I’ve never appreciated the fact that lots of great stuff is on youtube.  Case in point: live video of the Dead Milkmen.

I came across this article/handout today, and I thought it was pretty neat.  The idea is that dispositions aren’t simply triggered by the occurrence of an event:

Bad Solubility:

  • Trigger: Dunking in water
  • Manifestation: Dissolving
  • Causal Pattern: If T(x) then M(x), all things being equal.

Rather, dispositions are properties that sorta encourage the manifestation of a certain kind of event with a certain level of oomph.  So we have something like this:

Good Solubility:

  • Direction: Dunking in water –> Dissolving
  • Magnitude: 32

I don’t have access to the full article, so I’m missing a few important details (like what the magnitude is measuring).  Still, the idea interesting: dispositions are vectors in a vector space of qualities.  A quality (like dissolving) manifests if a certain threshold is reached (like 90).

Since we have a vector space, we can add the dispositions present in a state of affairs to determine whether a manifestation should be expected.  Some dispositions may reduce the chance of a manifestation (such as the level of saturation in dunking water), while others would combine to increase the likelihood (perhaps the temperature of the water).

With details locked away in a journal beyond my reach, there’s little left to do but wonder freely through the notion of a vector space of dispositions.

We could represent qualities like solubility and fragility in a way that created a nice network of causal relationships:
:Solubility a :Quality; :dispositionTo :BeDissolved; :dispositionVal 32 .
:Fragility a :Quality; :dispositionTo :BeShattered; :dispositionVal 46 .
:BeShattered a :Quality; :dispositionTo :HoldWater; :dispositionVal -600 .

Qualities are convenient here, because they’re almost always understood to be unary atomic predications.

States of affairs are a bit more complex, as a kind of state of affairs involves multiple n-ary predications. For example, consider what it is to be shattered by a soluble object.  In the grand scheme of things, that kind of state of affair can be construed as a single unary predication.

Despite being more complex, types of states of affairs are very interesting, and seem to be conducive to this vector space view of dispositions.

Let’s say that we’re looking at hockey game data (again), and tap the following into our ontology:

  • Shot by X –[+n]–> Goal by X
  • Power Play for X –[+m]–> Goal by X
  • Penalty against X –[-m]–> Goal by X

Shots and power plays increase the likelihood of goals, while penalties lead to a decrease.  If we have a shot during a power play, it seems that we can add the individual dispositions and get

  • Shot by X during Power Play for X –[+n+m]–> Goal by X

And likewise a shot during a penalty kill should be less likely to result in a goal that an even-strength shot.

The authors of the article/handout bring up the fact that lots of issues remain to be ironed out:

  • can dispositions always be added?
  • how should the magnitudes of disposition vectors be interpreted?

There seems to be plenty of interesting ideas here to play with for a bit, and it does strike me as somewhat similar to both Judea Pearl’s theory of causation and the structural equation modeling approach.

My god – there are tons of Dead Milkmen songs on youTube.