The Heap

Hackworth, R. (tr.), Plato’s Phaedo, Bobbs-Merrill, 1955.

Robert Nozick makes a slippery-slope argument that there is only a relative difference between someone who is forced to pay taxes and a slave. This is more or less true (though it’s even more true of people working for a wage) but slippery-slope arguments of this kind. This is a relative difference, but relative differences are real; to put it more strongly, only relative differences are intelligible. That is to say, t difference between hot and cold is relative and something we can think about, but there isn’t a lot to say about the more or less absolute difference between hot and green.


In my dream I grow taller and taller…. until at last I am completely tall.
Henri Michaux

A 7′ man is tall, a 4′ man is not tall. Somewhere in between there are people who may or may not be tall. When I was a kid the dividing line was 6′, and nowadays it’s probably 6’2″. There’s absolutely no rigorous way to tell exactly where the line is, but the fact remains that some people are tall and others are not.

This is the kind of thing that fuzzy-set theory works with. (George W. Bush’s “fuzzy math” jokes annoyed me, partly because they were so deliberately ignorant but also because his own numbers were usually so dishonest). I’ve been told that fuzzy sets play a big role in robotics and AI because they keep a system from freezing up when one of the values isn’t exactly right, while still making it possible to notice that there might be a problem.

In Plato there was an argument about this somewhere. Seemingly Plato’s Socrates had an idea of tallness which was not a relative one (i.e., not also an idea of shortness) and he had to use a very complicated method of saying that A was taller than B but shorter than C. ( “A participates in tallness in relation to B, but he participates in shortness in relation to C”). I believe that Plato had to do this because he didn’t want to allow a continuum where “good” meant “less bad” and “bad” meant “less good”. He wanted an absolute Good.

However, it’s absolutism which (paradoxically) leads to the slippery slope. With relative concepts you have known ends, and argue somewhat uncertainly about the middle. With absolute concepts you have one end which is perfect and basically imaginary; everything else is equally imperfect, and first trimester abortion is the same as murder. With two ends given, you can argue about the middle without making either end disappear entirely (i.e., without either making everyone tall, or everyone short). To my mind, Chuang Tzu and Lao Tzu in Chinese philosophy had solutions to this problem superior to Plato’s.

To me Nozick’s argument is just an example of what happens when an attempt is made to use the impoverished toolkit of analytic philosophy on any kind of reality. (Peter Singer is another instance.) Rorty has defined analytic philosophy simply as training in the techniques of valid argumentation, and analytic philosophers seem to choose the cases they advocate (animal rights, anarchism) strictly on whim, after which “making the case” becomes a professionalized technical operation. It’s like a court trial, and as in court trials, the players end up concentrating on winning the argument according to the rules in place.

Today’s philosophers are like public defenders sitting and waiting for a defendant to be assigned them by the court so that they can “make their case”. Philosophers (quite rightly) used to function ultimately as the judge and the jury, making the best possible real-world judgements of the actual truth of whatever was in question. But nowadays they’re just shyster advocates.


Socrates (102 c-d): “So that is how Simmias comes to be spoken of as both short or tall, being as he is between the two others: he offers his shortness to the tallness of Phaedo to be overtopped, and presents his tallness to Socrates to overtop the shortness of Socrates”.

Socrates (102 d –103 a): “Not only will tallness itself never consent to be simultaneously tall and short, but that the tallness in us can never admit shortness, and never consent to be overtopped; instead, one of these two things will happen: it must either retreat and withdraw when its opposite, shortness, advances, or it must perish at that advance; what it won’t consent to is to endure and admit shortness, and so to be something other than it was.”

In 104 b Socrates uses the mutually-exclusive, non-relative, binary example of odd vs. even as a supporting analogy, proving that nothing is relative and everything absolute. (Chinese Taoist philosophers tend to use the examples of relative concepts such as height to show that everything is relative and nothing absolute.)

My point, and Heraclitus’s, is that there is one Form for shortness / tallness, and that individuals are relatively tall or short according to where they are on the Form. It’s not that there are two Forms, shortness and tallness, and individuals simultaneously participate in both. And similarly for goodness and beauty, which was Heraclitus’ (and Chuang Tzu’s) point.

Alternatively, there is one “height” Form, with the comparative heights of individuals (“taller than” and “shorter than” relations) known by comparing their locations of the Form, and with the general ideas of “shortness” and “tallness” designated in terms of some conventional normative standard applied to the Form.