I have been intending to post on this topic. Now my hand has been “forced.” Sabio Lantz has a post:

at his blog, and there he displays a graph with usefulness (i.e. pragmatism) on one axis, and with accuracy (i.e. truth) on the other axis. I responded in a comment, saying that those two (usefulness and accuracy) are not orthogonal. My point appears to have not been understood. So this post will attempt to flesh out the details.

**Pragmatism**

To a first approximation, pragmatism amounts to making decisions on the basis of their usefulness. We all make pragmatic decisions from time to time. A person is often described as a pragmatist if that person is seen as taking usefulness as the most important criterion in decision making. I doubt that anybody is a pure pragmatist, in the sense of only making decisions on a pragmatic basis.

I see myself as a pragmatist. Many (perhaps most) scientists see themselves as pragmatists. In considering myself a pragmatist, I see that as opposed to being an idealist. That is, I do what seems to be useful and make practical sense, rather than what seems to be ideal but unachievable.

There is a philosophy of pragmatism. I have trouble making sense of it. I do not see myself as an adherent of a philosophy of pragmatism. But I do see myself as a pragmatist.

**Truth**

Decisions are often made on the basis of truth. It is hard to say what truth actually is. When asked, some people will mention the correspondence theory of truth

- a statement is true if it corresponds to the facts

but the correspondence theory looks circular to me. If you find someone who goes by the correspondence theory, ask them how they would tell whether a statement corresponds to the facts. And insist that they avoid any reference to truth in that explanation. You will quickly have them fumbling, or appealing to unexplained metaphysics.

**Reconciling truth and pragmatism**

Truth and pragmatism are both terms that we ascribe as the basis of some decision making. That’s about what Sabio Lantz seemed to be saying in his post. My disagreement was with the idea that those two are orthogonal (or mutually independent).

Other people see there as being only one way of making decisions. For some folk, that one way is truth. If I make a decision on the basis of its usefulness, those truth advocates will say that I really decided the truth of what was useful. So they see a pragmatic decision as a special case of a truth decision.

Others try to make pragmatism the source of all decisions, leading to the pragmatic theory of truth. This is sometimes crudely stated as “the truth of a proposition is its cash value”, sometimes with a reference to William James. The pragmatic theory of truth seems overly crude. We do come across cases where pragmatic decisions and truth-based decisions seem to disagree.

**Truth as the step child of pragmatism**

I see truth as a step child of pragmatism, albeit a somewhat unruly step child. That is to say, truth originates from pragmatism, but decisions based on truth do not always agree with decisions based on pragmatism.

Let’s take mathematics as an example. It’s a good example, in the sense that it is very precise so it is easier to see how decisions are made. On the other hand, it is a poor example in that it is unrealistic. But it is still a good starting point.

In mathematics, we prove theorems. And our proofs are entirely concerned with truth. However, the mathematics starts earlier than that. It starts with axioms. I see axioms as pragmatic instruments. Proofs, then, amount to exploring the consequences of axioms. So proofs are based on using conformance to axioms as the basis for the truth that they explore. It starts with the axioms, those instruments of pragmatism. But thereafter we use proofs on the basis of truth. So truth is the step child of pragmatism, in the sense that it is based on those pragmatic instruments, the axioms. It is an unruly child, in that it will often result in conclusions that were not envisioned at the time that the axioms were formulated.

In real life, we establish systems of weights and measures. And then we often make determinations of truth based on compliance to our standard system of weights and measures.

**Truth is a human artifact**

I see truth a conformance with societal standards and social norms. Quine has a philosophy paper “Truth by convention” in which he argues against the idea that mathematical truth is established by convention. From my perspective, as a mathematician, the trouble with Quine’s argument is that it interprets “convention” too narrowly. It works pretty well as an argument against formalism as a philosophy of mathematics. However, it fails to find a source, other than convention, as the basis for mathematical truth.

From my point of view, humans establish standards for pragmatic reasons. Some of those standards are formally adopted as defining standards, and those might reasonably be called conventions. Other standards are more in the form of social norms that are adopted by apparent consensus. The standards, whether adopted formally or by consensus, are effectively human artifacts. I see truth emerging as conformance with those standards. So truth is emergent, but it emerges from artifacts so should itself be seen as an artifact.