[me from before:]Does mathematics not do this more then any other branch of philosophy?
Interesting that you would think so, but no.
what math and science both have that philosophy and theology lack is a combination of usefulness, internal consistency, and cross cultural consensus.
Uhm, to the extent that mathematics and science came from philosophy, this is self contradictory. But granting your desired partition of the words your statement is still on shaky grounds.
Theology seems to be more cross cultural then science. Long before any cultures had science, just about all of them had theology. Specifically all cultures have many people who believe in the supernatural and had some kind of story that went with it. Not all cultures have people who even understand what science is.
Science and higher math (beyond simple arithmetic) are the same in China, Pakistan, Iran, Brazil, Canada and the United States, precisely because they were spread by Western style institutions. I would venture that Catholicism is the same in all the cultures it has spread for similar reasons. But I would not take this to indicate that Catholicism is therefore cross culturally universal in the same sense that you were trying to argue for science.
The only exceptions seem to be in subcultures that reject science because of religious dogma.
Before science came along other cultures didn't have science because it simply wasn't part of the culture. Who knows if and when it might have become part of any other culture without Western influence? How can we know then, what combination of things keeps science from blossoming when introduced?
Christianity isn't accepted everywhere the same either. Nor ping pong, nor soccer.
But back to my original point about mathematics. It is designed specifically to be internally consistent. Every axiom is simply accepted at face value. Every conclusion is derived by deductive reason alone without regard to anything at all in nature. And indeed, despite its highly contrived nature and complete disregard for empirical evidence, it is, as you have admitted, extremely useful in helping us understand nature.
In view of this, let us reexamine your claim:
"Logic is of little value when you set up your definitions so you can’t lose an argument."
Math uses logic, and with painstaking care sets itself up to be unassailable from counter argument, and you admitted it is useful. Seems an excellent counter example. The plausibility that your disdain for theology is rational no longer seems viable to me.
What math and science both have that philosophy and theology lack is a combination of usefulness, internal consistency, and cross cultural consensus.
Science is to philosophy what chemistry is to alchemy. It is a descendant, but it is also a new thing. Alchemy provided a number of useful observations, but chemistry has developed methods and theories that make its parent discipline obsolete.
Philosophy provides numerous questions worth pursuing, but no means of resolving them or validating resolutions.
Mathematics has much more going for it than internal consistency. It has applications. It is the applications rather than the internal consistency that make it cross cultural, and the same applies to science.
Both math and science are judged primarily by their usefulness.