What We Cut from Education—and Why It Matters for Cognitive Science and AI

How many years of education does it take to do truly groundbreaking work in cognitive science and AI? Not to produce incremental papers. Not to optimize benchmarks. But to develop the kind of deep, integrative understanding required to rethink the nature of mind, intelligence, and computation.

If your answer is something like 10 to 15 years—from undergraduate degree through PhD and a few postdoctoral projects—then Aaron Sloman thinks you are underestimating the problem.

Is our educational system producing thinkers of the kind that are required for solving some of the hardest problems in cognitive science and AI? In a remarkable Oxford interview, Aaron Sloman argues that it is not. Aaron Sloman is an Honorary Professor of Computer Science at Birmingham. He won the 2020 Jon Barwise Prize for his sustained contributions to philosophy and computing.

Sloman emphasizes two interrelated problems. First, key modes of reasoning—such as learning to construct and verify geometric proofs—have largely disappeared from standard education, replaced by more superficial or narrowly formal approaches. Second, and more fundamentally, the timeline of education itself has become far too compressed. We expect students to become productive researchers within a few years of leaving school, under intense pressure to publish, secure grants, and accumulate citations. In his view, this system produces competent specialists but not the kind of broadly educated, deeply reflective thinkers required for major conceptual breakthroughs.

Sloman argues instead for a radically extended educational trajectory—one that allows for sustained exploration across disciplines, including mathematics, philosophy, psychology, neuroscience, linguistics, and AI, with far less pressure to produce early outputs. He suggests assistant professors be given a decade to continue their learning and research without pressure to publish.

I experienced something close to that ideal. In my undergraduate degree, I took many courses in psychology, philosophy, computer science, mathematics, linguistics, neuroscience and English literature. (Yes, even English literature contributed to my understanding of mind. For instance, I took a course on Literature and Psychology. Compare this project.) Though formally I got a degree in Psychology, it was equivalent to a degree in cognitive science, which is by definition interdisciplinary (not just multidisciplinary). I did my PhD under Aaron Sloman at the University of Birmingham, England. I was formally in its School of Computer Science (which recently has been ranked as the top computer science program in the UK) though my Ph.D. was in Cognitive Science being co-supervised by Glyn Humphreys of Psychology. I read widely across disciplines. I did not suffer from the now-standard “publish or perish” pressures. I spent long days—and many nights, often into the wee hours—thinking, modeling, and programming in AI. The emphasis was on understanding, not output; on grappling with deep problems rather than optimizing for publication metrics. That environment made a lasting impression on my approach to research and intellectual work. Even as an adjunct professor, I am not under intense pressure to publish.

My research uses an integrative design-oriented (IDO) approach that I have been developing and advocating. As outlined in A Manifesto for an Integrative Design-oriented Approach to Understanding Humans as Autonomous Agents, the IDO framework explicitly calls for an education that spans multiple interacting domains. Such an integrative framework is not something that can be mastered quickly or within narrowly defined disciplinary tracks. It obviously requires a longer, broader, and more exploratory educational process.

Aaron Sloman was asked:

KI: Do you think then that we have the right approach to develop robots? I mean, we often take the most advanced methods in sensing, planning, reasoning, acting, language processing and so on and we try to integrate them into a single system. Should we instead rather adopt a more developmental approach and learn things incrementally?

He answered:

Perhaps my answer will surprise you. I think the main challenge is our educational system. It is not producing thinkers of the kind that are required for some of the hardest problems. There are various reasons for this. One is that the teaching of geometry as I learnt it as a child has changed. Bright school- children used to learn how to solve construction problems and prove theorems in Euclidean geometry using diagrams: it was a standard part of academic education. It was part of Immanuel Kant’s education. Some of his views about the nature of human minds were based on that sort of background.

Now many school-leavers may have learnt a little logic, set theory and algebra, and perhaps learnt to reason formally from axioms expressed using logic, but they have learnt only very shallow subsets of geometry and topology. E.g., I meet graduates who tell me that at school they simply memorised facts, such as the triangle sum theorem, or Pythagoras’ theorem, but have never learnt to find and check proofs. And if they do learn to prove theorems in geometry, for instance, at a university, they may only learn it in a logical framework, e.g. starting from something like Hilbert’s axioms.

I did not learn logic and abstract set theory until I was a graduate student, but I don’t think that hampered my early mathematical development, any more than not knowing such things hampered Archimedes, or Zeno. At school, before going to university, I benefited enormously from learning to find and check geometric proofs or constructions.

There are now impressive geometry theorem provers that start from logicised versions (or variants) of Euclid’s axioms, and then use formal reasoning to produce conclusions, e.g. (Chou, Gao, & Zhang, 1994). But that’s not what the ancient mathematicians did. For example, ancient mathematicians discovered the concepts and axioms for Euclidean geometry without deriving them from axioms! They also made discoveries that went beyond Euclid’s axioms, such as the neusis construction that enables arbitrary angles to be trisected—impossible in Euclidean geometry.

However, no current AI geometry theorem provers that I know of can make such discoveries because they can only start from (possibly extended versions of) Euclid’s axioms and work out logical consequences. They can do logical and arithmetic reasoning but not spatial reasoning or make discoveries of the sorts that originally led to axiomatised geometry, including discoveries like the neusis construction (see Neusis construction and How to trisect an angle (Using P-Geometry)), which was known to ancient mathematicians (e.g. Archimedes) but was excluded from the teaching of Euclidean geometry, apparently on the grounds that it combines properties of straight edges with properties of compasses, which reduced the purity of geometry. But excluding it reduced the power of geometrical reasoners!

The point of all this is to indicate how the creative mathematical power of biological minds (a) exceeds the power of statistics/probability based learning systems, which cannot discover, represent or reason about impossibility and necessity, as Kant seems to have understood, long ago, and (b) exceeds the heuristic power of logic+algebra based formal systems in certain domains of reasoning and problem solving concerned with impossibility and necessity in spatial structures and processes — despite the fact that sophisticated logic-based theorem provers outperform all humans on certain tasks, just as computers have outperformed humans on arithmetic tasks, sorting tasks, searching tasks, and others, for several decades. But I am not aware of any computer based machine that can start with something like the knowledge at birth of a baby human and achieve the understanding of numbers of a six year old child.

The fact that the old powerful ways of thinking are no longer a standard part of education, will inevitably restrict the abilities of future AI researchers attempting to find ways to replicate human mathematical creativity. And that is likely to restrict the AI systems they develop.

Another factor relevant to progress on hard research problems, is the enormous growth of human knowledge that is now available to be learnt by potential researchers, who need a much extended education to provide the breadth and depth of understanding required for important advances. We still expect students to leave school at about 18, spend three or four years getting a first degree, and then after five or six years of post-graduate education to be ready to become successful researchers, as demonstrated by ability to produce highly cited publications and win grants. Instead, the most able potential researchers need to spend at least another decade after their first degree broadening and deepening their knowledge, including knowledge of the history and philosophy of science and mathematics to help develop their judgement. Highly accelerated pressures on young researchers to publish, get grants and attract citations (pressures I did not encounter as a young university lecturer) seriously interfere with the continued learning and development required to produce ground-breaking thinkers who can significantly advance human knowledge, though the current system may train humans to be machines for generating conference and journal papers in restricted domains, often based on groups that form efficient mutual citing communities.

I believe this educational system is inadequate to produce the kinds of researchers needed for the deepest and most difficult ground-breaking advances in knowledge, as opposed to fairly shallow extensions of current knowledge flooding journals and conferences. In the UK, the problem was hugely exacerbated by the decision around 1990 to abolish polytechnics, which were performing important educational and industrial/ commercial training functions by turning them all into universities, thereby seriously diluting resources for funding university-level research, and depriving the nation of an important post-school educational resource: its polytechnics!

On the whole, current educational systems tend not to produce graduate researchers and university lecturers with the kind of broad and deep education needed for them to perform the future-oriented functions of universities, including inspiring and guiding future ground-breaking researchers. In particular, research on understanding cognition in all its forms requires an education encompassing mathematics, chemistry, physics, biology, neuroscience, psychology, philosophy (e.g. philosophy of mathematics, of science, of language, of mind) as well as a broad and deep understanding of varieties of forms of computation and their strengths and weaknesses. A lot of the education should be project-based, but without pressure to get publications or high citation counts, as opposed to critical and constructive reviews by supervisors and peers.

We need more bright learners leaving school to be exposed to a variety of additional disciplines, learning to combine information of very different kinds when appropriate, and working on deep and difficult projects without pressure to publish and attract funds. That may be slowly happening to a very small (lucky) subset of researchers. But it’s not happening on a sufficiently wide scale, and I suspect it is not happening to enough people to generate the new thinkers who can come up with ideas that will enable us to make deep new advances and also educate the next generation to continue the process.

I was very lucky as a young graduate, because I was allowed to switch from mathematics to philosophy, and later, as a young lecturer, to switch from philosophy to AI, without anybody chasing me to get grants or to produce publications. It took me a long time. My undergraduate degree (in mathematics and physics) lasted from 1953 to 1956. As a graduate student (1957-62) I moved from mathematics to logic, to philosophy of mathematics, then became a lecturer in philosophy. Later, thanks to psychology seminars where I met Max Clowes, I encountered AI in 1969 and began to do theoretical work in AI in 1972. My first substantial AI development project between 1975 and 1978 (with David Owen, Frank O’Gorman and Geoffrey Hinton) tested ideas about vision, reported in (Sloman et al., 1978). So, between 1953 and 1978 I was lucky to experience an extended educational process in which I was mostly learning, including learning about philosophy, biology, psychology, and linguistics, then programming and AI. The learning continued long after that, and accelerated after I (formally) retired, around 2002. Far more young researchers should have that kind of breadth of education without pressures to produce anything in particular, except to go on learning, teaching, and demonstrating progress to peers and mentors, with cross-institutional reviews (but no league tables) to maintain standards. Such a culture could encourage experienced researchers to share very hard unsolved problems with younger colleagues (as Max Clowes did with me), with the possibility of triggering something new and deep, even if it takes far longer than the duration of a typical grant or a temporary research fellowship.

Deep new advances in knowledge may emerge that, despite astounding advances in technology and physical and biological sciences, our current system does not encourage, as indicated by the widespread neglect of Kant’s deep ideas among researchers in AI, psychology and neuroscience. I wonder how many other cross-disciplinary bridges are waiting to be built that can support deep new advances. Is this already happening, without my knowing about it?

If the above intrigues you, I recommend taking the time to read the entire interview.

What are hard problem in cognitive science and AI?

Yo might be curious to know what Aaron and I mean by “hard problems” in cognitive science and AI. They include understanding capabilities (not just making predictions but modeling functionality) of the human mind and brain from an integrative design-oriented perspective. In 2014, Springer published a book of papers written by former students and colleagues of Aaron Sloman, including myself, on hard topics in AI. They were written based on presentations we gave at Aaron Sloman’s festschrift in Birmingham in 2011. The book is From Animals to Robots and Back: Reflections on Hard Problems in the Study of Cognition: A Collection in Honour of Aaron Sloman (J. L. Wyatt, D. Petters, and D. Hogg (eds.))

My paper in that book is Developing Expertise with Objective Knowledge: Motive Generators and Productive Practice. The late Maggie Boden wrote the foreword to the book: Aaron Sloman: A Bright Tile in AI’s Mosaic which is well worth reading.

Conclusion

Sloman’s reflections are not merely nostalgic; they are diagnostic. They point to a structural mismatch between the kinds of minds we need and the kinds of educational systems we have built.

If we take seriously the goal of understanding natural intelligence—and building artificial systems that approach its richness—then we must also take seriously the need for longer, broader, and less pressurized forms of education. Without that, we risk producing ever more technically proficient researchers who are nonetheless constrained by narrow training and limited conceptual reach.

I will return to some of these themes in future articles here on my Substack. In particular, next week I plan to explore in more detail the cognitive science of geometry and diagrammatic reasoning—topics that Sloman researched from his own Ph.D. onwards, and that I believe are central to understanding both human cognition and the limitations of current AI systems.