As someone with a postgraduate background in Philosophy I can say that, within at least the Western Analytic (mostly anglophone) tradition, that many do in fact think exactly that and I would tend to agree. Many Philosopher see their closest relations reside in Mathematics and to a lesser extent the hard sciences. They prize deductive reasoning and argument with truth as the aim.
They are not consciously engaged in a project of cultural preservation and would welcome say Indian or Chinese contributions, but the barrier to understanding their contributions are often very very high (conceptual and not just large linguistic barriers with lack of access to good translations) and so very few people bother to engage when grant applications need writing.
History of Philosophy, as the study of past traditions, thinkers, and arguments plays an outsized role in Philosophy 101 undergraduate courses, but in fact represents a minority of research activity. The majority of research philosophers are active in work relating to new work and living or recent figures such as David Chalmers, Saul Kripke, Ted Sider, David Lewis, Ruth Millikan, Dorothy Edgington, Timothy Williamson, David Parfit, and many many others. To demonstrate what I mean look at the citation network of the top journals in the subject:
Force graph visualisation: https://kieranhealy.org/philcites/
Blog post explainer: https://kieranhealy.org/blog/archives/2013/06/18/a-co-citati...
You mention one strand of western philosophy, "the Western Analytic (mostly anglophone) tradition" that believes its work is most closely related to math but then also point out that, while practitioners from that school are open to participation from non-westerners, they often face "conceptual and not just large linguistic barriers" at engaging with such contributions.
You seem to be saying that there may be value in these contributions but that we lack the cultural framework to understand and engage with them. If that is true, even though this is the portion of philosophy most consciously focused on mathematics-like deductive reasoning, doesn't that suggest an insufficiency in our current programs and perhaps argue that we need to expand our coverage if we are going to engage with practitioners in a global field?
I'm not going to pretend that there isn't some real problem with engagement with other cultures as you only need to look at the ongoing divide between the Analytic and continental traditions. That divide is partly artificial driven by politics and events in early 20th century Europe. At the same time, its is a misunderstanding of what philosophy is if you think its just about cultural preservation. Philosophy in the West is an active and living discipline that is not standing still. A philosophy wants to know what is true, not necessarily what Kant thought was true.
And you are right to do so, for the reasons I explained in my post above.
When you talk of current research, then sure, you talk of modern philosophers. But that's still studying a tradition: just the latest versions of it. When teaching students you reach further back in time (just as maths students learn ancient theorems rather than modern ones).
The conceptual barriers to entry that you say face Asian contributions are a consequenceof the whole discipline having learned more Aristotle than Kongzi in philosophy 101. Because the 101 class (in any field) is what sets the terminology and background assumptions behind even modern research.
"Causal theories of reference" looks interesting from an AI perspective. Do you know how it relates to the math discipline, causality (eg. Pearl)?
Philosophers working in metaphysics and especially causation are aware of Pearl, and the literature on causation in Philosophy is very large, old, and active. It is also clear that Pearl is also aware of the literature in Philosophy on causation and conditionals as he does cite people like Robert Stalnaker and David Lewis.
However, there is a slight difference in concerns on the topic of causation/causality. Philosophers are usually interested in providing a reductive account of causation by providing necessary and sufficient conditions for causation, as apposed to modelling known causal structures to predict what interventions might have on novel systems. That said I do know that L.A. Paul, Ned Hall, Hitchcock, and Menzies have done some work trying to incorporate the insights from the causal modelling approach done by Pearl and colleagues.
Some links in case you want to explore further. Standard Encyclopedia of Philosophy is an amazing free resource if you want to look something up:
http://www.philosophybites.com/
Check out Stanford Encyclopedia of Philosophy, which is free and edited by active research philosophers on pretty much every major topic and figure.
Naming and Necessity by Kripke is about reference and the causal theory of reference, but it assume a decent amount (in case that is what you were asking for specifically).
The Very Short Introductions series have some really good booklets if you want quick ways to jump into a topic.
A few other books:
B Russell The Problems of Philosophy. OUP (dated, but a classic general introduction)
Simon Blackburn Think. Oxford (nice general introduction)
Tim Crane The Mechanical Mind. Penguin (Nice introduction to phil of mind)
A J Ayer Language, Truth, and Logic. Penguin (dated, but a classic)
D Hume Enquiries
T Kuhn The Structure of Scientific Revolutions. Univ of Chicago Press
Philosophy students study study particular thinkers and the traditions in detail. And rightly so: theirs words are open to importantly varied interpretation. Students need to read read Plato because even today professors have non-trivial arguments about what he meant and how to apply the ideas.
So it is forgivably hard for philosophy to see beyond the western tradition it grew up in. But it is unforgivably dumb to try and justify the Euro-centrism by an by an false analogy to science.
I if a student is learning classical mechanics, she needn't read Principia Mathematica, and it doesn't matter what Newton was thinking when he wrote it. What matters is how you do physics today -- the various interpretations that physicists put on it can wait for some advanced course.