Mathematics is a weakness not a strength in the absence of operations. Mathematical logic is dependent upon ‘independence of scale’. But it remains dependent upon existential possibility. And existential possibility is the test provided by operational definitions. (And yes, despite this bit of brevity I can defend that argument.)
Something that is not well understood, even in computer science, is that just as they syllogism, the ratio, the calculus, and statistical relation were innovations in human thought, so was programming an innovation in the process of human thought.
It is hard to accept the fact that programming may be as important as mathematics, the scientific method, and logical reasoning, grammar and rhetoric.
For the single reason that unlike statistical relations programs consist of existentially possible operations.
The 20th century failure of operationalism, intuitionism and praxeology is due to the failure to grasp that justification (confirmation) is not meaningful, and that correlation provides us with a source of inquiry, but only a sequence of operations provide us with evidence of existential possibility. And only parsimony assists us in choosing truth candidates between existentially possible sequences of operations.
In other words, if statements of social science cannot be reduced to sympathetically testable, rationally decidable sequences of choices, they we have no idea if they CAN be true.
We train ourselves to be intolerant of inserting information that does not exist, because the entire purpose of science is to eliminate error, bias, wishful thinking and deception from propositions that we construct by means of free association. And that is what statistical analysis helps us do: extend our senses so that we can construct possible free associations from that which we cannot sense without such technological devices.