Unless you are a sci-fi author or some secret government agency, the question whether aliens would understand lambda calculus is probably not your main practical concern. However, the question is intriguing because it nicely vividly formulates a fundamental question about our formal mathematical knowledge. Are mathematical theories and results about them invented, i.e. constructed by humans, or discovered, i.e. are they eternal truths that exist regardless of whether there are humans to know them?
The question makes for a fantastic late night pub debate, but how can we go about answering it using a more serious methodology? Is there a paper one can read to better understand the problem? Occasionally, a talk or an online comment by a computer scientist comments on this question, but way too often, people miss the fact that the nature of mathematical entities is one of the fundamental questions of philosophy of mathematics. Alas, all those discussions are carefully hidden in the humanities department!
I believe that knowing a bit about philosophy of mathematics is important if we want to have a meaningful debate about philosophical questions of mathematics (sic!) and so I did a talk on this very subject at CodeMesh 2017. This article is slightly refined and hopefully more polished version of the talk for those who, like me, prefer reading over watching. Keep in mind that the question about the nature of mathematical entities is one of the fundamental questions of an entire academic discipline. As such, this article cannot possibly cover all the relevant discussions. Compared to some other writings in this space, this article is, at least, based on a couple of philosophical books that, I believe, have useful things to say on the subject!
The word "design" is often used when talking about programming languages. In fact, it even made it into the name of one of the most prestigious academic programming conferences, Programming Language Design and Implementation (PLDI). Yet, it is almost impossible to come across a paper about programming languages that uses design methods to study its subject. We intuitively feel that "design" is an important aspect of programming languages, but we never found a way to talk about it and instead treat programming languages as mathematical puzzles or as engineering problems.
This is a shame. Applying design thinking, in the sense used in applied arts, can let us talk about, explore and answer important questions about programming languages that are ignored when we limit ourselves to mathematical or engineering methods. I think the programming language community is, perhaps unconsciously, aware of this - one of the reviews of my recent PLDI paper said "this is a nice, novel design paper, and the community often wants more design papers in our conferences". The problem is that we we do not know how to write and evaluate work that follows design methodology.
To better understand how design works, I recently read The Philosophy of Design by Glenn Parsons. The book perhaps did not answer many of my questions about design, but it did give me a number of ideas about what design is, what questions it can explore and how those could be relevant for the study of programming languages...
As someone who enjoys being at the intersection of the academic world and the world of industry, I'm very happy to see any attempts at bridging this harmful gap. For this reason, it is great to see that more people are interested in reading academic papers and that initiatives like Papers We Love are there to help.
There is one caveat with academic papers though. It is very easy to see academic papers as containing eternal and unquestionable truths, rather than as something that the reader should actively interact with. I recently remarked about this saying that "reading papers" is too passive. I also mentioned one way of doing more than just "reading", which is to write "critical reviews" – something that we recently tried to do at the Salon des Refusés workshop. In this post, I would like to expand my remark.
First of all, it is very easy to miss the context in which papers are written. The life of an academic paper is not complete after it is published. Instead, it continues living its own life – people refer to it in various contexts, give different meanings to entities that appear in the paper and may "love" different parts of the paper than the author. This also means that there are different ways of reading papers. You can try to reconstruct the original historical context, read it according to the current main-stream interpretation or see it as an inspiration for your own ideas.
I suspect that many people, both in academia and outside, read papers without worrying about how they are reading them. You can certainly "do science" or "read papers" without reflecting on the process. That said, I think the philosophical reflection is important if we do not want to get stuck in local maxima.
If you read a about the history of science, you will no doubt be astonished by some of the amazing theories that people used to believe. I recently finished reading The Invention of Science by David Wootton, which documents many of them (and is well worth reading, not just because of this!) For example, did you know that if you put garlic on a magnet, the magnet will stop working? Fortunately, you can recover the magnet by smearing goats blood on it. Giambattista della Porta tested this and concluded that it was false, but Alexander Ross argued that our garlic is perhaps not so vigorous as those of ancient Greeks.
You can just laugh at these stories, but they can serve as interesting lessons for any scientist. The lesson, however, is not the obvious one. Academics will sometimes read those stories and use them to argue against something they do not consider scientific - arguing that it is like believing that garlic break magnets.
This is not how the analogy works. What is amazing about the old stories is that the conclusions that now seem funny often had very solid reasoning behind them. If you believed in the basic assumption of the time, then you could reach the same conclusions by following fairly sound reasoning principles. In other words, the amazing theories were scientific and entirely reasonable. The lesson is that what seems a completely reasonable idea now, may turn out to be wrong and quite hilarious in retrospect.
In this article, I will look at a couple of amazing theories that people believed in the past and I will explain why they were reasonable given the way of thinking of the time. Along the way, I will explore some of the ways of thinking that we use today about programming and computer science and why they might appear silly in the future.
This blog post is an edited and more accessible version of an article Thinking the unthinkable that I recently presented at the PPIG 2016 conference. The original article (PDF) has proper references and more details; the minimalistic talk slides give a quick summary of the article.
Our thinking is shaped by basic assumptions that we rarely question. These assumptions exist at different scales. Foucault's episteme describes basic assumptions of an epoch (such as Renaissance); Kuhn's research paradigms determine how scientists of a given discipline approach problems and Lakatos' research programmes provide undisputable assumptions followed by a group of scientists.
In this article, I try to discover some of the hidden assumptions in the area of programming language research. What are assumptions that we never question and that determine how programming languages are designed? And what might the world look like if we based our design method on different basic principles?
Combining philosophy and computer science might appear a bit odd. The disciplines have very little overlap. Both philosophers and computer scientists get taught formal logic at some point in their undergraduate courses, but that's probably as close as they get.
But the fact that the disciplines do not overlap much might very well be the reason why putting them together is interesting. In an article about Design and Science, Joichi Ito (from MIT Media Lab), describes the term antidisciplinary and nicely summarizes why looking at such unusual combinations is worthwhile:
Interdisciplinary work is when people from different disciplines work together. But antidisciplinary is something very different; it's about working in spaces that simply do not fit into any existing academic discipline.
[When focusing on disciplines, it] takes more and more effort and resources to make a unique contribution. While the space between and beyond the disciplines can be academically risky, it (...) requires fewer resources to try promising, unorthodox approaches; and provides the potential to have tremendous impact (...).
As you can see from some of my earlier blog posts, I think the space between philosophy and computer science is an interesting area. In this article, I'll explain why. Unlike some of the previous posts (about miscomputation, types and philosophy of science), this post is quite broad and does not go into much detail.
At the danger of sounding like a collection of random rants, I look at a number of questions that arise when you look at computer science from the philosophical perspective, but I won't attempt to answer them. You can see this article as a research proposal too - and I hope to write more about some of the questions in the future. I wish antidisciplinary work was more common and I believe looking into such questions could have the tremendous impact that Joichi Ito mentioned.
When I tell my fellow computer scientists or software developers that I'm interested in philosophy of science, they first look a bit confused, then we have a really interesting discussion about it and then they ask me for some interesting books they could read about it. Given that Christmas is just around the corner and some of the readers might still be looking for a good present to get, I thought that now is the perfect time to turn my answer into a blog post!
So, what is philosophy of science about? In summary, it is about trying to better understand science. I'll keep using the word science here, but I think engineering would work equally well. As someone who recently spent a couple of years doing a PhD on programming language theory, I find this extremely important for computer science (and programming). How can we make better programming languages if we do not know what better means? And what do we mean when we talk about very basic concepts like types or programming errors?
Reading about philosophy of science inspired me to write a couple of essays on some of the topics above including What can programming language research learn from the philosophy of science? and two essays that discuss the nature of types in programming languages and also the nature of errors and miscomputations. This blog post lists some of the interesting books that I've read and that influenced my thinking (not just) when writing the aforementioned essays.
If trials of three or four simple cases have been made, and are found to agree with the results given by the engine, it is scarcely possible that there can be any error (...).
Charles Babbage, On the mathematical
powers of the calculating engine (1837)
Anybody who has something to do with modern computers will agree that the above statement made by Charles Babbage about the analytical engine is understatement, to say the least.
Computer programs do not always work as expected. There is a complex taxonomy of errors or miscomputations. The taxonomy of possible errors is itself interesting. Syntax errors like missing semicolons are quite obvious and are easy to catch. Logical errors are harder to find, but at least we know that something went wrong. For example, our algorithm does not correctly sort some lists. There are also issues that may or may not be actual errors. For example an algorithm in online store might suggest slightly suspicious products. Finally, we also have concurrency errors that happen very rarely in some very specific scenario.
If Babbage was right, we would just try three or four simple cases and eradicate all errors from our programs, but eliminating errors is not so easy. In retrospect, it is quite interesting to see how long it took early computer engineers to realise that coding (i.e. translating mathematical algorithm to program code) errors are a problem:
Errors in coding were only gradually recognized to be a signiﬁcant problem: a typical early comment was that of Miller [circa 1949], who wrote that such errors, along with hardware faults, could be "expected, in time, to become infrequent".
Mark Priestley, Science of Operations (2011)
We mostly got rid of hardware faults, but coding errors are still here. Programmers spent over 50 years finding different practical strategies for dealing with them. In this blog post, I want to look at four of the strategies. Quite curiously, there is a very wide range.
Science is much more 'sloppy' and 'irrational' than its methodological image.
Paul Feyerabend, Against Method (1975)
Programming languages are a fascinating area because they combine computer science (and logic) with many other disciplines including sociology, human computer interaction and things that cannot be scientifically quantified like intuition, taste and (for better or worse) politics.
When we talk about programming languages, we often treat it mainly as scientific discussion seeking some objective truth. This is not surprising - science is surrounded by an aura of perfection and so it is easy to think that focusing on the core scientific essence (and leaving out everything) else is the right way of looking at programming languages.
However this leaves out many things that make programming languages interesting. I believe that one way to fill the missing gap is to look at philosophy of science, which can help us understand how programming language research is done and how it should be done. I wrote about the general idea in a blog post (and essay) last year. Today, I want to talk about one specific topic: What is the meaning of types?
This blog post is a shorter (less philosophical and more to the point) version of an essay that I submitted to Onward! Essays 2015. If you want to get a quick peek at the ideas in the essay, then continue reading here! If you want to read the full essay (or save it for later), you can get the full version from here.
As someone doing programming language research, I find it really interesting to think about how programming language research is done, how it has been done in the past and how it should be done. This kind of questions are usually asked by philosophy of science, but only a few people have discussed this in the context of computing (or even programming languages).
So, my starting point was to look at the classic works in the general philosophy of science and see which of these could tell us something about programming languages.
I wrote an article about some of these ideas and presented it last week at the second symposium on History and Philosophy of Programming. For me, it was amazing to talk with interesting people working on so many great related ideas! Anyway, now that the paper has been published and I did a talk, I should also share it on my blog:
- What can Programming Language Research Learn from the Philosophy of Science?
- Fairly minimalistic slides from my talk at the symposium
One feedback that I got when I submitted the paper to Onward! Essays last year was that the paper uses a lot of philosophy of science terminology. This was partly the point of the paper, but the feedback inspired me to write a more readable overview in a form of blog post. So, if you want to get a quick peek at some of the ideas, you can also read this short blog (and then perhaps go back to the paper)!