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.

I think your counterargument is conflating issues that need to be kept distinct.

Your interlocutor ((I'll call him or her your friend) said, correctly, that if morality is objective, the truth of moral claims doesn't depend on the person who makes them. That seems fine. To say that something is objectively true is to say that it's true whether or not anyone believes it.

Your response was to ask how we could know that there are objective moral facts, if there really are. But that's a separate issue, and in fact it has nothing in particular to do with moral claims. If there are objective facts about what's going on now (say, in the Earth's frame of reference) in some remote part of the universe, then those facts are facts whether or not we could ever be in a position to know them. Whether X is mind-independently true and whether anyone is in a position to know that X is true are different matters.

You ask: "how can a moral fact be known independent of a human mind to decide?" That's ambiguous. Obviously nothing can be known independently of minds, human or otherwise, because knowledge is a case of belief, and beliefs are mental states. But once again: whether something is true and whether it's known or even believed are different matters.

But your wording hints at something else. It suggests that as you see it, moral claims are special: they aren't the sort of thing that could be true at all independent of someone deciding that they are true or accepting them or committing to them.

If that's what you mean, then you and your friend don't necessarily disagree. You quote your friend as saying that if morality is objective, moral truths don't need to be believed to be true. However, that's a conditional claim. It's compatible with moral claims not actually being objectively true at all. It just reminds us of what we mean when we say that something is objectively true.

So I'm guessing that the real disagreement is over the question of whether moral claims could be objectively true, I'm guessing that your friend thinks the answer is yes, and you think it's no. Both of you are in good company. There are interesting defenses of both point of view.

Now there's a further idea that may or may not be in the background. It holds that truth can't float free of the possibility of knowing the truth. On this view, the idea that there might be some truth that no one could even possibly know is a confusion. Perhaps that's correct, though I'm not inclined to think so myself. But notice that it has nothing in particular to do with morality. Rather, it amounts to saying that a certain notion of objectivity is misplaced from the outset. I suspect that's not what you're saying. If I'm right, then what you would need to do to advance the argument is to say what in particular it is about morality that gets in the way of it's being objective in the sense that your friend has pointed out.

Here is a sampling of views on time that you'll find in recent literature:

Presentism: Only the present moment is real; neither the past nor the future exist. Among other things, this view is supposed to help make sense of our sense that time really passes, but it does that (to the extent that it does) by treating the present as an infinitely thin slice and not as something eternal.On the contrary: the present is utterly evanescent.

The Block Universe: On this view, all events exist eternally, as it were. That includes all events before my writing this post, all events simultaneous (in some frame of reference) with my writing, and all events after my writing. This view is claimed to fit best with the understanding of time that Relativity provides, but there is no eternal now. "Now" has no metaphysical interest whatsoever. "Now" is like "here": it's what is sometimes called an indexical term, picking out what it picks out only relative to its use. When you say "I am here" and I say "I am here," what you are saying is not what I am saying. You use "I" to refer to yourself; I use it to refer to myself. You use "here" to refer to where you are; I use "here" to refer to where I am. But there is no privileged "I" and no privileged "here." There are just speakers and locations. On the block universe view, "now" works the same way. It doesn't pick out anything special or privileged or metaphysically distinguished. On the block view, there are temporal relations (earlier than, simultaneous with, later than) but no special times and no unique, let alone eternal "now."

The Growing Block: This view takes seriously the worry that that really are facts about the past, and that if Presentism is true, this is hard to understand; on Presentism, the past does not exist. But this view also takes seriously the idea that time really does pass, and that it's hard to reconcile this with the Block Universe. So the Growing Block view says that the totality of existence keeps growing. The past is real, and that's why there can be truths about it. The present is continuously slipping into the past, but is indeed the present for an instant. The future doesn't exist, but will come into being, and once in being will not cease to be. Once again, however, no eternal now.

There is another view that's received some attention recently. It's called fragmentalism. Insofar as Presentism allows for truths about the past, there is an argument due to John McTaggart Ellis McTaggart (who wins the prize for nifty names) that time comes out contradictory on that view. In the past it was true that I am now in Canada. In the present it is true that I am not now in Canada. But the Presentist also wants to say that the word "now" is not like the word "here." It's not an "indexical" term but a way of picking out something metaphysically privileged. And so we apparently get a contradiction, which McTaggart takes to show that the view must be false. Fragmentalism embraces the contradictions but segregates things into "fragments" that are internally consistent but mutually inconsistent. We are never in a position to reason from more than one fragment, and so the worst logical consequences of inconsistency are avoided. But there is still no one eternal "now," though there may be some sense (I'm genuinely not sure) in which the fragments have something like eternal status.

There is also a view that some physicists take quite seriously, according to which time is not a fundamental feature of the world at all, but is "emergent" from more basic physical structure. This may (or may not) mean positing a fundamental and timeless reality, and in that sense might be sorta, kinda like an eternal "now." But since "now" is a temporal notion and time emerges out of the fundamental reality on this account, "eternal now" sounds like a bad way to put the idea.

So... there are views according to which there's no past or future, but the now—the present—isn't eternal. And there are views on which there's no "now," except in a metaphysically uninteresting sense, but there is something like an eternally (timelessly?) real collection of events. And there are a few more exotic views as well, but none that clearly fit the model of an eternal "now." I'm not sure whether any of these views are what you have in mind.

There is also, however, a more-or-less mystical notion that one sometimes runs into. One might think of it as dealing with how things are from God's timeless point of view and our capacity to get occasional glimpses of that. (I'm neither endorsing nor rejecting the idea.) The language of an "eternal now" is often used to capture the idea. The theologian Paul Tillich published a collection of sermons titled The Eternal Now. That said, though I have a soft spot for Tillich, I don't really see much connection between this idea of an eternal Now and the concerns that come up in contemporary philosophy of time.

If you obsess too much about more or less anything, it can be bad for you, but some of the topics that philosophy deals with can be more troublesome for some people. I have in mind especially some forms of radical skepticism. I have met people who've been obsessed with the possibility that they don't really know that there's an external world, or that there are other people. I've had them in my office, clearly distressed. I'd guess that there were already some underlying problems. I'd guess that it wasn't a case of someone who was otherwise fully functioning and then happened on Descartes' Meditations, but the skeptical questions provided something for their background issues to latch onto.

When I'm talking with such folk, I tend to stress two things. The first is philosophical: the fact that something is possible in some rarified sense isn't a reason for thinking it's at all likely. Yes: in some sense of "could," it could be that what's going on in my mind is all there is. But in this sense of "could," there are many, many things that could be true, including the overall possibility that my beliefs are broadly true and the infinitely many more specific variants on that possibility. Most philosophers who think about knowledge take it as given that we know lots and lots of things. The questions they're interested in are about the detailed structure of knowledge, not about whether we actually have any.

But aside from such philosophical commonplaces, when I've been in conversation with people for whom disturbing philosophical possibilities have become intrusive, I also offer a different suggestion: get out of your head. Get some exercise. Listen to music. Have lunch with a friend and talk about something fun. The great Scots philosopher David Hume wrote that he did just this sort of thing. When one is not just being a bystander to one's life, it's harder for philosophy's more outre speculations to hold their grip.

If by "philosophy" we mean something like having a view of reality and values then it is hard to imagine not having a philosophy. If we mean something more like "disciplined reflection on reality and values," then it also seems hard to imagine that doing more philosophy would be harmful. And if we go to the etymology of "philosophy" (from the Greek "philo," meaning "love" and "sophia" meaning "love") then it is (again) hard to imagine that doing philosophy would ever be bad. After all, if engaging in what we call philosophy was unwise, one should not do it.

Coming at your question from a different angle: let's say we define philosophy in terms of this site: should more people engage in AskPhilosophers? I think so, but we need to balance our tasks and responsibilities in life. Should a single parent of 6 children who is also a physician and caring for parents in hospice care, spend lots of time on this site? Well, I would like to believe it might provide a bit of relief / distracting stimulation, but some persons (alas) may be so stretched by various tasks that loving wisdom might involve moderating the drive to do philosophy.

Questions do not have solutions, so your question needs rephrasing. It contains a category mistake. Perhaps one could say that questions are to answers as problems are to solutions. At any rate, it is questions have answers, and problems that have solutions. So we can put your question as this: 'Is no philosophical question answerable?'

Your question has a history starting in classical philosophy, as the question whether there are insolubilia, or unanswerable questions, such as whether the statement made by the Cretan Liar is true, or whether it is false. But in modern philosophy the question about insolubilia expanded from logical annoyances into the entire world of metaphysics and epistemology. Can we ever find reality and know it as it is? Kant famously thought not, that we are somehow imprisoned within our own conceptual schemes. This is a big deal. His arguments are complicated and take some study to understand, if they can be understood. There is a possible lesson here, which is that we should look carefully at the reasons given for saying that reality is unknowable, rather than wallowing in that conclusion.

Suppose that the answer to your question is affirmative, so that no philosophical question is answerable. Then that is the answer to your philosophical question. But then the answer is wrong, since at least that question, the one you asked, has an answer. We have just given it!

So then suppose the answer to the question is negative. It is that some philosophical questions are answerable. So at least one philosophical question has an answer.

Either way, at least one philosophical question (yours!) has an answer. What goes for questions also goes for problems. So there is at least one philosophical problem with a solution.

It is interesting to see that to get an answer to your question we do not have to look at the specific arguments as to why philosophical questions might be answerable or as to why they might be unanswerable. We have an argument that cuts through any other argument, and delivers a reassuring result, even if it is a narrow one. But it would be a good thing to explore the historical question, 'What reasons have been given in the history of philosophy for thinking that there are insolubilia, of the narrower logical sort or of the wider metpaphysical and epistemological sorts?'

It would also be good to think about whether the argument I have given can somehow be generalized to all philosophical questions. A good place to start might be Moritz Schlick's "Unanswerable Questions?" of 1935. Schlick's view is that there are no unanswerable questions of an empirical kind, because the answers to such questions would be unverifiable, and hence meaningless. So the questions, being the answers with a question mark at the end, would also be meaningless.

You might also want to ask why you ask the question, what is your own reason for thinking that all it might be the case that all philosophical questions are unanswerable.

There's a problem with your symbolization. The word "since" isn't a conditional. It's more like a conjunction, but better yet, we can treat it as simply giving us another premise. So in a slightly modified version of your notation, the argument would be

N v D
F → N
D
∴ ¬F

But from the premises as given, the conclusion won't be derivable. The reason is simple. You are assuming that if it's day it's not night and vice-versa. That may be part of the meaning of the words, but the symbols 'N' and 'D' aren't enough to capture it.

The easiest fix is to treat "day" as "not night." That gives us

N v ¬N
F → N
¬N
∴ ¬F

In this case, the first premise is a tautology and not needed. The argument is just a case of Modus Tollens. If you want something less trivial, you can drop the first premise and add a premise like this:

D ↔ ¬N
F → N
D
∴ ¬F

The first premise amounts to making the "v" exclusive. From there it's easy to complete a proof.

A couple of extra comments. First, in the English version, you add a quantifier, and presumably you are quantifying over times—roughly "For every time, the time is either during night or during day." The argument can be symbolized accordingly, though it will be more complex. Second, you make one of your premises counterfactual with the "would"/"were" construction. That introduces issues you'd be better off avoiding.