Currently, I’m working on a dissertation on underdeterministic causation at the University of Pittsburgh, at the history of philosophy department. Before (and meanwhile), I got a few other degrees. I explain this confusing trajectory below. First thought, more on my research.

Underdeterministic causation

Most of my attention has recently been spent on investigating underdeterministic causal phenomena. Take an event that elevates the modal status of another event. For instance, if Breton hadn’t met Vaché, surrealism wouldn’t have come to be; if he had, it might have. He did. Surrealism began. Therefore, Breton meeting Vaché was a cause (or a causal background condition, if you prefer) of the advent of surrealism. These two counterfactual dependencies suffice to claim a causal relationship between the meeting and the movement. The relationship exemplifies a causal concept, which current theories of causation cannot account for: A new theory is needed: an underdeterministic cause elevate the modal status of its effects. And there’s more. Underdeterministic token causation is a member of an entire family of underdeterministic concepts: type causation, counterfactuals, causal modals, independence, underdeterministic structural equations. Read about them here.

The causal-causal theory

While developing the theory of underdeterministic token causation, I wanted to build it off the most successful deterministic theory; after all, deterministic causes are edge cases of underdeterministic causes, for they also elevate the modal status of their effects: from impossible to necessary. When I first encountered the structural equations literature on deterministic causation, I saw a project steadily progressing: the next new theory handled more cases, and although it also prompted new counterexamples, it successor would handle these too. And repeat. This clearly—or so I thought—was a flourishing research program. It’s built on two assumptions: that causation directly translates into a counterfactual dependence between the cause and the effect, and that this dependence is constrained by how normal the events involved are.

Now, however, I can’t but see epicycles upon epicycles. Consider Weslake’s partial theory of causation. The theory greatly improves on its predecessor by Halpern and Pearl, but the improvement is achieved by combining conditions that are seem independent; moreover, one of the conditions needs to be applied to every node along some path from the cause-node to the effect-node. The theory works, to the extent that it does, because it recovers the recursive structure of the causal judgment: a cause causes a distant effect in virtue of causing one of the effect’s direct causes. Add a constrain on asymmetry, and you captured the structure. The resulting theory, dubbed the causal-causal theory, is here. It’s not intended to handle cases that involve prevention, though it does handle some such cases. It also breaks down for some voting scenarios. Still, it seems to work better—i.e., account for more cases—than any previous deterministic theory. The next step is to deal with prevention and voting scenarios.

Typically, prevention cases have been handled with appeals to normality. However, I don’t think this works. Here, I argue that there are cases that such appeals mishandle, even though the cases involve the very same intuitions that normality was supposed account for. So, however I fix the causal-causal theory, the solution won’t appeal to normality.

The trajectory

The explanandum:

2022(expected) Ph.D., University of Pittsburgh, history and philosophy of science
2022(expected) M.A., University of Pittsburgh, philosophy
2022(expected) CMU/University of Pittsburgh, graduate certificate in neuroscience
2018Ph.D., Wrocław University of Economics, economics
2016M.A., Washington University in St. Louis, philosophy-neuroscience-psychology
2011fellowship at Rutgers University
2011B.A./M.A., University of Wrocław, philosophy
2010B.Sc./M.Sc., University of Wrocław, computer science
2008B.A./M.A., Wrocław University of Economics, management

And the explanans:

It is a truth universally acknowledged—or at least it was in Poland at the time I was applying to college—that philosophers starve and programmers don’t. So, despite my heart-felt intention to study philosophy, I enrolled in computer sciences studies. (A piece of background: in Poland, you apply to a particular major, which then you can’t switch, and you typically study it for five years and graduate with a master’s.). A year later, I realized I had enough energy to enroll in another major. Yet, since managing programmers makes the prospect of starvation even less likely, I was persuaded to study management. Fast forward two years. It became clear the desire to do philosophy wasn’t a phase I would grow out of or placate with an elective. The philosophy department luckily offered weekend studies—a weekend of classes twice a month. I enrolled. What may seem like lots of work was more like vacations: every other weekend I would forget about the outside world for two days—everyday life would give way to Plato.

Eventually, I graduated with three master’s degrees: management in 2008, computer science in 2010 (it took me some time to finish the thesis), and philosophy in 2011. But I don’t want to imply I did the first two for practical reasons, and only the last reveals my true preferences. That might have been how it started. But in computer science, I took classes in logic, abstract algebra, computational theory, modal logic, and elements of formal semantics; in writing my thesis, I used skills from all these classes. And understating Turing’s proof that there are problems no machine can solve is one of the most philosophically shaking experiences out there. In my management studies, I quickly realized that macro- and microeconomics and econometrics is where all the fun is. I redesigned my studies (thankfully, the university allowed for that if you found a professor who’d OK your plan) to focus on these subjects. Once I graduated, I enrolled in a Ph.D. program in economics. I wrote my thesis on economics of education (for knowledge is the highest good, I read somewhere), and I got a National Science Center grant to fund my empirical research. After what happened next, I put the research on the back burner for some time. Still, in 2018, I defended the dissertation; I write more about this research here.

In my fourth year of studying philosophy, I googled Bacon’s experimentum crucis while preparing for an exam. Experimental philosophy popped up in search results. Empirical research, but in philosophy—what’s there not to love? I organized an undergraduate interest group; soon enough, we ran our own experiments—the first xphi studies ever conducted in Poland. One of them married philosophy and economics. We put some people behind (our best approximation of) the veil of ignorance and asked them to discuss and decide on a distribution rule of unknown future payoffs. Our subject weren’t very Rawlsian, to be honest, but the results were interesting enough to submit an abstract to a conference in Japan. It got accepted. Months later, I attended my first international academic conference. There, Stephen Stich saw our presentation and suggested I should apply to graduate school in the U.S., eventually sponsoring a year-long visit in 2011 so I could audit classes and get recommendation letters.

That’s about that. I got into the philosophy-psychology-neuroscience program at Washington University; after three years, with a master’s, I transferred to Pitt HPS. There and here, I took some more classes than the curriculum demanded; I expect to graduate with a Ph.D. in history and philosophy of science, master’s in philosophy from the philosophy department, and a graduate certificate form the Center for Neural Basis of Cognition.

Underdeterministic causation

Three papers develop theories of underdeterministic phenomena.

The underdeterministic framework. Here, I lay foundations for the entire project. I introduces: underdeterministic causal models, where structural equations can return multiple values; causal modals and might- and would-counterfactuals; underdeterministic independence (an analogue of probabilistic independence); the underdeterministic Causal-Markov condition; and underdeterministic type causation. The paper is under review; download its current version here, but please mind that the final version might differ significantly. The other two papers use this framework.

Underdeterministic causation: a proof of concept. I propose an underdeterministic theory of token underdeterministic causation, which in underdeterministic settings reduces to Halpern and Pearl’s (2005) deterministic theory. The paper is under review; download its current version here.

Underdeterministic counterfactuals. I formulate a theory of underdeterministic counterfactuals, which can handle, with a single model, counterfactuals with disjunctive antecedents and ones with other counterfactuals in the consequent. I also offer a generalized formalism of what Fine (2012) and Briggs (2012) call truthmakers—representations of events. The paper is under review; download its current version here.

The causal-causal theory

In two papers, I begin developing a theory of deterministic token causation.

The recursive structure of causation. Here, I develop a recursive theory of causation: a necessary (but insufficient) condition for causes to cause their distant effects is that the causes cause the effects’ direct causes. The causal relation, as defined here, is transitive unless obeying transitivity would violate asymmetry. The theory isn’t intended to handle cases of prevention, though it happen to handle early and late preemption. The paper is under review; download its current version here.

Causation, normality, and conjoined cases. This paper is purely negative: it shows that invoking normality evaluations in theories of causation doesn’t work. The paper is under review; download its current version here.

The next step is to combine insights from both papers and adapt the causal-causal theory to cases that involve prevention.

Philosophy of cognitive science

Arguments over intuitions?. Deutsch (2010) claims that hypothetical scenarios are evaluated using arguments, not intuitions, and therefore experiments on intuitions are philosophically inconsequential. Using the Gettier case as an example, he identifies three arguments that are supposed to point to the right response to the case. In the paper, I present the results of studies ran on Polish, Indian, Spanish, and American participants that suggest that there’s no deep difference between evaluating the Gettier case with intuitions and evaluating it with Deutsch’s arguments. Specifically, I argue that one would find these arguments persuasive if and only if one is already disposed to exhibit the relevant intuition. The paper, published in the Review of Philosophy and Psychology, is here.

Normality: a Two-Faced Concept. Consider how we evaluate how normal an object is. On the dual-nature hypothesis, a normality evaluation depends on the object’s goodness (how good do you think it is?) and frequency (how frequent do you think it is?). On the single-nature hypothesis, the evaluation depends solely on either frequency or goodness. To assess these hypotheses, I ran four experiments. Study 1 shows that normality evaluations vary with both the goodness and the frequency assessment of the object. Study 2 shows that manipulating the goodness and the frequency dimension changes the normality evaluation. Yet, neither experiment rules out that some people evaluate normality solely based on frequency, and the rest evaluate normality solely based on goodness. Whence two more experiments. Study 3 reveals that when scenarios are contrasted—presented one after another—only frequency matters. But, as study 4 shows, when scenarios are evaluated alone, both frequency and goodness influence normality evaluations in a single person, although the more a person is sensitive to one dimension, the less she’s sensitive to the other. The dual-nature hypothesis seems thus true of uncontrasted applications of the concept of normality, whereas the single-nature hypothesis seems true of contrasted applications. The paper, published in the Review of Philosophy and Psychology, is here.

Philosophy of mathematics

Explanatory Circles, Induction, and Recursive Structures. Lange (2009) offers an argument that, according to him, “does not show merely that some proofs by mathematical induction are not explanatory. It shows that none are […]” (p. 210). The aim here is to present a counterexample to his argument. The paper, published in Thought, is here.

  1. Conjoined cases, causation, and normality.
    • 2022 Central APA, Chicago, USA.
  2. Underdeterministic causation: a proof of concept.
    • 2021, Philosophy of Science Association Biennial Meeting, Baltimore, USA.
    • 2021, Eastern APA, New York, USA
  3. Underdeterministic counterfactuals.
    • 2021 Central APA, New Orleans, USA.
  4. The delusive benefit of the doubt.
    • 2019 Central APA, Denver, USA.
    • 2018 The Neurobiology of Moral Conscience Workshop, Tübingen, Germany
  5. Causal judgments and model implementation.
    • 2019 International Association for Computing and Philosophy Meeting, Mexico City, Mexico.
  6. How to measure norms? A tool for an identity economist.
    • 2019 Philosophy of Social Science Roundtable, Burlington, USA.
  7. Production explanations in formal sciences.
    • 2019 Philosophers’ Rally, Cracow, Poland.
    • 2018 International Association for Computing and Philosophy Meeting, Warsaw, Poland
  8. Causes, cycles, equilibria.
    • 2018 Philosophy of Science Association Biennial Meeting, Seattle, USA.
    • 2018 Pacific APA, San Diego, USA
    • 2017 Philosophers’ Rally, Wrocław, Poland
  9. Intensions and intuitions.
    • 2018 Chalmers and Carnap on Metaphilosophy, Vienna, Austria.
    • 2018 Philosophers’ Rally, Łódź, Poland.
  10. Norms and college major choice.
    • 2018 Annual Meeting of American Economic Association, Philadelphia, USA (poster).
    • 2017 Conference of Economics Departments, Międzyzdroje, Poland.
  11. Normality: a two-faced concept.
    • 2017 Eastern APA, Baltimore, USA.
    • 2016 Experimental philosophy conference, Buffalo, USA.
    • 2015 European Society for Philosophy and Psychology conference, Tartu, Estonia.
    • 2015 CUNY Graduate Conference: Normativity and the Human Sciences, New York, USA.
    • 2014 Cross-Cultural Perspectives on Moral Psychology, Seoul, South Korea (poster)
  12. Seeing unreliably.
    • 2017 Southern Society of Philosophy and Psychology conference, Savannah, USA.
    • 2015 Experimental philosophy conference, Buffalo, USA.
  13. Mathematical induction, grounding, and causal explanations.
    • 2016 Central APA, Chicago, USA.
  14. The evidential value of p-values.
    • 2016 Pacific APA, San Francisco, USA.
    • 2015 Central States Philosophical Association conference, Lexington, USA.
  15. Arguments over intuitions?
    • 2015 Pacific APA, Vancouver, Canada.
    • 2014 Experimental philosophy conference, Buffalo, USA.
    • 2014 Experimental Philosophy: Philosophy of Mind and Action, Bristol, UK
Fig. 1. Quiz question № 3: what ethical theory am I?

At the University of Pittsburgh, I have independently taught morality and medicine, an introduction to medical ethics, and mind and medicine, an introduction to philosophy of medicine. Here’s the syllabus for the former, and here’s the one for the latter.

At Washington University in St. Louis, I TAed a few times for problems in philosophy, which is an introductory course in philosophy, and present moral problems, which is an introduction to ethics. At Wrocław University of Economics, I taught statistics and TAed a few times in microeconomics, macroeconomics, and international economics.

While TAing in macroeconomics, I developed a list of exercises. I find them more useful than the problems in standard textbooks, for here students develop, step by step, the two standard basic models in economics: the Keynesian cross and the IS-LM model. Someone might find the exercises helpful too (they are in Polish).

My research on underdeterministic causes began as a technical problem about non-recursive sets of structural equations. A quick introduction: the currently most successful deterministic theories of causation are formulated using causal models, which in turn use structural equations to represent counterfactual relationships between events. A typical causal model comes with an assumption that its structural equations are recursive: a variable cannot determine its own value.

But it seems that sometimes non-recursive systems of equations are called for: in the simplest model of an economy in equilibrium, (the quantity of) production causes (the quantity of) demand which causes (the quantity of) production. Curious thing happens now if you allow for such systems, however: one system of equations can have multiple solutions, and, importantly, the equations won’t tell you whether any solution is more probable than any other solution. That is, the causal relationships expressed with such equations determine only what equilibria are possible, but they won’t tell you how probable these equilibria are. This is where it first appeared to me that only a new causal concept affords a causal talk about such situations. If some parameter, say, X=1 makes a particular equilibrium possible, while X=2 makes this equilibrium impossible, then if the system is this equilibrium, X=1 rather than X=2 caused the system to attain this equilibrium. Yet, this cause is not deterministic because X=1 didn’t necessitate the system to attain the equilibrium. And it’s not probabilistic because no probabilistic measure is defined over the set of all possible solutions, and therefore the formalism doesn’t let you use probabilities. The whole thing looked new, important, and interesting.

Now, the correct strategy seems to be divorcing the underdeterministic causal part from the non-recursive part. This way first you can investigate causal underdeterminism without all the problems that plague non-recursive models. Once you do that, it turns out that an entire family of causal concepts is waiting to be studied.

The entire underdeterministic framework stems from one little change with respect to deterministic models: allow equations to return more than one value for the same output (economists call such functions correspondences). For illustration, consider a case: about to jump off the tower, Dedalus knows that he only may escape, but also that if he doesn’t try, he’ll stay imprisoned forever. Let J=1 mean that he jumps and J=0 that he doesn’t; and let E=1 mean that he (successfully) escapes, and E=0 that he doesn’t. The equation that describes the counterfactual relationship between whether he jumps and whether he escapes reads: E ← 0, J. For J=0, it returns exactly one value, E=0; therefore, the equation encodes a would-counterfactual: if Dedalus doesn’t jump, he won’t escape. For J=1, the equation returns two values, E=0 and E=1. Therefore, it also encodes two might-counterfactuals: if Dedalus jumps, he may escape, and if he jumps, he may fail to escape. Equations can also encode modal notions: J ← 0, 1 encodes that he may jump and that he may refrain from jumping.

The Dedalus model has three solutions:

σ1 00

Once you allow models to have multiple solutions, new causal concepts begin lurking at every corner. First come causal modalities: an event is causally possible if it happens on at least one solution, and it’s causally necessary if it happens on all solutions. E.g., it’s causally possible that he jumps and escapes, J=1 and E=1; it’s causally necessary that he jumps or he fails to escape, J=1 or E=0; and it’s causally impossible that he doesn’t jump but still escapes, J=0 and E=1.

Next comes underdeterministic independence, which, like every respectable independence relation, satisfies the graphoid axioms. One variable is independent from another iff every possible event over one variable is co-possible will every possible event over the other variable. For instance, J and E aren’t independent because J=0 and E=1 are possible but not co-possible. And like every respectable independence relation, underdeterministic independence facilitates inferences. E.g., if you know that Dedalus has escaped, E=1, you can infer that he has jumped, J=1.

Independence then allows you to state the Causal Markov Condition. The standard formulation states: every variable in a model is conditionally independent of its nondescendants, given its parents, where to be a variable’s parent is to figure as an argument in the variable’s structural equation. This formulation directly applies to underdeterministic causal models too, but now conditional independence refers to the underdeterministic version of the relation. All (recursive) underdeterministic causal models, it turns out, satisfy the condition.

Next, you can define type underdeterministic causation: what it means to say that one variable causes another variable (where variables denote categories of events). So, C causes E iff for some assignment of values to some of the remaining variables, switching between two values of C changes the set of causally possible values of E. In deterministic models, the definition reduces to Woodward’s (2003) theory from his Making Things Happen. I introduce all these concepts (underdeterministic models, causal modalities, …) here.

Token underdeterministic causation is much harder to define than type causation. I do it here. My definition reduces to Halpern and Pearl’s (2005), and therefore inherits their theory’s counterexamples. Very roughly: C=c causes E=e if under some suitable assignment of values to some of the remaining variables, C=c elevates the modal status of E=e from impossible to possible or from merely possible to necessary. Say, Dedalus jumps and escapes. The jump is an underdeterministic cause of the escape because the jump made possible what was otherwise impossible—Dedalus’s fleeing Crete.

The underdeterministic framework allows also for a generalized theory of underdeterministic counterfactuals. By generalized I mean here that the theory provides an interventionist semantics for both would- and might-counterfactuals; the semantics doesn’t require probabilities and allows for modeling counterfactuals with disjunctive antecedents and with other counterfactuals in consequents. The theory has a few virtues. Unlike other interventionist theories, it uses a single underdeterministic model to represent any counterfactual and works for variables with infinite domains (i.e., unlike other theories, it has no problems with, e.g., 0 < X < 8 in the antecedent, where X ranges over real numbers). I develop the theory here.

Subsequently, I used this theory of counterfactuals to engage with a problem in linguistics (von Fintel 2001) and philosophy of language (Moss 2012): how to model counterfactuals within a discourse. Notice it’s felicitous to say “if I wore glasses, I would see better; but if I wore glasses in pitch dark, I wouldn’t see better,” but not “if I wore glasses in pitch dark, I wouldn’t see better; but if I wore glasses, I would see better.” I propose a formal structure—trees of underdeterministic models—that can represent such sequences. This solution explains both classic examples from the literature and new examples, which other theories have a hard time accommodating. I put forward this dynamic theory of counterfactuals in the fourth chapter of my thesis; while substantially developed, the theory isn’t yet finished.

I also engage with another question from philosophy of language: how to interpret might-counterfactuals? Some propose that to say “Dedalus may succeed if he jumps” is to say “I don’t know that Dedalus won’t succeed if he jumps,” i.e., that all might-counterfactuals are would-counterfactuals that one can’t rule out (Stalnaker 1980, DeRose 1999). On this proposal, called the epistemic thesis, an epistemic operator (“I don’t know”) binds an individual counterfactual (“he won’t succeed if he jumps.”). I develop an alternative: the epistemic operator binds underdeterministic models, not individual counterfactuals. The proposal explains cases that support the competing theories as well as new cases that the competitors can’t handle. I also use this proposal to explain away the intuition many people have in the Morgenbesser coin case: that I would have won if I bet on a fair, genuinely nondeterministic coin landing heads if the coin in fact did land heads. I put forward this theory in the fifth chapter of my thesis; again, while substantially developed, the theory isn’t yet finished.

What’s next? Immediate future: after completing the last two extensions of the basic underdeterministic theory of counterfactuals, I’ll investigate cases from history, law, and the social and natural sciences. If the theories I propose predict the judgments made in such cases, the theories will be supported. Moreover, in cases where the predictions and the judgments disagree, it might turn out that the theories explain away the judgments, suggesting where and why mistakes where made. I also plan to test experimentally whether laypersons’ evaluations of thought experiments agree with the prediction of my theories. The first battery of experiments will just test if folk intuitions support the theories. More sophisticated follow-ups will test, for instance, reaction times; if the folk reasons faster with causal modalities rather than probabilities, it would suggest the underdeterministic concept is psychologically independent from the probabilistic one. An opposite result might in turn suggest that reasoning with underdeterministic causes is, at its core, probabilistic.

Less immediate future: because underdeterministic causal phenomena haven’t been hitherto modeled, there’s a lot of work to be done. First, notice that the underdeterministic framework provides all the necessary apparatus for an interventionist modal logic. This logic will be dynamic, where solutions to underdeterministic models behave roughly like possible worlds, and there are two kinds of accessibility relations. Two solutions are related with the first kind of relation iff they belong to the same underdeterministic model. One model is related to another with the second kind of relation if you can produce the latter mode from the former one with an intervention; these relations are indexed with interventions (whence the logic is dynamic). So, the first relation partitions all solutions into islands of mutually accessible solutions, the same way as logic S5 does; and the other family of relations lets you jump between these islands. Why work on this kind of logic beyond the sheer fun it? The logic will let us automatize causal inferences in underdeterministic settings.

Another theory that begs to be developed is an underdeterministic variant of a causal decision theory. Current variants of causal decision theory have been developed only for situations where distributions over variable values are defined. But there are situations—think bounded uncertainty—where the agent knows what possible outcomes of her decisions but the probabilistic distributions over these outcomes. A philosophically important version of this situation are Rawlsian agents behind the veil of ignorance. We don’t have a causal decision theory that specifies how one ought to behave in such situations; with the underdeterministic framework, such a theory should be fairly easy to formulate.

In 2018, I defended a dissertation in economics: Polish high-school graduates’ decision to enroll college—an analysis within the framework of identity economics (the original Polish title sounds much better) at Wrocław University of Economics. The project was funded with a grant from the National Science Centre. I haven’t gone around to it yet, but in some time I’ll post the empirical data I collected for anyone to use. Meanwhile, I’ll describe the project more.

In the last row of the classroom, a student is playing with his phone. He’s not paying attention to the lecture at all. You might think he’s just not interested in this very class, but if you follow him elsewhere, you’ll witness a similar behavior. And he’s not majoring in computer science, even though graduating in it would give him reasonably good job prospects despite a low GPA. He’s majoring in English literature, whose students you always imagined as literature enthusiasts who prefer pursuing their interests over acquiring skills that are in demand on the job market. But this student’s all interests seem to lie in his smartphone. You wonder: why does this guy even bother to enroll college?

When applied to students’ choice of major, the two main theories in the economics of education—human capital theory and signaling theory—predict that an agent will choose the major with the higher expected present value of lifetime earnings. That’s a reason, but hardly the main reason. A cross-national body of literature shows that an agent’s interests play a significant role in her choice of major (Altonji 1993, Arcidiacono 2004, Zafar 2009, Beffy, Fougère, & Maurel 2012). However—as I argue in my thesis—there’s yet another factor that influences high-school graduates’ decision to enroll college: the motivation from a social norm prescribing one to get a college degree, regardless of the major. I dub this norm the s-norm (‘s’ for study!). Were there a student motivated purely by the s-norm, he wouldn’t care what major he chose, provided the choice maximizes the probability of getting a degree. Though plausibly the motivation from the s-norm is never the only kind of motivation, it’s a live possibility that the s-norm plays a role in students’ choice of major along interests and the expected salary. My investigation shows that it is indeed so.

A working draft of the paper presenting the model and the results is here; working on this paper is currently on the back burner, however. Below, find the poster I presented at the American Economic Association meeting in 2017; its pdf version is here.

Poster for the 2017 meeting of the American Economic Association.

In 2011, I defended a master’s thesis at the University of Wrocław; it was on experimental philosophy. As it was the first thing in Polish describing studies by experimental philosophers, I put it up online. It turned out that some people have found it rather useful—I’ve seen courses that used it as a textbook (e.g., here and here). Therefore, I thought I would keep the document up. It is, obviously, super dated, and its sole value is that it might help Polish speakers who don’t feel comfortable with English. The vices notwithstanding, here it is.