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 These days, I mostly post my tech musings on Linkedin.  https://www.linkedin.com/in/seanmcgrath/

Friday, April 14, 2017

What is law? - part 8

Previously:  what is law? - Part 7.

A good place to start in exploring the Closed World of Knowledge (CWoK) problem in legal knowledge representation is to consider the case of a spherical cow in a vacuum...

Say what? The spherical cow in a vacuum[1] is a well known humorous metaphor for a very important fact about the physical world. Namely, any model we make of something in the physical world, any representation of it we make inside a mathematical formula or a computer program, is necessarily based on simplifications (a "closed world") to make the representation tractable.

The statistician George Box once said that "all models are wrong, but some are useful." Although this mantra is generally applied in the context of applied math and physics, this concept is incredibly important in the world of law in my opinion. Law can usefully be thought of as an attempt at steering the future direction of the physical world in a particular direction. It does this by attempting to pick out key features of the real world (e.g. people, objects, actions, events) and making statements about how these things ought to inter-relate (e.g. if event E happens, person P must perform action A with object O).

Back to cows now. Given that the law may want to steer the behavior of the world with respect to cows, for example, tax them, regulate how they are treated, incentivize cow breeding programs etc. etc., how does law actually speak about cows? Well, we can start digging through legislative texts to find out but what we will find is not the raw material from which to craft a good definition of a cow for the purposes of a digital representation of it. Instead, we will find some or all of the following:
  • Statements about cows that do not define cows at all but proceed to make statements about them as if we all know exactly what is a cow and what is not a cow
  • Statements that "zoom in" in cow-ness without actually saying "cow" explicitly e.g. "animals kept on farms", "milk producers" etc,
  • Statements that punt on the definition of a cow by referencing the definition in some outside authority e.g. an agricultural taxonomy
  • Statements that "zoom in" on cow-ness by analogies to other animals eg. "similar in size to horses, bison and camels."
  • Statements that define cows to be things other than cows(!) e.g. "For the purposes of this section, a cow is any four legged animal that eats grass."
What you will not find anywhere in the legislative corpus, is a nice tidy, self contained mathematical object denoting a cow, fully encapsulated in a digital form. Why? Well, the only way we could possibly do that would be to make a whole bunch of simplifications on "cow-ness" and we know where that ends up. It ends up with spherical objects in vacuums just as it does in the world of physics! There is simply no closed world model of a cow that captures everything we might want to capture about cows in laws about cows.

Sure, we could keep adding to the model of a cow, refining it, getting it close and closer to cow-ness. However, we know from the experience of the world of physics that we reach the point where have to stop, because it is a bottomless refinement process.

This might sound overly pessimistic or pedantic and in the case of cows for legislative purposes it clearly is, but I am doing it to make a point. Even everyday concepts in law such as aviation, interest rates and theft are too complex (in the mathematical sense of complex) to be defined inside self-contained models.

Again, fractals spring to mind. We can keep digging down into the fractal boundary that splits the world into cow and not-cow. Refining our definitions until the cows come home (sorry, could not resist) and we will never reach the end of the refinement process. Moreover many of the real world phenomena law wants to talk about exhibit a phenomenon known as "sensitivity to initial conditions"[3]. It turns our that really, really small differences in the state of the world when an event kicks off, can result is completely different outcomes for the same event. This is why, in the case of aviation for example, mathematical models of the behavior of an aircraft wing can only get you so far. There comes a point where the only way to find out what will happen in the real world is to try it in the real world (for example, in a wind tunnel.) So it is with law. Small changes in any definitions of people, objects, actions, events, can lead to very different outcomes. The sensitivity to initial conditions means that it is not possible to fully "steer" outcomes by refining the state of affairs to greater and greater depth. Outcomes are going to be unpredictable, no matter how hard you work on refining your model.

We can come at this CWoK problem from a number of other perspectives, each of which shine extra light on the representation problem. From a linguistics perspective, in searching for a definition of "cow" we can end up in some familiar territory. For Sausserre[4] for example, words have meaning as a result of their differences...from other words:-) Think of a dictionary that has all the words in the English language in it. Each word is explained....in terms of other words! Simply put, language does not appear to be a system of symbols that gets its meaning by mapping it onto the world. It gets is meaning by mapping back onto itself.

From a philosophical perspective, trying to figure out what a word like "cow" actually means has been a field of study for thousands of years. It is surprising tricky[5], especially when you add in the extra dimension of time as Searle does with the concept of Rigid Designation[6].

Fusing philosophy and linguisics, Charles Sanders Pierce noted that nothing exists independently. I.e. everything we might put a name on only exits in relation to the other things we put names on[9] . We can approach the same idea from an almost mystical/religious perspective and find ourselves questioning the very existence of cows:-) Take a look at this picture from Zen Master Steve Hagen for example[8] Do you see a cow? Some people will, some will not. How can we ever hope to produce a good enough representation of a cow unless we all share the same mental ability to split the world between cow and non-cow?

Echoing Charles Sanders Pierce, we find the ancient Eastern concept of dependent origination[10]. Everything that we think exists, only exists in relation to other things that we think exist. Not only that, but because everything is constantly changing with respect to time, the relationships between the things – and thus their very definitions - keep changing too.

This is essentially where philosopher John Searle ends up in his book Naming and Necessity[11]. For Searle, the meaning of nouns, ultimately, is a social convention and meaning *changes* as social convention changes. One final philosophical reference and then we will move on. Wittgenstein famously stated that the meaning of language can only be found in how it is used - not in dictionaries[12]. As with Pierce, the meaning can change as the usage changes.

This doesn't sound very promising does it? How can law do its job if even the simple sounding concept of rigorously defining terms is intractable? Law does it by not getting caught up in formal definitions and formal logic at all. Instead, the world of law takes the view that it is better to leave a lot of interpretation to a layer of processing that is outside the legal corpus itself. Namely, the opinions formed by lawyers and judges. The way the system works is that two lawyers, looking at the same corpus of legal materials can arrive at different conclusions as to what it all means and this is ok. This is not a bug. It is a feature. Perhaps the feature of law that differentiates it from classical computing.

The law does not work by creating perfect unambiguous definitions of things in the world and states of affairs in the world. It works by sketching these things out in human language and then letting the magic of human language do its thing. Namely, allowing different people to interpret the same material differently. In law, what matters is not that the legal corpus itself spells everything out in infinite detail. What matters is that humans (and increasingly, cognitively augmented humans) can form opinions as to meaning and then defend those opinions to other humans. This is the concept of legal argumentation in a nutshell. It is not just inductive reasoning[13], taking a big corpus of rules and a corpus of facts and “cranking the handle” to get an answer to a question. It is, in large part, abductive reasoning[14] in which legislation, regulations, caselaw are analyzed and used to construct an argument in favour of a particular interpretation of the corpus.

That is why parties to a legal event such as a contract or a court case have their own lawyers (at least in the US/UK common law style of legal system). It is an adversarial system [15] in which each legal team does its best to interpret the corpus of law in the way that best serves their team. The job of the judge then is to decide which legal argument – which interpretation of the corpus presented by the legal teams – is most persuasive.

This is what I think of as the Unbounded Opinion Requirement (UoR) of law. This UoR aspect, kicks in very, very quickly in the world of law because the corpus – for reasons we have talked about – doesn't feature the clear cut definitions and mathematically based rules that computer people are so fond of. The corpus of law, does not spell out its own interpretation. It cannot be “structured” in the sense that computer people tend to think of structure. It has as many possible interpretations as there are humans – or computers - to read it and construct defenses for their particular interpretations.

I have been arguing that a “golden” interpretation cannot be in the legal corpus itself, but I think it is actually true that even if it could, it should not be. The reasons for this relate to how the corpus evolves over time and how interpretation itself evolves over time and that this is actually a very good thing.

A classic example of a legal statement that drives computer people to distraction is a statement like “A shall communicate with B in a reasonable amount of time and make a fair market value offer for X.” What does “reasonable amount of time” mean? What does “fair market value” mean?

A statement like “reasonable amount of time” for A to communicate with B is a good example of a statement that may be better left undefined so that the larger context of the event can be taken into account in the event of any dispute. For example what would a reasonable communications delay be, say, between Europe and the USA in 1774? In 1984? In 2020? Well, it depends on communications technology and that keeps changing. By leaving it undefined in the corpus, the world of law gets to interpret “reasonable” with respect to the bigger, “open world” context of the world at the time of the incident.

In situations where the world of law feels that some ambiguity should be removed, perhaps as a result of cultural mores, scientific advances etc. it has the medium of caselaw (if the judiciary is doing the interpretation refinement), regulations/statutory instruments (if the executive branch is doing the interpretation refinement) and primary law (if the legislature/parliament) is doing the interpretation refinement.

One final point, we have only just scratched the surface on the question of interpreting meaning from the corpus of law here and indeed, there are very different schools of thought on this matter within the field of jurisprudence. A good starting point for those who would like to dig deeper is textualism[16] and legislative intent[17].

In conclusion and attempting a humorous summary of this long post, the legal reasoning virtual box we imagined in part 1 of this series, is unavoidably connected to it surroundings in the real world. Not just to detect, say, the price of barrel of oil at time T, but also for concepts like “price” and “barrel” and maybe even “oil”!

On the face of it, the closed world of knowledge (CwoK) and the Unbounded Opinion Requirement (UoR) might seem like very bad news for the virtual legal reasoning box 
However, I think the opposite is actually true, for reasons I will explain in the nextpost in this series.


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