You are right about "vetenskapen" being definite. However as far as I know, in English, you generally say "Science can (not) explain everything." while in Swedish you use the definite "Vetenskapen kan (inte) förklara allt.". Would a native English speaker say "the science" in that context?
You're totally right, I just want to note, for the non-native English speakers, that this example isn't a sentence that would really appear, and in fact sounds a little odd to a native speaker.
A native speaker using the word science twice like this would be unlikely. In this, the second one would almost always be replaced with "it". If the first part of the sentence did not include the word science, the second phrase becomes much more likely.
"Chemistry tells us a lot about the world, but can the science explain everything?"
Likka was totally right about this article question, just wanted to note this little thing for any non-native English speakers who wanted to use English structures like this
We would only use the definite if we were talking about a specific branch of science, like likka said.
The indefinite can be used in a connected context, Talking about a branch of science that is not an exclusive member of a group,
"Chemistry is a science that deals with the natural world"
Also, in agreement with the rest of English, and indeed other languages that use articles, the indefinite is used the first time a topic is introduced, then the definite must be used to refer back to it.
Talking about science in general would mean using no article at all, simply saying "science"