Do we learn abstractions, or just instantiate innate metaphysical templates?
It seems obvious (Or does it?)
Let’s consider a general rule that — clearly all of us, and since the early years of childhood — we come to learn, namely the metaphysical fact shown in the picture below.
Children do indeed come to know this metaphysical truth very early: if they move a bag from one room to another, then their baseball glove which is in the bag, must now be in the new room. We take it that this fact should not be controversial.
But how do children come to know such metaphysical truths very early? Empiricists (and thus statistical/data-driven enthusiasts) will of course argue that this is done bottom-up: a child comes to “know” metaphysical fact 1 by seeing so many instances of objects that take on the location of the objects they are contained in.
But this simple explanation has many problems, the most important of which is a circular logic that does not have any plausible answer.
What did we abstract first?
The data-driven empirical explanation of how a child comes to know of metaphysical fact (MF) 1 is problematic in this sense: either a child comes to know first that bags, suitcases, briefcases, trucks, cars, etc. can all be looked at as ‘containers’ that one can have objects contained in; objects that must also be ‘smaller’; or — in the absence of a type hierarchy that must be learned first — the child has to see so many instances of this metaphysical fact that involves various types of objects and various types of containers. But how many different objects and containers must a child see? If you consider also that this metaphysical fact applies to all objects regardless of their size; as long as the container is larger than the contained, then this would seem to be implausible. More problematic is the fact that knowing metaphysical fact 1 bottom-up means the child has also known that the ‘contained-in’ relation is transitive — so that if their baseball glove is in the bag, and the bag is in the car, and the car is being hauled by a truck, then their baseball glove must be wherever the truck is!
Note also that the above metaphysical fact has several facts that are associated with it: if a house is completely burned down, all (most?) of what it contains must also have been burned with it — in fact, the burning of the house is in effect the burning of all that it contains — or all that is ‘part of it’. Does a child also need to see examples of all of these? This also seems implausible, given how quickly a child comes to know metaphysical fact 1.
The metaphysical fact given above (an object y contained in an object x always assumes the location of x) is just one example of naïve physics that children come to know very quickly. Another one is the transitivity of so many relations: ‘LargerThan’, ‘OccursBefore’, etc. Or the metaphysical fact that an object must occupy some space/time and so if their toy truck is not in the vicinity of the child, then the child knows that the toy truck did not disappear or cease to exist, but that it must be somewhere else.
The data-driven empirical explanation of how a child comes to know of all of these metaphysical facts — namely bottom-up from seeing many instances, is very problematic; mainly because this is cognitively implausible and simply because one can easily see that this story will soon run into circular logic: to learn metaphysical fact (MF) 1 we must assume that we have already learned MF 2, and that might presuppose that we have learned MF 1.
But what else then, if the data-driven empirical explanation is implausible? If we don’t learn these abstract templates of thoughts bottom-up, what else could explain how a child comes to learn these these metaphysical facts very early?
Could our Learning be Top-Down?
A child knows very early on that if we paint a chair with red paint, then the color-of(chair) = red, but the child also knows this holds regardless of the object (chair, car, ball, etc.) and regardless of the color. Again, while this is a very simple metaphysical fact, learning this bottom-up also seems to be problematic since it would easily run into circular logic — as it would only work if the child has already classified various physical objects, as well as colors, and has already seen a massive amount of paintings of objects of various sizes painted with different colors.
Let us suggest an alternative (and what might at first seem to be an implausible) explanation. Could it be that many naïve physics facts have been genetically encoded as general rules of the commonsense world and that all that is needed to ‘master’ these templates are few instantiations? In other words, could the learning be happening in reverse, from general templates to instantiations that simply fit and confirm the general rule? Well, in the high-level cognitive world of language and mathematics that does indeed seem to be the case.
Abstract Language Templates
Consider this template of a a very simple nominal construction, that of a Noun-Noun compound:
Substance Artifact
Any such Noun-Noun compound, where the first noun is a Substance and the second noun is an Artifact satisfies the Artifact-made of-Substance template (function). Here are some examples:
plastic knife
paper cup
cheese cake
silver spoon
wooden stick
bronze statue
silicon chip
glass table
sand castle
brick house
etc.
I argue that we come to know of the Artifact-made of-Substance template by observing a few instances of an innate (already known) template and not by “seeing” a combinatorial number of (substance, artifact) pairs where (substance, artifact) are pairs in Artifact x Substance. Language is full of such templates that it would be unthinkable that they are all learned “bottom-up” — and not only because of the circularity argument, but also the speed by which these templates come to be known in early childhood does not seem to be consistent with learning these templates by seeing a combinatorial number of examples.
Besides language, the world of mathematics — and by extension, computing, also suggests that all we do in many cases is in fact insatiate already known true facts, rather than learn these universally true facts bottom-up. For example, if you ask a child to put an object in a bag and it did not fit, you will make a child baffled if you asked her to put the same object in a smaller bag and that’s because the child seems to already know that “BiggerThan” is a transitive relation (if x did not fit in y; then it will not fit in a z that is smaller than y).
Or, take the simple mathematical fact that the length (or size) of a container is less than the length (or size) of the container that has an additional object added to it. If the container is a list, then a (polymorphic) formal statement of this fact would like this:
for any list L, len(attach(x, L)) > len(L)
Even a child knows that if they add a toy to their bag, they have more toys in their bag than they had before they added another toy. A child also knows that if a group of people G going on a trip split into two groups g1 and g2 so as to fit into two cars, then |G| = |g1| + |g2| or, more formally:
for all G, g1, g2,
if G = (g1 ++ g2),
then len(G) = len(g1) + len(g2)
Thus, a child knows that the sum of the number of people in g1 and the number of people in g2 is exactly the total number of people that split. This is not a trivial metaphysical fact: the child apparently knows that the len function distributes over addition!
There are many such mathematical, linguistic, conceptual and just plain commonsense facts that children seem to know very early on and that suggests that perhaps we do not learn everything bottom-up, but perhaps we come endowed with some templates of naïve physics (that I called here metaphysical facts) that we come to “own” by seeing a few instantiations of them. This certainly explains the speed at which children come to know many facts about the physical world, and it also explains how fast children instantiate the language module, and how we come to “discover” mathematical facts (including computing rules) and relate them to our physical world.
Another lengthy discussion that I did not get into here is that of metaphor and how we come to relate abstractions to the physical world we live in by metaphorical mappings (heat/anger/up, source-path-goal, etc.) but I will leave that for another article.
Final Word
If we do learn (or, if we do come to know) many metaphysical facts in a top-down fashion (by instantiating available/innate templates), then we have a lot to re-think about how we are doing AI.
__
Keep AI’ing.
ONTOLOGIK — Medium
