Zeno was not worrying about specifications or formal systems

By -


Reader Alex Small writes:

"the fact that we can specify a process via an infinite list of statements does not mean that it is impossible for such a process to happen. There is an implicit assumption that the only physically feasible processes are those with finite specifications in some particular formal system."

But this is mistaking what the Greeks were worried about. There concern was not with specifications or formal systems. There concern was with the nature of space. And they were puzzling over whether space, in reality, was infinitely divisible, or was it somehow chunky, or atomic. And some among them noted that, if it is infinitely divisible, that seems to create some problems, such as it seemingly making it impossible for things to get moving.

The difference between worrying over this and worrying over specifications in formal systems might be clarified by my stating that I have no quarrel with the mathematical concept of the continuum at all. The fact that in a formal system, something might be specified as taking an infinite number of steps, and that we then treat those steps as if they were completed, leaves me as serenely unperturbed as the Buddha under the bodhi tree*. We can have a model of space as a continuum, and if it proves useful, well, for a model, that's all that counts.

The issue here is not about our specifications or any formal system: it is about reality.

* Remember his big hit, "Don't sit under the bodhi tree / with anyone else but me / anyone else but me"?

Comments

Post a Comment

Popular posts from this blog

Libertarians, My Libertarians!

By -
Cruel to be kind means that I love you . Because, while I think you are mistaken, your hearts are in the right place -- yes, even you, Silas --  unlike some people . This Breitbart fellow (discussed in the link above), by all appearances, deliberately doctored a video of Shirley Sherrod to make her remarks appear virulently racist, when they had, in fact, the opposite import. I heard that at a recent Austrian conference, some folks were talking about "Callahan's conservative turn." While that description is not entirely inaccurate, I must say that a lot of these people who today call themselves conservative give me the heebie-jeebies.
Read more

"Pre-Galilean" Foolishness

By -
 I am currently reading The Master and His Emissary , which appears to be an excellent book. ("Appears" because I don't know the neuroscience literature well enough to say for sure, yet.) But then on page 186 I find: "Asking cognition, however, to give a perspective on the relationship between cognition and affect is like asking astronomer in the pre-Galilean geocentric world, whether, in his opinion, the sun moves round the earth of the earth around the sun. To ask a question alone would be enough to label one as mad." OK, this is garbage. First of all, it should be pre-Copernican, not pre-Galilean. But much worse is that people have seriously been considering heliocentrism for many centuries before Copernicus. Aristarchus had proposed a heliocentric model in the 4th-century BC. It had generally been considered wrong, but not "mad." (And wrong for scientific reasons: Why, for instance, did we not observe stellar parallax?) And when Copernicus propose
Read more