Cognitive-Science on digikar's microblog

4-year Undergraduate Program in Computation and Behavioral Sciences

Sun, 20 Sep 2026 20:49:01 +0200

If you have ever discussed Cognitive Science with me for extended periods of time, then you’d know that I have often lamented about the need for a 10 year cognitive science “pre-graduate” program. However true it may be that acquiring relevant knowledge from all the different subdisciplines of Cognitive Science – Psychology, Computer Science, Neuroscience, Philosophy, Linguistics, and Anthropology – takes a long amount of time, such a program would be impractical for at least two main reasons:

Impracticality of long-term planning: To be employable by mid-20s at the latest requires starting by the age of 14 or 16. No sane person in this age group commits to a program so long, that too, with questionable financial or employment utility, especially in the 21st century.
Inclination towards financially-wise choices: It cannot be denied that everyone is trying to find a way or two to earn money by doing activities that aren’t so unpleasurable. In particular, people usually choose undergraduate (or even graduate) programs by the extent of their financial utility they generate. That’s not to say interests have no role. But given two things that look equally enticing in non-monetary terms, one is inclined to choose one that yields them better money.

Time and again, almost all the (senior) researchers I have come across in the field of Cognitive Science over the last 4 years have expressed that mathematical maturity goes a long way in any field of research including Cognitive Science. Interestingly, a related skill concerning programming is also an immensely useful skill in the 21st century in terms of its financial utility. Putting these two together, it seems that it might actually be possible to propose a standard 3- or 4-year undergraduate program that has both utilities (i) financial/employment (ii) research/higher-studies.

As a doctoral student of Cognitive Science, I still lack any background in Linguistics, Neuroscience, or Anthropology. Whatever little I might have gained through occasional exposure is lost through time. So, it’s difficult to judge the below resources by myself. I invite readers to either leave comments below, or on the public post from which you found this page, or email them to me.

By labeling the program as “Computation and Behavioral Sciences”, I have already split the curriculum into two parts. Thus, anyone with a sufficient exposure from these other disciplines of Linguistics, Neuroscience or Anthropology might be able to suggest the appropriate changes to the second part to come up with a corresponding “Computation and XYZ”. In fact, MIT itself has a curriculum focusing on Neuroscience. My own preference for the curriculum comes from my exposure to Cognitive Science at IIT Kanpur and my ongoing PhD at CEU.

Semester	Computation	Behavior
1	Introduction to Algebra	Introduction to Cognitive Psychology
	Introduction to Geometry	Fundamentals of Biology
	Introduction to Programming
2.0	Paradigms of Programming	Introduction to Neuroscience
2.1	Polynomials and Equations
	Basic Statistics
2.2	Coordinate Geometry	Philosophy of Mind
3	Probabilty Theory	Hypothesis Testing and Frequentist Methods
	Single-variable Calculus	Philosophy of Science
	Practical Programming
4	Multivariate Calculus	Basic Experimental Methods
	Linear Algebra	Bayesian Statistics
	Discrete Structures
5	Data Structures	Computational Modeling
	Machine Learning	Embodied, Embedded, Enacted, Extended Cognition
	Databases
6	Non-Classical Logic	Neural Data Analysis
	<Computational Elective 1>	Causal Models and Explanations
		<Behavioral Elective 1>
7	<Computational Elective 2>	<Behavioral Elective 2>
	<Research Project 1>	<Research Project 1>
8	<Research Project 2>	<Research Project 2>
	<General Elective 1>	<General Elective 2>

The nice thing about the above is even if one drops out by year 1 (semester 2) or year 2 (semester 4), they would already be familiar with numerous topics that are part of the computer science curriculum or its prerequisites. As teachyourselfcs.com says: There are 2 types of software engineer: those who understand computer science well enough to do challenging, innovative work, and those who just get by because they’re familiar with a few high level tools. The courses listed above are motivated for the later kinds of programmers.

One objection to this curriculum can be that this is too heavily focused on Computer Science and Mathematics. The reasons are two-fold: Firstly, because many students opting for Behavioral Science due to a spite with Mathematics. Unfortunately, Mathematics comes back to bite people during their Graduate Studies, if not eventually in life. Secondly, an exposure to Data Structures, Discrete Structures, and Databases serves to provide more examples of “structures that the mind might use for computation”, thus helping the student and the eventual researcher keep an “open mind” once out of college.

With that said, let me now list some resources that may be used for the courses themselves. This is still a work in progress, and is the most time and effort consuming part of this page. Reader discretion is advised for improved suggestions. The audience in mind is a class 12th graduate who may not be good with mathematics; or who may be good with mathematics at the expense of other topics:

No.	Course & Prerequisites	Resources
1	Introduction to Algebra
2	Introduction to Geometry
3	Introduction to Programming
4	Introduction to Cognitive Psychology	Cognitive Psychology: A Student’s Handbook by Michael W. Eysenck, Mark T. Keane
5	Fundamentals of Biology	Campbell Biology by Lisa A. Urry, Peter V. Minorsky, Kerry L. Hull, Rebecca B. Orr
6	Paradigms of Programming
	Strong: Introduction to Programming
7	Polynomials and Equations
	Strong: Introduction to Algebra
	Weak: Introduction to Geometry
8	Basic Statistics
	Strong: Introduction to Algebra
9	Introduction to Neuroscience	Neuroscience: Exploring the Brain by Mark Bear, Barry Connors, Michael A. Paradiso
	Strong: Fundamentals of Biology
	Weak: Introduction to Cognitive Psychology
10	Coordinate Geometry
	Strong: Introduction to Geometry
	Strong: Polynomials and Equations
	Weak: Introduction to Algebra
11	Philosophy of Mind
	Strong: Introduction to Cognitive Psychology
	Strong: Introduction to Neuroscience
12	Probability Theory
	Strong: Basic Statistics
	Strong: Introduction to Algebra
	Weak: Polynomials and Equations
13	Hypothesis Testing and Frequentist Methods
	Strong: Basic Statistics
	Strong: Probability Theory
14	Single-variable Calculus
	Strong: Polynomials and Equations
	Strong: Coordinate Geometry
	Weak: Introduction to Algebra
15	Practical Programming
	Strong: Introduction to Programming
	Strong: Paradigms of Programming
16	Philosophy of Science
	Weak: Introduction to Cognitive Psychology
	Weak: Basic Statistics
17	Multivariate Calculus
	Strong: Single-variable Calculus
	Weak: Coordinate Geometry
	Weak: Linear Algebra
18	Linear Algebra
	Strong: Introduction to Algebra
	Weak: Coordinate Geometry
	Weak: Single-variable Calculus
19	Discrete Structures
	Strong: Introduction to Algebra
	Strong: Introduction to Programming
20	Basic Experimental Methods
	Strong: Hypothesis Testing and Frequentist Methods
	Strong: Introduction to Cognitive Psychology
	Weak: Probability Theory
21	Bayesian Statistics
	Strong: Probability Theory
	Strong: Hypothesis Testing and Frequentist Methods
	Weak: Basic Experimental Methods
22	Data Structures
	Strong: Introduction to Programming
	Strong: Paradigms of Programming
	Weak: Discrete Structures
23	Machine Learning
	Strong: Probability Theory
	Strong: Linear Algebra
	Strong: Practical Programming
	Weak: Single-variable Calculus
	Weak: Data Structures
24	Databases
	Strong: Introduction to Programming
	Strong: Data Structures
	Weak: Practical Programming
25	Computational Modeling
	Strong: Machine Learning
	Strong: Introduction to Cognitive Psychology
	Strong: Introduction to Neuroscience
26	Embodied, Embedded, Enacted, Extended, Cognition	The New Science of the Mind by Mark Rowlands (book)
	Strong: Introduction to Cognitive Psychology
	Strong: Philosophy of Mind
	Weak: Introduction to Neuroscience
27	Neural Data Analysis	Analysis of Neural Data by Robert E. Kass, Uri T. Eden, Emery M. Brown (book); Analyzing Neural Time Series Data: Theory and Practice by Mike X Cohen (book)
	Strong: Introduction to Neuroscience
	Strong: Machine Learning
	Weak: Linear Algebra
	Weak: Machine Learning
	Weak: Computational Modeling
28	Causal Models and Explanations	Making Things Happen by James Woodward (book); Explaining the Brain by Carl F. Craver (book); Pseudo-mechanistic Explanations in Psychology and Cognitive Neuroscience (paper); Mechanistic Explanation in Psychology (paper); Cognitive science as an interface between rational and mechanistic explanation (paper)
	Strong: Philosophy of Science
	Strong: Basic Experimental Methods
	Strong: Computational Modeling
	Strong: Neural Data Analysis
	Strong: Embodied, Extended, Enacted Cognition
29	Non-Classical Logic	An Introduction to Non-Classical Logic by Graham Priest (book); Non-Axiomatic Logic by Pei Wang (book)
	Strong: Introduction to Algebra
	Weak: Philosophy of Science

ESPP Conference 2026

Wed, 08 Jul 2026 21:43:36 +0200

The past week I had the opportunity to attend the ESPP Conference 2026. This one is by European Society for Philosophy and Psychology.

As someone who has half-jokingly been called a philosopher on different occasions, it was a very neat experience. And while I hate philosophizing without a practical purpose (ironic, isn’t it? such is my life), the conference was great. I enjoy philosophy being used to guide practical action and, since I’m a cognitive-science researcher in-training, I also enjoy philosophy being used to guide research in psychology and cognition. The conference was a mix of sparsity and density. The mornings were light, the afternoons packed, but still plenty of time for lunch in the middle. The timetable and abstracts are available from this page.

The conference itself was held in Boothstraat Church in Utrecht.

As a memoir, and perhaps, as a future note, here are some of my personal highlights:

Day 1 - Tuesday

The section on Compositionality reminded me of Greenberg (2023). This is a paper on the iconic-symbolic spectrum in representations. This was first brought to my (our) notice during Susan Carey’s visit to CEU in January. The topic of representations has, however, been on my mind almost since the time I started cognitive science during my masters, and was made more interesting by chapter 3 of Pylyshyn (2007) on conceptual vs nonconceptual representations.
- Greenberg, G. (2023). The Iconic-Symbolic Spectrum. Philosophical Review, 132(4), 579–627. https://doi.org/10.1215/00318108-10697558
- Pylyshyn, Z. W. (2007). Things and Places: How the Mind Connects with the World. MIT Press.
Further sessions on the topic of non-linguistic thought were good and informative, albeit like much research at most places and fields, not satisfying. Even though we have evidence (what exactly?) that human thought is very unlike proposition or first order logic, people still remain obsessed with it. There are a number of non-classical logics developed over the past century (Priest, 2008; Wang, 2013), these sadly remain obscure.
- Priest, G. (2008). An introduction to non-classical logic: From if to is. Cambridge university press.
- Wang, P. (2013). Non-axiomatic logic: A model of intelligent reasoning. World Scientific.
Another complaint I have had with psychological research on compositionality and combinatoriality is that it seems very ill-defined. Is composing of functions like add and multiply the same as composing a red color with square shape? Perhaps, someone somewhere has tried to work out the ontology of compositionality, but it hasn’t yet penetrated mainstream research on the topic.
As someone interested in programming language design (see moonli and peltadot), and also language of thought, I also felt a jolt of inspiration to use Gardenfors’ Conceptual Spaces to design a language of thought. If feasible, it should resolve both the issues I have with the vagueness of various philosophical and psychological terms, as well as some issues I have with Conceptual Spaces. Though, it still remains uncertain when exactly I’d undertake this venture.
Quilty-Dunn and Eliasmith were names I had heard before. The conference has again been a nice reminder for me to visit their works.
In the context of Quinian Bootstrapping, again, it seemed an actual programming language of thought could resolve some of the issues that came up.
I had explored Woodward (2016) before regarding the problem of (causal) variable choice. While the problems that I’m concerned with for my doctoral thesis concern variable choice at a personal level, some talks (particularly, Pommer) were a nice reminder that Woodward’s work is primarily concerned with variable choice for scientists. I also need to checkout Woodward (2008).
- Woodward, J. (2008). Mental Causation and Neural Mechanisms. In J. Hohwy & J. Kallestrup (Eds.), Being Reduced: New Essays on Reduction, Explanation, and Causation (pp. 218–262). Oxford University Press.
- Woodward, J. (2008). Invariance, modularity, and all that: Cartwright on causation. In Nancy Cartwright’s philosophy of science (pp. 210–249). Routledge.
- Woodward, J. (2016). The problem of variable choice. Synthese, 193(4), 1047–1072. https://doi.org/10.1007/s11229-015-0810-5
Further, as someone also interested in the nature of scientific explanations, Kaplan and Craver were names I probably hadn’t heard of before, but whose work seems very very interesting.
As someone also currently interested in the relation between intuitive physics and visual cognition at large, Balaban’s work also seems very very interesting. In case you like big names, Balaban also has some recent work with Ullman.
I have also been interested in Amartya Sen’s Development as Freedom (2000). The basic idea is that development should not just mean an increase in GDP (combined, per-capita, or media), but it should be a multidimensional target that revolves around different kinds of freedom. Interestingly, I learnt from Karki that the same notion of freedom that led to Amartya Sen’s work has also led to the notion of education as freedom or autonomy-enhancing enterprise (my paraphrase). In today’s context of constantly progressing AI that risks deskilling, the idea then is that at least those skills should be preserved which are freedom-enhancing for the student. This looks like a potentially nice attitude to decide which tasks one should allow students to handover to the AI, and which tasks and skills they should prioritize learning. Finally, something that might seem obvious in hindsight, but wasn’t easy to see before I attended Koi’s talk was that (my extension perhaps) freedom implies the individual having a particular decision set. A decision set refers (and this is where Koi comes in) not to options that an external observer can see, but to options that the individual herself can see. In evaluating freedom, it matters whether the policy evaluator thinks “some people can go to university” in contrast to whether you can think “I can go to the university”.
- Sen, A. (2001). Development as freedom. Oxford University Press Academic UK.

Day 2 - Wednesday

Since Day 1 was so exciting, I wasn’t exactly in a receptive state on Day 2. Nonetheless -

There was an interesting talk that since consciousness perhaps depends on the substrate and autopoesis, machines cannot be conscious. (Although, artificial life can be conscious if it were autopoetic.) This isn’t exactly a new point, and probably dates back to Lycan (1995) and even before. If there was more subtlety to the point, I was unable to grasp it.
- Lycan, W. G. (1995). Consciousness. MIT Press.
This was followed by a symposium that covered different topics including explanatory pluralism. These again referred to Woodward as well as Craver and Kaplan, and a number of other authors I probably hadn’t heard before. Since we were discussing explanations themselves, there was also a reference to a Theory of Explanation (I’m sure there are several of them).
- Behrens, S., Krämer, S., & Roski, S. (2024). Introduction: difference-making and explanatory relevance. Philosophical Studies, 181(9), 2047–2061. https://doi.org/10.1007/s11098-024-02213-8
For my own self, two further points I felt relevant included:
- “Explanations are hyperintensional relations.” The exact meaning is lost on me, but I’ve been dipping my toes into hyperintensionality in causal judgments this past year, so this ringed a bell.
- The explanations I seek about cognition are computational simulations of mechanistic models rather than computational models themselves.
Going to the afternoon sessions, I found some more interesting points for my broader interests: (i) The same brain region is involved in multiple activities. See Poldrack (2006) and Anderson (2010) for neural reuse. As someone who’s been part of cognitive science departments (both, my old at IITK and current at CEU) that have professors that are skeptical of neuroimaging claims, these look like interesting papers. (ii) That there is something to be said about the numerous (78+) neuron kinds in the brain – see Anderson & Pessoa (2011).
- Poldrack, R. (2006). Can cognitive processes be inferred from neuroimaging data? Trends in Cognitive Sciences, 10(2), 59–63. https://doi.org/10.1016/j.tics.2005.12.004
- Anderson, M. L., & Penner‐Wilger, M. (2012). Neural reuse in the evolution and development of the brain: Evidence for developmental homology? Developmental Psychobiology, 55(1), 42–51. https://doi.org/10.1002/dev.21055
- Anderson, M., & Pessoa, L. (2011). Quantifying the diversity of neural activations in individual brain regions. Proceedings of the Annual Meeting of the Cognitive Science Society, 33(33).
Pylyshyn (1986, 2007) had mentioned that representations are only useful explanatory tools when non-representations cease to be helpful. But these are relatively short remarks on the topic that are seldom discussed in cognition. Through Garbayo’s talk, I also learnt about Clark & Toribio (1994) that points out two conditions for representations to be explanatory useful, as well as Saigusa (2008).
- Clark, A., & Toribio, J. (1994). Doing without representing? Synthese, 101(3), 401–431. https://doi.org/10.1007/bf01063896
- Pylyshyn, Z. W. (1986). Computation and Cognition: Toward a Foundation for Cognitive Science. The MIT Press. https://doi.org/10.7551/mitpress/2004.001.0001
- Saigusa, T., Tero, A., Nakagaki, T., & Kuramoto, Y. (2008). Amoebae Anticipate Periodic Events. Physical Review Letters, 100(1). https://doi.org/10.1103/physrevlett.100.018101
Finally, there was also reference to Godfrey Smith’s work, who is another big name I had heard before but had forgotten about. Thanks for the reminder!

Day 3 - Thursday

The afternoon of the third day I was met with a slight headache, and decided to take a precautionary break, since my own talk was still 24 hours away. The result was that I missed some very interesting sessions on consciousness :’). Can’t catch ’em all I guess.

I’ve tried reading Sperber’s work, but every time I drift off to something. (This happens with all voluntary things though; there are just too many interesting things!) This time, there was a reminder to Sperber & Wilson (1992), but also lots of other work – 1986, 1997, 2019. The 2019 chapter is a concise review in particular.
- Sperber, D., & Wilson, D. (1986). Relevance: Communication and Cognition (Vol. 142). Harvard University Press Cambridge, MA.
- Wilson, D., & Sperber, D. (1992). On verbal irony. Lingua, 87(1), 53–76.
- Sperber, D., & Wilson, D. (1997). Remarks on relevance theory and the social sciences.
- Sperber, D. (2019). Personal Notes on a Shared Trajectory. In Relevance, Pragmatics and Interpretation (pp. 13–20). Cambridge University Press. https://doi.org/10.1017/9781108290593.002
Perhaps, most usefully, there is now a diamond open access journal for Experimental Pragmatics. Thanks to Ira Noveck for sharing.

See https://journals.uclpress.co.uk/jxprag/

Day 4 - Friday

That humans don’t just learn from each other, but also teach (and shape) is each other seems obvious to a non-psychologist. Yet psychology research on this topic is relatively non-mainstream outside education. Thus, the fourth day was particularly interesting for bringing this topic to the forefront. See the program for more details!
Being situated in a Cognitive Science department that also focuses on theory of mind and social cognition, I also come across Apperly & Butterfill’s work from time to time. Apperly, Devine & Butterfill (2026) is another addition.
- Apperly, I. A., Devine, R. T., & Butterfill, S. A. (2026). Mindreading as asynchronous coordination: The MAC account of theory of mind performance, and individual differences. Cognition, 274, 106569. https://doi.org/10.1016/j.cognition.2026.106569
As a supporter of neurodiversity, I remain puzzled by a paradox that I was quite pleased was elucidated in Castro’s talk. Or at least they attempted an elucidation that I failed to grasp, and did not quite find the opportunity to clarify. But I revisited the presentation now and I still fail to grasp it.

So, perhaps, I’ll describe my own view on the paradox. The paradox is roughly as follows (i) Neurodiversity implies there is no single “right” mind, and that neurodiverse minds are just as right as neurotypical minds. The inconveniences and difficulties that neurodiverse individuals face are because neurotypicals dominate the world. These difficulties are in the similar spirit as those that men would face in the lack of urinals and women would face in the lack of standard toilets. (ii) If all neurodiversity is to be explained by diversity of minds, there should be no need for medications or, perhaps, even diagnosis.

And while I agree with the suggestion by Castro (if I understood correctly) that there is a social-normative aspect to what is dubbed as a disorder, I think it is useful that a neurodiverse child (or adult) be provided with sufficient resources so that they do not fall behind their peers for reasons beyond their control. The notion of falling behind can itself be defined in terms of the freedom and capability-development that was mentioned on day 1 of the conference. Finally, the notion of sitting in an office environment being hyperfocused on some or the other task seems so different to the natural wild environment that humans (or life in general) evolved in for the past million years (or hundred million).
In the last session, I had my own talk. Unfortunately, the attendance was quite low. I also felt a bit out of place given that my talk and work was a weird mix of formal philosophy, computational modeling, and psychology. In particular, it was about a non-counterfactual account of actual causation, and particularly, the presence or absence of hyperintensional effects therein. Put in simpler words, it concerned whether (graded) causal judgments differ even if the logical structure of events (in terms of their truth-tables) differ. Such hyperintensional effects are known about actual causation. And while I have enjoyed this, apparantly, there weren’t many people at ESPP into actual causation. Nonetheless, Sarah Beck suggested the role of temporal proximity for causal judgments. This is actually a fairly researched topic I hadn’t looked into before, so it’d be exciting to see if I delve deeper into it.
The very last talk was by Sarah Beck and was perhaps the most fun talk of the conference given a demonstration similar to this :):

Source: reddit

Your browser doesn't support HTML5 video. Here is a link to the video instead.

The explanation is that kids learn the functions (to sit inside) of artefacts (such as car). And the scale is then irrelevant until the child is of a certain age.

The talk itself concerned if children search for multiple solutions to physical problems. It was based on similar prior research in animal cognition:

Perhaps, the best part of attending the conference was I got to enjoy some very good dahi puri, it’s been a rarity outside Pune.

I guess I’ll leave you at that! Have a nice day, or night :).

Some issues with Probabilities and Bayesianism for Unified Models of Cognition or Artificial General Intelligence

Fri, 14 Nov 2025 13:49:34 +0100

Bayesian Methods provide a reasonable model of updating Probabilities of Beliefs in the face of upcoming information. Taken as a framework theory (unfalsifiable) of cognition or intelligence for a particular task, these can be pretty good for providing a precise null theory to compare cognition against (citation needed). Similarly, it also provides a good alternative to the Frequentist approaches to statistical inference.

However, it becomes problematic when it starts being used as a model of unified cognition or general intelligence.

Wikipedia provides the motivation for Probability Theory as:

Probability is a way of assigning every “event” a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) be assigned a value of one. To qualify as a probability distribution, the assignment of values must satisfy the requirement that if you look at a collection of mutually exclusive events (events that contain no common results, e.g., the events {1,6}, {3}, and {2,4} are all mutually exclusive), the probability that any of these events occurs is given by the sum of the probabilities of the events.

This already presents several issues:

You require a well-specified set. There’s no specification how to assign probability to a new event that is outside the set.
Probabilities should be kept consistent with each other, respecting its axioms. Not doing so leads to Dutch books.
The uncertainties quantified by probabilities are relative uncertainties rather than absolute ones. This relates to the first point. I have argued about this before.
When one tries to quantify the uncertainty of all beliefs by probabilities, and tries to remain consistent, this can require updation across a wide range of beliefs. This can be computationally expensive. It is also dissimilar to humans who seem to be able to hold mutually contradictory beliefs (as long as they are “far apart” in reasoning chains).

To actually state the resulting unified model of cognition or general intelligence rigorously, one needs to specify what the probabilities are of, that is, what are the elements of the set? I have seen zero discussion of this in Cognitive Science. Fortunately, there is a relevant entry in the Stanford Encyclopaedia of Philosophy that discusses Modal Probability Logics and First-order Probability Logic.

Classical mathematical (first-order) logic has several issues. Chapter 1 of Pei Wang’s book on Non-Axiomatic Logic discusses these. Several of them remain even after mixing probabilities and first order logics:

The truth-value itself may be dependent on assumptions. Thus, a change of assumptions (which a unified model of cognition must be able to handle) can necessitate revision of truth-values.
Reasoning involves induction, abduction, analogy, and other types of inference beyond deduction itself.
Classical logic leads to logically correct but intuitively problematic inferences. See Paradoxes of Material Implication.

There is talk on how bayesian updates provides revision. There is work on how hierarchical bayesian models can be used for induction, abduction, etc. There is work on incorporating causality into probabilities. Intuitively, until they are fully specified, that is, as good as a mathematical theory, they are simply models of cognition with unspecified assumptions in the researchers’ heads. They are not yet unified models of cognition that can be implemented in a machine to yield artificial general intelligence. Concretely, I still do not grasp the arguments.

Is there an alternative? There are already many branches of logic. There’s also a book written by Graham Priest on Non-Classical Logic. And finally, the one that introduced me to these issues is Pei Wang’s work on Non-Axiomatic Logic that tries to draw upon several non-classical logics at once.

Software Development as simultaneous Prediction and Explanation

Wed, 05 Nov 2025 19:34:01 +0100

There is often the talk that prediction and explanation can be opposed to each other. Simple models aid explanability but may hinder prediction. Complex models aid prediction but may hinder explanability. Or so the story goes in my understanding.

However, consider software development. Particularly of large softwares. Take this for example.

Google has 2 billion
Mac OS has 80 million
Microsoft Office has 40 million
…

Perhaps, no Googler understands all of Google’s codebase, no Mac OS core-developer understands all of Mac OS, no developer of Microsoft Office understands all of Microsoft Office. Yet it is true that these are more-or-less reliable products produced by humans. It is true that individual humans fix bugs or add features to these behemoths.

It is true that individual humans do not understand these softwares in their entirety. However, an individual human can understand different aspects of the software once they put their mind to it. The task of combining the different aspects into an interactable whole is left to the computer. Most well-maintained softwares have potential understandability even if they are not understandable.

In a similar manner, scientific explanations too can use the computer to construct potentially understandable models without giving up on complexity. Taking inspiration from software development, one can build complex scientific models that may be non-understandable but be potentially understanable.

Of course, the task of coming up with a language to program scientific explanation might be a lifetime of work in itself. Though, see Structure and Interpretation of Classical Mechanics. (Might be unrelated – I haven’t read it!)

A non-equivalence between Non-Axiomatic Logic and Probability Theory (Nov. 2025)

Wed, 05 Nov 2025 18:32:41 +0100

People have beliefs about the world*. The beliefs have uncertainties. How do we characterize or represent these uncertainties?

In both the (computational) cognitive and computational sciences, beliefs are often represented as a parameter value $\theta = \theta_0$. The truth value of the belief may be true or false characterized by a scalar value $P(\theta = \theta_0)$, called the probability of the belief. The spread of the probability distribution $P(\theta)$ (often the standard deviation $\sigma$) gives us the uncertainty of the belief.

However, note that this uncertainty is characterized in the context of a belief space, that is, the set $\mathit S$ of values of $\theta$. The uncertainty then is with respect to other beliefs $\theta_0' \neq \theta_0$.

The non-axiomatic logic framework by Pei Wang et al. instead characterize the truth-value of the belief by a two-length tuple $(f,c)$, the frequency and the confidence respectively. This allows us to characterize beliefs independently of each other. The different beliefs may later be compared against each other.

Contrast the two situations:

10 coin tosses with 8 heads
1000 coin tosses with 800 heads

It is true that the bias of the coin in the second situation may be judged as being less uncertain than the first. Probability theory explains it as the two probability distributions same mean but different variations. Non-axiomatic logic explains it as two beliefs having the same frequency but different confidence.

For the class of situations involving coin tosses, it is also the case that different values of $\theta$ are mutually exclusive. It is this mutual exclusivity that allows the use of Probability theory to model belief updates. In cases where mutual exclusivity fails, Probability theory becomes misapplied. NAL can take-over in those situations with contradictory beliefs.

However, events can always be modeled so that they are mutually exclusive. To talk about the uncertainty of a particular belief $\theta = \theta_0$ independent of other beliefs $\theta = \theta_0'$ requires assigning each belief to its individual probability distribution. ~~Often this could be a normal distribution $\sout{\mathit N(\theta, \sigma)}$ characterized by a mean $\sout{\theta}$ and standard deviation $\sout{\sigma}$.~~ However, this implies that the set of mutually exclusive alternatives is $\mathit S: \{\theta = \theta_0', \theta \neq \theta_0'\}$ and likewise for each value of $\theta$. Each of the two elements of the set can then obtain a probability independent of other values of $\theta$. But, this does not allow us to represent what might be considered the uncertainty in probability.

Even besides this non-equivalence, the two frameworks diverge a fair bit. Pei Wang has also talked about Belief Revision in Probability Theory discussing other issues with probabilities. I remain failed to grasp anything beyond intuitive ideas, perhaps, lacking a background in philosophy and history of probality theory or my own peculiarities. While Non-axiomatic Logic has seen a lot of development, it remains true that the research developments in Probability Theory has been humongous.

*Or if you are a Cognitive Semanticist like Gardenfors, I’d restate as: these are beliefs about represented features of the world.

Memory (Oct. 2025)

Fri, 31 Oct 2025 13:00:08 +0100

How humans learn and store information and knowledge has been interesting to me. Although not enough to pursue a doctoral research on it. Although, it is also the case that I was advised not to silo myself into a “topic of cognition” but rather to start from an intriguing phenomenon and let that phenomenon guide my investigation. I think I like that advice.

So, how do I think human learning and memory work? Here’s an attempt.

Given an organism in an environment, the organism’s sensors make (transduce) sensory representations $S$ from the environment. This could involve electromagnetic radiation such as light, or vibrations such as by sound or ultrasound, or tactile such as by touch, or something more exotic. The environment may be external to the organism or it could be internal, to account for hunger, thirst, etc. For simplicity, one may assume that the same environment produces the same sensory representations. Thus, its sensors may be said to be functional (as in functional programming). If we allowed sensors to be non-functional in characteristic, it seems possible to attribute the entire process of cognition to sensors alone (citation needed). Such a sensory representation may also have a temporal component.

Such a sensory representation $S$ only lasts very briefly (citations on classic sensory memory experiments). It must be transformed into a conceptual representation $C_S$ for it to be available in the long run. The conceptual representation in turn may depend on an earlier conceptual structure, so we label the conceptual representation with a timestamp $t$: $C_{S,t}$. Doing so devoids the conceptual representation from a temporal component.

It is ubiquitous that episodic (layman speak: contextual) and semantic (layman speak: context-free) memories are two aspects of our experience. How do these two aspects arise?

A conceptual representation $C$ is a structure built out of concepts available from an existing concept-database $\mathcal C$. The structure may be atomic or compound. The concept databases includes atomic-concepts (nouns) as well as relation-concepts (adjectives, verbs, prepositions) to describe or combine existing structures into new compound structures. This raises several questions:

What are atomic-concepts? Or what determines whether some concept is atomic?
How are relation-concepts created?

The concept database also allows us to compute the probability $P(C' | \mathcal C_{S,t}, S)$ of new conceptual structure $C'$ given the current concept-database $\mathcal C$, the current conceptual representation $C_{S,t}$, and sensory representation $S$. I use probability for convenience, but it could be any other measure of uncertainty.

To answer the questions, we require postulating two concept-learning processes.

The first process $\mathcal P_{\text{atomic}}$ can make new atomic concepts out of sensory representations. An atomic concept $C'$ is characterized by traces of sensory representations that were used to make the concept, as well as some conditional probabilities $P(C' | \mathcal C_{S,t}, S)$. What exact conditional probabilities are involved might be an open question. Perhaps they correspond to the concepts $C_{S,t}$ used to predict this new concept $C’$? Additionally, what do I mean by traces?
The second process $\mathcal P_{\text{relational}}$ can make new relational concepts out of sensory representations as well as existing concepts.

Stating this also partly answers question 2: A concept is atomic if it depends solely on sensory representations. A concept is relational if it depends on both sensory representations or other concepts. But this raises yet another question: what do I mean here by depend on?

Semantic Memory is identical to the concept database $\mathcal C$.

We say that a concept is active if it is a part of the current conceptual representation $C_{S,t}$.

Episodic Memory works as follows:

The organisms cognitive system produces a sequence of conceptual representations $(C_1, …, C_t)$ from the sucessive sensory representations its sensors produce. In a well-functioning organism, the production of such a sequence also creates a sequence of activations corresponding to different concepts. This sequence of activations is recorded by some cognitive-subsystem (perhaps hippocampus?).
During recall, this sequence of activations is replayed back by the cognitive-subsystem that had recorded the activations. Because recall involves relations to concepts that are earlier or later in the sequence, episodic memory is conceptual.

Open questions include:

What exactly do I mean by depend?
How exactly do the concept-generating processes operate? This needs to be specified in (much) more detail.
What do I mean by traces?

And finally, what predictions does this make?

Of course, comparison with existing literature is an open task on its own.

Advice for (Psychology) Graduate Students

Fri, 24 Oct 2025 08:45:32 +0200

I recently received an email from one of my professors titled Some non-obvious advice for psych graduate students. I wanted to share it publicly, but found no obvious public links in the email that was forwarded from one of Substack’s mailing list. Though, after inspecting the url for Varun Shennoy’s substack varunshenoy.substack.com this morning, the critical part seemed to be obtaining some username, and then the website should be at <username>.substack.com. And there it was paulbloom.substack.com that I could share publicly. Enough Meta!

If you are a psychology graduate student (or perhaps even a postdoctoral researcher or someone in their early career), definitely check it out!

Some non-obvious advice for psych graduate students

Another of Paul Bloom’s post I liked and can suggest reading is

The only interdisciplinary conversations worth having

To be honest, that’s a strong take. I think from an interdisciplinary research perspective, it still makes sense. However, I also think there’s more to interdisciplinary research. I should share an article I had found another day; it’s a tangential topic on philosophy of interdisciplinary research rather than advice for graduate school.

Coming back to graduate school advice, I had come across a book last year. I suspect it was this, but it could be different. It is slighly hefty at 400+ pages, but given that they are plain english rather than academic jargon, it should be an easy read over lunch hours or a weekend or two. Goodreads reviewers rate it quite highly.

A Field Guide to Grad School: Uncovering the Hidden Curriculum

Good luck!