I have recently been involved in a series of tutorials with a team from a law firm, involving mapping the arguments found in Federal or High Court judgements in the area of competition law.   For example we mapped the arguments presented by Chief Justice Gibbs of the High Court in the case Castlemaine Tooheys Ltd v Williams and Hodgson Transport Pty Ltd (1986) 68 ALR 376.  Here is the map in Rationale format:


Figure 1.  View full size image, or the Rationale file.

Mapping these judgements is quite hard work.   This is due in part to the complexity of the arguments and their often turning on subtle conceptual distinctions.  However the difficulty is also largely due to the manner of expression, i.e. the way in which judges present complex legal arguments in traditional legal prose.  In a number of ways, this style of writing makes it very challenging to determine what the arguments are, at least at the level of clarity and rigour required for a well-developed argument map.

Sparse use of logical language

When we we present arguments in prose, we can use logical language to clearly indicate the logical connections between the parts of the argument.  So for example I might say

A brewer cannot sell beer on the condition that the buyer engage a particular transport firm for delivery.  The reason is that this would amount to exclusive dealing.

Here I have used the locution “The reason is” to help the reader understand that what follows is an argument for the preceding proposition.

However if you look closely at the Gibbs judgement, you’ll find that there is surprisingly little logical language of this kind.   Argument pieces are provided, but with little clear and explicit flagging of their logical relationships.  For example:

It is even more clear that there was no exclusive dealing of the kind mentioned in s.47(7).  The appellant did not refuse to supply the beer to any retailer.  It was already ready to supply any retailer, either by delivering it from the brewery to North Queensland, or by allowing it to be picked up from a regional depot.

The phrase “it is even more clear that” does suggest that the following proposition (there was no exclusive dealing…) is a point being established or supported.  The following sentences constitute (in part) the argument for that proposition.  Note however that those sentences are simply stated immediately after the proposition to be established.  There is no explicit verbal flag that they constitute an/the argument.   You, the reader, are supposed to just “see” that.  The cue is contextual (proximity) rather than verbal.  Gibbs could have said something like “This is because…” – but he didn’t; he relied on non-verbal cues instead.  The trouble is that non-verbal cues to logical relationships are generally quite weak and ambiguous, and impose a heavy interpretative burden – and hence cognitive load – on the reader.

Diverse or unclear logical language

Even when logical language is used, there are innumerable different forms, with subtle differences in meaning.   Readers would have a much easier time identifying complex arguments if there were standard, unambiguous verbal conventions for signposting logical relations.  Unfortunately, there are not.  Of course there are some locutions that are used more often than others and are relatively unambiguous – e.g. “It follows that”.  But you also find obscure or archaic expressions like “does not gainsay”, and use of ambiguous terms like “however” and “but”.  Both of these common expressions can be functioning as argument structure indicators, but might be playing quite different role.

Missing premises

Another problem is that only some pieces of the argument are actually presented in the prose.  The rest are left unstated, with the expectation that the reader will be able to fill in the gaps.

Consider again the passage quoted above.  What’s missing – at the very least – from this presentation of the argument is something like

Exclusive dealing of the kind mentioned in s.47(7) would require the appellant to refuse to supply beer.

Gibbs is assuming that the reader will understand that some proposition of this kind is part of the argument.  In this case it may seem a reasonable enough assumption.  However we know in general that people find it very hard to identify these missing parts, and when they try, there is huge variation in what they come up with.   In other words, it is dangerous to assume that readers will properly “read in” the missing pieces.  Even if they can do it correctly, it often takes signficant mental effort (though it is worth noting that very often, in simple cases, filling in the missing pieces is seemingly effortless).

Missing intermediate pieces (“leaps of logic”)

There are at least two kinds of missing pieces.  The first, just illustrated, is unstated co-premises; in other words, the argument is enthymematic.  The other kind are intermediate steps in the argument.  Here, in Rationale format, is an alternative rendering of the argument, making clear that between the general conclusion Gibbs is drawing (no exclusive dealing) and the  particular fact offered by way of proof (no refusal to supply beer) there is really an intermediate level of argument.


Figure 2.  Click on the thumbnail to view full-size version.

In other words, judges often expect readers to fill in missing pieces both alongside and between the pieces that are provided.

In fact, the first premise at the intermediate level had been provided, but many pages  before.  It was not (re)stated in the immediate context of the argument, though it did appear in the text, in a rather remote location, with many other pieces of the larger argument appearing in between.   Which brings up the next point…


Consider an argument structure of the kind displayed in Figure 1.  Suppose you had to present that argument in ordinary prose.   Ordinary prose is essentially just a “linear” sequence of sentences – one sentence after another – though of course we can use some formatting to break up the monotony.    An issue you would be forced to address is: in what order do you present the pieces of the argument?

There is a systematic way to map a hierarchical structure into a sequence.  In fact there are many such ways.  However, every such way necessarily involves placing items adjacent in the sequence when they are not adjacent in the hierarchy.  This is simply a topological fact, with an interesting consequence for presenting arguments in prose.  It means that pieces of the argument with no direct relationship to each other must end up adjacent to each other in the text (though there may be other material, not part of the pure argument structure, separating them).  In other words, the prose will “bounce around” the argument structure.

puzzledWhen we study real examples of presentation of complex arguments in prose, such as the Gibbs judgement, and we look carefully at the order of presentation of pieces, we find that the author “bounces around” even more than is required mathematically.  In other words, in terms purely of ordering, the pieces are all “jumbled up”, almost as if pieces of a jigsaw had been thrown in a bag and drawn out one by one.

Of course, there will generally be some kind of logic in the madness; the author is trying to present the pieces in an order which, with the surrounding text, will help the reader understand the argument.  The issue is whether the author has done as well as he could in this.   Other things being equal, the more the “dis-order” or jumbling, the more trouble the reader will have in reassembling the hierarchical structure.


Intermingling with other material – and purposes

Another problem is that a written judgement is not solely concerned with transparently presenting the argument.   First, there is other material needing to be presented.  For example, there are the facts of the case, including both the facts that are immediately involved in the argument as well as other information providing important context.  Also there will be related issues which the judge may feel should be discussed, even though they are not part of the core arguments.

The trouble is that the presentation of the argument is intermingled with all this other material.  This means that the reader must pull apart what is argument, what is background, what is peripheral, etc..

On a related point, the judge has purposes in addition to transparent presentation of argument.  There is a certain amount of rhetoric involved in presenting a judgement, since the goal is to persuade others such as the parties to the case, their lawyers, and other judges.  Further, most judges would like to think that their written judgements are well-crafted, readable, perhaps somewhat entertaining, and possibly even literary, in a legal fashion.   It turns out that these goals are somewhat in tension with the goal of presenting the argument transparently.   It is certainly possible to present complex arguments in prose in such a way as a suitably trained reader can see, without inordinate effort or doubt, exactly what the argument is.  The problem is that such text is not pleasant to read, and it may not be as persuasive as more mellifluous discourse.   It requires a true master of argumentative writing to simultaneously reward the reader’s taste for literature or entertainment, and their desire to understand a complex argument with crystal clarity.

Argument Structure vs Essence

I’ve been writing as if judges’ primary ambition, in drafting written judgements, is to transparently display a complex argument structure.  But often when reading these judgements it seems that the authors are  more concerned to convey the “conceptual essence” of the argument – the key insight(s) such that, if the reader get that insight, then they’ve grasped the real heart of the argument.  The key that unlocks the case.   How exactly that essence is embedded in a larger structure of argument may not be so important.   So you find judges “talking around” that key insight or argument step, doing multiple “takes” on the presenting the point so that if the reader doesn’t quite get it one way, they’ll get it another, gaining understanding through a kind of triangulation.

Clearly conveying the conceptual essence of the case is of course a very important thing to do.  However it that is what the judge is primarily trying to do, then the effort devoted to this may be at the expense of, or even interfere with, transparent display of the rest of the case.

Summing up

Judges use written judgements to convey the complex set of arguments supporting their decision.  However it is difficult to extract the arguments from those written judgements, at the level of clarity and rigour demanded by good-quality argument mapping.   This difficulty is due in large part to various aspects of traditional legal prose.

  • Judges make surprisingly little use of verbal indicators of logical structure, and often use obscure or vague indicators
  • Judges present only some pieces of the arguments, expecting the reader to fill in the rest
  • The pieces necessarily appear in the text in a “disrupted” order, compared with their proper relationships in the argument structure
  • When producing their written judgements, judges have multiple purposes in addition to clearly conveying a complex structure; and the argument is intermingled, in the text, with other material
  • Judges may be more focused on conveying the conceptual essence of the argument than the full argument structure.

These observations are based on a fairly small sample – a handful of judgements in the current round of tutorials, plus my occasional experience over the past few decades  grappling with similar legal writings.  Still, I’m confident that the factors listed would be in play in most legal argumentative writing, and indeed almost any time an author attempts to convey a complex argument in prose.

If this is right, then if we’re faced with the challenge of presenting a complex argument in prose, we can help our readers by:

  • Making generous use of logical structure indicators, and trying to use a limited range of relatively standard, unambiguous ones
  • Explicitly stating more pieces of the argument
  • Trying to present the pieces in as coherent an order as possible, given the logical relationships among the pieces
  • Being aware of one’s purposes, and trying to avoid compromising the clear expression of the argument by other purposes
  • Disentangling the presentation of the argument from presentation of other material
  • Not neglecting overall argument structure while conveying the conceptual essence.

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