loading . . . Philosophy of science is fascinating Interesting things happen at intersections. That’s my answer when people ask me how I find interesting problems to work on. It’s one of the things that I love about computational biology - molecular biology, disease etiology, genetics, computer science, statistics, chemistry, math, and technology all collide. But many other areas of academic research also have this unique collision of expertise and traditions, too.
A recent area of intersection that has caught my interest is the philosophy of science. Since the Enlightenment, people have noted that mathematicians and scientists do a kind of academic research that seems different from other disciplines. What differentiates these disciplines? What makes them unique compared to other historical traditions? Is there a clear demarcation line between scientific thinking and ethics or theology? When does something cross the line from science into pseudo-science?
Answers to these questions are surprisingly more complicated than you might think. They are certainly more difficult to answer than popular science media would lead you to believe. I don’t want to recite a history of the philosophy of science, here. I’m not a historian and nor am I a philosopher, so I don’t think I’d be of much help, there. What I do want to talk about is some of the philosophers I have read and how these philosophies connect to some of my experiences today.
# Falsificationism
If you’ve heard anything about the philosophy of science, you’ve probably heard of Karl Popper and his philosophy of “falsification”. The idea is that a scientific theory should be rejected if it makes predictions that do not match what is observed in nature. One of the inspiring ideas behind this philosophy was the success of Albert Einstein’s general relativity and its accurate prediction of Mercury’s orbit around the sun, especially compared to Isaac Newton’s inverse-square law of gravity. Newton’s theory made a prediction about Mercury’s orbit, which wasn’t correct, even when accounting for technical limitations of the measurement devices. Newton’s theory had been “falsified” by experimental observations.
Falsification has been a very influential philosophy. But “falsificationism” didn’t come from nowhere. Falsificationism was a response to the previous wave of philosophical thought called “positivism”. A central theme of positivism is that knowledge is solely derived from knowledge or facts - humanity’s knowledge of the world is always increasing. The Vienna Circle was a group of logical positivists in the 1920s through 1960s who attempted to make a meta-theory for science. Popper certainly knew about them and his work on “verisimilitude” (proximity to truth), “corroboration” (evidence that supports or does not refute theory), and falsificationism was a rejection of some of these ideas.
Similarly, falsification is not the be-all-end-all of philosophy of science. There were alternative philosophies at the time, like Thomas Kuhn’s The Structure of Scientific Revolutions.
# Scientific revolutions
Kuhn’s paradigmatic view discusses how different theories compete through their successes and failures. Scientists, as a group, determine what a successful theory is. Some scientists will ardently support an older theory, despite it’s inability to explain the results of new experiments. Some scientists will adventurously support a newer theory, even if it can’t explain everything the older theory can because they believe it will be able to, eventually. Others, waiting to be convinced, eventually pick one when enough people and evidence convince them. There is a period where both old and new theories are viable and proponents of each theory try to interpret results of experiments that are difficult or impossible for the other theory to explain (“commensurability”). All of this leads to quite a lot of disagreement until a single paradigm emerges victorious (the “paradigm shift”) and the field can return to its “normal science”, which means asking interesting questions and doing regular work under the prevailing theory. Kuhn didn’t invent the word “paradigm”, but it certainly became popular as a result of his work.
Kuhn’s work speaks to how scientists view theories given some logical framework to evaluate them. He doesn’t claim to have found _the_ logic that scientists use. What matters to Kuhn is that there is _a_ logic. Falsificationism _may be_ the logic scientists use, but it doesn’t have to be. Any philosophy that is understood by enough scientists in the field will do.
What also matters is that the elevation of individual researchers to influential “leading scientists” may come from a distinct logic than what is used to evaluate scientific theories. You can judge theories by one logic and leading scientists by another. Those leading scientists can go on to encourage a new philosophy for judging theories, which shapes future scientific research. Quantum theory is a good example of this. Niels Bohr held radically different views of how subatomic particles behaved from predecessors Ernst Mach and Max Planck, and from contemporaries like Einstein. Einstein may have beileved that “God does not play dice”, but Bohr’s Copenhagen interpretation of quantum mechanics has outlasted many of these criticisms, despite all the epistemological and physical issues it raises.
Importantly, who is selected as the leading group of scientists that dictate the internal logic _does not_ need to be a logical choice, itself. To paraphrase Planck, science advances one funeral at a time. Cultural influence is a valid mechanism to select a leading group of scientists. To quote someone I’m going to talk about next:
> Kuhn came up with a highly original vision of irrationally changing rational authority.
# Research programmes
Popper’s falsificationism and Kuhn’s scientific revolutions inspired many subsequent philosophies. One of the people who was inspired by these two philosophies was Imre Lakatos, the author of the above quote. Lakatos greatly admired Popper and called him one of the greats of philosophy. However, Lakatos still found falsificationism too naive and paradigm shifts too irrational. Let’s return to the example of gravity to see why falsificationism doesn’t solve everything.
Astronomers knew for hundreds of years that Newtonian gravity didn’t explain certain observations, like Mercury’s orbit around the sun. Newtonian gravity had already been falsified, almost as soon as it was proposed. And yet, it hung around. Why would scientists hold onto ideas they knew were false? According to Lakatos, there are two main reasons for this.
The first reason (called the “Lakatosian defence”) concerns running experiments in the real world. If you have an underlying theory that you think is true, you need real experiments to test them. But, as scientists know, real experiments require all kinds of engineering and planning and technology to get right. If an experiment gives you results that contradict your theory, do what anyone would do who tries to avoid responsibility - blame the tools!
It’s necessary to question the experimental setup, confounding factors in your experimental design, and all kinds of other effects you haven’t accounted for before attacking the theory. This gives you some wiggle room to play defence and protect a theory. Contradicting results don’t necessarily falsify a theory, so you need not abandon it right away, like naive falsification suggests you should. If there is a sufficient amount of contradictory evidence and you can’t blame to tools, then Lakatos’ defence has been thoroughly beaten and you need to abandon the theory. However, abandoning a theory isn’t an easy thing because that theory often produces other predictions _that are true_. How do you continue to explain those phenomena if you’re forced to abandon the best theory you have that predicts them?
That brings us to the second reason Lakatos focused on, which concerns having _any underlying theory at all_ to work with. Yes, physicists knew Newtonian gravity couldn’t explain Mercury’s orbit. But Newtonian physics was a monumental foundation to build on and you don’t just let that go easily. It wasn’t until general relativity came around to pull the rug out from _everything_ that anyone had sufficiently better theories that _still explained everything that Newtonian physics did_. In philosophical terms, general relativity had more “truth-content” than Newtonian physics, while still being “commensurate” with it. Falsificationism focuses on single theories, but like Kuhn noted in his work, scientists shift from one theory to another. Lakatos understood that it doesn’t make sense to only focus on a single theory - you need to focus on a series of theories, which he called a “research programme”.
A “research programme” can be understood as a series of theories, where all theories share some postulates that Lakatos called the “hard core”. This “hard core” is central to all tests of legitimacy, but each individual theory will vary in some way. These variations between theories in the same programme are called the “auxillary”. The auxillary can build on the hard core, but they don’t need to be certain logical derivations of the hard core. The auxillary can also include facts from other scientific fields to include instrumentation, measurement practices, the interactions between well-established phenomena and new ground being explored with the hard core. The auxillary is a bit more flexible than the hard core, and only once enough evidence has gathered with different auxillary theories can you really begin to poke at the hard core and evaluate its veracity.
Newton’s three laws of motion comprised the hard core of Newtonian theory and his law of universal gravitation was an auxillary theory that worked incredibly well to describe the orbits of objects in space. Einstein’s special relativity encapsulated Newton’s laws under the banner of an “inertial reference frame” and famously added an additional postulate that the speed of light is the same in all inertial reference frames. Through a decade of differential geometry and calculus of variations, Einstein, Hermann Minkowski, Hendrik Lorentz, and many others showed that objects don’t actually move in straight lines, like Newton thought, but along geodesics of the spacetime manifold. Physicists didn’t need auxillary theories to explain gravity, they already had it through the mechanism by which mass warps the spacetime manifold. When the objects of interest don’t have a lot of mass or they are very far apart, this manifold is approximately flat, like Euclidean space, and things behave like Newtonian theory predicts. Even then, you have to reinterpret Newton’s laws quite a bit. “Stationary objects” as a concept doesn’t mean anything if everything is relative, and “stationary” and “instantaneous” in a Newtonian sense were separate spatial and temporal concepts, respectively. Both concepts had to be reworked as part of a four-dimensional “spacetime”. Special and general relativity were as much philosophical works as they were physical ones.
There were all sorts of _ad hoc_ theories that could explain Mercury’s orbit better than Newtonian gravity did, like epicycles. But it wasn’t until the theory of general relativity that physicists could reimagine all of Newtonian physics as a special case of a different theory that had much more truth-content. Physicists, swinging from theory to theory, didn’t want to let go of the Newtonian branch until they found a sturdier one to grab onto. And this transition from theory to theory, grounded in ideas about truth-content, corroboration, and verisimilitude were the philosophical ideas Lakatos focused on.
I like “research programmes” a lot. This makes a lot of sense to me and matches my own historical understandings of physics and biology. Lakatos has other interesting writings, like Proofs and Refutations that focuses on philosophies of mathematicians.
# Philosophy as historiography
Lakatos was also a historian of math and science, and some of his posthumously-published work focuses on how conceptions of “rationality” influences historiography - the evolution of methodology in history, itself. The importance that a historian of science places on certain experiments, theories, or researchers, is influenced by both logic and culture. The logic that a historian uses to determine what theories are successful will also influence their understanding of how that theory developed and what experimental and theoretical works were important for its development. Similarly, the historian’s connection to the culture around the people and theories of interest will also colour their views of who is an influential scientist.
Take for example, all of the philosophers I have talked about so far. They are all men of European ancestry and they are all publishing these ideas in the 1950s and 1960s. Fallout from WWII, recognition of physics as both a scientific and geopolitical powerhouse, and the role of white men in patriarchal (neo-)colonial nation states were the cultures these philosophers grew up in. Popper, Kuhn, and Lakatos write about philosophies of _science_ , but they almost exclusively refer to _physics_ in their historical examples. These philosophers viewed physics as top quality science, so naturally they used physics to develop their philosophies and interpret theories and experiments in light of their ideas.
But physics isn’t the only science, and white men in neo-colonial countries aren’t the only people doing it. For example, I haven’t found a single mention of a woman cited by the above philosophers. Yes, women were far less prevalent in science at this period of history, but Marie Curie won her two Nobel Prizes 40 years prior! Ada Lovelace had completed her pioneering mathematican and programming work a century earlier, and women like Grace Hopper and Emmy Noether had already produced influential works and taking on important roles in universities. At the time, genetics was undergoing a revolution, coming to understand how cells inherited genetic information from their ancestors. Rosalind Franklin and her graduate student Raymond Gosling had recently discovered the double helix structure of DNA, countering decades of high profile work about DNA’s structure 1. Even my own examples here are of European and American women because I’m not that knowledgeable about science history, especially in other regions and cultures.
I hope you can imagine how different fields of science operate distinctly from physics and that there are various ways to approach science than solely what is drummed up in the minds of white men. Lakatos wrote more about the influence of logic on historiography than culture, but culture is a big part, too.
# Acting irrationally
Taking a very different approach to Lakatos, Paul Feyerabend looked at Kuhn’s cultural influences behind successful theories and applied that thinking to older scientific works in Against Method. Scientists are ordinary people, which means they act irrationally, too. And if you look at revered scientists like Galileo, you can make the case that everything Galileo did went against good logic!
Galileo made observations that no one else could replicate; used faulty instruments that others knew were bad; cherry-picked data to support his arguments; and was such a loud-mouth that he pissed off everyone, most notably the church who famously imprisoned him for blasphemy. And yet, his work was incredibly influential. His measurement devices with water droplets were physical manifestations of calculus and inspired accurate time-keeping; his telescopes pioneered work in optics; and his thought experiments produced Galilean frames of reference, which were instrumental for understanding Lorentz contractions and Minkowski metrics in general relativity. US astronauts on the moon famously performed one of Galileo’s experiments, dropping a feather and a hammer to show they fall at the same rate. Galileo was able to convince scientists, engineers, and mathematicians about his ideas, and they eventually won out, despite how poor the evidence was to support them at the time! Feyerabend references other examples in scientific history to make the case that “anything goes”. Convincing scientists is what matters, but you don’t have to be a pure logician to do it - popularity, colonialism, or propaganda work just fine, too.
Feyerabend was a contemporary of Lakatos’, and they were friendly with each other, despite having opposing philosophies. Lakatos describes Feyerabend like so, in The methodology of scientific research programmes:
> If a historian’s methodology provides a poor rational reconstruction, he may either misread history in such a way that it coincides with his rational reconstruction, or he will find that the history of science is highly irrational. Popper’s respect for great science made him choose the first option, while the disrespectful Feyerabend chose the second.
Here again is Lakatos’ emphasis on historiography. Feyerabend focused on different historical details than Popper did and conlcuded that scientists were, by and large, irrational.
There are more modern versions of this irrationality, especially when it comes to marginalized communities. Scientists in the global south have a hard time getting their work recognized in the global north, despite it being just as rigorous and creative while on a shoestring budget. Similarly, Indigenous peoples and ethnic minorities struggle to have their philosophies of knowledge recognized by western establishments. Robin Wall Kimmerer highlights an example of this in ecology in her 2013 book Braiding Sweetgrass. Even your everyday graduate student will have a hard time convincing their supervisor, committee members, and reviewers that certain ideas the older generation takes for granted are false because they haven’t evaluated relevant literature.
# Philosophy and statistics
The application of statistics in the sciences is another area where these tensions can arise. Although null hypothesis statistical testing (NHST) originated in the early 1900s – long before Popper’s work in the 1950s and 1960s – you can see how the language around NHST plays nicely with falsificationism. You set a null hypothesis and a significance threshold (a “demarcation line”) at which you reject your null hypothesis. You also don’t “accept” your null hypothesis if your statistical test stays below your significance threshold, you “fail to reject” it. Everything is fallible and can be discarded at a moment’s notice if the data doesn’t fit well enough. But different scientific fields use this same mathematical formalism in very different ways. Naturally, this has very different consequences!
Paul Meehl was a psychologist who approached philosophy differently than others mentioned, above, because of his experiences. Much philosophy of science has focused on math, physics, and chemistry – the so-called “hard sciences”. But there was much less philosophizing about the “soft sciences” like sociology and psychology 2. In a widely cited paper from 1967, Meehl noted that physicists tend to use the null model in the way statisticians intend. Physicists genuinely believe the null model to be accurate and experiments are designed to meet assumptions of the statistical tests they intend to use.
However, in psychology, experiments are different. There are mixture distributions, confounding effects, invalidated statistical assumptions, smaller effect sizes, confounding between subjects, and more. Most of the time, there aren’t even meaningful ways to quantify important concepts. This makes null models not very useful. Even the best null models in this scenario are routinely rejected under a NHST framework.
See how different the null model is in a hypothesis test between these two fields? Hypothesis testing in physics is much more falsificationist in practice, whereas in psychology it’s much more confirmationist. These are two very different philosophies! Naturally, this will lead to very different interpretations. It also means that statistics is at the centre of these tensions between different fields of science.
Statistics is a crucial part of any scientist’s work, today, but this was not always the case. Much monumental scientific work happened before probability theory and statistics even existed as mathematical fields! Yes, people had been gambling and thinking about “probability” in a crude sense for centuries. But Henri Lebesgue didn’t publish his work on integration until 1902 and Andrey Kolmogorov didn’t publish his axioms of probability theory until the 1930s. These are foundational works, yet people were able to do a lot of important thinking without them!
Rudolf Carnap, a logical positivist, wrote about the interpretation of probability theory in the 1950s. Importantly, he described two main perspectives for understanding what a “probability” is, and how the term confounds two ideas:
1. “Probability 1” is a philosophical concept that describes the relationship between a hypothesis and its evidence.
2. “Probability 2” is the relative frequency of an event happening within a space of events.
The reason he made this distinction is that “probability 2” concerns objects in a semantic language describing the rules and outcomes of the experiments, but “probability 1” concerns the meta-language of statements, themselves, in the philosophy of science. If you view science as a game akin to gambling, then “probability 2” focuses on the rules of a game, whereas “probability 1” focuses on strategies for all kinds of games at the casino.
You can also see how these two interpretations of “probability” map onto “Bayesian” and “frequentist” perspectives. It’s not a perfect mapping, to be clear. “Likelihood functions” and “posterior distributions” are a kind of inversion of a “data generating probability distribution” that aligns much more closely with “probability 1” than it does”probability 2”. And in frequentist NHST, we use the “probability 2” origins of test statistics and impose a “significance threshold” that sometimes functions as a “demarcation line” to assess theories, which is the realm of “probability 1”. One reason I, personally, find Bayesian statistics more relevant for scientific research is because it largely maps more cleanly to “probability 1”, which is what I care about more for scientific purposes. Both of these _philosophical_ concepts intersect _statistical_ concepts in non-trivial ways.
Another important philosophical contribution to statistics in the sciences is the _ceteris paribus_ clause. One implicit assumption that all statistical analyses of scientific data make is that repeated observations or experiments will come from the same probability distribution. You can meaningfully compare results from different experimental conditions because you, as the experimenter, have controlled for all the relevant variables and that everything else is equal between the observations. _Ceteris paribus_ literally means “all else being equal”. All kinds of chaos ensued when physicists measured the spin of subatomic particles and found that this common assumption was violated! Born’s rule is now a fundamental postulate of quantum mechanics and is crucial for making any sense of a quantum wave function.
_Ceteris paribus_ is also important in causal inference, which is a branch of statistics that connects to graph theory and machine learning. When modelling the causal relationships between variables, you try to create a causal graph that is complete enough to describe all the variables of interest, but simple enough that the graph doesn’t go on forever. To paraphrase Einstein, you want a model that is as simple as possible, but no simpler. Everything in your system should be described by everything in the causal graph, and everything outside the causal graph is irrelevant. All the excluded stuff is what’s treated as “all else being equal”. The _ceteris paribus_ clause, then, corresponds to the variables without ancestors in the causal graph! That correspondence then allows you to make sense of your observations and fit them into whatever statistical model you use that is compatible with the causal graph.
I find it fascinating that so many concepts in statistics can be viewed in such different philosophical perspectives. It’s also surprising that philosophy helps me understand statistics. Crucially, philosophical and statistical concepts don’t always map to each other in one-to-one correspondences. As noted above, both Carnap and Meehl stress how the same mathematical tools can be understand by different people in different manners, which leads to different interpretations of the same results. That relationship between objective quantities and subjective interpretation is a recurring motif in philosophical works, and is one that remains important to this day.
# Re-emergence of instrumentalism
I’m routinely surprised at how relevant these works are to my everyday scientific work 60 years or more after these articles were written. It goes to show how difficult these concepts are, even to the people who spend decades thinking about them. Imagine how muddied your thinking can be if you haven’t spent any time at all!
Meehl’s assessment is right on the mark for many biologists. Biological theories are harder to pin down than physical ones and are often limited in scope due to the tangled mess of biological systems. Naturally, predictive quantitative models aren’t terribly accurate, so fold changes and statistical analyses are preferred. Biologists, like psychologists, tend to use NHST in a confirmationist manner, even if they think they’re acting like falsificationists. High-dimensional measurements and machine learning models are changing this – but those changes rarely result in comprehensible, predictive, quantitative models rooted in biological theory.
This isn’t a surprise to me because computer scientists, in my opinion, aren’t scientists at all 3. Especially in the current wave of machine learning research, most computer scientists I see have a wildly “instrumentalist” regard for science. Who cares what the model is or how it works? Why do I even need to talk with domain experts? As long as a model makes accurate predictions, that’s all that matters. Anyway, can I sell you on my new “AI scientist” product?
Computer scientists often lack expertise in the field they’re creating computational models for, yet they’re still able to produce accurate 4 results for loosely defined concepts like social networks or language. If they haven’t interrogated why and how those predictions fail and only see paper after paper of amazing benchmarks, why wouldn’t they feel a little arrogant? They’ve taken the rationalism-empiricism debates of the 1600s and 1700s and thrown most of their weight behind empiricism, rarely understanding the centuries of philosophical debate behind their stances.
This disregard for philosophy of science 5 is a going concern of mine, as machine learning and computer scientists devour scientific disciplines. In previous decades, hypotheses were abundant but data was scarce. Now, journal articles are bloated with high-dimensional datasets and scientists are compelled to use machine learning models to interpret it all. These models are often incomprehensible and contribute less to the theoretical foundations of each discipline than what they extract. Larger models necessarily abstract away semantics into an embedding space where only machines can process what’s happening. This is a form of full-throated instrumentalism that doesn’t add to our understanding.
There’s a reason why science used to be called “natural philosophy”. If we only build simulations that mimic the natural world, then we are approaching the end of theory. In the same manner that AI corporations strip-mine art, privacy, and aquifers, unrestrained AI undermines the entire purpose of scientific research. If humans are a means by which the universe understands itself, we discard our humanity when we renounce our ability to think. We _need_ theory to make sense of anything, even if it’s incorrect. Amazing things can happen when you think outside what your mere eyes can see.
# Conclusions
Many of us practicing scientists rarely interrogate the philosophical bases of what we’re doing. We’re too busy focusing on doing what we think science is to think about the philosophical influences behind methodologies and the kinds of questions we ask. Left unexamined, these biases invade our practice. All these different philosophies discussed above are being practiced by all kinds of people all at once, knowingly and otherwise!
I hope you can see that what actually makes science _scientific_ is not straightfoward, at all. Like all things, the more you know about it the more complicated it gets. Intersections of different fields is such an abundant source of inspiration for creativity, and I, for one, just love it.
# Further reading
* _Against Method_ , Paul Feyerabend, 1993
* _Proofs and Refutations_ , Imre Lakatos, 1976
* _The methodology of scientific research programs_ , Imre Lakatos, 1978
* _The Structure of Scientific Revolutions_ , Thomas Kuhn, 1962
* _Braiding Sweetgrass_ , Robin Wall Kimmerer, 2013
* _Logical Foundations of Probability_ , Rudolf Carnap, 1950
* Paul Meehl’s 1989 course on philosophical psychology
* Dr. Fatima’s “How Galileo Broke the Scientific Method”
# Footnotes
1. To be fair to historians at the time, it would be many years before James Watson’s theft of Franklin’s work made it into common-enough knowledge that her discoveries would be valued in a historical account of molecular biology. ↩
2. Aside from derision. Popper thought that psychological theories like Freudianism and sociopolitical theories like Marxism were both anti-scientific. Lakatos, interestingly, was a Stalinist in the 1940s and it wasn’t until his interactions with Popper’s philosophical work in the 1950s and 1960s did he become disillusioned with communism. His disillusionment may have also been a result of the Soviet Union invading Lakatos’ home country of Hungary, but some of Lakatos’ posthumous notes discuss Popper’s philosophical influence on his political views. ↩
3. I like to say that “computer science” is a misnomer on both parts. It’s not a science and it’s not about computers either! It’s a branch of math concerned with computation and algorithms. ↩
4. Depending on your definition(s) of “accuracy” or other metrics you care about. ↩
5. In addition to the many _many_ environmental, human rights, privacy, legal, and artistic abuses that AI corporations and the company they keep have committed. Just ask Timnit Gerbu and Emile Torres about their TESCREAL bundle paper and some of the horrors they have encountered. ↩
https://jrhawley.ca/2026/02/03/philosophy-of-science-is-fascinating
