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A Philosophy of Science Primer

Naively one would expect science to adhere to two basic notions:
  • common sense, i.e., rationalism,
  • observation and experiments, i.e., empiricism.
Interestingly, both concepts turn out to be very problematic if applied to the question of what knowledge is and how it is acquired. In essence, they cannot be seen as a foundation for science. But first a little history of science...

Classical Antiquity

The Greek philosopher Aristotle was one of the first thinkers to introduce logic as a means of reasoning. His empirical method was driven by gaining general insights from isolated observations. He had a huge influence on the thinking within the Islamic and Jewish traditions next to shaping Western philosophy and inspiring thinking in the physical sciences.

Modern Era

Nearly two thousand years later, not much changed. Francis Bacon (the philosopher, not the painter) made modifications to Aristotle's ideas, introducing the so called scientific method where inductive reasoning plays an important role. He paves the way for a modern understanding of scientific inquiry. Approximately at the same time, Robert Boyle was instrumental in establishing experiments as the cornerstone of physical sciences.

Logical Empiricism

So far so good. By the early 20th Century the notion that science is based on experience (empiricism) and logic, and where knowledge is intersubjectively testable, has had a long history. The philosophical school of logical empiricism (or logical positivism) tries to formalise these ideas. Notable proponents were Ernst Mach, Ludwig Wittgenstein, Bertrand Russell, Rudolf Carnap, Hans Reichenbach, Otto Neurath. Some main influences were:
  • David Hume's and John Locke's empiricism: all knowledge originates from observation, nothing can exist in the mind which wasn't before in the senses,
  • Auguste Comte' and John Stuart Mills' positivism: there exists no knowledge outside of science.
In this paradigm (see Thomas Kuhn a little later) science is viewed as a building comprised of logical terms based on an empirical foundation. A theory is understood as having the following structure: observation -> empirical concepts -> formal notions -> abstract law. Basically a sequence of ever higher abstraction. This notion of unveiling laws of nature by starting with individual observations is called induction (the other way round, starting with abstract laws and ending with a tangible factual description is called deduction, see further along). And here the problems start to emerge...

The Problems With Logical Empiricism

The programme proposed by the logical empiricists, namely that science is built of logical statements resting on an empirical foundation, faces central difficulties. To summarize:
  • it turns out that it is not possible to construct pure formal concepts that solely reflect empirical facts without anticipating a theoretical framework,
  • how does one link theoretical concepts (electrons, utility functions in economics, inflational cosmology, Higgs bosons,...) to experiential notions?
  • how to distinguish science from pseudo-science?
Now this may appear a little technical and not very interesting or fundamental to people outside the field of the philosophy of science, but it gets worse:
  • inductive reasoning is invalid from a formal logical point of view!
  • causality defies standard logic!
This is big news. So, just because I have witnessed the sun going up everyday of my life (single observations), I cannot say it will go up tomorrow (general law). Observation alone does not suffice, you need a theory. But the whole idea here is that the theory should come from observation. This leads to the dead end of circular reasoning. But surely causality is undisputable? Well, apart from the problems coming from logic itself, there are extreme examples to be found in modern physics which undermine the common sense notion of a causal reality: quantum nonlocality, delayed choice experiment. But challenges often inspire people, so the story continues...

Critical Rationalism

OK, so the logical empiricists faced problems. Can't these be fixed? The critical rationalists belied so. A crucial influence came from René Descartes' and Gottfried Leibniz' rationalism: knowledge can have aspects that do not stem from experience, i.e., there is an immanent reality to the mind. The term critical refers to the fact, that insights gained by pure thought cannot be strictly justified but only critically tested with experience. Ultimate justifications lead to the so called Münchhausen trilemma, i.e., one of the following:
  • an infinite regress of justifications,
  • circular reasoning,
  • dogmatic termination of reasoning.
The most influential proponent of critical rationalism was Karl Popper. His central claims were in essence
  • use deductive reasoning instead of induction,
  • theories can never be verified, only falsified.
Although there are similarities with logical empiricism (empirical basis, science is a set of theoretical constructs), the idea is that theories are simply invented by the mind and are temporarily accepted until they can be falsified. The progression of science is hence seen as evolutionary process rather than a linear accumulation of knowledge. Sounds good, so what went wrong with this ansatz?

The Problems With Critical Rationalism

In a nutshell:
  • basic formal concepts cannot be derived from experience without induction; how can they be shown to be true?
  • deduction turns out to be just as tricky as induction,
  • what parts of a theory need to be discarded once it is falsified?
To see where deduction breaks down, a nice story by Lewis Carroll (the mathematician who wrote the Alice in Wonderland stories): What the tortoise Said to Achilles. If deduction goes down the drain as well, not much is left to ground science on notions of logic, rationality and objectivity. Which is rather unexpected of an enterprise that in itself works amazingly well employing just these concepts.

Explanations in Science

And it gets worse. Inquiries into the nature of scientific explanation reveal further problems. It is based on Carl Hempel's and Paul Oppenheim's formalisation of scientific inquiry in natural language. Two basic schemes are identified: deductive-nomological and inductive-statistical explanations. The idea is to show that what is being explained (the explanandum) is to be expected on the grounds of these two types of explanations. The first tries to explain things deductively in terms of regularities and exact laws (nomological). The second uses statistical hypotheses and explains individual observations inductively. Albeit very formal, this inquiry into scientific inquiry is very straightforward and commonsensical. Again, the programme fails:
  • can't explain singular causal events,
  • asymmetric (a change in the air pressure explains the readings on a barometer, however, the barometer doesn't explain why the air pressure changed),
  • many explanations are irrelevant,
  • as seen before, inductive and deductive logic is controversial,
  • how to employ probability theory in the explanation?
So what next? What are the consequences of these unexpected and spectacular failings of the most simplest premises one would wish science to be grounded on (logic, empiricism, causality, common sense, rationality, ...)? The discussion is ongoing and isn't expected to be resolved soon... After the unsuccessful attempts to found science on common sense notions as seen in the programs of logical empiricism and critical rationalism, people looked for new ideas and explanations.
the thinker

The Kuhnian View

Thomas Kuhn's enormously influential work on the history of science is called the Structure of Scientific Revolutions. He revised the idea that science is an incremental process accumulating more and more knowledge. Instead, he identified the following phases in the evolution of science:
  • prehistory: many schools of thought coexist and controversies are abundant,
  • history proper: one group of scientists establishes a new solution to an existing problem which opens the doors to further inquiry; a so called paradigm emerges,
  • paradigm based science: unity in the scientific community on what the fundamental questions and central methods are; generally a problem solving process within the boundaries of unchallenged rules (analogy to solving a Sudoku),
  • crisis: more and more anomalies and boundaries appear; questioning of established rules,
  • revolution: a new theory and weltbild takes over solving the anomalies and a new paradigm is born.
Another central concept is incommensurability, meaning that proponents of different paradigms cannot understand the other's point of view because they have diverging ideas and views of the world. In other words, every rule is part of a paradigm and there exist no trans-paradigmatic rules. This implies that such revolutions are not rational processes governed by insights and reason. In the words of Max Planck (the founder of quantum mechanics; from his autobiography):
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.
Kuhn gives additional blows to a commonsensical foundation of science with the help of Norwood Hanson and Willard Van Orman Quine:
  • every human observation of reality contains an a priori theoretical framework,
  • underdetermination of belief by evidence: any evidence collected for a specific claim is logically consistent with the falsity of the claim,
  • every experiment is based on auxiliary hypotheses (initial conditions, proper functioning of apparatus, experimental setup,...).
People slowly started to realize that there are serious consequences in Kuhn's ideas and the problems faced by the logical empiricists and critical rationalists in establishing a sound logical and empirical foundation of science:
  • postmodernism,
  • constructivism or the scoiology of science,
  • relativism.


Modernism describes the development of Western industrialized society since the beginning of the 19th Century. A central idea was that there exist objective true beliefs and that progression is always linear. Postmodernism replaces these notions with the belief that many different opinions and forms can coexist and all find acceptance. Core ideas are diversity, differences and intermingling. In the 1970s it is seen to enter scientific and cultural thinking. Postmodernism has taken a bad rap from scientists after the so called Sokal affair, where physicist Alan Sokal got a nonsensical paper published in the journal of postmodern cultural studies, by flattering the editors ideology with nonsense that sounds good. Postmodernims has been associated with scepticism and solipsism, next to relativism and constructivism. Notable scientists identifiable as postmodernists are Thomas Kuhn, David Bohm and many figures in the 20th century philosophy of mathematics. As well as Paul Feyerabend, an influential philosopher of science.


To quote the Nobel laureate Steven Weinberg on Kuhnian revolutions:
If the transition from one paradigm to another cannot be judged by any external standard, then perhaps it is culture rather than nature that dictates the content of scientific theories.
Constructivism excludes objectivism and rationality by postulating that beliefs are always subject to a person's cultural and theological embedding and inherent idiosyncrasies. It also goes under the label of the sociology of science. In the words of Paul Boghossian (in his book Fear of Knowledge: Against Relativism and Constructivism):
Constructivism about rational explanation: it is never possible to explain why we believe what we believe solely on the basis of our exposure to the relevant evidence; our contingent needs and interests must also be invoked.
The proponents of constructivism go further:
[...] all beliefs are on a par with one another with respect to the causes of their credibility. It is not that all beliefs are equally true or equally false, but that regardless of truth and falsity the fact of their credibility is to be seen as equally problematic.
From Barry Barnes' and David Bloor's Relativism, Rationalism and the Sociology of Knowledge. In its radical version, constructivism fully abandons objectivism:
  • Objectivity is the illusion that observations are made without an observer (from the physicist Heinz von Foerster; my translation)
  • Modern physics has conquered domains that display an ontology that cannot be coherently captured or understood by human reasoning (from the philosopher Ernst von Glasersfeld); my translation
In addition, radical constructivism proposes that perception never yields an image of reality but is always a construction of sensory input and the memory capacity of an individual. An analogy would be the submarine captain who has to rely on instruments to indirectly gain knowledge from the outside world. Radical constructivists are motivated by modern insights gained by neurobiology. Historically, Immanuel Kant can be understood as the founder of constructivism. On a side note, the bishop George Berkeley went even as far as to deny the existence of an external material reality altogether. Only ideas and thought are real.


Another consequence of the foundations of science lacking commonsensical elements and the ideas of constructivism can be seen in the notion of relativism. If rationality is a function of our contingent and pragmatic reasons, then it can be rational for a group A to believe P, while at the same time it is rational for group B to believe in negation of P. Although, as a philosophical idea, relativism goes back to the Greek Protagoras, its implications are unsettling for the Western mid: anything goes (as Paul Feyerabend characterizes his idea of scientific anarchy). If there is no objective truth, no absolute values, nothing universal, then a great many of humanity's century old concepts and beliefs are in danger. It should however also be mentioned, that relativism is prevalent in Eastern thought systems, and as an example found in many Indian religions. In a similar vein, pantheism and holism are notions which are much more compatible with Eastern thought systems than Western ones. Furthermore, John Stuart Mill's arguments for liberalism appear to also work well as arguments for relativism:
  • fallibility of people's opinions,
  • opinions that are thought to be wrong can contain partial truths,
  • accepted views, if not challenged, can lead to dogmas,
  • the significance and meaning of accepted opinions can be lost in time.
From his book On Liberty.


But could relativism be possibly true? Consider the following hints:
  • Epistemological
    • problems with perception: synaesthesia, altered states of consciousness (spontaneous, mystical experiences and drug induced),
    • psychopathology describes a frightening amount of defects in the perception of reality and ones self,
    • people suffering from psychosis or schizophrenia can experience a radically different reality,
    • free will and neuroscience,
    • synthetic happiness,
    • cognitive biases.
  • Ontological
    • nonlocal foundation of quantum reality: entanglement, delayed choice experiment,
    • illogical foundation of reality: wave-particle duality, superpositions, uncertainty, intrinsic probabilistic nature, time dilation (special relativity), observer/measurment problem in quantum theory,
    • discreteness of reality: quanta of energy and matter, constant speed of light,
    • nature of time: not present in fundamental theories of quantum gravity, symmetrical,
    • arrow of time: why was the initial state of the universe very low in entropy?
    • emergence, selforganization and structureformation.
In essence, perception doesn't necessarily say much about the world around us. Consciousness can fabricate reality. This makes it hard to be rational. Reality is a really bizarre place. Objectivity doesn't seem to play a big role. And what about the human mind? Is this at least a paradox free realm? Unfortunately not. Even what appears as a consistent and logical formal thought system, i.e., mathematics, can be plagued by fundamental problems. Kurt Gödel proved that in every consistent non-contradictory system of mathematical axioms (leading to elementary arithmetic of whole numbers), there exist statements which cannot be proven or disproved in the system. So logical axiomatic systems are incomplete. As an example Bertrand Russell encountered the following paradox: let R be the set of all sets that do not contain themselves as members. Is R an element of itself or not? If you really accede to the idea that reality and the perception of reality by the human mind are very problematic concepts, then the next puzzles are:
  • why has science been so fantastically successful at describing reality?
  • why is science producing amazing technology at breakneck speed?
  • why is our macroscopic, classical level of reality so well behaved and appears so normal although it is based on quantum weirdness?
  • are all beliefs justified given the believers biography and brain chemistry?
This was originally posted as three parts in February 2009 in my tech blog...

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