
Imre Lakatos and the philosophy of bad science - Hooke
https://aeon.co/essays/imre-lakatos-and-the-philosophy-of-bad-science
======
rjrodger
I wrote my final year thesis on Lakatos’s book “Proofs and Refutations”[0].
It’s a short, mind-blowing book that answers the question: “Is mathematics
discovered or invented?”

You may think the abstract structures that you learn about are fixed
fundamental truths, but just read Lakatos’s account of the multi-decade
_debugging_ of the Euler characteristic for polyhedra and you will realise
that maths is both created and discovered.

How do ya like them apples for yer epistemology!

Another example would be limits vs infinitesimals - which is the “true”
foundation of calculus? [1]

Or have you ever struggled with the Axiom of Choice?

[0]:
[https://en.m.wikipedia.org/wiki/Proofs_and_Refutations](https://en.m.wikipedia.org/wiki/Proofs_and_Refutations)

[1]: And the correct answer, as all you Coventry City fans will know, is:
_trick question_

~~~
coolgeek
So, first off, Model Theory teaches us that there are an infinite number of
ways to represent calculus (or any other branch of mathematics). So there is
no 'true' way. There are only ways that we have discovered and used.

Second, I don't know anything about the debugging of the Euler characteristic,
but I suggest that the issue here is better characterized as taking decades to
discover the correct representation. Sort of like Edison finding 1000
lightbulb ideas that didn't work, before finding one that did. (Don't take
that analogy too far... I'm not suggesting that physical things are discovered
in the same way that mathematical things are discovered. (But I'm also not
suggesting that they are not.))

~~~
rjrodger
And the interesting question is, for each of those conceptions, did we call it
into being, or was it “there already” in some sense. Consider the case where
aliens on the other side of the universe got there first (we consider only
possibilities, not probabilities!).

With respect to the debugging of the Euler characteristic, one might ask what
truth value formulations _during_ those decades of debugging had, from the
perspective of those on the ground at the time. Are we so sure in our present
age that there no bugs in Andrew Wiles’s work?

Even if you use automated machine proofs (Mathematica and friends) you still
can’t be sure that stray cosmic rays don’t flip a bit every damn time.

Fun times.

~~~
coolgeek
I already spend more time than I should in considering how to prove that math
exists. So if you're talking about physical things in your first paragraph,
that's one of those things that I have to prohibit myself from contemplating
for reasons of self-preservation.

I will say, though, that acknowledging that math exists independent of its
observation makes it more difficult to argue that possible arrangements of
atoms do not exist prior to their physical manifestation.

History is, of course, replete with examples of things that we got wrong for
thousands of years - the existence of zero, the existence of negative numbers,
"real" numbers, as distinct from "imaginary" numbers. These things are now
considered trivial, and are taught to children.

I can't imagine Wiles's proof ever being understood by 1% of humanity. I hope,
and believe, that there are no catastrophic errors in it, but I wouldn't bet
more than $20 that there aren't.

------
guscost
This is one of my favorite subjects, and I love the idea of negative and
positive heuristics. On the other hand, has _anyone_ ever seen this happen?

> But, according to Lakatos, when the time comes, a revolution is driven by
> logic and method, not irrational mob psychology: ‘the Kuhnian “Gestalt-
> switch” can be performed without removing one’s Popperian spectacles’.

Even the consensus adoption of General Relativity took decades (long enough
for an entire generation of older scientists to die), and the author provides
no other examples to back up his claim that "results were mixed" in the
history of science. I'd love to hear some counterexamples.

~~~
pdonis
_> has anyone ever seen this happen?_

My take on this, largely from reading Kuhn, is that the picture of "scientific
revolutions" that philosophers have doesn't really apply to anything that has
happened in any particular field of science since that field became a science.
That's not an accident: it's because the examples the philosophers were
actually thinking of in a particular field happened before that field became a
science.

For example, when Kuhn talks about paradigm shifts in physics, what he's
actually thinking of is the shift from Aristotelian to Galilean/Newtonian
physics. That _was_ a truly revolutionary shift, but it was a different _kind_
of shift from, say, the shift from Newtonian physics to relativity, or from
classical physics to quantum physics. Steven Weinberg, in a review of Kuhn's
book published years ago in the New York Review of Books, notes that, in the
latter cases (i.e., in any transition to new paradigms in physics since
physics really became a science), the old theory lives on as a special case or
particular approximation within the new theory. Newtonian physics still gets
used extensively today, because it's a valid approximation to relativity when
gravity is weak and speeds are slow compared to the speed of light, and
classical physics still gets used extensively today because it's a valid
approximation to quantum mechanics when there are a large number of degrees of
freedom and quantum interference effects are negligible.

By contrast, nobody does Aristotelian physics today, nor has anybody done it
since Newtonian physics took over. Aristotelian physics is not a special case
or an approximation to any physical theory we have today; it's a totally
different theory of physics that simply is not useful any more, because we've
found a much better and more accurate way of modeling the world. So comparing
Aristotelian to modern physics is much, much _more_ of a "gestalt switch" or
"paradigm shift" than trying to compare Newtonian physics with relativity, or
classical physics with quantum physics. And that kind of shift is what Kuhn
was actually describing.

Lakatos seems to recognize that there are limitations to Kuhn's approach, but
I don't think he really grasps the degree to which all modern science is one
thing, and all fits together, and the sort of "revolution" that took us from
Aristotelian to modern physics simply doesn't happen once a field becomes a
science.

~~~
guscost
Modern science is absolutely not a single paradigm. QM has been in conflict
with GR since its invention. Lambda-CDM is in conflict with MOND and other
cosmological paradigms. String theory is a paradigm. And that's _just_ talking
about theoretical physics. I appreciate your argument, and yes if there have
been no paradigm shifts in the past few centuries that would neatly resolve
the problem. But I can't possibly agree, and regardless I would still love to
find a counterexample where something which _anyone_ considers a paradigm
shift happened in a non-political manner.

For a great example outside of physics, I can't imagine how anyone could read
the story of plate tectonics and not understand it to be exactly what Kuhn was
talking about:
[https://en.wikipedia.org/wiki/Plate_tectonics#Development_of...](https://en.wikipedia.org/wiki/Plate_tectonics#Development_of_the_theory)

~~~
pdonis
_> Modern science is absolutely not a single paradigm._

I think you're confusing "paradigm" with "model". See below.

 _> QM has been in conflict with GR since its invention._

"Conflict" in the sense that neither one can possibly be a final fundamental
theory, yes.

But whatever final fundamental theory we come up with is going to have our
current QM and our current GR as special cases/approximations in the relevant
regimes. In terms of any such final fundamental theory, current QM and current
GR would simply be particular models built for particular applications.

So current QM and current GR are not different or conflicting "paradigms" in
the sense that Aristotelian and Newtonian physics are. They're just our best
current models.

 _> Lambda-CDM is in conflict with MOND and other cosmological paradigms._

These aren't paradigms, they're models. Both of them accept the same
underlying framework for model building. They just make different claims about
which models are more accurate.

 _> String theory is a paradigm._

String theorists like to make it seem that way, but it's really not any
different from any other quantum field theory in the fundamentals. It's just
QFT using strings instead of point particles. The original justification for
it as a fundamental theory candidate was that gravity just pops out (since the
simplest closed string mode looks like a massless spin-2 particle at low
energies, and that's the graviton), so it seemed to be an easy way to get a
quantum theory of gravity that would reduce to GR in the classical limit. (I
think it's fair to say that the jury is still out on whether this promise has
been realized.)

~~~
guscost
How do you get rid of renormalization? Are those not incompatible paradigms to
the best of our knowledge?

About string theory, "really not any different" and "strings instead of point
particles" don't seem compatible. I agree that it is largely an attempt to
explain the fine-tuning in the Standard Model, not to overthrow it. But it is
in conflict with other paradigms that attempt to "complete" the Standard Model
in other ways.

~~~
pdonis
_> How do you get rid of renormalization?_

First, why do you need to?

Second, renormalization only has to be done at all in perturbation theory, and
perturbation theory is just an approximation anyway. There is plenty of work
done in non-perturbative QFT, in which renormalization doesn't even arise at
all.

 _> Are those not incompatible paradigms to the best of our knowledge?_

I'm not sure what you mean. Different approximations to the same underlying
theory don't _have_ to be compatible unless their domains of validity overlap,
and even then the only compatibility they have to have is that they have to
make predictions that are consistent with each other.

More generally, s/approximations/models/ in the above, since approximations
are one kind of model.

 _> "really not any different" and "strings instead of point particles" don't
seem compatible_

Why not? There's nothing about the fundamentals of QFT that says it can only
apply to point particles, or that applying it to point particles and applying
it to strings are inconsistent. They're different models.

 _> it is in conflict with other paradigms that attempt to "complete" the
Standard Model in other ways._

To the extent that the different attempts at a fundamental theory are
inconsistent with each other (e.g., string theory vs. loop quantum gravity,
which AFAICT are not consistent with each other), yes, I suppose they could be
considered different paradigms. But there will never be a transition from one
of them to the other. The most that could happen is that we transition from
our current theories as the best we have, to our current theories being
approximations to whichever more fundamental theory wins out. (Or it's
possible that none of the current candidates will win out.)

~~~
guscost
> why do you need to [get rid of renormalization]?

What does renormalization actually represent? Why does nature do that? Those
rules seem kinda tacked-on after the fact, to me...

> There's nothing about the fundamentals of QFT that says it can only apply to
> point particles

String Theory does not present a serious challenge to QFT or the Standard
Model _yet_ , but it is a _massive_ set of additional ideas that are
completely unnecessary for either one, and it is a paradigm in vigorous
conflict with all of the other proposed completions to the Standard Model
right now. If any of these completions ever wins conclusively, it will also
"win" against the Standard Model, in the sense that the Standard Model will
turn out to be a higher-level approximation of some truer lower-level theory,
one which will _never_ explain any of its fine-tuning, and therefore one which
will fail.

It's very similar to GR vs. Newtonian Dynamics, and I would argue that
Newtonian Dynamics _is_ in fact a failed paradigm, and it _has_ been replaced
by a better paradigm, no matter how useful it may remain.

~~~
pdonis
_> What does renormalization actually represent? Why does nature do that?_

We don't know whether nature "does that"; renormalization is a feature of our
models of nature, but not all features of our models of nature are features of
nature itself. That's true of any model.

 _> I would argue that Newtonian Dynamics is in fact a failed paradigm_

You can argue that by defining "failed paradigm" in your preferred way, but
you cannot argue that it is a failed paradigm in the sense that Aristotelian
physics is a failed paradigm. So by using the term "failed paradigm" to
describe both, you are ignoring a very important difference between the two.

Similar remarks would apply to the Standard Model in the scenario where one of
our candidates for a more fundamental theory has been confirmed and the SM is
now just an approximation to that theory in an appropriate regime.

~~~
guscost
> not all features of our models of nature are features of nature itself.

Bingo! Therefore our models are each wrong in some way. Paradigm shifts happen
when a new model (theory, paradigm, etc) that is "less wrong" conquers an
older _incompatible_ model that is "more wrong". That incompatibility is the
defining characteristic, not the usefulness or the scope of the model. Of
course I consider Newtonian Dynamics to be incompatible with GR, one uses a
single frame of reference and the other uses infinite frames of reference.

~~~
pdonis
_> our models are each wrong in some way_

Yes.

 _> Paradigm shifts happen when a new model (theory, paradigm, etc) that is
"less wrong" conquers an older incompatible model that is "more wrong"._

If you had left out the word "incompatible", I would have agreed with this as
a description of what happens as science progresses, though I would still not
like the term "paradigm shift" as a term for it.

But you included "incompatible", and that makes a huge difference. By your
definition, for example, no paradigm shift has happened in physics since
Newtonian physics replaced Aristotelian physics, because "incompatible"
requires that the old model _not_ be usable as an approximation or special
case of the new model. I realize you don't mean "incompatible" to mean that,
since you say:

 _> Of course I consider Newtonian Dynamics to be incompatible with GR_

And I disagree with that, for the reason I gave above (and have stated several
times elsewhere in this discussion). The reason I consider that factor so
important is the same reason Weinberg, in his review of Kuhn's book, took Kuhn
to task for ignoring it: that ignoring it means ignoring how _progress_ is
made in science: by coming up with new models that _still take advantage of
all the true things we learned from the old model_. As Weinberg says, if you
have one of those T-shirts with Maxwell's Equations on it, you may have to
worry about it going out of style, but not about its becoming false. But
Maxwell's Equations are "wrong" and "incompatible" by your definition, since
they're classical, not quantum, and classical electrodynamics is now replaced
by quantum electrodynamics.

So your definition basically agrees with Kuhn that no progress is ever made in
science; all we can do is lurch from one paradigm to another, each
incompatible with the last and throwing away all the knowledge we gained from
the last. And in the transition from Aristotelian physics to Newtonian
physics, that _is_ what happened. Whatever true things Aristotelian physics
had taught people, nobody has been taught since we got rid of it. The same is
_not_ true of Newtonian physics. And it will not be true of GR, QFT, or the
Standard Model in some future time when we have found a new fundamental theory
to which those are all approximations.

------
pfdietz
I've wondered if this same approach can be taken to technology projects,
rather than pure science. We can see examples of long term efforts that
degenerate in a way very similar to what happens to a degenerating scientific
program.

~~~
guscost
You're gonna _love_ incompleteness if you can grok it:
[https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theor...](https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems)

~~~
dwohnitmok
At risk of being a bit uncharitable here, I think you may be overstretching
the implications of the incompleteness theorems here.

FWIW I think the usual presentations of the incompleteness theorems that talk
about truth may it sound much more mysterious than it is (and lead people
without a grounding in model theory very far astray). In fact I don't like to
really talk to about truth or really even too much about proof since again
they often lead people astray.

Here's the informal-ish presentation I prefer:

First incompleteness theorem: Given a formal system of axioms expressive
enough to do arithmetic, there will always be theorems which are independent
of these axioms, i.e. adding that theorem or its negation as a new axiom are
both consistent with the other axioms (but of course not adding both at the
same time).

Second incompleteness theorem: Assuming that system of axioms is itself
consistent, one of those aforementioned independent theorems will always be
the theorem "all previous axioms listed are consistent with each other."

Side note: a closer inspection of the second incompleteness theorem is perhaps
slightly mind-bending. Note that we're talking _independent_ here! That is the
theorem "the previous axioms are inconsistent with each other" is also a valid
axiom to add and results in a system of axioms that is consistent overall!

~~~
danharaj
You can easily adapt the incompleteness theorem to empirical science: take its
computational analogue, undecidability. There is no scientific method that can
answer whether a computer emulating a turing machine, a physical phenomenon,
will end with the computer accepting. If the fact that turing machines are
infinite bothers you, then just restrict to some plausible but large amount of
memory. It's still out of reach of science. We don't have to do much, we just
have to show that there is a well posed physical question that no human
scientific method could answer.

But we go further than that, because incompleteness and its many guises say
more: not only are there questions you can't reasonably answer, _you can 't
separate the unreasonable questions from the reasonable ones_. This applies to
all science.

So, all science which attempts to answer questions either is surefooted and
facile or sophisticated and destined to make "mistakes" of pursuing questions
that it won't be able to answer. But then what exactly counts as a "good"
mistake which advances science and a "bad" one which is pseudoscience?

~~~
dwohnitmok
There are two aspects I disagree with here.

The first is formal relevancy. These questions only make sense if we already
assume we have a theory of everything. We know we don't. From a formal
perspective the totality of the formal theories behind modern science are
inconsistent. So results like Godel's incompleteness theorems don't apply
formally.

Okay, but what if we do get a theory of everything? What happens if a string
theorist comes out and says they've solved it? Well let's examine the Game of
Life, where we do have its theory of everything (the game rules) and it
happens to be undecidable. In particular, given an initial configuration, a
pixel X might be eventually shaded in if and only if ZFC is inconsistent.

Let's assume the game is playing in a screen. So is an investigation into
whether pixel X on the screen will be shaded scientific?

This brings me to my second point. Popper would probably say yes. This is a
classic example of the problem of induction that is falsifiable. Kuhn would
probably say he needs more information about how the study is going to be
carried out and the underlying metatheory of the researchers. Lakatos probably
would say something similar to Kuhn in this case.

Yet I have a hard time believing any of these people would be hung up on the
decidability part of the problem. As an empirical phenomenon whether pixel X
on the screen will be shaded seems little different from whether a bowling
ball on a plank will start spontaneously levitating. It probably won't, but oh
boy will it be interesting if it does! And crucially in both cases I think,
given the right setup, most everyone could agree that staring at the pixel or
staring at the bowling ball for a long long time constitutes a scientific
experiment, albeit a boring one.

Perhaps the objection might be raised that these are different. We don't have
a theory of everything behind the bowling ball, but we do have a theory of
everything behind that pixel.

Well if your theory is fundamental enough to completely obviate the need for
empirical experimentation, I don't think many people would agree the
subsequent logical work would qualify as science.

To put it another way decidability and incompleteness are not very helpful
sociological explanations of science.

There's nothing stopping someone from saying that the definition of science is
intrinsically tied to decidability. After all people can make whatever
definitions they want.

But it doesn't seem useful to me, because it doesn't explain what it is that
people who call themselves scientists applaud and what they frown on. That is
it's not a very useful descriptivist framework. That is whether a question is
decidable or not does not seem to be the criteria of whether a question is
reasonable or not.

Indeed let's not talk about hypotheticals.

What do scientists who are familiar with the incompleteness theorems have to
say? Well Hawking talks about it: [http://www.hawking.org.uk/godel-and-the-
end-of-physics.html](http://www.hawking.org.uk/godel-and-the-end-of-
physics.html) but doesn't use it to split the scientific from the
unscientific. In fact he seems to derive joy from the incompleteness theorems.

Indeed I have a hard time finding people who view logical completeness or
decidability as the differentiating factor between pseudoscience and science
as ways of thinking and acting, rather than as potential limiting results on
what the theory of everything would look like.

~~~
danharaj
I think we're speaking past each other. What I'm trying to argue is that
before we even talk about a scientific experiment, we have to ask "Is this
question scientifically well posed?" and that this question is unbelievably
complex, to the point that you can't answer it ahead of time, so scientific
activity will necessarily pursue questions it can't answer. And either it will
give up on questions that are well posed but take an enormous amount of time
to answer, or it will pursue forever questions that it can never answer
because they don't even really make sense.

I'm not going to try to elaborate on what the consequences of that would be
for any given theory of science, I just want to show that whatever the
difference is between science and pseudoscience, in the small scale they can
look quite the same.

Tangentially, the incompleteness theorems are not scientific knowledge
according to Popper. They are metamathematical propositions that suppose the
consistency of mathematics as one of their hypotheses. If they could be
falsified, we would have discovered an inconsistency in mathematics, and so we
have nevertheless validated the theorems. You literally can't falsify them.

------
everybodyknows
Misposted: Title of the Aeon article is "How science fails". Which makes more
sense than "... the philosophy of bad science" \-- since how can bad science
be said to possess any philosophy at all?

~~~
jfengel
Philosophers consider the problem of distinguishing good science from bad to
be not solved. That's what the article is about.

For more, see
[https://en.m.wikipedia.org/wiki/Demarcation_problem](https://en.m.wikipedia.org/wiki/Demarcation_problem)

------
knolax
> The average scientist’s acquaintance with philosophy tends to be of the
> passing variety. This is a great pity.

This is not a "deep pity" but proof that modern society has progressed beyond
the sophistry of the humanities.

~~~
DapperZoom
A knowledge of the historic and philosophical background gives that kind of
independence from prejudices of his generation from which most scientists are
suffering.

\-- Albert Einstein

~~~
knolax
The fact that a random unbacked claim in the form of a quote is the top reply
proves my point. The best argument the humanities mode of thinking can come up
with is an appeal to authority.

