Sunday, August 06, 2006

The Arrows of Inference and Causality

Sorry for the dearth of recent posts. I've been working on a big one, and it's been "almost done" for more than a week now.

In the meantime, my big post has forced me to consider another concept.

Question: Does our understanding of triangles come from the axioms of geometry, or is it the other way around?

Answer: It depends on the meaning of the expression "come from."

The axioms of geometry were not invented before we knew anything about geometry. Our observation of geometric figures led us to the understanding that the axioms of geometry predicted the theorems we already knew.

It works the same way in physics as it does in mathematics. Our knowledge of experimental regularities is used to infer the axioms of physical theories.

Thus, there is an arrow of inference that reasons from a collection of phenomena to a handful of axioms that predict those same phenomena.

This implies that there is an arrow pointing in the reverse direction, an arrow of causation. For the axioms to predict the phenomena, the axioms must define laws of causation that do the predicting. We follow the arrow of inference with induction, and follow the arrow of causality with deduction.

So, when we say "A comes from B" we need to be clear about the arrow to which "come from" refers.

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