From Popper to Gödel: Your Questions Answered
Claire Berlinski, Ed. ·
Jun 16, 2011 at 3:38am
My father very much enjoyed reading the comments here in response to his earlier comments. He had a specific response for Peter Robinson, who asked whether Karl Popper's definition of scientific propositions as necessarily falsifiable struck him as valid:
He was also intrigued by the discussion of Gödel's incompleteness theorem. Paul, Midget, this one's for you:
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Nov '10
Re: From Popper to Gödel: Your Questions Answered
Claire,
Is it obvious that "All men are mortal" is unfalsifiable?
I think it is unfalsifiable, but not quite obviously so. The reason could be spelled out.
First consider "All men are immortal". This is falsifiable. Just wait long enough and see. Now, it might not be falsified by any particular time. But it could be falsified in principle.*
In contrast, "All men are mortal" isn't falsifiable. To falsify it, at least one man would have to live forever. But no one can live forever as a fait accompli. Hence, no fact could ever falsify it. Same for "All cats are mortal".
But I wonder about your Pop's extrapolation. As "All men are mortal" invokes eternity, is it seriously atypical of scientific claims in general. So, Popper's criterion of falsifiability may still hold for scientific claims in general.
Could he provide, to confound Peter and myself, a direct example of a scientific claim that is both unfalsifiable and investigatively viable?
* For simplicity, suppose God were available to falsify it, if we weren't.
Edited on Jun 16, 2011 at 5:51amRe: From Popper to Gödel: Your Questions Answered
I almost wish this "stranglehold of falsifiability" was the first of these videos.
It clarifies the nature of the overall argument.
Re: From Popper to Gödel: Your Questions Answered
And be sure to check out this post about what Leo Strauss and Eric Voegelin thought of Popper over on the member thread
May '10
Re: From Popper to Gödel: Your Questions Answered
Ray Kurzweil thinks "All men are mortal" will be falsified very shortly. Well, I guess "shortly" is a little optimistic if you require actual eternity as proof. But if it appears that we can reverse engineer the human body, then immortality is just an engineering problem.
Aug '10
Re: From Popper to Gödel: Your Questions Answered
Profuse apologies for using the word "unprovable" as a vague shorthand for stuff I didn't have space to write on the previous thread. It was abuse of terminology, and I feel suitably chastised for it.
What I meant in the earlier thread is that by studying the Incompleteness Theorems, Midge also learned some epistemological modesty. For once a small serpent learns that you can prove there are limits to (self-contained) provability in a system as simple as Peano arithmetic... well... it changes her epistemological expectations of the world.
Dr Berlinski put it much more eloquently than I ever could. Thanks.
Jan '11
Re: From Popper to Gödel: Your Questions Answered
Note to Claire: please keep these coming -- I love them.
Let’s address the question squarely. What is the relationship between reality and human knowledge? The answer plays in several threads recently.
If philosophy is so academic and impractical, why does it show up everywhere?
Apr '11
Re: From Popper to Gödel: Your Questions Answered
If such is the case , for the integers case , then what can be said of what's complex instead ? From what stems what's valued , and also what's free ?The clouds of uncertainty renders all we hold dear , for transcendent reasons , which are lost in the smear. For if uncertainty , indeed did not exist, then stagnation of our passions , would extinguish all our bliss . The quest for what's true , is a truth without doubt , yet the reason this quest does Emerge from the mist ,can't be proven , of that there's no doubt . The endeavor's in place , explained only by grace . It is true , one can argue ,that it happened by chance - But the "chance " which exist in an endless aegis , randomness for our bliss , could only transpire - - violent birth from quagmire , commencement required time and space from the fire - bridled freewill installed-pursuant to laws , which transcend us all - - -by decreed endless splendor , by whose power do render ,all that humans engender .
Oct '10
Re: From Popper to Gödel: Your Questions Answered
Wow. First, my thanks to Dr. Berlinski Sr. for addressing my comment! Thanks also (again) for "A Tour of the Calculus."
Second, to Midge: I must apologize. Typography is the wrong medium in which to convey an "Arrrrrgh!" that should sound a lot more like it came from a Monty Python sketch than from actual exasperation. :-) Heaven knows I've used the Incompleteness Theorems as a convenient shorthand myself, and you're right: epistemological humility is warranted, on my part as well as everyone else's.
Finally, Dr. Berlinski Sr. is obviously correct that the theorems are extremely important. One of the things they tell us is that not all information (in the Shannon/Kolmogorov sense) already exists, otherwise we could just turn the modus ponens crank forever to get it. [Jaynes 2003] clarifies that Cox's "theorem" tells us how to proceed upon the acquisition of new information, and this turns Cox's "theorem" into a theorem.
Aug '10
Re: From Popper to Gödel: Your Questions Answered
Let's break it down a bit:
The consensus in this thread seems to be that the hypothesis "all men are mortal" is indeed a "scientific" hypothesis. However, I have yet to read a reasonable argument why that should be true. So far in this thread, it seems to have been treated as a given.
I would tend to agree with Popper that "all men are mortal" is not a "scientific" hypothesis. I would seem to me to be a "philosophical" hypothesis.
That does not mean that the hypothesis has no value. A question does not need to be "scientific" in order to have value.
I find Popper's argument about falsifiability very useful when "scientists" (particularly a few popular theoretical physicists) make philosophical arguments but claim that they are "scientific" arguments.
Stephen Hawking's recent musings about the existence of God come foremost to mind. His theories on the existence of God are not falsifiable, yet they are treated as "scientific".
Aug '10
Re: From Popper to Gödel: Your Questions Answered
Paul Snively:
Second, to Midge: I must apologize. Typography is the wrong medium in which to convey an "Arrrrrgh!" that should sound a lot more like it came from a Monty Python sketch than from actual exasperation. :-) Heaven knows I've used the Incompleteness Theorems as a convenient shorthand myself, and you're right: epistemological humility is warranted, on my part as well as everyone else's.
Apology accepted, and more than accepted :-)
After all, you aren't telepathic (right?), so there wasn't any way for you to tell what I was thinking when I whipped out a drive-by reference to Gödel. For all you knew, I might have been claiming something asinine like "the Incompleteness Theorems prove that we can't prove whether God exists" instead of just observing that math has taught me an important life-lesson (epistemological humility).
I think being on guard for Gödel-abuse is a good thing. As it is, the poor guy's theorems already get more abuse than a cheap hooker. And I've put that book on uses and abuses into my Amazon shopping cart. Thanks.
Re: From Popper to Gödel: Your Questions Answered
Immensely grateful, Claire--immensely. I asked for "Twinkle, Twinkle, Little Star." Your father gave us this:
Jun '10
Re: From Popper to Gödel: Your Questions Answered
Misthiocracy:
I would tend to agree with Popper that "all men are mortal" is not a "scientific" hypothesis. I would seem to me to be a "philosophical" hypothesis.
That does not mean that the hypothesis has no value. A question does not need to be "scientific" in order to have value.
I find Popper's argument about falsifiability very useful when "scientists" (particularly a few popular theoretical physicists) make philosophical arguments but claim that they are "scientific" arguments.
Exactly my thoughts! Another example that comes to mind: history. History is not (by definition) repeatable, therefore it's not amenable to the methods of the empirical sciences. We cannot repeat the Battle of Gettysburg to see how it would have turned out under different initial conditions, and so conclusions of historical research can never be "scientific" in the same sense as gravity or quantum mechanics.
That doesn't mean the study of history is worthless pseudoscience, merely that it uses different methods than the natural sciences. It also means people like Karl Marx who claim to have discovered "scientific laws" of history and economics should be read with great skepticism, as Popper himself argues in "The Open Society and Its Enemies."
Mar '11
Re: From Popper to Gödel: Your Questions Answered
One of the problems that arises from these various fundamental statements is that people don't understand that they are most specific in their scope. Popper does not seek to limit the scope of inquiries nor invalidate them but merely says that you can't call them science.
I find this most annoying when people invoke, for instance, thermodynamics to support their arguments for things that have noting to do with what those laws specifically address. They are committing the logical fallacy of false analogy.
May '10
Re: From Popper to Gödel: Your Questions Answered
I can't conceive of how to design an experiment to test a non-disprovable hypothesis. If you can't subject something to scientific study, it is by definition unscientific. That's not to say it is false.
Nov '10
Re: From Popper to Gödel: Your Questions Answered
I wonder, has your dad read any of Penrose' recent series of books proposing a number ofstartling things pertaining to the science of human consciousness, and in the process ends up bucking experts in almost every major scientific field -- math, psychology, theoretical physics and biology. And yet, his work is hard to dismiss as crankery considering his stature, which I can't recite in a mere 200 words, but let us just say that Penrose is Hawkings' principal mentor and at least his equal.
I am interested in your dad's take on the starting point for Penrose' meanderings, which is a certain meta-analysis of, not Godel's theorem exactly, but an element in the proof of that theorem, in which he demonstrates that we can "see" that a certain thing is so, while that proof demonstrates that a Turing machine cannot decide this. If his analysis is correct, it proves that we are not Turing machines. Not controversial, you would think? No, this is precisely where he discovers that in order to understand consciousness it is necessary to toss out significant assumptions in contemporary physics.
Edited on Jun 17, 2011 at 1:41amNov '10
Re: From Popper to Gödel: Your Questions Answered
I have read critiques of Penrose' argument by several people with various kinds of expertise -- philosophical, mathematical, psychological and even by his friend, colleague and sparring partner Stephen Hawking. I am struck that in every case I have seen thus far the "expert" in question appears simply to misunderstand Penrose' argument. He is, anyway, quite gentle in explaining where they have gone astray in picking up the argument in The Emperor's New Mind, and deals with critics at length in the sequel, Shadows of the Mind.
A few years ago I gave a series of seminars and colloquia here on the subject that drew not only my colleagues in the math department but also physicists and psychologists -- probably the first time our venue was inadequate for the audience. While many are in doubt there is no doubt that he has the attention of significant figures in these fields. In preparing for these talks I read widely and discovered that Godel had, much earlier, come to the same conclusion as Penrose, in almost precisely the same way.
I'm just looking for insight that may help in presenting this argument clearly to both the scientifically literate and the general public.