One Cannot be Rigorous by Merely using Rigorous -Looking Things
Cause and prediction no longer fit the requirements of mathematical rigor.
Two aspects of science that can no longer fit the requirements of mathematical rigor are cause and prediction.
Cause, as in an internal description of a phenomenon’s workings, and prediction as in some forward guess as to what will happen, when.
Mathematical rigor should only apply to a phenomenon’s properties; as an analogy for the system of constraints a phenomenon appears to adhere to.
There is no lack of mathematical rigor to discuss something as complex as the climate, the market, or Edna’s rising cornbread, as long as one refrains from obtuseness, such as trying to say how something occurs causally, or when some event will take place.
The wrong discussion always happens, because people want the evidence. But there is no grand accumulation of truth obtained through experiments because what accumulates here are the pieces of whatever myopic lens the experimentalist has designed. The “cause” to climate change, market moves and starch leavening have been covertly predetermined by choosing a ridiculously small subset of possibilities and watching for change.
I will subscribe to math inasmuch as I subscribe to human cognition and language. We need symbols and abstraction to converse and be precise, so sure, math. But applying math to the guts of phenomena that have never given us a morsel of internal causality, or using it to foretell an experimentalist’s narrowly defined and fabricated values deserves no subscription to an intelligent mind. I have no delusions that I could use a ruler to measure the shape of a cloud.
One cannot be rigorous by merely using rigorous-looking things. The rigor is in how a thing is applied.