Essay:Learned sets

Sort of a follow up to the much larger Essay:Painting the World.

What is a set?

A Set is just a group of interrelated things. Mathematics has the most formal version of this concept. So {1, 2, 3, 4...} is a set of positive integers, and {2, 4, 6, 8...} would be a set of positive even integers. We usually distinguish whether something is part of a set or not through a membership test. So if we divide by 2 and have no remainder we can say that it belongs in the second example. 68, 858, 94,282 pass the test, 77, 98.67, 0.533 don't. But mathematics is (usually) nice to us in this respect.

What if the set in question was {3, 9, 66.75, π, xylophone...}? Why? Well, why not? Let's just assume it is for the sake of argument, because some ancient Greek mathematician laid this set down thousands of years ago.

Forming a membership test for this bizarre combination would be a challenging task, it might not even be possible, really. We have a set that just is, but doesn't have a membership test - which violates the concept of set in a mathematical sense, but it still happens elsewhere. We can only populate this set through a combination of existing knowledge, or, by being motivated to put a object into that set for some reason other than a direct membership test.

What is art?

So consider questions like "what is music?" or "what is art?" or "what is religion?". These things, art, music, religion (these are just examples, too), aren't really sets with membership tests. They're things we've learned. We recognise a song in an album chart as music, but is John Cage's 4:33 "music"? It puzzles us to think about it, so we try to come up with a membership test to describe it. "Sounds, heard" and "organised sound" is sometimes the definitions given for music, but what do they accomplish? If someone answers "what is art?", it's a better indication of their personal preference than what art is as they might demand that art have a point, or emphasise creativity - so people who merely paint aren't artists, despite their skill, but someone who presents an empty room with a blinking lightbulb in it is an artistic genius. This hints at the concept of motive behind forming a category.

This "motive" is concerned not with the observed properties, but with the inferred properties of a category. If the inferred property of "art" is that it can be sold for a lot of money, that's pretty strong motive to alter the membership test to match what "art" you have to sell.

Is atheism a religion?

Is atheism a religion? Perhaps, perhaps not - but then we have to ask what is "religion" and what is "no religion", and most importantly what do we accomplish by defining these things. Because there's no actual membership test readily available, we hit problems when trying to make one. We recognise Christianity and Islam as religions because self-definition and experience has reinforced that these things belong in the set marked "religion". We don't recognise walking under ladders, black cats crossing in front of us, or finding four leaf clovers, or touching wood to be part of "religion". Yet it's difficult to come up with a description of such superstitions that doesn't also include the major (and minor) religions, and it's difficult to come up with a description of the religions that doesn't also include those superstitions. We might also talk of religion meaning "God", but where does that leave Taosim, or Buddhism, or Jedi? So we can't ask what a religion is, until we answer why we want to draw a box around it and label things as a religion. At least once we've done that we can proceed with a bit of honesty as to our intentions.

We might struggle to generate an inclusive membership test because one didn't actually exist when the set, or category, was actually created - or at least it's become decreasingly relevant as more things have been shoehorned into the category over time and we've learned to accept them as part of it. Alternatively (and I think this is the most common and easiest to illustrate case), we learn a category and a membership test, but then find through subsequent examination of reality and further accumulation of knowledge that this test doesn't quite set out to do what we think it should do. Again, motive for why we want to put something into "Category X" becomes important.

What is life?

An strong example of the latter case is "life". Ask "what is life?" and you will get a thousand different answers from a thousand different people, it's hardly helpful. This is because we evolved and grew up with a simple dichotomy of "alive" and "not-alive" because we could eat or be eaten by other living things, but not really by non-living things. If it moved, it was alive, if it didn't it wasn't alive. We ascribed this concept of "life" to the animate, but not to the inanimate and a quick and accurate judgment of this would be a life or death decision. The motive was clear for why we had to make this distinction; our concept of life and being alive was never about a magic property called "life", it was about finding food and avoiding becoming food.

Fast forward a few thousand years and we've since developed a broad knowledge range that transcends such a simplistic dichotomy. Consider the many examples that confuse people when they ask "is it alive?" - A computer with advanced AI that passes the Turing Test; a brain-dead person in a vegetative state; viruses, prions and other microscopic life; symbiotic and parasitic life; gametes, zygotes and embryos; artificial DNA that replicates with mutation so undergoes natural selection; reanimated cells that posses artificially created DNA. The list goes on for things that don't cleanly fit our old and outdated membership test of "does it move", so we look for a new membership test for a set that just doesn't have relevance any more. Yet, we've learned that set, and we've learned its members, so we continue to use it anyway. It then transfers to different motivation that drives whether something is included in the set. Some people think freshly fertilised human eggs are "human life", even though they'd fail any meaningful membership test of this, all because someone, somewhere, decreed that abortion was wrong. Does this mean one can't make a meaningful case against abortion? No, but it does mean you can't do it by lumping in a zygote with a fully grown human and say that this is an objectively derived conclusion, a la personhood laws.

It's simply a capital mistake to confuse a strong biased motive and desire for an actual and accurate representation of reality.

Is that a man or a woman?

The same thing happens with the gender binary; as we have become more accepting of sexuality and identity, a simple 1 or 0 doesn't help us as much any more. Our knowledge and the way it's decided has simply altered, but we've clung onto the categories still because they have a certain simplicity and we've been informed what they are. Anything that doesn't fit that dichotomy becomes a little weird, even though that's exactly what reality is telling us. We've been told that there are certain properties of "male" and "female", we've learned them - and if reality doesn't match very bad things can happen. It's the root of discrimination; our internal model doesn't match with what we see, it's weird, it must be destroyed.

Is Pluto a planet?

There is an analogous situation to all these with Pluto and the definition of "planet". We used "planet" quite haphazardly until only a few years ago, and then a few new cases made us realise we hadn't actually defined a "planet" yet, not properly at least. So a definition was made, and Pluto was excluded. Science has luxury of being able to do this, however. The objections to any particular definition were due to attachment to Pluto as a planet and the concept of 9 - and only 9 - planets in the solar system. We had spent so long simply learning the set of 9 planets rather than learning the membership test - as one didn't really exist. No membership test could be built to include Pluto but exclude Ceres and Eris. Something had to give, and Pluto was lost except on historical grounds (incidentally, Ceres was considered a planet at the time of its discovery). But as I said, science has the luxury of being able to do this and adapt its definitions in a meaningful manner as we gain more information. People themselves? Not so much, it seems.