h&f 0037 Book Review 001: Proofs & Refutations by Imre Lakatos

{or…by Lakatos Imre, if you’re Hungarian.}

The Logic of Mathematical Discovery

Proofs and Refutations: The Logic of Mathematical Discovery

When you finish this short book, it will put a reckoning wrench in the way you think.  It is about mathematics, but you’ll easily fall into the critical thinking platform that it is.  And then you’ll get past that and just enjoy it.  No, for real.  That’s what makes it art.  It doesn’t start by proclaiming itself art, but simply plies its trade and ends up at the art that lies at the end of any true effort to dive into a given discipline.

I should also note that it’s an easy read, if not easy reading (there will be some formulas – very light, though), since it’s written as screenplay.  You can follow a particular line of reasoning just by following the comments of specific characters.  He gives each a Greek alphabet name: Alpha, Beta, Gamma, etc. are students in a classroom debating whether or not Euler’s theorem [v-e+f=2, vertices minus edges plus faces equals two] holds true for all polyhedra.

You can tell by all this nonsense that I am a dangerous and probably frustrating kind to the true scientist or mathematician: the layman who grabs math and science for analogs, pleasure, or some other non-math reason.  Imagine an 8-year old using a jackhammer.  …mad fun.

But I do take heart at the unexpected affirmation from John Seely Brown who, when I mentioned this book during a Socrates Society Seminar at the Aspen Institute said that it changed his way of thinking.  Whew!  Gimme my jackhammer back.

My only possible redemption is that I acknowledge that weakness and try not to use those analogs gratuitiously when I write about them. And I won’t talk to you about them when we’re playing ball, fishing, running, surfing, or just sitting on the rooftop for coffee.  That’s right, not even coffee.

What I am not hestitant about, though, is what I have experienced as application of this stuff to the way I think.  Proofs and Refutations gave me access to a new system for analysis through, yes, Proofs, Refutations, but also local and global counterexamples along any specific line of thinking that I have.  A whole lot more is in this book.

Check how he uses footnotes – The best example I’ve seen of stuff that would clutter the text but is necessary at the point you would insert them.  He gives historical anecdotes and clarifications in the footnotes that are pretty dang powerful.

I’ll stop here.  I hear the scientists and mathematicians gathering forces against lay, and possibly misinformed enthusiasm.  And I really don’t want to go toe to toe with those dudes on whether or not Polya acutally gave a better perspective or whether or not, per Paul Feyerabend , “Lakatos’ methodology {is} not a methodology at all, but merely “words that sound like the elements of a methodology and no different from epistemological anarchism, Feyerabend’s own position.”

Just read it and lemme know how it moves ya…..

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~ by ericjhenderson on August 28, 2008.

One Response to “h&f 0037 Book Review 001: Proofs & Refutations by Imre Lakatos”

  1. […] The Complete Review Book Review The Philosophical Quarterly Book Review Mathematical Association of America Book Review Hustle and Flow Book Review […]

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