Some Philosophy of Science

The Bayesian approach to the philosophy of science was developed in the first half of the twentieth century. Karl Popper and Thomas Kuhn are twentieth-century philosophers of science who later proposed alternative approaches.

It will be convenient to start with the Bayesian approach since we already talked about probability and Thomas Bayes in this post. The Bayesian approach (mainly associated with Ramsey and Savage) can be regarded as a verification-based philosophy of science; it is based on different scientists gradually updating, according to new empirical evidence, their (different) prior (subjective) probabilities of scientific explanations and theories, until the cumulative evidence is strong enough to reach a common conclusion.

One difficulty with the Bayesian approach is that in cases of disagreement, there are also disagreements on the interpretation of the evidence.

Bayesian view does not give a way to test a scientific theory but rather to update our beliefs in the theory given new evidence. In practice, scientific theories primarily explain existing observations. For example, the main motivation of Newtonian mechanics and the main support for its validity was the explanation of Kepler’s laws. Kepler’s laws concerning the elliptic orbits of planets around the sun were discovered seventy years before they were explained by Newtonian mechanics.



              Karl Popper                          Thomas Kuhn

 Popper is famous for basing philosophy of science on the notion of falsification. According to Popper, the mark of a theory as scientific is falsifiability: the possibility to empirically refute the theory – in principle. This is in contrast with other approaches that can be viewed as basing philosophy of science on confirmation or verification. Famously, two principal examples of non-scientific theories according to Popper are the Marxist theory of capital and Freudian psychoanalysis.  

If the Bayesian approach, like approaches based on verification, suggests that the optimal way for a scientific theory to proceed is by making safe conjectures which may lead to small incremental progress, Popper’s approach suggests making bold and risky conjectures. One concern about practical implication of the Popperian approach is the fact that bold conjectures and theories that pass the falsifiability test are of little value if they are absurd or simply false to begin with.

Critics assert that neither Popper’s theory nor earlier approaches based on verification give a proper description of how science is practiced. Also, they have limited normative value regarding how science ought to be practiced. It is especially difficult to use the insights from philosophy of science for scientific theories under development.

Thomas Kuhn is famous for his notions of paradigm shifts and scientific revolutions. According to Kuhn, science is normally carried out inside a certain paradigm that is shared by a community of scientists, and it is furthermore characterized by “paradigm shifts,” which occur when the current paradigm is no longer capable of explaining the new evidence.  Kuhn referred to the process of switching from the common paradigm to a new one as a “scientific revolution.” An important example of a scientific revolution analyzed by Kuhn is the shift from Newtonian mechanics to Einstein’s theory of relativity.

It may be useful to put things described here in a larger context and give a few more details.

Verification approaches towards philosophy of science: Verification- (or confirmation-) based approaches to scientific theories were developed in the first half of the twentieth century and became quite dominant in the philosophy of science until today. An important role in their development was played by the Vienna circle, a group of philosophers, who shared common basic attitudes towards philosophy, and who gathered in Vienna mainly between the two world wars.  According to most of these verification-based approaches, scientific theories are gradually examined and updated in view of new empirical evidence.

Philosophy and logic: The Vienna circle approach towards philosophy of science is part of their larger approach to philosophy centered on the rejection of metaphysics (and religion, in particular). This approach, called “logical positivism,” is related to a greater move associated with Bertrand Russell and others to base mathematics, science and philosophy on logic. Logical positivism has led not only to distinctions of “what is scientific” and “what is unscientific”, but also to an attempted classification of “what is meaningful” and “what is meaningless”. As a result, for many decades the central interest in philosophy moved away from traditional issues like “justice,” “ethics”, and “beauty” which were labeled as unscientific and even meaningless. (At a later time, attempts to distinguish “meaningless” from “unscientific” were made, and eventually the main interest in philosophy moved back to where it was before “logical positivism”.)

Critiques of early versions of confirmation approaches in the philosophy of science were made, at the beginning of the 20th century, by French philosopher Pierre Duhem and by Henri Poincaré. Duhem’s approach asserts that the main test of a scientific theory is its internal coherence and consistency. Both Duhem and Poincaré gave much weight to “intuition” and “insights.” This dispute is related to a famous debate between Poincare and Russell on the role of logic in mathematics.  

Probability: Probability plays an important role in some of the verification-based approaches to the philosophy of science. Often they rely on a logical (objective) notion of probability rather than “subjective probability” which is central to the Bayesian approach. Foundational questions regarding probability theory again come  into play. Logical probability (also referred to as “partial deduction”) is based on the idea that probability can describe a logical relation between two statements. This idea goes back to Wittgenstein, Caynes, and perhaps even to Leibniz. Rudolf Carnap, a central member of the Vienna circle, had a programme which he believed could lead to a whole logical calculus of probability starting with answer to the question: “What is the probability of a statement A given the validity of statement B?” and ending with an answer to “What is the probability that a theory X is correct?”. 

Popper deliberately diminished the role of probability in his approach to philosophy of science. A (parhaps familiar) critique of Popper was expressed by Oded Schramm who wrote (after reading an earlier version of this post): “I remember when I read Popper, I was very disappointed with his treatment of probability. It was totally unsatisfactory. (This was much before I became seriously interested in probability.) Probability statements are never falsifiable.”

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14 Responses to Some Philosophy of Science

  1. Gandolf says:

    This is an interesting post, but I would consider most of the questions addressed as pertaining to the sociology of science and not the philosophy of science.
    The latter is inherently related to a philosophical worldview or system, and as far as I understand, cannot be detached from it (e.g., Kantian philosophy induces a certain philosophy of science, and this philosophy of science is totally dependent on other questions addressed by the Kantian philosophical system).

  2. proaonuiq says:

    Interesting post and a deep comment from Gandolf. In fact the two main worldviews or cosmo-visions, science and religion originates from the same proposition: the later asserts what the former denies. Religion asserts that the supernatural exist (religions are in fact global explanations of the relations between the supernatural level of reality and the natural levels); science denies the supernatural and therefore claims that natural explanations exists.

    Philosophy of science in a more narrow sense is the theory of scientific theories. A scientific theory is ideally a potentially infinite set of inputs (systems of the same reality level) and a mathematical structure, code generator or algorithm that outputs code words or descriptions of the system´s structure and behavior or dynamics (predictions and eventually ways of control it). According to this view philosophy of science is a meta-theory: its inputs are specific theories and its outputs descriptions of these theories structure and dynamics (this is the structural approach of the philosophy of science: Sneed, Stegmuller, Moulines, Balzer…; i ignore if it still active as a research program). By reading this literature one can see how hard is to formalize (using set theory) even the simplest scientific theories. Popper and Kuhn programs were in fact very ambitious and abstract (valid for all scientific theories): Popper tried to find a general structural property wich could sieve scientific theories from not scientific theories (demarcation problem); Kuhn tried to build a meta-theory of the dynamics of scientific theories. For criticism of misleading applications of bayesan approach Bunge is a must (see for example “In chase of reality”, chapter 4). Not surprisingly he is also a pitiless critic of game theory as a social theory (afaik, not as a mathematical theory). Mainstream game theorists share this view.

    Going back to Gandolf, on the urderground of the scientifist ontologic (realism, naturalism) and epistemologic positions lies an emerging debate. All scientifists seems to agree that reality comes in four levels (physical, biological, neuromental and sociocultural), that in each level there are organized systems (wich are the way they are, or are not; by necessity) and aggregated systems (wich are the way they are by accident, either deterministic or random) and that the most we know about the organised systems of different levels of reality, the most its structure and behavior admits a mathematical description. But this general scientifist position comes in four varieties:
    –unilevel-unicode or reductionism (there is only one reality level (physical) and one possible code generator; if not wrong, this view is embraced by most physicists),
    –unilevel-multicode or relativism (there is only one reality level but several, potentially infinite codes, one for each posible world; inw this view is shared by the multiverse theories supporters),
    –multilevel-multicode or emergentism (there are several levels, each one with its own emergent properties, explained by independent and different codes; inw this is the view supported by complexity theorists “á la Santa Fe Institute”),
    –multilevel-unicode or “unicodism” ( there are several levels, but only one code wich explains for organised systems; i.e. the same mathematical structure wich explains the structure and dynamics of matter as approximated by SM and GR, explains the structure and dynamics of life as codified by DNA, explains perception as decodification etc…although the units of systems at each level changes (it could be photons in atoms as systems, atoms in cells as systems, cells in brains as systems, and brains in societies), when organized in systems its structure and dynamics follows the same code).
    I would say this last one will turn out to be the correct one.

  3. Gil Kalai says:

    Dear Gandolf and Proaonuik, many thanks for the comments.

  4. kulic says:

    I was working on a proper reply to this post but got sidetracked. So this is the incoherent, rambling, abreviated, incidental thought version:

    The essential thing about science as opposed to philosophy and art (working Deleuze&Guattari’s 3-part rubric, which I’m not totally in cahoots with, but …) is that the objects under discussion are well defined, or ‘Well-Defined’. There is ‘Rigour’. (!) This is the essential thing about science, and falsifiability and/or verifiability follow from this, so they’re merely secondary, follow-on affects; it is easy to see that you can’t refute something which isn’t well-defined. Or verify it, (whatever ‘it’ actually is; if not well-defined ‘it’ may be different things to different people)
    That was the whole Russel, Whitehead, Godel thing at the beginning of the 20th century, trying to reduce everything to logic, essentially/eventually to reduce everything to science. D&G have some fascinating things to say on this in “What is Philosophy”; though again, even to the extent that I understand what they have to say, I’m far from any kind of full endorsement, thus my disclaimer of responsibility on that…
    My main point was that the essential properties of science are rigour/definition; the field which has been characterized as constituting a discursive and internally-referential (and hopefully, at least ‘mostly’ internally consistent) system of definition. From the primitive objects you can build higher order objects, propositions. The possibility of verification/refutation follows from that.

  5. kulic says:

    “In fact the two main worldviews or cosmo-visions, science and religion originates from the same proposition: the later asserts what the former denies. Religion asserts that the supernatural exist (religions are in fact global explanations of the relations between the supernatural level of reality and the natural levels); science denies the supernatural and therefore claims that natural explanations exists.”

    I’d disagree with this conception of things, on more or less aesthetic grounds:
    First of all, why ‘worldviews’? Surely science contains and has harbored many worldviews, they don’t seem to be unified by much of a common thread, except that be in method. Maybe there is a bit of a worldview in there, in the method of definition and analytics, but it remains that there have come and gone in the natural sciences some radically different worldviews, conceptions of the universe. Inasmuch as religion could harbor worldviews, we have the same situation: ‘religion’ as such does not constitute a unified worldview, there are and have been a vast number of widely varied worldviews harbored under religious auspices. It’s tedious to argue that the essential thing about religion is that it proposes the existence of the ‘supernatural’, whereas science refutes it; some religions propose a natural order to the universe which is demanded of their dogmatic setup, including angels, demons, protoplasms, whatever; the linguistic artifact of ‘supernatural’ vs. ‘natural’ is contingent/accidental, and merely serves to highlight the conflict in assertions about the nature of the universe. In that sense, we could argue that religion (an ill-defined set of phenomena,..but do what we can) is merely a failed science; but others more persuasively argue that religion(in the West) is essentially and principally a structure of political power; furthermore, that with the decline of the Church a kind of popular-‘scientism’ and any of a variety of humanistic complexes(in conjunction with a kind of contemporary scientism) have taken over much of the socio-political power that the Church had. It’s even more difficult to describe the (socio-political) situation in the early 21st century, in a rigourous and well-defined way. I think it’s fair to say that the technical vocabulary and ontological framework has not yet been developed that can describe/model succinctly this contemporary ‘state of affairs’. Surely the ‘social-sciences’ have their work cut out for them. Will it happen? Hope so.

    “Reality comes in four levels.” No! Only our thinking makes it so. 😉 Actually I’m not disagreeing. I find this stuff fascinating and largely intractable.
    One substance, many attributes? Spinoza?
    Chomsky’s lecture “Language and Thought” dealt with some of these issues, at that time there was some need to defend linguistics against overzealous reductionism; his point was that you can (have to) scientifically study reality at varying levels of abstraction, and that the history of science showed that for the most part what is needed is not reductionism but unification. (not reduction to primary substance, but unifying frameworks for translating knowledge and results from one level of abstraction to another). A similar conversation to this “uni-codism”, which I’d not heard of before. But it does sound like something related to CAS, or complex adaptive systems (SFI), similar laws/dynamics governing complex systems at wildly divergent scales, such as economies, ecologies, immune system responses, etc..

    I do like the rubric:

    Art, Science, & Philosophy
    3 ways of dealing with chaos, each irreducible to the other. Pure philosophy in this way of thinking creates concepts to describe events on a plane of immanence, science creates functions/propositions to describe states of affairs on a plane of reference, and art creates compositions on a plane of sense. …Deleuze has quite a bit to say about the Logical Positivists and their relation to philosophy; in essence, I think Deleuze puts Russell in a position of trying to reduce all thought to the scientific mode of operation; add Godel, he failed at that. But I’m overgeneralizing…

    Thanks for the conversation and stimulation!

  6. Jr says:

    I had exactly the same reaction regarding probability when I read about Popper. It does not seem to be a very common criticism of him however, neither Wikipedia nor my textbook in the philosophy of science mentions it.

    I think also that falsificationism is a terrible desription of how a social science like history works.

  7. proaonuiq says:

    First let me correct Bunge´s book title “Chasing reality:strife over realism”.

    1. If your philosophical grounds are D&G it is likely we will never reach agreement, but i won´t discuss that one of the essential things about science is rigour. Tedious or not both scientific and religious views start from the same proposition. This proposition is an ontological option you can assert or denie but never prove (that´s a matter of faith!) and this has consequences. If you assert that a fifth level exists (the supernatural) then there are still many other options to make: this is why there are so many religions. But i agree that the scientifist worldview is clearly still under construction; this is why its inverse worldview, religion, is still valid as a worldview.

    4. Regarding unicodism (uggly name !) let me be concrete: if the code generators were mathematical structures (i.e. systems of equations, cellular automatas…)
    –reductionists would assert that everything could be explained by the same system of equations which explains the physicall level (matter): concepts such as reproduction, evolution, perceptions, intentions, sense, cultural products…can be described and explained by the dynamics of atoms; i would say that Weinberg and most TOE seekers (including string theorists) fall into this category.
    –relativists would assert that each possible world would have been generated by its own different mathematical estructure; in general multiverse theories has a reductionistic flavour, but Deutsch seems to combine both relativism with emergentism;
    –emergentists would assert that entities of each level behaves according to its own different and independent mathematical structure; if i´m not wrong CAS, SFI, Mainzer, Zuse-Fredkin-Wolfram, Schmidhuber etc…are all emergentists.
    –Unicodists (again, sorry) asserts that there are only four levels; that in each of the four levels you can find aggregated systems (such as light, minerals, climate, ecosystems) of whom you will never have a complete knowledge, and organized systems (exactly atoms, cells, brains, societies) of wich you can have exact knowledge since this 4 organized systems are generated by an unique and same mathematical structure or code generator; according to this to talk about organised systems of the 4 different levels you need new concepts. I´m interested in knowing which thinkers (of the scientifist side) have defended this position; i´m not sure about Spinoza…

    Of great interest regarding this subject is Max Tegmark´s paper
    “The Mathematical Universe” and his thesis about the Ultimate Ensemble.
    He leads the scientifist position up to its ultimate consequences

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  13. Jon Awbrey says:

    C.S. Peirce developed an alternative framework for understanding the “logic of science”, reviving a triadic scheme of abductive, deductive, and inductive reasoning that goes back to Aristotle in the light of what Peirce called the “laws of information”. Peirce’s theory of inquiry, integrated with his theory of signs, affords a very different perspective on the usual problems of induction.

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