Several physics textbooks and even the SI-The International System of Units Brochure(8th-edition) says that, ''The division of quantities into base quantities and derived quantities is a matter of convention''. Now this means that one can also choose some other physical quantities to be the base quantities.
BUT HOW'S THAT EVEN POSSIBLE !
For instance let speed and time to be the base quantities and then length to be a derived quantity.
Then in this scenario a unit length will be the distance traveled at a unit speed in unit time and for time one can define it's unit independent of any other physical quantities but how come can someone define the unit of speed independently without involving the lengths?
I hope I'm able to keep my point clearly i.e. if speed is defined to be the base or fundamental quantity then how come can someone account for the unit of speed, how will speed then be quantitatively expressed?
Note: The SI Brochure(chapter 1 section 1.1 third paragraph) more precisely says "From a scientific point of view, the division of quantities into base quantities and derived quantities is a matter of convention, and is not essential to the physics of the subject''. The beginning and ending of this statement was becoming hard to digest for me so I left it above.