Kuhn vs. Popper by Steve Fuller, Part 2

Part 2? Take Two, rather (This is Take One). It surprises me how difficult it is to get to grips with this book, particularly given its apparent brevity (the main body of the book runs through page 215 in a relative small format). Of course, I’m not even an amateur philosopher of science, but still.

A part of the difficult lies in the chaotic or at least hidden structure of the book. Fuller announces his motives in the introduction (‘to recapture the full range of issues that separate [Kuhn and Popper],’ see p. 3*). The ‘full range’ is presumably a lot of material; the already mentioned brevity is thus surprising. But Fuller do not list nor declear the ‘issues’ he wants to address. There seem to be no plan or structure. Rather, he seems to move from issue to issue in a haphazard fasion, and the motive or aim of the discussion is often out of sight and elusive. The conclusion of the book is also something of an anti-climax. The last chapter seemingly only discusses one of the issues separating Kuhn and Popper; there are no final remarks, no conclusion, or anything that resembles a closure.

Kuhn vs. Popper did increase my understanding and knowledge of the ideas of both Kuhn and Popper, and also how their ideas connect to the ideas of other important thinkers. Perhaps more importantly, Fuller has helped me see the important differences between Kuhn and Popper. Throughout the book, for one thing, Fuller comes up with comparative statements.

Kuhn and Popper represent two radically different ways of specifying the ends of inquiry: What drives our understanding of reality? Where is the truth to be found? [p. 56].

Kuhn was indeed authoritarian and Popper liertarian in their attitudes to science. This point has been largely lost, if not inverted, by those who regard ‘Kuhn vs Popper’ as a landmark in 20th-century philosophy of science [p. 13]

Popper was a democrat concerned with science as a form of dynamic inquiry and Kuhn an élitist focused on science as a stabilising social practice. Nevertheless, they normally appear with these qualities in reverese. How can this be? [p. 68].

To dig deeper into these differences, one has to dig into the actual ideas. Kuhn first:

For Kuhn, science begins in earnest with the adoption of a ‘paradigm’, which means both an exemplary piece of research and the blueprint it provides for future research [...] Kuhn deliberately selects the phrase ‘puzzle-solving’ (as in crossword puzzles) over ‘problem-solving’ to underscore the constrained nature of normal science [...] A ‘revolution’ occurs [upon a 'crisis'] when a viable alternative paradigm has been found. The revolution is relatively quick and irreversible. In practice, this means that an intergenerational shift occurs [pp. 19-20].

An important aspect of Kuhn’s philosophy of science is how history is rewritten after a scientific revolution, such that the scientific development appears streamlined and meaningful. In Kuhn’s view, Fuller writes,

[...] the secret of science’s success – its principled pursuit of paradigmatic puzzles – would be underminded if scientists had the professional historian’s demythologised sense of their history. After all, in the great scheme of things, most actual scientific work turns out to be inconsequential or indeterminately consequential [p. 20].

Another important feature of Kuhn’s ideas regards how people become scientists. One becomes a scientist through a “conversion experience or ‘Gestalt switch,’ whereby one comes to see the world in a systematically different way” (p. 21).  These features, combined with the conservative flavor of Kuhn’s The Structure of Scientific Revolutions, led Popperians to liken Kuhn to ‘religious and politcal indoctrinators’ (p. 21).

But of course, this was not how Structure was read by most of its admirers – if they actually did read the book. For while Kuhn’s examples are drawn almost exclusively from the physical sciences, these are the disciplines that have probably paid the ‘least’ attention to Structure, even though Kuhn himself was qualified only in physics. Kuhn’s admirers are to be found instead in the humanities and the social and biological sciences [p. 21].

Kuhn’s admirers persisted in wrenching Structure from its original context and treating it as an all-purpose manual for converting one’s lowly discipline into a full-fledged science. These wishful readings of Structure have been helped by its readers’ innocence of any alternative accounts of the history of science – often including their own – with which to compare Kuhn’s [p. 22].

When Fuller turns to discuss Popper, his sympathies with Popper become obvious:

[Popper] was always a ‘philosopher’ in the grand sense, for whom science happened to be an apt vehicle for articulating his general world-view [pp. 22-23].

For the ‘grand philosopher,’ philosophy of science is only a reflection of more fundamental attitudes:

Once Popper’s philosophy of science is read alongside his political philosophy, it becomes clear that scientific inquiry and democratic politics are meant to be alternative expressions of what Popper called ‘the open society’ [p. 26].

Popper grew up intellectually among the positivists in the Vienna Circle, but disagreed with them on their attitude towards the role of logical deduction.

For the positivists, deduciton demonstrates the coherence of a body of thought, specifically by showing how more general knowledge claims explain less general ones, each of which provide some degree of confirmation for the more general ones. For Popperians, deduction is mainly a tool for compelling scientists to thest th econesequences fo their general knowledge claims in particular cases by issuing predictions that can be contradicted by the findings of empirical research. This is the falsifiability principle in a nutshell [p. 25].

Fuller neatly sums up the difference between the 20th century’s giants in the philosophy of science:

Whereas actual scientific communities existed for Popper only as more or less corrupt versions of the scientific ideal, for Kuhn the scientific ideal is whatever has historically emerged as the dominant scientific communities [p. 6].

* Page numbers refer to the Icon Books 2006 paperback edition.

Related post:

• Kuhn vs. Popper by Steve Fuller, Part 1
• Dense Philosophy of Science: A Necessity?

Kuhn vs. Popper by Steve Fuller, Part 1

In Kuhn vs. Popper, Steve Fuller discusses and compares the two most important philosophers of science in the 20th century; Thomas Kuhn and Karl Popper. The book is not what I expected it to be (what I expected is not entirely clear, but that is not the point). The book as a broader view than I expected, for example, revisiting philosophers from Plato to contemporary and, to me, new names like Rorty, and shuffles over themes from theology to nazism. The broad view is indeed intentional and announced in the introduction:

This book is designed to recapture the full range of issues that separate these two self-styled defenders of science [Kuhn and Popper, of course].  Many of the issues plumb the depths of the Western psyche: What is the relationship beteween knowledge and power? Can science bring unity to knowledge? Can history bring meaning to life? At the same time, these issues are entangled in more secular concerns about economy and society, politics and war  most of which are still very much with us today [p. 3].*

While I cannot say I found every twist of the book equally interesting, it did help me understand the the ideas of Kuhn and Popper better than before and even correct things I got wrong. For one thing, I used to think of Popper as the normative and Kuhn as the descriptive; Fuller claims I was wrong:

It was not, as is often said, that Kuhn was more ‘descriptive’ and his rivals [the Popperians] more ‘prescriptive’ with respect to the history of science [p. 208].

Thomas Kuhn (1922 - 1996)

According to Fuller, the Popperians appeared ‘perversly contrarian’ to the public when they imposed a normative perspective on the history of science; to the public, science’s authority was self-evicent. Kuhn, on the other hand, ‘never articulated the norm’ he imposed when he selected and arranged the historical examples he used in his arguing (p. 209). In other words, one needs a rather good idea of the history of science in order to see and understand that Kuhn presents only the examples that fits with his theory; according to Fuller, hsitory is abound with examples less in accordance with Kuhn’s theory.

A thing I do not like about the book is that it is densely written, and in order to follow it, one need to at least be acquainted with the theories of Kuhn and Popper up front; Fuller only briefly summarizes the ideas. I find this surprising, as the cover is littered with acclaim from newspapers like the Economist and the Financial Times with the obvious purpose to attract the general reader. According to Fuller, this involved writing, presupposing knowledge of the issue at hand was a trademark of Popper, and, I’m afraid, many philosophers:

Popper and Adorno [another philosopher Popper locked horns with] shared the critic’s tendency [not entirely clear to me what 'the critic's tendency' is supposed to point to here] to presuppose that the audience already knows the target of criticism in some detail, so that one’s own discourse becomes a series of reflections on the hidden opponent. This feature made it frustrating for listeners who sought  constructive advice on the conduct of social research [p. 154].

Frustrating indeed, do you listen, Fuller? (I guess not.)

Now, while flipping through the book, I realize I’ve underlined too many quotable passages and marked too many passages to address them all in one post. I will thus try to focus my opinion of this book in a later post; stay tuned.

* To be sure, page numbers refer to the Icon Books 2006 paperback edition.

Related post:

• Dense Philosophy of Science: A Necessity?

Dense Philosophy of Science: A Necessity?

What we call the ‘modern’, and distinctly Western, sensibility emerged as people tried to organise the conduct of the sciences in light of second-order condsiderations of what might be common to all the sciences. The result was a Galilean zeal for spotting latent contradictions between bodies of knowledge, the pretext for eliminating the social, lingusitic and practical barriers to their proper integration into one system of thought. Popper promoted a version of this strategy in his attack on the ‘myth of the framework’, the Kuhnian idea that the presence of incommensuarable theories rendered any explicit normative comparison so difficult that one simply had to wait for history to take its course, as individuals come to adopt one or another theory for their own reasons. In contrast, Popper argued that if the incommensurable theories are truly scientific, they aspire to universality, which means that there will be cases that they have yet to explain or predict. These cases may then serve as relatively neutral ground for designing a crucial experiment to decide amonst the theories.*

I’m reading Steve Fuller’s truly interesting account of ‘The Struggle for the Soul of Science,’ the legendary debate between Kuhn and Popper. Although I enjoy the book, I cannot help but marvel at the dense style Fuller, and many in his field, pledge to. I wrote an essay once, on what I’ve late learned is known as the underdetermination hypothesis (data can be explained by any number of mutually incompatible theories, see, f.eks. pp. 61-62 in Kuhn vs. Popper). I wrote rather dense myself, I seem to remember (I’ll post an example if I can dig it up). I wonder if a complicated style is necessary to philosophy of science, if it is impossible to iron it out more, if it’s somehow inherent to the subject. Philosophy of science is, in a weird way, depending on itself for its own existence. (See; I came up with something rather dense just writing about how dense it is!)

* Steve Fuller (2003), Kuhn vs. Popper, pp. 66-67, Icon Books 2006 edition.

Reason and Rationality by Jon Elster

A while ago, I read the little book Reason and Rationality (2009) by Jon Elster. Jon Elster is a Norwegian philosopher and social scientist. He has also  authored more than thirty books. A recent and relevant one is Explaining Social Behavior (2007); an older and perhaps less relevant one is Making Sense of Marx (1985).

In Reason and Rationality, Elster ‘proposes a unified conceptual framework for the study of behavior.’ Further, Elster provides ‘a brief, elegant, and accessible introduction to his work’ (both quotes from the back-cover). The latter first; to someone not familiar with Elster’s writings, nor with the writings of moralists and philosophers in general, I do not find Reason and Rationality particularly elegant nor accessible apart from its brevity. Perhaps his language and choice of words are elegant, but his way of arguing and demonstration does not communicate well with me. And perhaps my poor ability to perceive Elster is why Elster’s ‘unified conceptual framework’ eludes me. However, it is necessary to be aware (which I was not) that Reason and Rationality was originally Elster’s inaugural lecture at Collège de France. ‘Given formally in the presence of his colleagues and a large audience, this lecture provides him with an opportunity to situate his work and his teaching in relation to that of his predecessors and to the most recent developments in research’ (pp. 78-79). In other words, Elster’s language and choice of words did have additional tasks to proposing a ‘unified conceptual framework’ (whatever that means, anyway). With that in mind, I find his concluding paragraph less cryptic:

What, finally, are the functions of reason and rationailty in human behaviours? They are the functions, respectively,of the prince’s tutor and his councilor. The tutor teaches the prince to promote the public good in the long term. The councilor tells him how to act in order to achieve his goals, whatever they might be, in the most efficient way. It is not incumbent upon the councilor to impose the demands of reason; but if the tutor has done his job well, the prince will make them his own (p. 68).

It is somewhat unclear to me what the unifying framework consist of, other than that Elster thinks reason (the actual, human, internal reason for an action) and rationality (an analytical concept which demands a system of preferences weigthed against each other) are deeply connected; I cannot disagree. What strikes me as interesting (and perhaps a bit disappointing), is Elster’s extended argumentation through examples. An argument with examples at its core leaves me dissatisfied, although, perhaps, everything is, deep down, nothing but examples. Anyway, I found one of his examples interesting; the voter’s paradox:

Is it true, is it coherent, to say that the common good can be realized only through the pursuit of private goods? Is it true that the more rational actors are, the better reason’s demands are met? Or must we see, inversly, the rationality of individuals as an obstacle to reason? Take, for example, the “voter’s paradox,” which results from the fact that the rational actor has no reason to vote. In fact, the chance of having an influence on the outcome of the election is clearly less than the risk of dying in a traffic accident on the way to the polls. Moreover, those who are in the best position to understand the logic of this line of reasoning-in particular, professional economists-choose the cooperative strategy less often in the “prisoner’s dilemma,” of which voting is a classical example (pp. 6 – 7, footnotes with references are omitted).

Although a bit hard to follow, Reason and Rationality is an interesting book. Among other things, he touches upon hyperbolic discounting, a concept I myself find very interesting. Elster also seems to be a likeable guy. According to this article, (in Norwegian), he cannot small talk, he thinks social scientists must have lesser ambitions than their current ‘grand theories,’ and he has some interesting views on how research is managed and funded in Norway today. Anyway, read Reason and Rationality! It will leave you curious!

Philosophy of Taekwon Do Fundamentals

The five fundamental principles or tenets of (ITF) Taekwon Do are courtesy, integrity, perseverance, self-control, and indomitable (unconquerable) spirit. Once, a 3. Dan (third level black belt) asked me which of the principles was the most important. After some contemplation, I realized self-control embodies the other four principles and concluded that self-control is the most important fundamental principle of Taekwon Do.

After further contemplation, however, I realized that my conclusion depends on an unsettling premise; it requires that self-control is necessary to be courtly; that self-control is necessary to maintain integrity, and so on. In other words, that self-control is the most important principle implies that humans are inherently impolite, corrupt, lazy, and have a weak  spirit; self-control is needed to control the in-built human features.

The premise that humans are inherently impolite, corrupt, lazy, and spiritless is not necessarily wrong, but certainly implies a negative view of things. If, instead, the premise was that humans are polite, honest, persevere, and spirited, as part of a more positive view, self-control would not be required, it would not embody all other principles, and the five principles would be of equal value.

Economics: A Science or Not?

I came across this truly interesting book, Truth Versus Precision in Economics (1993) by Thomas Mayer. I’m still only on p. 16, but endnote 1 in chapter one provided fodder for my thinking about economics and science:

I see no purpose in discussing whether economics actually is a science. Philosophers have not succeeded in finding a criterion that distinguishes science from non-science [...], and the question whether a field is an empirical science may even lack clear meansing [...]. Fortunately, nothing hinges on whether one calls economics a science or not, and the question can be left to lexicographers. Knowing whether economics is a science would not allow us to decide whether  it should use the same methods as the natural sciences, since not all sciences necessarily us the same methods. What methods economics should use can be decided better by looking at specific methods and specific problems than by talking in general about ‘scientific method’. Similarly, knowing whether economics is a science would not allow us to say whether it provides answers that deserve a high degree of credence. The science of weather forecasting does not, while the non-science of history does [p. 8, paperback edition].

I agree that nothing really important hinges on whether economics belong to the (hard) sciences or not (what matters is that it is scientific). But, Mayer doesn’t seem to recognize that the English science has lost it’s propper meaning (here’s McCloskey’s explanation): Science means ‘systematic inquiry’ in any other language.

Related posts:

• Economics IS a Science!
• What is Science?

More on Knowledge & Weinberger

I’ve been thinking more about David Weinberger’s ideas of knowledge and how it is formed and communicated. (I’ve discussed Weinberger earlier; see sort-of-review and on knowledge, and an excerpt from his book.) Weinberger seem convinced that the emergence of the internet, and particularly user oriented knowledge bases such as Wikipedia, will change the shape of knowledge: We need to adapt to the new shape of knowledge (see the excerpt).

First of all, what is knowledge, and how is it formed (not shaped; created)? I don’t have the answer to those questions, and they require more space and time than what I intend to spend: There is an entire philosophical branch devoted to knowledge and its structure; it’s called epistemology. (And I don’t know much about it, so what is to follow is amateur epistemology; consider yourself warned.)

My first thought is that there are two types of knowledge: personal knowledge and external knowledge. The personal kind of knowledge is basically the content of your brain, and consist of both external knowledge and memories of experiences. Memories of experiences form skills, for example; a type of knowledge that is not external. External knowledge is knowledge as recorded in books, on film, and so on. (External is probably a terrible word, but I could not come up with a better one; suggestions?) Weinberger is primarily concerned with external knowledge, and so is epistemology as far as I understand.

I described external knowledge as recorded knowlegde, and that is important. Knowledge on the internet is recorded in some form, mostly in writing. When it is recorded, it is communicated. Communication is crucial to knowledge. If I’m not wrong, Weinberger touches upon the importance of communication somewhere in his book. My point is that it is extremely hard to communicate knowledge. Anyone who has tried to put an idea down in writing knows how hard it is. Knowledge is often complicated and involved with other knowledge, which makes it harder. Bad writing is unclear; my personal opinion is that much of the writing on Wikipedia is not particularly good. I’m not certain that millions of anonymous editors can make it better. Weinberger argues that when people stop editing an article on Wikipedia, it constitutes the knowledge ‘we’ agree on. Agreement does not necessarily imply clearly written prose. To the contrary, it may be easier to agree on something fluffy and unclear, which may even mean different things to different people.

Who are ‘we’, by the way? If I’m not mistaken, only about every sixth person has daily access to the internet in the world today. How many of those who do have access devote time to edit articles on Wikipedia? The fact that certain kinds of people may be more interested in Wikipedia can lead to bias. The fact that a lot of smart people never contribute to Wikipedia leads to incompleteness.

Finally, Weinberger underscores the problem of statements which may constitute knowledge to some, but not to others. I don’t see how Wikipedia can solve that: In the end, there is only one article on each topic. It may be broad and change through time, but I simply don’t believe one source can ever be enough.

Related posts:

• Everything is Miscellaneous by David Weinberger
• Four Characteristics of Knowledge
• Wikipedia vs. Public Restrooms, and Social Knowledge

Everything is Miscellaneous by David Weinberger

It’s been a while since I finished ‘Everything is Miscellaneous’ by David Weinberger, and I’ve been planning to put down some thoughts on it. It’s an interesting book; it forced me to think about stuff in new and different ways than before. I don’t always agree with Weinberger, though.

The book is about how the web and its new ways of organizing and connecting things changes how we think, how we work, how knowledge forms, and, ultimately, us. That last point, how the web 2.o (which is a fancy buzzword for web pages and appliances letting its users contribute in different ways) changes us is actually never discussed in the book, but it certainly is understood and implied in Weinberger’s grandiose views. After all, how we think is a part of who and what we are.

Weinberger main topic is order. There are three orders: The first order is the order of physical things, like how books are lined up on shelves in a library. The second order is the catalogue order. A catalogue typically refers to a physical order; it is still physical, but one can make several catalogs of the same physical order. Weinberger’s prime example is the card catalog of libraries. The third order of order is the digital order, where there is no limit to the number of possible orderings. The digital order frees itself from physical reality, and in it, everything can be connected and related to everything else: Everything is miscellaneous.

‘Everything is Miscellaneous’ is, naturally, the topic of numerous blog entries and online discussions. For example, I stumbled across the blog ‘Experiencing Information’ by James Kalbach, and he has some interesting thoughs on Weinberger’s book. In one post, he discusses an analogy between Weinbergers three orders of order and Karl Popper’s theory of reality: I was unaware of Popperian cosmology, but the analogy is striking. In another post, he critizises Weinberger’s use of the library card catalogue as example and illustration of how backward the second (and first) order is. Instead, he suggests that the real topic of interest is the Time of Information in the third order, and not the order itself:

I agree with Weinberger that the third order of organization the web affords is different, but not because other means of accessing books (just to stick with that example) don’t exist. That vision was already there in the paper world.

There are indexes that provide access to Bach cantatas by the first line of text, for instance. Same for poetry. And then there are the countless literature guides in just about any discipline and sub-discipline.

So what the web really changes is:
a.) Who is doing the organizing. Now it’s everyone instead of information professionals
b.) The time it takes to create new lists of access points to books, to then find those list, and to use them effectively.

The Time of Information in the third order, then, is the real thing to focus on.

I would say it is also worth to foucs on who organizes, and who contributes content. Weinberger thinks highly of Wikipedia, for example, where any user can add, change, tag, comment, and link to any material. It sounds chaotic, and it often is. However, over time, stuff tend to settle down. In Weinberger’s view, it’s all fantastic:

[I]magine it is ten years from now. New topics are still being added to Wikipedia an old ones edited, but not at the rate of the early years. The big arguments have mainly been settled. There are continuous small edits polishing the more popular articles, but big changes have become more rare. Wikipedia then constitutes the body of knowledge about which we agree. [...] Wikipedia is commoditizing knowledge, continuing a trend that search engines such as Google began. Text-books also present settled knowledge, or at least present it as settled, but the Internet makes knowledge as instantly available as a calculator’s “equals” button [pp. 214-215].

In fairness, Weinberger admits that Wikipedia will never be complete, and there will always be something to argue about. I think there are several reasons to be skeptic towards Wikipedia. Interestingly enough,  Wikipedia itself has a discussion of some of its problems (here), and most of my concerns are in fact covered there.  (I’ve quoted more of Weinberger’s ideas about how the internet changes knowledge in an earlier post.)

Weinberger sees potential value in every link, tag and comment added to the third order. Personally, however, I often find the links distracting. I should just ignore them, of course, but when I click them, it’s not because I don’t think its interesting to me. That is not the point. A thought experiment illustrates the problem: In a hundred years, there may exist articles on Wikipedia, or elsewhere on the web, where every word links to something else. Every word. And, even worse, and we don’t even have to do time travel to experience another problem; the same word may link to different things at different places. (Of course, that can be a strengt as well, but it can certainly be a problem.)

I want to go back to James Kalbach: In a third post he claims that libraries are not as useless as Weinberger seem to think:

Missing from Everything is Miscellaneous, then, is a discussion of the user experience you have while in the stacks of a DDC library. [Dewey Decimal System: A very common classification system used by libraries.] Namely, the books are arranged by subject. If you find one book on Muslims, others around it are likely to be about Muslims too.

And if you think people don’t look left and right when retrieving a book from a shelf, you’re wrong. They do. It’s an important type of information discovery in physical libraries. Let’s say you go to the stacks for a biography of J.S. Bach. You may then see biographies of C.P.E. Bach and J.C. Bach, perhaps whom you didn’t know much about or even existed. That’s an interesting connection you may not have seen online or in a card catalogue.

I love to go to the library, the only problem is that it takes more time than I usually have.

Without going into more detail, I disagree with Weinberger on a lot of issues. I still found the book very interesting; a lot of it is philosophical discussions related to order, knowledge, information, and communication. A particularly interesting discussion is the one on ‘The Span of Meaning’ (p. 169 and onwards). I end this post with a short quote from it:

Meaning‘s own meanings span a range unique in our language. On the one end, a meaning is a simple definition one can look up in a dictionary. At the other end, meaning is the broadest term for what gives value to our lives [p. 169].

Related posts:

• Four Characteristics of Knowledge
• Wikipedia vs. Public Restrooms, and Social Knowledge

Wikipedia vs. Public Restrooms, and Social Knowledge

The user who visits Wikipedia to learn about some subject, to confirm some matter of fact, is rather in the position of a visitor to a public restroom. It may be obviously dirty, so that he knows to exercise great care, or it may seem fairly clean, so that he may be lulled into a false sense of security. What he certainly does not know is who has used the facilities before him.

The words belong to Robert McHenry, a former editor in chief of the Encyclopædia Britannica. I found the quote in David Weinberger’s book ‘Everything is Miscellaneous’ (p. 132). The quote is taken from an article McHenry wrote on TechCentralStation.com back in 2004. I’m sure it makes interesting reading. 2004 is five (5!) years ago, however, and a lot has happened since then.

Another skeptic towards Wikipedia is (or, was) Stephen J. Dubner of Freakonomics; he discovered himself on a list of well-known economists. That was 2005, however, and Dubner’s skepticism has faded (if my memory serves me right, that is; I’m sure he mentioned his newly won trust in Wikipedia somewhere, but I wasn’t able to find it; I need a backward-link seeking tool to find entries linking to the post I link to above, because it was when he mentioned his new view of Wikipedia he linked to the old post with his Wikipedia skepticism I found that; confusing I know, but it’s not important, so just forget about it).

Wikipedia may be great, but it also may be wrong from time to time. To know, you need to find out whether an entry is disputed or not. If it is, I’m sure the relevant discussion page suffices to make sure what is trustworthy and what is not, and eventually what side of the dispute you want to sympathize with. However, if the subject is a bit odd, Wikipedia may be wrong and still not disputed because so few people ever looks up the entry.

So, can Wikipedia be trusted on the big, important entries, but not the small ones? When is an entry big; when is it small? My conclusion is that Wikipedia may be a good starting point, but usually I rely on Wikipedia to take me somewhere else, to ‘real’ sources. Wikipedia doesn’t feel real to me, but it collects threads to a lot of real stuff.

The old rule of not relying on only one source remains. Paradoxically, Wikipedia, which is generated from innumerable sources, needs to be checked towards different sources before one can rely on it.

Weinberger concludes his section containing the McHenry quote with the following sentence:

Knowledge – its content and its organization – is becoming a social act [p.133].

I twisted when I read that. When was knowledge, its content and organization, not social? I’m certain dear Deirdre wrote somewhere (probably in ‘The Rhetoric of Economics’) that research is social; research is supposed to produce science, and if we’re strict about knowledge, it comes from science. Not all kinds of knowledge, for sure, but certainly the kind Weinberger is talking about. Research IS social. It’s not objective; it’s colored by the subjects involved and the social environment they do their research in. What Weinberger tries to tell us, I think, is that more people may take part in the process he calls knowledge (the social act). No initial requirements to participate are necessary, or rather, requirements (I’m thinking education; position; image) doesn’t matter, or matter less. Whether that is a good thing or not, I haven’t yet decided.

Related post:

• Four Characteristics of Knowledge

A Mathematician’s Apology by G.H. Hardy

I just finished G.H. Hardy’s ‘A Mathematician’s Apology,’ and I intend to jot down some thoughts on it. I’ve been wanting to read this book for quite a while (I’ve had it for over a year) as it has been mentioned in several other books and texts that I’ve read earlier. From what I’d read about it beforehand, I expected some sort of philosophical discussion and understanding of mathematics. I also expected a mathematician’s position in relation to some fundamental philosophical questions like religiousness. Hardy do discuss mathematics in what you may call philosophical way. I was, however, disappointed.

Hardy was a successful mathematician, working as a professor at both Cambridge and Oxford from circa 1900 until his death in 1947. One of his greatest achievements was to prove that the Riemann zeta function has infinitly many roots with real part equal to one half. According to himself, however, was his most important contribution (whether to mathematics or in general I’m not sure, but he probably meant both) the discovery of the Indian mathematical genius Ramanujan.

Hardy was a peculiar man. He had an intense interest in cricket, for example. Within a week of his death, he allegedly said to his sister: ‘If I knew that I was going to die today, I think I should still want to hear the cricket scores.’ Among other peculiarities was his games with God, which become even more peculiar since he claimed not to believe in God. One a trip abroad, he once sent a postcard to a colleague claiming that he had proven the Riemann hypothesis. The idea was that God would not let Hardy’s boat on the return journey sink and, according to some accounts, allow him the same, mytic fame Fermat achieved with his last theorem. Other accounts claims that the idea was that God would not let such a discovery as the solution to the Riemann hypothesis die with him.

I cannot help but to include this list of New Year’s resolutions Hardy once sent to a friend. It shows both ambition and humour. I am sure Hardy meant every word:
1. To prove the Riemann hypothesis,
2. To make a brilliant play in a crucial cricket match,
3. To prove the nonexistence of God,
4. To be the first man atop Mount Everest,
5. To be proclaimed the first president of the U.S.S.R., Great Britain, and Germany, and
6. To murder Mussolini.

Now, the book. First of all, I didn’t like the foreword by C.P. Snow. The foreword was not part of the original book, but was added long after Hardy’s death. It is much too long, particularly for a short book like the Apology, and it draws an untimely picture of Hardy in particular, and of early 20th century British academics in general, as shy, helpless brainies unable to deal with the real world. The only interesting parts in the foreword are the biographical facts about Hardy’s life.

The Apology was published in 1940. By then, Hardy had become a bitter, old man, deprived of his powers as an imaginative mathematician. Obviously, mathematics was one of two truly important things to him, the second being cricket. Feeling that his life is essentially over, he finds it necessary to write the Apology. The book seem to serve as some sort of justification of his life as a mathematician, and, as he claims some sort of generality of his arguments, justification of all mathematicians and of mathematics itself.

I found the topic of the book interesting enough; a discussion of why mathematics is worthwhile; mathematics, the only enterprise of man where absolute truths exist. I found Hardy’s conclusion a bit discouraging, however; I’ve been a student of mathematics myself, and have caugth a glimpse of true, mathematical beauty. I’ve been a fool, it seems, to think there’s something more to it. That depends, however, on my acceptance of Hardy’s position in relation to a range of issues. In most cases, I don’t.

First of all, I don’t like his tendency to claim his position to be common to all pure mathematicians. He may be right, but I won’t accept that just like that. The Apology is generally acclaimed as one of the best insights into the mind of a working mathematician available to laymen, and that may be an indication that Hardy is indeed talking for most mathematicians. Anyway, in his very first paragraph (§1), he claims that exposition and criticism is work for second-rate minds. I wholeheartedly disagree, and I am actually a bit offended by that. Hardy’s problem is his limited understanding of exposition and criticism which is revealed in the Apology. (I won’t argue this case, but I believe any experienced writer would agree that the exposition of the Apology has room for considerably improvement). How can he claim a mind to be second-rate when he does not understand what it does or how it works?

However, the following passage from §2 I agree with and will try to carry with me in my pursuit of a doctoral degree:

Good work is not done by ‘humble’ men. It is one of the first duties of a professor [...] to exaggerate a little both the importance of his subject and his own importance in it. [...] He must shut his eyes a little and think a little more of his subject and himsleft than they deserve.

In the following paragraph (§3), Hardy essentially brings forth the one reason he finds sufficient to justify his life’s work as a mathematician; he’s good at it. Moreover, anyone who is really good at something should ‘make almost any sacrifice in order to cultivate’ his talent. Hardy also claims that very few men are able to do something rather well. I can accept Hardy’s personal justification to pursue his talent. I cannot, however, accept it as a general thesis; many talents aren’t desirable, neither personally nor socially. And, while it is tempting to think that few people have extraordinary talents (it seems plausible, for example, from a probabilistic position), all have the urge to survive embedded in their genes. Given the extreme complexity of the human brain, who knows what other talents lies hidden? Maybe it is more about discovering a talent than having it.

Towards the end of §6, Hardy again demonstrates his condemnation of rhetoric;  he seem to think that content, or substance, doesn’t depend on form. That is simply not true. It may be that mathematicians in particular, and natural scientists in general, believe that they deal with substance only. However, substance and form are two sides of the same coin, and substance is what is read into a certain form. If there’s a problem with the form, or rhetoric, there’s a problem with the substance.

In §22, Hardy writes that he believes mathematical reality to lie outside us, and our (that is, mathematicians, I presume) function is to observe it. I’ve already written that mathematicis is the only scientific enterprise that deals with absolute truths; truths outside ourselves. (Think prime numbers.) Any mathematical discovery, however, depend on axioms, and axioms depend on us (mathematicians, that is). Axioms are supposed to be ‘natural,’ but as long as mathematicians seem to differ in opinion on the ‘intuitivity’ of axioms, I am skeptic. An example of such disagreement may be the Parallel Postulate, which has been subject to centuries of debate.

In §24, Hardy argues that mathematical reality lies outside us:

A chair or a star is not in the least like what it seem to be; the more we think of it, the fuzzier its outlines become in the haze of sensation which surrounds it; but ’2′or ’317′ has nothing to do with sensation, and its properties stand out the more clearly the more closely we scrutinize it. [...] Pure mathematics [...] seems to me a rock on which all idealism founders: 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

I have sympathy with the prime number argument; I cannot imagine prime numbers being anything else than prime numbers. So, with my limited knowledge of mathematics, I may agree that some of what Hardy calls mathematical reality, like prime numbers, lies outside us. I still have problems with the axioms, though, but in the interest of time I’ll leave that discussion for now.

My ‘review’ is far too long already. I need, however, to discuss one more claim Hardy makes to complete my discussion of the Apology. Hardy makes a clear distinction between ‘real’ mathematics and ‘trivial’ mathematics. With trivial, he means all type of applied and school mathematics. This may seem to be a clear distinction, and it is crucial to Hardy’s final conclusion. Hardy goes on to claim that real mathematics is not harmful in any way, as long as it is ‘useless.’ And with useless, he means not applicable to real world problems. There is no clear distinction, however, between real and applied mathematics, and while it may be difficult to realize the applied potential in pure mathematical discoveries, history has shown it otherwise. Numerous results from real mathematics has proved useful in applications. Crown examples are the role of prime numbers in cryptography and Einstein’s theory of relativity. And as long as there is no clear distinction between pure mathematics and applied mathematics, Hardy cannot escape the truth that mathematics as a whole is useful and, more severe to his conclusion, may be harmful.

To Hardy’s defence, it may be asserted that he lived in a different time than ours, and, if they ever were, that his views are probably no longer are representative of mathematicians in general. Indeed, I do hope that present day mathematicians are more in contact with reality than what Hardy seemed, and realize both the potential value and danger in pure mathematics.

Hardy’s conclusion, then, is that mathematics is nothing more but a creative art, and that his achievements

[...] differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any of the other artists, great or small, who have left some kind of memorial behind them.

It seems clear that Hardy, despite all his devotion and appreciation of it, reduces mathematics to an art, and resembles great mathematicians like Hilbert and Abel with other great artists like Mozart and Picasso . Not that I don’t think highly of art. Art, to me, is a product of the human mind; meant to please or provoke; meant to mean something; meant to influence someone; and, not the least, a product of an urge to create. Art is a sign of prosperity and abundance, not necessarily a necessity. Pure mathematics, however, is different; it is an expedition into the absolute; investigating and observing logic; not meant to please or provoke, but a necessity to progress. It may resemble art, nonetheless, depending on creativity and inspiration, but still being different, and, in my eyes, more important; while any artist or may be much more important to any one individual, the great mathematicians are much more important to the human kind.

Those interested can download the book for free (luckily, without the foreword by C.P. Snow) and make up their own mind.

Replication in Economics

Despite the voodoo noise, a different and lot more interesting debate about replication in economics has started on Environmental Economics. The debate on Env-Econ is a response to a post on Market Movers, which opens like this:

Falsifiability and replicability are key cornerstones of any academic research. If you’re running an empirical study, and your results aren’t replicable, your study is largely worthless.

First of all, the claim that falsifiability is a key cornerstone of academic research is simply not true, or at least not agreed upon. I understand falsifiability in the Popperian sense:

For Popper, a theory is scientific only if it is refutable by a conceivable event. Every genuine test of a scientific theory, then, is logically an attempt to refute or to falsify it, and one genuine counter-instance falsifies the whole theory.

(Read more about Popper and his ideas at the Stanford Encyclopedia of Philosophy.) Popper’s philosophy of science has been subject to extended debates. Thomas Kuhn, for example, claims that science consist of problem solving within a paradigm, and that paradigms change through scientific revolutions. In particular, Kuhn did not think that a statement had to be falsifiable to be scientific, as Popper did.

I am more willing to agree on the importance of replication. In the hard sciences like physics and chemistry, replication was truly important and researchers (ideally) remained sceptic towards new results until they had been replicated independently from the initial study. Since most research in physics and chemistry are conducted in laboratories, controlled experiments could fairly easily be replicated and results compared.

In economics, however, only recently have researchers started to conduct controlled experiments in laboratories. Tim Haab writes (On replicability in economics and the validation of models)

With economics models, at least until recently, we don’t have labs.  We are working with real observations from highly complex systems.  As such, we are forced to rely on modeling by assumption and measurement through statistical force rather than isolated direct observation.  This makes external validation of economic models extremely difficult.

This is changing over the past decade or so with the advent of experimental economics research in which researchers are testing fundamental economic results in a controlled setting.  Unfortunately, these experiments often suffer from over control which makes generalizability and practical applicability of laboratory results difficult at best. [...]

To me, lack of replicability is not a condemnation of economics as a field, rather a challenge to the field to continue the unending pursuit of defensibility.

As Tim also points out, the post on Market Movers is primarily concerned with duplication of results (instead of independent replication), which requires the same data set and statistical tools. Such research is quite rare in economics, and it has different reasons (see Tim’s post). What is more common in economics, however, is that researchers collect their own data and see if they can find the same kind of conclusions as those available in the literature. John Whitehead puts it like this:

Why bother with replication with someone else’s data when you can publish your own study with your own data? The only time you ask for someone else’s data is if you really think they’ve made a horrible mistake or if you have an ax to grind.

However, I do agree with Market Movers that in general, replication and duplication is more important than what it seems to be in academia today.

Hat-tip: Env-Econ

What is Science?

Despite my earlier efforts, the strange usage of ‘science’ in the English language still obstructs the discussion over on Climate Progress. John McCormick writes

Here is a definition of the word ‘science’

“1. the systematic observation of natural events and conditions in order to discover facts about them and to formulate laws and principles based on these facts. 2. the organized body of knowledge that is derived from such observations and that can be verified or tested by further investigation. 3. any specific branch of this general body of knowledge, such as biology, physics, geology, or astronomy.”

Academic Press Dictionary of Science & Technology [...]

Economics does nto [sic] fit the definition of science, in my opinion. So, scientific norms do not apply [when it comes to economics.]

McCloskey tracks the current use of ‘science’ back to 1867 (p. 20 in ‘The Rhetoric of Econmics,’ 2nd ed.). Earlier ‘science’ meant ‘studies,’  in line with its counterpart in other Indo-European languages. The weird thing is that today,  its counterpart in most languages hasn’t really changed meaning; it means ‘systematic inquiry’ and is not explicitly chained to ‘natural events.’ It is thus used to describe, e.g., philosphy and studies of poetry and language, as well as physics and chemistry. It is thus absurd that economics is a science in other languages, but not in English. What are we supposed to make of this? I let McCloskey explain (p. 21).

The point is that the foreigners have gotten it right. [...] “Economics is a science” should not be the fighting words they are in English. The fighting lacks point because, as our friends across the water could have told us, nothing important depends on its outcome. Economics in particular is merely a disciplined inquiry into the market for rice or the scarcity of love. Economics is a collection of literary forms, some of them expressed in mathematics, not a Science. Indeed, science is a collection of literary forms, not a Science. And literary forms are scientific. [...] The idea that science is a way of talking, not a separate realm of Truth, has become common among students of science since Thomas Kuhn.[*]

So, what’s important is that economics is scientific. Economics might not be a science in the U.S., but it is certainly scientific and scientific norms do apply.

* Thomas Kuhn (1922 – 1996) was maybe the most influental philosopher of science in the twentieth century. Anyone slightly interested in science, philosophy or generally should read his book ‘The Structure of Scientific Revolutions.’

The English problem

Daniel Hamermesh asks some interesting questions about the position of the English language in academic circles over on the Freakonomics blog. (Many of the comments are worth reading if you’re interested.) I think it is safe to say that English is the most widely used language in scientific articles these days; maybe some Russian mathematicians still publish in Russian and I think Chinese research is published in Chinese. However, English is the new ‘lingua franca,’ as Hamermesh points out (English dominant position goes beyond the academic world, ofcourse). ‘I feel guilty about this,’ Hamermesh writes,

and all American economists should: It’s easier for us to write our scholarly papers than it is for other economists; it’s easier for us to function internationally.

That exact problem bugs me every single day. In the recent year I’ve put efforts into improving my english; this very blog is one of my training facilities. Had English been my mother tounge I would be able to put more efforts into the research I’m supposed to conduct and less into studying English. Notwithstanding, a lot of American economists could with advantage pay more attention to how they use their language (just ask McCloskey). And, ofcourse, I’m in the same boat as all other researchers who have an other mother tounge than English. Still, however, the English problem bugs me every time I read an English word or sentence that is not immediate to me.

Would I prefer a world with a world language? Well, I don’t know. For one thing, if you don’t know what you’re missing, you don’t miss it. And, an instant switch from 200+ languages (I’m sure there’s more, but I think there’s at least 200 languages around in active use) to one world language is impossible. So the question is hypothetical (I’ve realized that most (philosohical) questions are, and I have to work on my ‘distaste’ for them). Another thing is that in todays world, a situation with one world language is not a sustainable situation; different corners that are more or less unconnected, say, Inner Mongolia and Outer Sahara, would develop dialects and words independent of each other and soon one could not talk of only one world language anymore. But  apart from these problems, I think Yes, I would prefer a one language world.

A Smilansky paradox: Beneficial Retirement

This is my second post on Saul Smilansky’s ’10 Moral Paradoxes.’ My first post addressed the paradox of Fortunate Misfortune. Now, I would like to address the second paradox Smilansky discusses in his book; the paradox of Beneficial Retirement.

 Smilansky claims that a large share of those in a particular job/position should consider retirement because of the likeliness of someone better than them replacing them; a better replacement would be beneficial. Particularly, this applies to typical ‘offical’ jobs (e.g., doctors, researchers) that often are less exposed to competition than many jobs in the private sector (at least once you are in the job). I don’t like this idea. This implicitly demands that everyone (because the argument really applies to everyone) put everyone else above themselves, and I think that is to demand (and hope) for too much from people. And, the situation does not exactly support a stable society, where half the workforce (at any given time, the way I read Smilansky) gave up their job and went searching for other jobs or did not contribute at all. It hardly sounds like a beneficial situation. I guess that since Smilansky writes books on philosophy (instead of applying vacant jobs), he considers himself at least in the top half among philosophers. I am alarmed; me, an amateur philosopher, easily finds holes and problems in much of his thinking. On p. 28, Smilansky claims that the difficulty can be seen when he claims that a doctor cannot ‘sensibly and consistently’ make the following statements:
1. I am a doctor because I want people to be healthier; and
2. I will continue to work as a doctor.
(Smilansky presents the statements for three different examples, but that does not make any difference and is unecessary, I think.) Well, I conjure that many doctors are not doctors because they want people to be healthier, but rather because of a range of reasons, possibly, but not necessarily including wanting people to be healthier. Also, I disargee with Smilansky’s claim that the replacement is probably better than those employed for half the workforce. (Half is very much; where do all those people come from; is there enough buss drivers in Norway to replace half of them currently employed with those unemployed?) Of course, half is just a number and could have been whatever, the point is that it is relatively large. This particular issue requires some refinement, and I am surprised that Smilansky does not discuss this. The betterness of a replacement employee depends on the time scale the skills are measured; I am certain that seniority and experience is very important in many jobs, and when a replacement has gained that seniority and experience he might turn out to be better than the first employee. Ironically, he would never get the chance, because all these recently retired competitors with a lot of experience is knocking on the door and the newcommer is morally required to give up his job, according to Smilansky. Secondly, the benefit of the better replacement has a large time lag compared to the inital retirement of the previous emploee; the benefit is less worth when we have to wait for it.

Following my arguements above, I think there are two big problems with the paradox of Beneficial Retirment. First, it would not be beneficial if people were to consider retirement all the time. Second, it doubt the benefits to be reaped. Paradoxically, Smilansky may be aware of these problems, because he imposes a set of ‘underlying conditions’ for the paradox which avoids the problems I raise (p. 24). I find no reason to excuse Smilansky, however, for imposing unrealistic conditions. The conditions turns the paradox into a hypothetical paradox which may find its best use as entertainment.

Fortunate Misfortune, a philosophical paradox?

I’m reading Saul Smilansky’s ’10 Moral Paradoxes’. It is a very small book, and according to Smilansky it addresses a neglected field in ethics (p. 2). I enjoy philosophy (or at least I think I do; I’m afraid I’m don’t really know what philosophy is; what I’m familiar with is mainly philosophy of science), and I find paradoxes entertaining, so ’10 Moral Paradoxes’ caught my attention at some point.

I have many problems with this book (more than I remember actually; I have to start to keep notes) and I want to discuss some of them here on my blog. Before I get to ‘Fortunate Misfortune’, however, I should make (somewhat) clear what Smilansky thinks of as a paradox. There’s two extreme and oposite ideas of a paradox; a paradox is a logical contradiction, or merely something unexpected or ironic. Smilansky deliberatly places himself somewhere inbetween these extremes, and does not require a strict logical contradiction but still wants to be ‘quite rigorous’ in what he considers a paradox (p. 3). The way I see things, what he discusses is often merely hypothetical paradoxes, and I ask: Is a hypothetical paradox a paradox, and, more important, is it interesting? I could give you an example of what I mean, but I won’t; I trust you are able to conjure a hypothetical paradox yourself. Is it interesting?

So, the first chapter in ’10 Moral Paradoxes’ concerns Fortunate Misfortune (capitalized to be safe). Smilansky claims that sometimes, misfortune can be fortunate and that such fortunate misfortune is paradoxical. Well, I do not disagree to the paradoxical figure of speech (fortunate misfortune), but I do only agree to it in the ironic sense of paradox; if one should be more strict in what one regards as a paradox, Fortunate Misfortune is not a paradox.

Let me be more specific. To illustrate what he means by Fortunate Misfortune, Smilansky provides examples (p. 12) (I observe that philosophers more than anyone argues through examples and I find it highly dissatisfying; I touched upon my dissatisfaction with examples as ‘definitions’ earlier). His main example is that of Abigail who were born with breathing difficulty and a muscle disease that made it hard for her to use her legs. Her doctor told her to swim alot. Later, her breathing and legs became normal, but she continued to swim and became a world champion swimmer. The point is that Abigail had misfortune early in life, but in the end it turned out to be a fortune for her because it introduced her to swimming. (Smilansky provides deails to ensure that she would probably not swim much if she was normal as a child.) First of all, for there to be a paradox, the misfortune has to be the deterministic cause of her later fortune. Such determinism is impossible in practice (to become a world champion swimmer you need the right genes; with those genes she might have become sucessfull in some other sport or something else for that matter; only getting those genes is fortunate as beeing conceived is a lottery; fortunate circumstances made it possible for her to start swimming at an early age, and I can go on listing necessary fortunes in her life for her to become a world champion swimmer) and Smilansky’s Fortunate Misfortune paradox is at best hypothetical, and not a very interesting one. Second, Smilansky points out that he only considers cases where the misfortune has been severe or serious to qualify for his sense of paradox (p. 13). The later fortune has to be equally ‘severe’ as it is supposed to compensate Abigail for her sufferings in her childhood. Can later fortune compensate one for earlier misfortune? (A technical argument here is discounting, and makes the paradox dependent on whether Abigail is forward or backward looking (I just realized that I don’t really know how to treat backward looking discounting!), or whether it is an independent philosopher who observes and assesses the paradox. Abilgail, by the way, is most probably backward looking as anything else would remove the example so far away from reality that it might not be interesting anymore; the Fortunate Misfortune paradox looses interest value as it removes itself from reality in my eyes. And then I haven’t mentioned risk aversion.) And is seriousness truly necessary? I think it would be much less problematic to conjure examples of small misfortunes that were compensated by later fortunes that is conditional on the first misoftunes. The causal issue would also be much easy to establish with smaller events. I am disappointed that Smilansky does not realize this. Another problem is that we cannot observe Abigail’s alternative lives; maybe her illness was only a mild case of what was most probable given whatever conditions that lead to her illness; maybe she could have had an even better life had she never been ill (she could have been an even better swimmer; or been good at something more rewarding altogehther).

I think what Smilansky struggles with in chapter 1 of his ’10 Moral Paradoxes’ is merely a hypothetical paradox. I also wonders what he (and others) put into the words ‘fortune’ and ‘misfortune’. In a lottery where each draw is independent of each other, one can only talk about fortune and misfortune per draw; later fortunes are not dependent on neiter earlier fortunes nor misfortunes. In life, however, things are more complicated. Things depend on each other in ways we don’t understand, and on things we don’t realize matter at all. ‘Fortune’ or ’misfortune’ then has to apply to a specific set of events. It is misfortunate to become sick. It is fortunate to have a great talent. But when one combines events, like ‘become sick, start training, get well, be stronger than before’, one may call that chain fortunate since one ends up stronger than before (here I go, arguing in examples myself, jeez), and still consider it unfortunate to become sick. I don’t see a paradox here; the fortune and misfortune applies to different sets of events; they operate on different scales.

Even though (or maybe because) I have several problems with ’10 Moral Paradoxes’, I still find it an interesting and rewarding read. Particularly, I enjoy its brevity. If there’s one thing many academics (myself included (ok, semi-academic), see above for example; not exactly brief) need to pay more attention to, it is the art of brevity. Many of the paradoxes under scrutiny spur ideas and new thoughts, and I plan to discuss some of these later. So stay tuned for more Smilansky!