This post can be viewed as a companion piece to my one about “proof.” Proof is a kind of test to which a certain, rigidly constrained, set of ideas can be subjected. While it is important within that limited context, proof mostly stands out as an all-but-unachievable ideal, the kind of ideal that suggests the outside limit for the types of tests that might be applied to ideas, concepts, claims, hypotheses, and so forth. There are a great variety of such tests, and they do not line up along a single unimodal, univocal spectrum. But it does seem to me that they do converge at the far ends of this lattice, this partially ordered set of possibilities, to proof as the highest ideal at one end, and vapid opinion, as the most dispensable example at the lowest (and, sadly, commonest) end.
There are primarily three families of tests for ideas, and each such family breaks out in a variety of ways: logical coherence, empirical adequacy, and narrative intelligibility. Following Whitehead’s argument in the early pages of Process and Reality, I take “logical coherence” to be something that is vastly larger than just proof-theoretic completeness or model-theoretic semantic sufficiency. Both of these latter are formal ideals, part of the above, generalized concept of “proof,” that seldom realize themselves in the real world. Logical coherence is not such a desiccated abstraction; rather, it is the requirement that ideas “hang together,” at least “locally” (in metaphysics, this requirement becomes “globally.”) Continue reading
