(2026-08-11) Brander Llms For Theory Building

Gordon Brander: LLMs for theory-building.

Three kinds of reasoning:

• Deductive reasoning: All beans in this bag are white. These beans are from this bag. Therefore these beans are white. (Rule + Case → Result)
• Inductive reasoning: These beans are from this bag. They are white. Maybe all beans in this bag are white? (Case + Result → Rule)
• Abductive reasoning: All beans in this bag are white. These beans are white. Maybe they came from this bag? (Rule + Result → Case)

Deduction proves, induction generalizes, abduction explains. Or, put another way, abductive reasoning tries to match an observation to the best available hypothesis that could explain it.

LLMs are not very good at abductive reasoning. They aren’t great at deduction either, but we can patch this up with tool use, with automated reasoning, and by burning more thinking tokens.

Where LLMs truly shine is inductive reasoning. This is surprising, because before we had LLMs, computers were not inductive at all

But LLMs are intuitive, like us. This is what makes them seem so human!

System 1 excels in constructing the best possible story based on ideas currently activated

When information is scarce, which is a common occurrence, System 1 operates as a machine for jumping to conclusions.

if LLMs are good at induction, and they can be made to do deduction, can they also be coached into abductive reasoning? This matters, because abductive reasoning is a core move in theory-building, debugging, and discovery

It goes like this:

• You encounter something surprising that violates your current model of reality
• Suddenly–eureka!—a mechanism pops into your head which explains it (abductive).
• You figure out what else would be true if the theory were to hold (deductive)
• Then you test empirically to gather evidence (inductive).

Abductive reasoning gets us from epicycles to elliptical orbits. It’s where new ideas come from. If an LLM can do all three kinds of reasoning, we have the raw ingredients for fully-automated research.

I also have a stake in this, because abductive reasoning is an important part of strategic foresight. Scenario planning isn’t just about predicting discrete events. It’s a theory-building exercise.

what about all those math breakthroughs LLMs have been making? These seem to be examples of abductive reasoning

formal and verifiable domains such as math and coding. Might the constraints of mathematics make abductive reasoning more tractable?

Another clue: when solving these math problems, the LLM seems to take a lot of shots in the dark, just trying a lot of things and checking the results. This is sometimes called “repeated sampling” or “test-time compute scaling” in the lit. It sort of brute-forces abductive reasoning, but hey compute is cheap, so why not? Take 100 guesses. Take 1000 guesses. Who cares?

This goes some way toward explaining why formally verifiable domains are getting automated first. The LLM vibes out a bunch of tests, the compiler verifies them. So inductive reasoning can simulate abductive reasoning by generating enough data points to hit on a solution, or to curve-fit.

What about non-verifiable domains? Funnily enough, training LLMs in verifiable domains like code seems to make them better at reasoning in general.

Beyond transfer learning, LLM-as-judge can be surprisingly effective. The LLM judge acts as a substitute verifier in domains without any formal verification method

humans aren’t always correct in their judgements, so human-level doesn’t mean “correct”. Then again, many questions have no single “correct” answer. Most of life is navigated by taste. Either way, we want to ground our judges with external signals wherever we can.

Another promising idea, I think, is to collect a library of mechanisms and theories for the LLM to search through. When confronted with a problem, an LLM could search through this database for likely candidates. A judge could extrapolate what else might be true if the hypothesis holds, and ground its score by searching for confirming and disconfirming evidence on the web or in curated datasources.

Once you have that database of mechanisms, you might use combinatorial methods such as morphological analysis or cross-impact analysis to generate new candidate hypotheses. In strategic foresight, we often do this by identifying high-impact drivers of change (thematic clusters of events, trends, issues) and mapping the interesting ways they might collide (“what happens if declining birth rates collide with advances in robotics?”).

While it’s often valuable to get humans out of the loop, it doesn’t hurt to cheat. Indeed, sometimes human-in-the-loop is the whole point. If I’m doing strategic foresight, I want my agents to expand my OODA loop, not cut me out of it.

How else might we integrate human intelligence? We can ground LLM-as-judge by using techniques like the Delphi method to source expert judgement

We can also have LLMs surface candidate explanations, but down-rank them until they get human peer-review

We’ve gotten LLMs to deduce using bolt-on aftermarket harnesses. Abductive reasoning is trickier, but I think we can get there.