Why is length considered a fundamental (base) quantity?

[anorlunda]

You are confusing the definition of quantities with the definitions of the units used to measure those quantities.

That's the best answer. Position is a physical quantity. Length is the difference in two positions. But the units used to measure position can be anything convenient, and can be defined by any valid procedure. The units are not the same as the quantity. Inches, meters, and light-seconds are all interchangeable units of length.

 

[f95toli]

Ok so these seven base dimensions can be inter-related (without violating the definition of base dimension)?

Yes, of course.
The only base unit that does not at least in principle somehow rely on any other base unit for the realization is the second.

Btw, "realization" is metrology speak for the actual experiment that is used to measure a quantity which is then used for e.g. calibrating secondary standards.
One difference between the new system and the old is that since we have now defined the fundamental constants there are multiple legitimate ways to realize most of the base units; in the past the SI prescribed one specific realization.

 

[jfmcghee]

The only base unit that does not at least in principle somehow rely on any other base unit for the realization is the second.

Is this in reference to the second being based on a cesium transition?

 

[vanhees71]

Indeed, if you think about the entire SI as it is defined today, everything starts and depends on the realization of the second as a unit of time. The reason for this is that time measurements are the most accurate measurements that can be done today. The other 5 physical base units are then fully defined by choosing the natural constants that can be realized also with sufficient accuracy ($c$, $\hbar$, $e$, $N_{\text{A}}$, $k_{\text{B}}$).

That time is still defined by referring to a specific substance (Cs-133 atoms) and not by also defining Newton's gravitational constant, $G$, is due to the impossibility to establish $G$ at satisfactory accuracy.

The 7th base unit, the candela, is more a physiological than a physical unit.