Doubt thou the stars are fire.

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?!

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