anything, so it comes out (vacuously) true even in worlds lacking any red or colored things.

Your comment runs together two things that ought to be kept distinct: (1) Can we choose our preferences? (2) Could we have chosen otherwise than we in fact chose? I'll take them up in turn.

I'm not a psychologist, but I take it as common knowledge that we do have some long-term control over at least some of our preferences. Even if you now prefer Bieber to Beethoven, you can choose a program of listening and study that will fairly reliably end up reversing that preference. But the more important point is this: You needn't have chosen your preferences in order to choose freely in light of them. I prefer Beethoven to Bieber, and on that basis I can choose to listen to an hour of Beethoven's music rather than an hour of Bieber's if given those options. I would be unfree if I couldn't choose according to my preferences. Moreover, in some cases we form strong preferences -- e.g., for one job-offer rather than another -- as a result of careful deliberation, and it would be silly to think "Even though my deliberations resoundingly favor job A over job B, I wish I could choose to prefer B instead."

Whether we can choose our preferences, and whether free will requires our being able to do so, are separate issues from whether we could have chosen differently than we in fact chose. I'm inclined to think that we couldn't have chosen differently than we in fact chose under exactly the same conditions, even though we could have chosen differently had our desires been different from what they in fact were. But the important point is this: The freedom and control that it makes sense for us to want don't require the ability to have chosen otherwise under exactly the same conditions. For discussion and defense of this position, see this SEP entry: https://plato.stanford.edu/entries/compatibilism.

According to many (but perhaps not all) Christians and many secular philosophers (and persons of other faiths) marriage is fundamentally based on the vows that persons make to each other. So, for many Christians in the west, the church does not actually marry two persons; the church recognizes and proclaims (and blesses) the marriage. Insofar as "the married man" and his spouse have ended their vow (whether they think of this as breaking the vow or releasing each other from their vow), the marriage has ended, even if it is still a legal matter of divorce. One reason why the state has an interest in the legality of making and ending marriages is to protect persons from harm and insure fair benefits (e.g. see to it that there is proper child support and a fair distribution of property) that might not happen on a voluntary basis. Apart from such a legal matter, however, it sounds to me that the soul of his earlier marriage (so to speak) has been dissolved in virtue of the two of them releasing each other from their marriage vow.

Your mention of a priest and being in Mexico suggests the context of Roman Catholic religious culture. The Roman Catholic Church currently does not approve or recognize divorce, but it does believe that some supposed marriages are not authentic if, for example, one of the couple did not fully intend to keep (or make a solemn) vow. "Marriages" can also be dissolved (or rendered null and void) if they are not consumated or it is consanguinity is discovered (the couple are related, e.g. siblings or first cousins). Still, many other Christian communities (Lutherans, Baptists, Anglicans, Methodists...) recognize divorce as a sad reality and allow for re-marriage. My own view is that "a divorce" can occur once either or both parties divorce themselves after their solemn vow to each other has ended (or is no longer binding). For some Christian churches that recognize divorce (the Eastern Orthodox for example in Greece and Russia), it is still held that one aspect of the original vow is still binding, the vow to love one another. So, the Orthodox (who hold that you can legitimately be divorced up to three times) maintain that formerly married couples should still pray for their former husband or wife for the rest of their lives (assuming this does not impose an undue burden, e.g. the divorce occurs because of some horrific violence).

Anyway, probably more information than you wanted. I wish you the very best during a difficult time.