Debunking of Modern Evolutionary and Cosmological Theories

[Hatshepsut]

...  But, being a rigid materialist, I don't see there being anything there which is in principle not subject to an empirical methodology. ...  Suppose that one can be found in which thought is reproducibly explained as patterns of ion density in bi-lipid membranes, ... all of which is material and all of which is subject to empirical investigation.  At that point, does what was previously transcendent, mathematics, logic or rationality itself, become base?

If that happens, I'm afraid the mathematicians will blanch because two major assumptions they have made will suddenly be as vulnerable to melting as ice cream in a hot car in July. You can do addition by experiment, using only marbles if you don't have a lipid bilayer handy. 2  + 3  = 5  becomes visually evident as marbles. But if you repeat the experiment next week, will you get the same result? Mathematicians assume that once you've established something like 2 + 3 = 5 you never have to prove it a second time. In other sciences that's not so. Anything done empirically is subject to re-investigation and possible overturn.

The other assumption is trickier: If you do math with apples instead of marbles, then what is the "sixness" that connects 6 apples with 6 marbles? Somehow, mathematicians feel that 6 ought to be 6 whether it's represented by marbles, apples, or dancing electrons on a bi-lipid membrane. They call it the principle of isomorphism.

Do rationalism and empiricism then meet in the middle?

I'm a centrist, so I'll vote yes. They should call a truce at Panmunjom. 

The nature of what it even really means for something to "exist" is still a battle far from won by either side, or so I have been told. To paraphrase what my philosopher professor said, "Thinking about abstract objects is difficult. Because they're abstract."

I agree, and questions of "meaning" and "existence" get glossed over smoothly in our hurry to argue. One thing in argument is we have to agree certain words and terms will remain undefined. We don't ask what they mean. Otherwise you have to keep going back and back defining stuff, and because we have a finite vocabulary, you're really going around in circles. Two of these undefined terms happen to be "meaning" and "existence" themselves. We don't ask what it means to exist, and we don't ask what it means to mean.  

Although it's way over my head, quantum logic introduces nothing "weird" because it's rules are still deterministic like in any other logic. Just different rules is all. Of course the outcome of rolling a die is uncertain, but probability doesn't care. It just says that fair odds on boxcars is 5 to 1.

Since ordered sets, lattices, and Hilbert spaces are all prerequisites for quantum logic, I don't see why someone who's got that far in math even worries about empiricism or lack of it in what they are doing. They're too busy! Shroedinger cats neither alive nor dead might amuse Neils Bohr in the coffee shop, but they won't piss on the papers on his desk.