Willard Opens a Can of Worms
In the comments, Willard asks if formal propositions, phrased in a logico-mathematical language, a predicate logic, would improve communication about such questions as “is the Earth warming.” In short, I doubt it.
People have an intuitive sense of what they mean when they use a phrase such as “warming.” This intuition will differ for different people, or even the same person addressing different audiences, leading to confusion. Trying to wring out the ambiguities by reaching for formal logic might work for technical audiences working from a common starting point, but it will only lead to greater confusion amid the general public unused to peculiarities of predicate logic. I count myself among them.
But there is a deeper problem …
There is nothing more dangerous or powerful in the philosophical process than selecting one’s axioms, especially given that they are nearly invariably expressed in sloppy old human language. There is nothing more useless than engaging in philosophical, religious, or social debate with another person whose axioms differ significantly from one’s own.
And that’s the nut, isn’t it? Not all disagreements in “the debate” are based in the science. The guppies feeding on the chum at WUWT, who swim the blogosphere swarming the comments on every global warming article, aren’t really interested in the science. Instead they create a polarized world, an artificial binary division, with two sides which accuse the other of engaging in religious belief. “Man’s impact is too small to matter” is hurled up against “Models and natural history tell us enough to be afraid.” The “climate is always changing” sings out against “we are causing climate change.” In the public-at-large, the positions surrounding global warming incorporate many different axioms, many different world views, many different fundamental beliefs that aren’t going to be changed by formal logic. Don’t get me wrong – I strongly believe that there is such a thing as climate science, that the science is sound, that it is evolving, that it provides a better description of the world as it evolves, and that it might be subject to disruptive discoveries, and that it should be subject to skeptical critiques. But without an agreement on the axioms, there is no way forward in rational discussion.
To see this process in action, just take a look at McKitrick’s paper asking “what ‘is’ is” and Benestad’s response, “Yes, Ross, there is a Santa Claus.” Do you think that these two could ever come to an agreement on the axioms of the proposition “Is the Earth warming?” much less agree on the conclusions. (More fun here, note the additional links in the title.)
However, I don’t think I can dismiss the whole idea of using predicate logic that simply. As I approach statistical analysis, I realize that many problems are posed as propositions with null or alternative propositions. That these propositional statements, these hypotheses, seem to mirror the formalism found in predicate calculus. Indeed, as an outsider to both subjects, there appears to be a great deal of similarity between predicate logic and formal statistical analysis.
But logic is it’s own field of study – one with its own language and symbolism to learn. I’ve got enough on my plate just learning statistical methodology. So while I can see some potential in Willard’s call for predicate logic in structuring claims that can be tested, I don’t see it being much help in developing understanding between those with fundamentally different world views. And if Willard takes a closer look at the how statistical propositions are made, I think he will see a surprising resemblance to predicate logic.