Footnotes to Plato from the foothills of the Superstition Mountains

Why Be Consistent? Three Types of Consistency

A reader inquires:

This idea of the necessity to be consistent seems to be the logician's "absolute," as though being inconsistent was the most painful accusation one could endure. [. . .] What rule of life says that one must be absolutely consistent in how one evaluates truth? It is good to argue from first principles but it can also lead one down a rat hole.

Before we can discuss whether one ought to be consistent, we need to know which type of consistency is at issue. There are at least three types of consistency that people often confuse and that need to be kept distinct. I'll call them 'logical,' 'pragmatic,' and 'diachronic.' But it doesn't matter how we label them as long as we keep them separate.

 1. Logical or Propositional Consistency. To say of two propositions that they are consistent is to to say that they can both be true, where 'can' expresses logical or broadly logical possibility. To say of two propositions that they are inconsistent is to say that they cannot both be true, where 'cannot' expresses logical or broadly logical impossibility.

I am blogging but not wearing a hat. My blogging is obviously consistent with my not wearing a hat since both propositions are true. But my blogging is also consistent with my wearing a hat since it is possible that I both be blogging and wearing a hat. But I am blogging now and I am not writing now are inconsistent since they cannot both be true. The first proposition entails the second, which implies the impossibility of the first being true and the second false.


Posted

in

, ,

by

Tags: