David Barner

Numerical Cognition

Happy to share this new entry on numerical cognition for the OECS. Thanks to @hbaum.bsky.social and @mcxfrank.bsky.social for making this happen! Apologies if your work isn’t cited! Had to limit cites!!! oecs.mit.edu/pub/rek9756r...

Very fun review from Jean-Charles Pelland on how base structures in number systems impact learning, thinking, & culture.

On official UC letterhead: UNIVERSITY OF CALIFORNIA James B. Milliken President Office of the President 1111 Franklin Street Oakland, CA 94607 universityofcalifornia.edu CAMPUSES Berkeley Davis Irvine UCLA Merced Riverside San Diego San Francisco Santa Barbara Santa Cruz MEDICAL CENTERS Davis Irvine UCLA San Diego San Francisco NATIONAL LABORATORIES Lawrence Berkeley Lawrence Livermore Los Alamos DIVISION OF AGRICULTURE AND NATURAL RESOURCES November 18, 2025 Dear Chancellors: I'm writing with regard to the President's Postdoctoral Fellowship Program (PPFP) and the program's associated faculty hiring incentive. As you know, for more than 40 years, PPFP has provided postdoctoral research fellowships, professional development, and faculty mentoring to scholars in all fields whose research, teaching, and service advance the academic and research missions of the University of California. Since 2003, UC campuses that hire current and former PPFP fellows into ladder-rank positions have been eligible for a hiring incentive funded by the University that provides support for newly hired fellows for five years. Since the creation of the incentive, more than $162 million has been invested by the University to support PPFP faculty hires. This commitment has enabled our campuses to successfully recruit and retain outstanding faculty across a range of disciplines. Given the myriad challenges currently facing UC - including disruptions to billions of dollars in annual federal support, as well as uncertainty around the state budget- reasonable questions were raised in recent months about whether the University could maintain the commitment to current levels of incentive funding. After considering a recommendation to sunset the incentive program due to these significant fiscal constraints, I consulted with all of you as well as faculty and campus academic administrators and systemwide Academic Senate leadership. [continued on next image]

After learning more about the history and success of the program and weighing the thoughtful perspectives that have been shared, I have concluded that barring extraordinary financial setbacks, the PPFP faculty hiring incentive program will continue while the University continues to assess the program's structure as well as its long-term financial sustainability. As a result of our continuing consultation and review, there may be consideration of some changes to elements of the program including the total number of incentives supported, a number that has fluctuated significantly over the years, and how the awards are distributed among campuses. In the meantime, the University will continue to fund the PPFP faculty hiring incentive program and campuses may continue to take advantage of these incentives. We will have an opportunity to discuss any potential changes prior to adoption. As we look to the future, I will continue to engage with faculty leaders, program stakeholders, and UC community members about this important program. I especially appreciate the thoughtful perspectives shared in recent weeks by Academic Council Chair Palazoglu and Vice Chair Scott, the Council of Graduate Deans, UC faculty members, and you as our campus leaders. Sincerely, James B. Milliken President

WE JUST KEEP WINNING. (UC President's Postdoctoral Fellowship Program RESTORED!!!!)

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periodic reminder of the existence of Atkinson Hyperlegible, a free font available from the Braille Institute designed to improve readability for people with low vision

I use it in talks because it's pretty and also because, as an audience member, I am perpetually squinting at people's slides

Shopping for a hot take on nativism? Here's an argument that "strong nativist" accounts of concepts (here, numerical concepts) often fail to explain ontogenesis because they lack an account of "rational causation" - i.e., how innate contents are brought to bear in experience osf.io/preprints/ps...

This will appear in a collection edited by Joon Park, Eric Snyder, and Richard Samuels called Numerical Cognition: Debates and Disputes with a ton of other great papers.

In this spirit I discuss one example of an empiricist model of concept learning that also struggles with rational causation. I also try to work through how constructivists try to resolve the problem, getting the method right, even if the details are still fuzzy in many places.

I note, following Braine, that this isn't unique to nativism but is more like a cultural difference that also explains why some ppl identify as nativists and others as empiricists. The former often care more about characterizing the final structure of thought, the latter about processes of change.

"...This internal connection between concept learning and epistemic notions like evidence is the source of the strong intuition that concept learning is some sort of rational process.” This, kind of rational/causal connection, I argue, is what many strong nativist accounts lack.

In LOT2 Fodor muses, "Perhaps COW is learned from experiences with cows? If so, then experiences with cows must somehow witness that it’s cows that COW applies to...."

They posit innate counting principles, magnitude representations, or even arithmetic principles that define integer concepts, but struggle to explain how these contents get expressed in language or behavior during development. What they lack, I argue, is a model of rational causation.

Prominent nativist accounts of number word learning address one problem of ontogenesis (i.e., providing models capable of describing the abstract content that humans come to have), but often lack detailed accounts of developmental change, and how innate content is deployed.

I explore Martin Braine's question "Is Nativism Sufficient", related to Fodor's point that "there must be a mechanism by which an organism determines which of its innate concepts is contextually appropriate... or innate representations remain inert, contributing nothing to cognition.”

Shopping for a hot take on nativism? Here's an argument that "strong nativist" accounts of concepts (here, numerical concepts) often fail to explain ontogenesis because they lack an account of "rational causation" - i.e., how innate contents are brought to bear in experience osf.io/preprints/ps...

IMO tactics that emerged in war time became simple dispositions of ideological intolerance. It’s fairly common in psychology to breeze past theory you don’t find aesthetically pleasing in a paper to accept it if it shows something interesting. Not nearly as much in linguistics.

For me it's 99.9% in linguistics. Psych ppl are mostly critical but nice

,

6. Month 21-25: Resubmit and wait
7. See 5.

collecting new data (though they won't test the hypothesis), citing Reviewer, and workshopping individual sentences to avoid triggering the reviewer, wondering if any your ideas are actually any good or if you really are an imposter, while telling students they DEFINITELY ARE NOT.
...

Project Joy/Dread Lifepan:
1. Month 1 (study conception): Pure joy
2. Months 2-4: pilots, methods, pre-reg. Hard, but so fun.
3. Months 5-7: Data collection, analysis writing: I'm in heaven
4. Months 8 - 14: Waiting in anxiety
5. Months 15-20: Dread, healing, reconsidering life choices,
...

YOU'RE RUINING OPEN SCIENCE!

I want an metric that automatically scores the severity of Reviewer 2's remarks, and then weights the significance of actually publishing the paper on this basis. This would start to reflect the true work that goes into publishing!

Super fun paper on the role of sensorI-motor procedures in 1-to-1 set matching in blind children and adults, with the effulgent @urvi.bsky.social . Procedures that blind kids use for counting 1-1 don’t help set matching 1-1 unlike in sighted kids!

Exact numerical reasoning in blind children and adults What is the origin of exact numerical reasoning in humans? Previous studies report that innumerate humans are unable to recognize that two sets placed…

Just in: @drbarner.bsky.social & I find that blind adults and children who have symbols for large numbers, and use 1:1 correspondence to count, do not extend a similar 1:1 strategy to a set-matching task, which assesses their knowledge of Hume’s principle. A 🧵:

www.sciencedirect.com/science/arti...

Super fun paper on the role of sensorI-motor procedures in 1-to-1 set matching in blind children and adults, with the effulgent @urvi.bsky.social . Procedures that blind kids use for counting 1-1 don’t help set matching 1-1 unlike in sighted kids!

Right - and the worst part is, when you reduce a pool this profoundly, you end up missing out on the best candidates, most creative work, and so on. The best money right now is on hiring in any area BUT ai.

My career has finally made contact with the culture wars. I can now start a podcast and start plotting an exclusive counterculture college.

I do not object to any of this in this context. The issue is the hiring fad and what it will do to research programs, grants, and students who think that similar jobs will exist in 10-20 years. Our field thrives under diversity of views, not when we go all in on one idea.

Exactly.

We can reap the benefits of everything LLMs have to teach us without hiring LLM “people”.