This paper came out of a workshop called "What makes a good theory?", organized by
@Iris, @devezer, J Skewes, S Varma, and T Wareham; and an engaging discussion with @AnyDes, @NeuroStats, F Oude Maatman, S Heignen, J Rawski, and C Wright.

So, what makes a good theory?

One answer comes from Larry Loudan, who said that "science is essentially a problem-solving activity", and "the first and essential acid test for any theory is whether it provides satisfactory solutions to important problems."

I like this answer because it matches what we say we *do* in science. "Problems" are everywhere. Grants and papers are written around them (cf.
@kordinglab's 10 rules for writing). They shape our day-to-day research decisions.

But what's a problem? And what makes one scientific?

For this, we turn Steve Elliott, who summarizes the history of answers to "what's a problem?" and proposes an all-encompassing account:

A problem is a situation in which an agent's aims are unmet, with a set of constraints on what counts as a solution.

journals.uchicago.edu/doi/abs/

Elliott's account well-captures the problems of everyday and professional life. But what about the problems encountered in scientific research?

What is the situation?
Who are the agents?
What are their unmet aims?
What are the constraints on their solutions?

To answer this, we consider a research community to be a collective "agent": a group of researchers joined by a communal aim: to build a body of knowledge that can be used to solve others and future problems in a specific domain.

Scientific problems can then be seen as problems-for a research community, or "field".

The situation is the state of the field's knowledge (a paper's "background").

The constraints are designated by a research question, the answer to which would constitute a solution.

Scientific problems are "wicked" problems – research questions aren't sufficient to specify their constraints, which are often unstated and change over time.

Unless specified, they can only be provisionally solved via community-based methods of evaluation and acceptance.

In addition to the phenomena that are subject of their research (e.g. biology studies living things), a field's domain includes the set of problems related to those phenomena - what we call a field's "problem-space".

Some of these are problems-for other agents. These are "external" problems for the field. Others are about the field's body of knowledge itself. These scientific problems are “internal” for the field.

Cf. Frankel (1980) for this distinction: jstor.org/stable/192551

Internal problems can be e.g. a gap in the field's knowledge, a methodological challenge, or a disconnect between its theories. They range from pure to applied concerns per their relevance to external problems, and include what Laudan called empirical and conceptual problems.

To solve a problem, we use theories from a relevant body of knowledge. E.g. an engineer combines Newtonian mechanics & specialized theories to design a bridge.

These "thoery-users" judge a theory based on problem-sufficiency: can it meet the constraints of my problem-at-hand?

Scientists are theory-users too. We use to theories to explain our data, to design experiments and experimental apparatus, and even to build new theories. (e.g. we use Cajal's neuron doctrine to build a theory of visual processing)

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@dlevenstein I think this is a generally good way of talking about theory, but I do have one criticism: the focus on humans, bringing up research communities, and all of that.

It's not to say that they don't exist, but I would simply want to downplay their existence, not emphasize it, as I think one of the big values of the scientific method is countering the human factors that are, again, definitely in there and unavoidable.

Yes, the scientific enterprise is about humans solving problems identified by humans, but I would just avoid that wording and talk about the method addressing problems in the abstract.

All too often people get sidetracked about the value of science based on focusing on the human factors, so I would avoid that sort of language.

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