Wednesday, December 13, 2017

Zeno for the computer age

If you wish to better understand Zeno's worry about the continuum, you could do worse than to consider loops in software.

Case 1: You want to loop over 10 records. You write:

for i from 1 to 10

What could be simpler? OK, let's loop over the positive integers, finding the prime numbers:

for i from 1 to ∞

This loop will run forever, but it is a perfectly valid loop. We can even set it up to loop over all integers:

j = 0
for i from 0 to ∞
    j = j - 1
    print i
    print j

And with only a little more trouble, we could loop over the rational numbers as well.

But what if I ask you to loop over the real numbers between, say, 0 and 1? The problem here is much worse than the loop running forever: the loop can't even get started. We could print out "0"... and then what? There is no "next" real number to which we can proceed. And note: the concept of a limit does not help with this problem at all.

And this is what Zeno was noting about motion in the continuum.

Tuesday, December 12, 2017

Open Source Software and Skin In the Game

I have been tinkering in the Haskell programming language recently. Trying to up my game, I have begun reviewing and working on issues in the Cabal project. Soon after submitting a (very) small pull request, the project admitted me to being a full contributor. I was surprised. I'm a Haskell newbie, and it's not my project.

A developer linked me to this post which argues for promoting random contributors to full collaborator status. Its author argues that if someone owns the project as his own, he's a better developer for that project. Admittedly the promoted contributors are not completely random. The author looks for signs showing the developer is responsible and can be held accountable for his work. And (in the author's experience) this has led to higher quality programs than his overseeing all commits.

Friday, December 08, 2017

Why so many died

"Tired of waiting for heaven — that is, for a condition where the transcendent would no more have to compromise with the immanent — these men and women [of the European wars of religion] tried to render it here on earth. Because this cannot be done, they could not agree on how to do it; because they could not agree on how to do it — and yet agreed that it needed to be done — they tore one another to shreds." -- Daniel Sportiello, "Rationalism in Eric Voegelin"

Saturday, December 02, 2017

What is the Friggin' problem with the imagination?

I have been going back over my review of Philosophy of Science in Practice: Nancy Cartwright and the Nature of Scientific Reasoning, and want to note an interesting problem, or perhaps pseudo-problem, that I did not have space to bring up in the review.

Roman Frigg and James Nguyen, in their essay in the reviewed work, have a very enlightening discussion of how scientific models "represent" some phenomenon. (Roman was one of my lecturers when I studied the philosophy of science at the LSE, and an excellent lecturer at that, so I hope he will forgive my pun on his name in the post title! Also, I am writing this post without the book in front of me, so I beg forgiveness if my rendition of the authors' terminology is not exact.)

Frigg and Nguyen's primary criterion for how a scientific model represents is that it is "declared" to represent some class of events: for example, a histogram of adult heights in the United States represents those heights because it has been declared to do so. (This simple declaration does not make a model a good model: to be a good model, it must further exemplify some salient aspects of the thing being modeled.)

But, per this definition of a model, the authors feel embarrassed by entities like "a map of Middle Earth" or "a drawing of a unicorn": since there just is no such thing as Middle Earth or unicorns, what do such models "represent"? Their solution seems to me to be unnecessarily convoluted: they claim that such models, while being "representations," do not "represent" anything: they are "representations" only because they resemble other things that truly do represent (e.g., a map of France, or a drawing of a horse). (And here is where I may have screwed up the exact terminology, since I can't locate the book at present, but nevertheless I think I have their sense correct.)

I can't see why they choose this solution, rather than going for what to me is the more straightforward answer: a map of Middle Earth represents the way J.R.R. Tolkien envisioned Middle Earth in his imagination, and a drawing of a unicorn represents what people imagine unicorns to look like. Of course, imaginary things are not real in the same sense that the furniture of the physical universe is real, but so what? Surely, the creatures of our imagination exist in some sense, even if in a more shadowy sense than do real animals and real countries.

And I think that my solution to this problem sidesteps a serious difficulty facing the solution offered by Frigg and Nguyen: let us imagine that no histograms had ever been created before Tolkien, but that Tolkien himself invented the histogram to "model" the distribution of hobbit heights. Per Frigg and Nguyen, this would not have been any sort of representation at all since, at the time Tolkien created it, it would have borne no resemblance to any representation of a "real" phenomenon: hobbits "do not exist." (I use the scare quotes because my contention is that they did exist at the time of the model creation, in Tolkien's imagination.) However, later on, if other people picked up on Tolkien's idea, and began to represent the distribution of the values of "real" entities with histograms, Tolkien's histogram would mysteriously, post-facto, turn into a representation, since it would now resemble models that actually do represent.

And that post-facto transformation of non-models into models, I think, renders the Frigg and Nguyen model of models less plausible than the one I offer here.

Tuesday, November 28, 2017

Single causes come first...

and general causal laws are derived from them:

"I maintain that the Hume programme has things upside down... Singular causal claims are primary. This is true into senses. First, they are a necessary ingredient in the methods we used to establish generic causal claims. Even the methods that test causal laws by looking for regularities will not work unless some singular causal information is filled in first. Second, the regularities themselves play a secondary role in establishing a causal law. They are just evidence -- and only one kind of evidence is that -- that certain kinds of singular causal fact have happened." -- Nancy Cartwright, Nature's Capacities and Their Measurement, p. 2

Tuesday, November 21, 2017

An orgy

“The advancement of science and the rationality of politics are interwoven in a social process that, in the perspective of a more distant future, will probably appear as the greatest power orgy in the history of mankind.” -- Eric Voegelin, “The Origins of Scientism”

Zeno for the computer age

If you wish to better understand Zeno's worry about the continuum, you could do worse than to consider loops in software. Case 1: You...