Exactly. I have a liberal arts degree and studied math basically only through first year calculus. The strange thing is, compared to most people around me, I am relatively skilled at math. I can do algebra, some calculus perhaps at least pulling some estimates of integrals and derivatives, but my real love is in humanities.
The reason why algebra is important has nothing to do with the GP's idea that it is the most objective of studies. Algebra is useful. That's it. People who know basics of algebra can use it constantly. I could see replacing geometry with a deductive logic class since that's all one studies with HS geometry anyway. I could see teaching less plane trig and more spherical trig too (I tried to teach myself spherical trig in order to better follow some writings of Ptolomy and others, and failed). But these aren't going to happen. But if you don't know algebra these doors are all closed.
What I think the GP is getting at is that it may not be the case that these students are really that stellar at the other subjects that are failing algebra. It's just easier to get passed along. A teacher can more easily allowing gibberish to pass for an analysis of The Great Gatsby than let pass someone's completely wrong attempt at solving a linear equation. It happens. Everyone knows it; it's not a controversial thing.
"The reason why algebra is important has nothing to do with the GP's idea that it is the most objective of studies."
I said neither that algebra is important, nor that it is the most objective.
What I'm saying is very non-controversial: failing at algebra is not just a problem but also a symptom of a general educational failure in an individual.
Even if algebra served no other practical or intellectual purpose at all, the fact that it reveals educational problems is valuable in and of itself. And that quality is due to its objective nature.
This is true, but when you look at geometric proofs all you are doing in HS geometry is deductive logic using an abstraction which is a general approximation of the real world. That's why I could see getting rid of HS geometry and just having a deductive logic class too, perhaps with a unit of Euclidean Geometry included in it.
Algebra and calculus are different though. They are tools for finding unknown information and thinking about changing values.
The reason why algebra is important has nothing to do with the GP's idea that it is the most objective of studies. Algebra is useful. That's it. People who know basics of algebra can use it constantly. I could see replacing geometry with a deductive logic class since that's all one studies with HS geometry anyway. I could see teaching less plane trig and more spherical trig too (I tried to teach myself spherical trig in order to better follow some writings of Ptolomy and others, and failed). But these aren't going to happen. But if you don't know algebra these doors are all closed.