Have you looked at Reuben Hersh's _What is Mathematics, Really_, and his proposed alternative, humanism? He claims:
Humanism sees that constructivism, formalism and platonism each
fetishizes one aspect of mathematics, insists that one limited
aspect is mathematics.
This account of mathematics looks at what mathematicians do. The
novelty is conscious effort to avoid falsifying or idealizing.
If we give up the obligation of mathematics to be a source of
indubitable truths, we can accept it as a human activity. We give
up age-old hopes, but gain a clearer idea of what we are doing,
and why.
1. Mathematics is human. It's part of and fits into human culture.
2. Mathematical knowledge isn't infallible. Like science,
mathematics can advance by making mistakes, correcting and
recorrecting them. (This fallibilism is brilliantly argued in
Lakatos's Proofs and Refutations.)
3. There are different versions of proof or rigor, depending on
time, place and other things. The use of computers in proofs is a
nontraditional rigor. Empirical evidence, numerical
experimentation, probabilistic proof all help us decide what to
believe in mathematics. Aristotelian logic isn't always the only
way to decide.
4. Mathematical objects are a distinct variety of social-historic
objects. They're a special part of culture. literature, religion
and banking are also special parts of culture. Each is radically
different from the others.
Music is an instructive example. it isn't a biological or physical
entity. Yet it can't exist apart from some biological or physical
realization -- a tune in your head, a page of sheet music, a high
C produced by a soprano, a recording, or a radio broadcast. Music
exists by some biological or physical manifestation, but it makes
sense only as a mental and cultural entity.
What confusion would exist if philosophers could conceive only two
possibilities for music -- either a thought in the mind of an
Ideal Musician, or a noise like the roar of a vacuum cleaner.
... and he goes onto build this case, explaining that there's a "backstage" to mathematics which mainstream philosophy don't know about, where the makeup comes off, and things are less cut-and-dried as the orderly arrays or theorems would lead us to believe:
The purpose of separating front from back isn't only to keep
customers from interfering with the cooking. It's also to keep
them from knowing too much about the cooking.
Everybody down front knows the leading lady wears powder and
blusher. They don't know exactly how she looks without them.
Diners know what's supposed to go into the ragout. They don't know
for sure what does go into it.
Traditional philosophy recognizes only the front of
mathematics. But it's impossible to understand the front while
ignoring the back.
Incidentally, I once mentioned other math/philosophical books on this list, and I have a weird feeling you'd like Gian-Carlo Rota's book: http://mailman.lbo-talk.org/2007/2007-September/018355.html
Tayssir