Thursday, 28 October 2021

Are Affordances Plausible? Updating Some Intuitions

In the previous post, I laid out the basic distinction between direct and indirect theories of perception. The basic issue is how to get to behaviourally relevant properties. Such properties of the world have to be partly about the organism, and not just the world; not just 'mass', which is something about the world, but 'moveability' which is something about the world, relative to the organism. If there are properties like these out in the world, and we can perceive them, then perception can, in principle, be direct. If there aren't properties like these there to be perceived, we would have to invent them, and perception would have to be indirect. The ecological hypothesis has to begin by finding behaviourally relevant properties out in the world, ready to be perceived without having to be invented; we need to find affordances

The problem is that this seems to be madness, right off the bat. It seems bizarre to think that things separate from the organism could possibly have properties that have anything to do with the organism. Why would they have such things? Surely things can only have properties that are about themselves and make them what they are? 

This post will talk about some pieces of information that make this at least plausible; the next post will talk about the specific ecological hypothesis about affordances that tries to implement that plausibility. To get to that plausibility, I am going to have to update your intuitions about what is simple, and what sorts of things can be physically real, and along the way introduce some useful vocabulary I will do everything I can to use clearly. 

1. Predicative and Impredicative Properties (A Little Vocab)

Where do properties live? The obvious answer is that they live in the thing that 'has' that property; that's what 'having that property' means. There are lots of properties that happily work this way; we can sensibly say that an object 'has' a certain mass and that's a complete story, no further information required. In the lingo, we can predicate the property 'mass' to an object. 

Other properties are more complicated. For example, 'moveability' isn't a property that we can predicate to just an object. For the full story, we need to include some information about the thing trying to do the moving. I can't move a 1-ton anvil but a crane can - same object, different mover, different moveability. 'Moveability' is an impredicative property, defined not just with respect to a single object but with respect to the more distributed physical system that is implementing the property. 

For 300 years or so, physics has considered predicative properties to be objective and primary, while impredicative properties are subjective and secondary. Primary properties are what's out there regardless of who's observing, and secondary properties have to be constructed by some kind of negotiation between the primary properties and observers. They are different in kind, and differ in status - primary properties are what's real, secondary properties are the kinds of weird things cognition has to invent. If this is correct, no affordances for us. 

One of the big changes to physics in the 20th and 21st century, however, has been discovering that the universe is basically made of impredicative properties. We call this quantum mechanics. For example, is a photon a wave or a particle; which set of properties can we predicate to the photon? Neither, and both; the (slightly terrifying) answer is that it depends on how you measure the photon. If you ask it wave questions, it behaves like a wave, but it you ask it particle questions, it behaves like a particle. In terms of our spoken language, this inability to assign properties to things is a worrying absurdity, but in terms of the mathematics its perfectly acceptable and, most importantly, a central reason why quantum mechanics works so incredibly well.

So we have accomplished one thing - at least some physical properties can be impredicative and be perfectly real. But are they just weirdos living in the quantum scale? The specific mechanism that supports impredicative properties at the quantum scale only lives and works there; at that scale, all properties are indeterminate until measurement resolves the uncertainty one way or another. At larger (e.g. ecological) scales, the uncertainty is already resolved prior to measurement. However, measurement does affect which properties can be taken as given, and which have to be figured out.

2. The Lesson of the Polar Planimeter (Runeson, 1976)

Imagine you have a pond, and you would like to know what area it has. Area is a higher-order (order 2) property; it is made of two lower-order measurements of length (order 1) that we use in a multiplication operation to make area. A priori, length is 'simpler' than area. 

However, it turns out that which of the two is the 'simple' property depends on how you are measuring. If you measure your pond with a length-ometer (e.g. a ruler), area is nowhere to be seen and has to be constructed via a mediating process. However, if you measure your shape with an area-ometer (e.g. a polar planimeter), then length is nowhere to be seen and has to be constructed via a mediating process. Importantly, polar planimeters exist and are therefore options. 

The lesson is this: how the world presents itself, which properties it makes immediately available, depends on the measurement device. The a priori analysis of 'simple' vs 'complex' is incomplete, and as in quantum mechanics, the full specification of what properties are present in what ways requires details of the measurement device.

Summary

Behaviourally relevant properties are a worry. It seems that by definition they aren't just properties we can predicate to things in the world, but that they are impredicative properties that are defined with respect to the organism-world system which makes them the kind of properties that have to be made by some process operating on the simpler elements. But we have learned a couple of things. 

First, impredicative properties are legitimate options for physical properties; everything at the quantum scale is impredicative and that is the single most reliable fact in science. Second, this kind of impredicativity is enabled by measurement. At the quantum scale, measurement is part of how properties are constituted, and while this part isn't true at the ecological scale, which properties of the world are 'simple' (i.e. don't need to be created) still depends on the measurement device at all scales. You can build a device that considers a higher order property as simple and the lower order properties as complex, or derived. Therefore, a measurement device that considers an impredicative behaviourally relevant property as simple is, in principle, a legitimate option. 

I tried really hard to write this post without getting into quantum physics or impredicativity. But I couldn't, because as I say at the start, making things like affordances plausible requires updating a few notions about what is allowed. This post is weird in another way; I've talked about quantum properties and polar planimeters but perception is not a quantum phenomenon nor is it made out of planimeters. So bear with me; at this point I am just laying out some concrete examples to show the things I need access to are physically possible. In the next post, I will go through the theory of affordances-as-dispositions, which is the particular attempt to implement all these ideas at the ecological scale. Yes, yes, I know - there's also affordances-as-relations. I'll get into how these do not hold up as a successful implementation of what affordances have to be in order to support direct perception too.

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