Since you are reading this article in English, the odds are you already know what the conjunction “so” means. You probably also know that “thus”, “therefore”, and “hence” mean basically the same as “so”, and you are wondering what the difference is. If this is the case, this article is just for you.
Before moving on to the particular words, it should be noted that “thus”, “therefore”, and “hence” are all rather formal and much more common in writing than in everyday conversation, where they are almost always substituted by “so”.
“Thus” and “so”
The most important difference between “thus” and “so” is that “so” is a conjunction (meaning “and for that reason”, “and because of that”), whereas “thus” is an adverb (synonymous with “consequently”). For example, the sentence
He is not satisfied, so we must prepare a new proposal.
can be rewritten using "thus" as follows:
He is not satisfied. Thus, we must prepare a new proposal.
He is not satisfied; thus, we must prepare a new proposal.
He is not satisfied, and(,) thus(,) we must prepare a new proposal.
He is not satisfied with it, thus we must prepare a new proposal.
“Thus” is usually separated from the rest of the sentence by commas, but the commas are often omitted if this would lead to three commas in a row (as in the third example).
The last example is not correct because “thus” cannot join two independent clauses.
“Thus” also has another meaning, followed by the -ing form of a verb: “in so doing”, “as a consequence of doing” (in which case it does not introduce a clause). For example:
They have developed a new technology, thus allowing them to reduce costs.
The comma here was appropriate because what follows “thus” is not a clause. It is just a parenthetical expression extending the preceding clause.
“Hence”
Just like “thus”, “hence” is an adverb, not a conjunction, so it cannot join two independent clauses (note that it is more common to omit the commas around “hence” than after “thus” in formal writing):
He is not satisfied. Hence(,) we must prepare a new proposal.
He is not satisfied; hence(,) we must prepare a new proposal.
He is not satisfied, hence we must prepare a new proposal.
“Hence” used in this sense is rather uncommon, and such usage persists mostly in specialized fields, such as scientific writing.
There is, however, another, more common meaning of “hence”, which substitutes a verb but is not a clause in itself and is always separated from the rest of the sentence by a comma:
Our server was down, hence the delay in responding.
The chemicals cause the rain to become acidic, hence the term “acid rain”.
As you can see, “hence” substitutes phrases such as “which leads to” or “which is the reason of”.
“Therefore”
Finally, “therefore” is also an adverb meaning “as a logical consequence”. It is used mostly in argumentation when one statement logically follows from another, and it is common in scientific literature.
Again, style guides usually recommend to set it off with commas, but when this would break the natural flow of the sentence, most authors tend to omit the commas:
The two lines intersect. Therefore(,) they are not parallel.
The two lines intersect; therefore(,) they are not parallel.
The two lines intersect, and(,) therefore(,) they are not parallel.
The two lines intersect, therefore they are not parallel.
Some people argue that “therefore” functions perfectly well as a conjunction (like “so”) and separating it with a comma instead of a semicolon is acceptable. However, none of the major English dictionaries (such as Oxford English Dictionary or Merriam-Webster) endorses such usage.
Note that “therefore” does not sound natural when there is no apparent logical connection between the two statements, especially in an informal context. You should use “so” in such cases:
The trip was cancelled, so I visited my grandma instead.
The trip was cancelled; therefore I visited my grandma instead.
A few more examples for each of the words mentioned above:
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Jakub Marian