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People like to see logic and computing in this way and the author is a great storyteller. But it is a somewhat misleading perspective that is kind of similar to

People like to see logic and computing in this way and the author is a great storyteller. But it is a somewhat misleading perspective that is kind of similar to "Whig historiography" (https://en.wikipedia.org/wiki/Whig_history https://en.wikipedia.org/wiki/Whig_history): > Whig is an approach to historiography that presents the past as an inevitable progression towards ever greater liberty and enlightenment, culminating in modern forms of liberal democracy and constitutional monarchy. Just replace the "greater liberty" bit with what computer scientists (and the author) argue is the right way of doing computer science today. I'd love to read a historical treatment of the topic that is written by someone who is a historian rather than computer scientist twisting history to support their world view.

pron 10y ago
I would recommend Andrew Hodges. Read this to get a taste: Did Church and Turing Have a Thesis about Machines?[1] (spoiler alert: probably) For the history of logic, Jean van Heijenoort's[2] annotated anthology, From Frege to Gödel[3] is fascinating. And, BTW, I think your hunch (about Whig history) is correct. [1]: http://www.turing.org.uk/publications/ct70.pdf http://www.turing.org.uk/publications/ct70.pdf [2]: https://en.wikipedia.org/wiki/Jean_van_Heijenoort https://en.wikipedia.org/wiki/Jean_van_Heijenoort [3]: https://www.amazon.com/Frege-Godel-Mathematical-1879-1931-Sciences/dp/0674324498 https://www.amazon.com/Frege-Godel-Mathematical-1879-1931-Sc...
tikhonj 10y ago
That's not a charitable interpretation ("twisting history to support their world view"), and your comment seems to be conflating the language-logic view itself with the history presented here. The relationship between programs and logic is compelling for many reasons and can stand independent of how the two happened to be developed; my take is that the historical story here—which is definitely too pat—is presented more as an illustration of the idea than anything else. This is no different than how math textbooks present the history of any particular mathematical abstraction or theorem: they don't go in depth on all the false starts and dead ends people explored before making real progress. That's certainly something interesting but it has no place—and no room—in textbooks dedicated to explaining abstractions. The simplified story of how something could have been developed is, I believe, more relevant to understanding the importance of an idea than the way it was actually developed. The real history is full of noise, a function of the person who first happened upon the idea. It's not hard to image thousands of alternate worlds where the exact development of an idea was slightly different, but reflecting the same fundamentals—those differences end up as irrelevant details due to chance.
- pron 10y ago
  > This is no different than how math textbooks present the history of any particular mathematical abstraction or theorem: they don't go in depth on all the false starts and dead ends people explored before making real progress. That's true, but it is important to point out when the story is told in a specific way to promote a certain ideology. I'm not saying it's wrong to promote an ideology (on the contrary; ideology is often very important) or that it's rare, but readers should be aware that a certain ideology is being promoted. Wadler is trying to promote functional programming by presenting it as a natural result of logic, and in many ways the essence of his story is correct (from other, more neutral accounts that I've read). But what readers may not know is that logic has not been the only motivating force in theoretical computer science (nor the most powerful), that there are other useful analogies between computation and other phenomena, and that what's presented here is just one perspective on computation. For example, Turing, the father of theoretical computer science which only gets a brief mention in this account[1], turned his attention to neural networks, biological computation and possibly even quantum computation (although he died while working on some physics results). Much of the main thrust of theoretical computer science was similarly influenced by information theory and the search for the "physical laws" of computation which led to complexity theory, something that is nearly entirely missing from the logical treatment. [1]: Both Wadler and Bob Harper often try to downplay Turing's role for ideological reasons (which, I think, is pretty funny considering the history of computer science), and neglect to mention that Church's relatively narrow perspective caused him to miss something very basic about computation, while Turing, who was opposed to logicism[2], i.e. reducing math to logic, was able to therefore grasp something much more fundamental about computation than Church. Interestingly, Brouwer, who is another figure that provides inspiration to proponents of FP, actually did not fall into this trap, and had the philosophical breadth that had led him to come closer to Turing's more general view of computation than Church, by trying, like Turing, to think -- philosophically rather than formally -- how the mind of a mathematician works regardless of a specific formalism. [2]: https://mdetlefsen.nd.edu/assets/201037/jf.turing.pdf https://mdetlefsen.nd.edu/assets/201037/jf.turing.pdf Some interesting quotes: > On 1 December 1933, the minutes in the Moral Science Club records: “A.M. Turing read a paper on ‘Mathematics and Logic’. He suggested that a purely logistic view of mathematics was inadequate; and that mathematical propositions possessed a variety of interpretations, of which the logistic was merely one.” > He was engaged in a program of putting Russell’s new logic into place, critiquing, not only its position or office, but perspectives on mathematics being forwarded by the “purely logistic” views. Turing was insisting that mathematical discourse stand on its own autonomous feet. And he was rejecting the idea that Principia — or any other construal of mathematics as a whole in terms of symbolic logic — offers mathematics a “foundation” of any ultimate or privileged sort, or reduces it to logic. A “purely logistic view” is but one (philosophically tendentious) “interpretation” among others, and is therefore “inadequate”. This is thoroughly consonant with the opening of Wittgenstein’s 1932 Cambridge lectures “Philosophy for Mathematicians” we have quoted above: Principia is simply part of mathematics, and there is nothing wrong with mathematics before its foundations are laid. > Turing developed an “anthropological” approach to the foundations of logic, influenced by Wittgenstein, in which “common sense” plays a foundational role.
kmicklas 10y ago
Ooof, this is too true. As someone greatly interested in type theory and the advancement of programming, I think this is definitely an issue to watch out for. Side note: an even better example than Whig history might be Marx's historical materialism. (Also an analysis I am sympathetic to but equally fraught with this peril.)

pron 10y ago

I would recommend Andrew Hodges. Read this to get a taste: Did Church and Turing Have a Thesis about Machines?[1] (spoiler alert: probably) For the history of logic, Jean van Heijenoort's[2] annotated anthology, From Frege to Gödel[3] is fascinating. And, BTW, I think your hunch (about Whig history) is correct. [1]: http://www.turing.org.uk/publications/ct70.pdf http://www.turing.org.uk/publications/ct70.pdf [2]: https://en.wikipedia.org/wiki/Jean_van_Heijenoort https://en.wikipedia.org/wiki/Jean_van_Heijenoort [3]: https://www.amazon.com/Frege-Godel-Mathematical-1879-1931-Sciences/dp/0674324498 https://www.amazon.com/Frege-Godel-Mathematical-1879-1931-Sc...

tikhonj 10y ago

That's not a charitable interpretation ("twisting history to support their world view"), and your comment seems to be conflating the language-logic view itself with the history presented here. The relationship between programs and logic is compelling for many reasons and can stand independent of how the two happened to be developed; my take is that the historical story here—which is definitely too pat—is presented more as an illustration of the idea than anything else. This is no different than how math textbooks present the history of any particular mathematical abstraction or theorem: they don't go in depth on all the false starts and dead ends people explored before making real progress. That's certainly something interesting but it has no place—and no room—in textbooks dedicated to explaining abstractions. The simplified story of how something could have been developed is, I believe, more relevant to understanding the importance of an idea than the way it was actually developed. The real history is full of noise, a function of the person who first happened upon the idea. It's not hard to image thousands of alternate worlds where the exact development of an idea was slightly different, but reflecting the same fundamentals—those differences end up as irrelevant details due to chance.

pron 10y ago
> This is no different than how math textbooks present the history of any particular mathematical abstraction or theorem: they don't go in depth on all the false starts and dead ends people explored before making real progress. That's true, but it is important to point out when the story is told in a specific way to promote a certain ideology. I'm not saying it's wrong to promote an ideology (on the contrary; ideology is often very important) or that it's rare, but readers should be aware that a certain ideology is being promoted. Wadler is trying to promote functional programming by presenting it as a natural result of logic, and in many ways the essence of his story is correct (from other, more neutral accounts that I've read). But what readers may not know is that logic has not been the only motivating force in theoretical computer science (nor the most powerful), that there are other useful analogies between computation and other phenomena, and that what's presented here is just one perspective on computation. For example, Turing, the father of theoretical computer science which only gets a brief mention in this account[1], turned his attention to neural networks, biological computation and possibly even quantum computation (although he died while working on some physics results). Much of the main thrust of theoretical computer science was similarly influenced by information theory and the search for the "physical laws" of computation which led to complexity theory, something that is nearly entirely missing from the logical treatment. [1]: Both Wadler and Bob Harper often try to downplay Turing's role for ideological reasons (which, I think, is pretty funny considering the history of computer science), and neglect to mention that Church's relatively narrow perspective caused him to miss something very basic about computation, while Turing, who was opposed to logicism[2], i.e. reducing math to logic, was able to therefore grasp something much more fundamental about computation than Church. Interestingly, Brouwer, who is another figure that provides inspiration to proponents of FP, actually did not fall into this trap, and had the philosophical breadth that had led him to come closer to Turing's more general view of computation than Church, by trying, like Turing, to think -- philosophically rather than formally -- how the mind of a mathematician works regardless of a specific formalism. [2]: https://mdetlefsen.nd.edu/assets/201037/jf.turing.pdf https://mdetlefsen.nd.edu/assets/201037/jf.turing.pdf Some interesting quotes: > On 1 December 1933, the minutes in the Moral Science Club records: “A.M. Turing read a paper on ‘Mathematics and Logic’. He suggested that a purely logistic view of mathematics was inadequate; and that mathematical propositions possessed a variety of interpretations, of which the logistic was merely one.” > He was engaged in a program of putting Russell’s new logic into place, critiquing, not only its position or office, but perspectives on mathematics being forwarded by the “purely logistic” views. Turing was insisting that mathematical discourse stand on its own autonomous feet. And he was rejecting the idea that Principia — or any other construal of mathematics as a whole in terms of symbolic logic — offers mathematics a “foundation” of any ultimate or privileged sort, or reduces it to logic. A “purely logistic view” is but one (philosophically tendentious) “interpretation” among others, and is therefore “inadequate”. This is thoroughly consonant with the opening of Wittgenstein’s 1932 Cambridge lectures “Philosophy for Mathematicians” we have quoted above: Principia is simply part of mathematics, and there is nothing wrong with mathematics before its foundations are laid. > Turing developed an “anthropological” approach to the foundations of logic, influenced by Wittgenstein, in which “common sense” plays a foundational role.

kmicklas 10y ago

Ooof, this is too true. As someone greatly interested in type theory and the advancement of programming, I think this is definitely an issue to watch out for. Side note: an even better example than Whig history might be Marx's historical materialism. (Also an analysis I am sympathetic to but equally fraught with this peril.)