Again my response is too long. Part the first:

This is eating up enough of my time, and I think we're making little enough progress, that I'm going to turn my attention to other responsibilities. I may or may not get back to this discussion.

"I don't want to bicker about what property is. Here's one idea: property is value that you want to control. For example, if you write a SaaS app, you don't want anyone else to get the source code, because then they could make money off of your work, against your will."

I definitely reject that definition of property. For one thing, I might want to control the laptop you paid for, so it's clearly leaving something important out. I also don't like the collapse of value caused by pretending non-rival goods are rivalrous.

'Another idea is that property is a "rivalrous" resource that you have exclusive control over. In this case, rivalrous means that only one person can control that resource at a time, and thus, there may be "rivalry" over the resource.'

That's better - and certainly rivalousness is an important motivator for why we need some system to mediate access ("property"), but it doesn't speak to why it's your property instead of my property or Jim's property.

"But this is all perfectly aligned with our intuitive sense of what property is. If you've got an apple in your hand, everyone else will automatically consider it your property, and so on."

Not really. Even that example depends very much on social context. If I am in a grocery store, standing in front of a pile of apples, with a shopping basket in one hand and an apple in the other people won't assume the apple in my hand is mine to do with as I please. It would still be rude for them to snatch it from my hand (or basket) though - there is a distinction between possession and property that is occasionally important.

"What you're doing here, is muddying the definition of property in an attempt at scraping together some semblance of legitimacy for taxation."

Absent the normative content, yes, that's more or less what I'm trying to do. I am trying to make sure every part of what we label "the right to property" is in fact useful to our aims in having rights, because otherwise we will be restricting people in ways that are not well motivated and permitting retaliation in situations where it is not justified.

I think that some parts of what we lump together as "the right to property" are more important than others. I think most important (in no particular order) 1) valued work being rewarded, 2) everyone playing by the same rules, and 3) no arbitrariness in deprivation of property. Reasonable levels of taxation, determined democratically and enforced fairly, don't violate any of these. I'm open to the idea that other aspects are important to, but I don't see it as being clearly the case so you'll have to explain why.

'"Heyyy, if everything everywhere is the government's property, then taxation is not extortion!"'

That is not where I was going, and it's unnecessary to my argument here. It just requires that portion that is taxed to be considered "the government's property", or even "temporarily my property but legitimately owed to the
government". You can continue to hold to the illigitimacy of the social contract, but with normal contracts this is certainly an ordinary thing - if I make a deal to sell sweaters you've made on contingency, people pay
me for the sweaters but only some of that money is legitimately mine - some is owed back to you.

"Well, next we'd need to delve into what constitutes legitimate property."

Yes, precisely. And I would argue that we socially determine that, and particular systems can be objectively better or worse when measured against various metrics. We should individually push toward the system we expect to give the best outcome, and we should abide by the system that is in place for the most part.

"Common sense suggests that anything acquired through coercion is not legitimate property."

I think I agree that common sense suggests that, but I'm not sure that's not the result of poor reasoning. It is absolutely the case that there are examples of transfer by coercion that are completely illegitimate, and these spring readily to mind. I am not confident it is correct to
generalize it to "all transfers through coercion are illegitimate". Restorative transfers (giving you your laptop back) seem clearly legitimate, there may be other examples where it is also obvious.

"Furthermore, if everything really were the government's property, would taxes need to be collected by force?"

I'll note again that "everything is the government's property" is not the framework I'm suggesting, but your question is still interesting in mine.

The answer is quite emphatically "Yes" - even if taxes are legitimately (and popularly seen to be) the property of the government before collection, we would expect force to occasionally be necessary (and thus it to be "ultimately backed up with force" in the general case). It is quite clearly the case that not everyone respects the property
rights of others, even in the most clear cut cases. We ultimately enforce your right to your laptop with force, as well.

"Wouldn't people acknowledge that in fact, whenever they produce value to someone else in exchange for a payment, the money they receive is actually the government's property?"

Noting again - some of the money they receive.

I think that it's not terribly uncommon for them to acknowledge this. Most people feel that some amount of taxation is legitimate - you earlier bemoaned the poor, deluded people accepting their own extortion; my position is that they are not deluded. You'll certainly get complaints about the money being spent poorly - and some of it certainly is, and that should be fixed - but the basic notion that some taxation is legitimate is commonly held.

"But that makes no sense whatsoever, of course. It's not the government that just produced value to whoever paid you for it - it was you."

The government did many things that helped enable you to produce that value. They paved roads, they enforce contracts, they protect your property... While there are potential private ways to get some of that done, they would themselves involve paying out more money (eg. use fees
for the turnpike). It's not crazy that you owe some money in proportion to the amount you're benefiting from the shared infrastructure, which is partly expressed by how much you're being paid for what you're doing.

For the record, I agree that "all property is actually owned by the government" is not a very good model.