etymology of TFP (total factor productivity)

Question

In economics, total-factor productivity (TFP), also called multi-factor productivity, is usually measured as the ratio of aggregate output (e.g., GDP) to aggregate inputs.1 Under some simplifications about the production technology, growth in TFP becomes the portion of growth in output not explained by growth in traditionally measured inputs of labour and capital used in production.

https://en.wikipedia.org/wiki/Total_factor_productivity

How can factors "not explained by growth in traditionally measured inputs of labour and capital" come to be described as "total"? Etymology, please. It would seem like "not explained" implies "complements" and "complementary" so CFP sounds better than TFP.

Addendum... It turns out that TFP has another name... the "Solow residual". A quote from the Economist on 2022 May 7.

Statistical techniques that try to measure the concept of “knowledge” typically bundle all the variation in growth that cannot be explained by changes in the workforce or investment into the black box. Hence TFP’s other, less flattering name—the “Solow residual”. Rather than a reliable metric of society’s level of knowledge, TFP so far seems to remain, in the words of a Solow critic, a “measure of our ignorance”.

Answer 1

It is total because it takes into account all output per all inputs - hence it is the total productivity of all factors.

Total factor productivity as that excerpt from Wikipedia states is given as:

$$TFP=\frac{\text{GDP}}{\text{All Factors}}$$

that is where the total comes from. In practice, the factors used in denominator are capital and labor, but they are measured very broadly to include other factors (e.g. human capital will often be 'hidden' in the labor variable). However, this being said some factors are very hard to measure (e.g. some economists consider entrepreneurship a factor of production), this is why some economists prefer to call it multifactor productivity (i.e. it is productivity of multiple factors but not all), as mentioned in the OECD glossary. However, it has nothing to do with complementarity which in economics has completely different meaning than what you imply in the question so CFP would make no sense.

Also, the passage you cite as reason for your confusion is actually not about total factor productivity but about growth in total factor productivity, i.e. not TFP but $\Delta$TFP. Those are two different variables in the same way as GDP and growth rate of GDP are not the same.

The idea here is simple, if output (GDP) grows, but all factors remain same, that means that the productivity of all the factors used must have increased. However, in real life things usually don't remain constant so you will observe that quantity of inputs economy uses increases over time, but if output increases even faster that has the same implication as the case when inputs remain constant and output grows, namely it means productivity of all those factors is increasing.