There is a rather convenient absence of an object in this sentence. We can assume that everyone loves. Even if it’s only the taste of cherries warmed by the sun.
I love. You love. Even the cruelest of dictators loves. The thing that a man’s lover wants to be assured of though, is that OBJECT part – that he loves HER.
The question is not that he loves but if she stands in the sights of that loving. He may love his mother. He may love his dagger. He may love Erasmus. He may love telescopes. He may love his dog. He loves. There is no doubt of that. But who? But what?

There’s that old riddle about the two brothers at a crossroads, the one in which one always lies and the other always tells the truth but you don’t know which; you can only ask one question to figure out which way you should go. If you don’t know this riddle and want to work it out on your own, read no further and do that. If you’ve heard this riddle as many times as I have, you may recall that the solution is (SPOILER ALERT) to ask what his brother would say. In lying, the lying brother will reveal the truth and the truth teller will illuminate his brother’s lie.
The trouble with this thought experiment is how absolute it is. There was never yet a human who was so reliable a liar that you could tell the truth by his lies – nor was there ever a truth-teller so rock solid that you couldn’t find some reason to doubt him. Even the most die-hard radical honesty advocate might slip off the rock of truth, if only by accident. But apart from that, a person you could set your Truth Watch by, ceases to be human somehow – you certainly wouldn’t want to chat with him at a party. Maybe this riddle would work better with robots.

Doubt that the sun doth move.

Don’t tell anyone but I’m a little bit of a glosser. I can easily gloss right over lines like this. I’m a big batch organizer, I guess. As in, I read a couple of lines in what is meant to be a love poem, put them in the box marked “love poetry” and dismiss them with, “Yeah, yeah, standard poem, Next!”
I have been known to do this when reading novels, as well, especially with descriptions, nature particularly. Give me a detailed description of the wheat bending in the wind across the plains and I batch it up with – Nature. Wheat. Wind. Next!
Which is partly why I’m doing this project because it is with this discipline that I catch my short-cuts. Thinking about the science of doubting the stars and the sun raises a whole host of questions about what in the heck Hamlet is up to in this poem, if in fact, he wrote in it the first place. It does not read: Doubt the existence of stars. Doubt the existence of the sun. Doubt the existence of truth. This is the sort of standard batching way I read it. Yeah, yeah. Stars. Sun. Truth. Love. It points at all of those things in a world where all of those things are newly questionable. Including Hamlet’s love.

This is actually good scientific advice; Doubt of accepted norms being one of the things that really moves science along. And if I’m not mistaken, we know now that stars are not, in fact, fire, so it’s a pretty good bet to doubt in this case. It is curiously fascinating to think about what was undoubtable for Shakespeare. Stars were fire. That’s it. There was no way to know that this was so, it simply was. Was fire the accepted fact of the moment? What did the Renaissance scientists think?
The evolution of the telescope taught us a great deal about the celestial bodies and their materials but I’m thinking, if I remember my science history correctly, that it was about 100 years after this that we got a really good look at the sky.
I will point out that the next line is, “Doubt that the sun doth move, “which is another thing that one really really should doubt – and makes me wonder at what point the news from Galileo made it over to England. (Fun fact: Galileo and Shakespeare were born the same year!)
It feels like there are few possibilities here:
1) Shakespeare knew of the developments in astronomy and was giving Hamlet some scientifically interesting things to say or
2) The scientific news had not yet hit and Hamlet is here asserting things he holds to be true – as in Doubt that the table is wooden. Doubt that we breathe air – which poetically is much more effective than telling someone to doubt things that are already in doubt
3) Shakespeare is giving Denmark a more medieval worldview than his Renaissance England where the sun still revolves around the earth and the stars burn with fire in the darkness.

Science scholars and Renaissance lit scholars unite! What is likely going on here?!

Et cetera!?! Now is this what Polonius actually says, or is this, perhaps an opportunity for a lazzo? It could easily just be the line. It’s logical for Polonius to skip through some of Hamlet’s letter to get to the juicy stuff – but there are a couple of other possibilities raised by this et cetera, as far as I’m concerned.
1) Depending on where it fell on the page (and I haven’t seen this page on either the folio or the Quarto recently) it could be as simple as the printers running out of space.
2) The printer/actors use et cetera as a placeholder while they try to remember the actual text.
3) Et cetera becomes a cue for Polonius to improvise. Polonius being essentially a Pantalone, could easily slip into the lazzo of reading a love letter. He could escalate the praise of his daughter until Gertrude stops him in the next line.
The improviser and comedian in me likes this last idea best – because I can imagine it bringing some exciting energy into the scene. The writer in me assumes Shakespeare meant exactly what he wrote. But because Shakespeare was also an actor, perhaps both parts lived side by side in him.

And here we begin with one of the big questions I have about Hamlet.

Why is he such a shitty writer and such an excellent talker?

A man who can come up with “What a piece of work is a man, etc” on the fly should be able to come up with some better damn verses than this nonsense.

This is like, Hallmark generic introduction.

This is like, photo of a sunset over a beach, printed in swoopy sappy calligraphy on the front. And the Roses are Red, Violets are Blue crap in the middle isn’t much better.

How is it POSSIBLE that a man who thinks in paragraph long parenthetical sentences would be satisfied with this? Polonius’ criticism of the writing is not unwarranted. This shit is DUMB, man!

And listen, if I’m in love with someone and he calls me celestial, his soul’s idol and/or beautified, I will probably be flattered and appreciate being held in such an exalted state. But I don’t know if I’d believe him. Because this is love generalities 101. And granted, love can make fools of us all – but does it make a brilliant thinker a crappy writer, too? It just doesn’t make any sense. Why would a man whose TOP STRENGTH is his way with words, use such cloddish language to woo his love? The thick lords in Love’s Labor’s Lost do better. Orlando (who’s a WRESTLER and by all accounts not a good poet) does better. Hell, Maria does better love letter writing as a joke!
So what is up with Hamlet’s letters? Are they really his? But to whom else would they belong? The only part of this missive that sounds like Hamlet is his sign-off. The rest? Clumsy. Cliché. Not worthy of the man they come from. It’s like he sent her greeting cards and just signed his name.