A third chunk of the work-in-progress paper.

Draft only. As always, comments welcome.

3.3 Semiformality

A third theme in explaining how using an argument mapping package such as Rationale can improve reasoning centres on the notion of semiformality. In a nutshell, the idea is this: human thinking is typically informal. In certain areas, such as general reasoning and argumentation, it can be improved by moving into a semiformal, rather than formal, mode. Argument mapping is reasoning conducted in a semi-formal mode.

The contrast between formality and informality, in the sense relevant here, is familiar enough. Modes, domains, systems, languages or whatever count as formal to the extent they have characteristics such as:

  • a finite set of basic symbols or primitives
  • are digital (Haugeland)
  • are governed by strict rules or algorithms
  • have well-defined concepts or “semantics”
  • achieve complexity through combination
  • support effective procedures

Mathematics, formal logic, programming languages, artificial intelligence, and many games such as chess are all formal. Natural language, conversation, politics, and humour on the other hand are informal, even if they exhibit a few of the features of formality to some extent.

Now human reasoning and argumentation are standardly informal. There are primitives (words, or propositions), meanings, and principles or norms, but these are not defined with the kind of precision, rigour or reliability one finds in formal modes such as mathematics or chess. In this respect, human reasoning is often reflecting the nature of the domains or issues about which the reasoning is being conducted. For example, politics is an inherently informal domain, and this informality is reflected in the nature of our default intellectual tools for thinking about and debating over political topics.

Noting on one hand the problems associated with ordinary human reasoning and argumentation, and on the other the often impressive achievements of their formal counterparts, the temptation has often been to recommend shifting human reasoning into a formal gear. Thus introductory logic textbooks are usually dominated by elementary formal logic (Aristotelian syllogisms, propositional logic, predicate calculus), making the assumption that people would reason more effectively if they replaced their instinctually informal thinking habits with logical formulae and proofs. This tendency culminates in the aspiration of mainstream artificial intelligence to recreate human-grade intelligence in the formal medium of digital computation.

Unfortunately this generally doesn’t work. AI research has discovered that it is extremely difficult, and perhaps impossible, to engineer formal systems capable of reliably making the mundane inferences underlying everyday conversation or humour, let alone engaging complex argumentation of the kind found, for example, in legal practice. Conversely, when people struggle with everyday reasoning and argumentation, they are not helped by attempting to translate their premises into some logical calculus and draw inferences by reference to its official rules. Indeed for innumerable commonplace reasoning challenges, formal techniques are so hopelessly impractical that recommending their use seems like a kind of sophistical sadism, another sad manifestation of Bacon’s Idols of the Theater.*

There are of course notable exceptions to the claim that human reasoning is not improved through the adoption of formal techniques. Clearly, for example, the proper use of statistical methods can help us draw better conclusions about subtle correlations and causal relationships. Formal modes of thought certainly have broad and important areas of application. The point being made here is that in general our practices of informal reasoning and argumentation cannot be enhanced by transposing into a formal key.

It may be, however, that some degree of formality can be helpful even where full-blown formal modes such as mathematics, formal logic and computation get no useful traction. The distinction between formality and informality is not a binary opposition. Rather, there is a spectrum of cases depending on which of the characteristics of formality are adopted and how those characteristics are manifested.

In the case of reasoning and argumentation, there have been many contexts in which these practices have been made more formal than they would normally be. Consider for example the medieval theory of disputation, which presented a sophisticated framework of rules governing moves in argumentation. Or consider contemporary high-school debating or “forensics;” etc. These sorts of elaborations of our ordinary practices are aimed, at least in part, at improving those practices; i.e., at enabling us to reason and argue more effectively. Implicitly they are proposing that the optimal mode for human reasoning is not the informal or the formal, but rather something intermediate, a “best of both worlds” scenario.

The conjecture, then, is that for general reasoning and argumentation there is a “sweet spot” somewhere on the spectrum between ordinary informal practices at one end, with their sloppiness and disorder, and purely formal techniques at the other, with their rigidity and limited range of application.
Argument mapping pushes reasoning in a formal direction by forcing relatively high level of explicitness and rigour in articulation. It generally requires that:

  • The claims involved be rendered discretely in full grammatical sentences
  • Material not directly involved in the reasoning be stripped away
  • The central contention or point in dispute be identified as such
  • All direct evidential links between claims be specified
  • Unstated claims or “assumptions” be identified and explicitly stated

In Rationale, these activities are scaffolded by providing a graphical format or “syntax” for the articulation of reasoning, with a limited set of “primitives” (claims, reasons, objections etc.) and strict rules about how those primitives can be combined.

Beyond the basic constraints, there are a number of principles of good mapping which cannot be specified as strict, universally-applicable rules. For example there is the principle of abstraction: generally, in a well-developed argument map, claims “higher” in the map (i.e., closer to the main contention) should be more abstract, and claims lower down should be more particular or concrete; and claims at a given level should be approximately the same in their degree of abstraction. While this principle is easy enough to state and understand, and with some practice is easy enough to apply in most cases, it involves inherently vague notions and is subject to a wide variety of exceptions, such that any attempt to articulate in a fully precise way what the principle is and how it applies ends up floundering in a quagmire of uncertainties and exceptions.

The principle of abstraction its ilk depend fundamentally for their successful application on intuitive human judgments based on experience and practice. To the best of our knowledge it is impossible to cash them out as formal rules capable of mechanistic implementation. Thus, argument mapping has irreducibly informal dimensions even as it makes reasoning activities more formal than they would normally be.

So argument mapping is semi-formal; it introduces aspects of formality while acknowledging its limits and retaining essentially informal dimensions.The idea is that disciplining reasoning practices to observe this degree of formality is the most feasible way to, if not eliminate, at least substantially mitigate the typical failures or difficulties standing in the way of good reasoning, argumentation and deliberation, such as:

  • not making reasoning fully explicit, including in particular the failure to articulate key assumptions
  • not applying relevant principles of good reasoning
  • not coping with the complexity of “real world” debates
  • not achieving common understanding among participants in argumentation

From what has already been said it should be clear that argument mapping confronts these failures head-on, which is why we can be optimistic that argument mapping practices, if widely and properly adopted, can lead to better reasoning.

What is the optimal level of formality to introduce into our reasoning practices? Where precisely is the “semi-formal sweet spot”? We don’t yet have definitive answers to these questions. Argument mapping as supported by a package such as Rationale constitutes one take on where the sweet spot is. It may have erred in one direction or the other. However evidence of the kind discussed in section X above suggest that Rationale’s take could well be approximately correct.


* “Lastly, there are idols which have immigrated into men’s minds from the various dogmas of philosophies, and also from wrong laws of demonstration. These I call Idols of the Theater; because in my judgment all the received systems are but so many stage-plays, representing worlds of their own creation after an unreal and scenic fashion.” From Novum Organum