So what's left in philosophy is the stuff that no one has gotten very far in solving in 3K years. Why is life worth living? What is a good life? What is the best beer?
Astronomy and medicine are two very obvious examples. Primitive cultures didn't need philosophical underpinnings to notice and record the patterns in the sky or to figure out which plants helped with fevers or how to set broken bones. Philosophy might have helped science in places with structural issues, but it's reaching too far to say that nothing would be around without philosophy.
The philosophy of information is a great example of where it's incredibly important [1]. I seriously, seriously doubt that information theory would have come about without many of the philosophical underpinnings that came before it. It's not just about structure.
[1] http://plato.stanford.edu/entries/information/
edit: interestingly enough, some of the posts in your blog would be considered "philosophy". ;)
PS: The two most widely used and useful parts of math where completely unknown to the anchent Greeks. Aribic numerals are the first example of useful information theory after writing.
When I talk about information theory, I'm talking more about the more generalized forms of it (Shannon, etc), not necessarily something that could generally be described as 'information' in a more classical definition. Specifically, https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Commu....
(this is a subject I'm actively learning over time, so please correct me if I'm wrong!)
Shannon was more an outgrowth of having already abstracted information and looking for ways to encode that for transmission. I don't want to downplay the value, but in historical context it's very different from how you learn about such things after the fact.
It is, and as I said sometimes doing that is _good_ despite the derogatory connotations of calling it as such.
There's a point I'm trying to make which is not coming across, and I'm not sure I'll be able to.
That doesn't make it any less worthy of study of course.