For the Sake of Argument

5 February 2014

When Professor Jeremy Gibbons presented a seminar on his work to the College last year I joked with him that he was suggesting we should hang a notice over the door to the college: “Let none ignorant of logic enter here”. Indeed, we have many Fellows and students within the College who are associated with the Software Engineering programme run out of the University of Oxford’s Department of Computer Science – a department that is renowned for the development and practical application of formal, logical methods. Such disciplines may seem esoteric to you only until you realise that they are often at the core of the security of your payment cards and to the safety of complex systems such as aircraft and medical devices. You have almost certainly trusted both your life and your wallet to those ‘esoteric’ logics practiced with such diligence on Parks Road.

However, I intend here to take a somewhat contrarian view to my colleagues on the Software Engineering programme (and only partly to provoke them into a response). I have a view that logic is the lesser form of argument; that logic sits at a lower rank in the trivium than that occupied by rhetoric. After all, is not logic really more than repeated tautology? A sufficiently smart person does not need the mathematical proof, since the truth or falsehood of the conclusion is entailed immediately from the premise: TRUE = TRUE. I am thinking here perhaps of Srinivasa Ramanujan who seemingly without effort created mathematical theorems of the most wonderfully beautiful and yet (to folk like me) incomprehensible kind.

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(We shall, of course, forgive the great Ramanujan for being a fellow of The Other Place)

However, such things are beyond me. And therefore, since I cannot prove a logician to entertain these fair well-spoken days, I am determined to prove a villein. As I shall explain.

The greater form of discourse, and that which is practiced most frequently within the walls of this University, is that of Defeasible Argumentation. A defeasible argument is one in which two equally intelligent, informed and ethical individuals may reasonably come to a different conclusion.

My current research interest spans these two great edifices of argumentation: Computation on the one side and defeasible argumentation on the other. I have found that the unfurrowed middle ground between disciplines can often be the most easily productive – fertilized as it is by great minds in both fields but otherwise left available for opportunistic cultivation by us farmers of lesser degree. Those who know me will be aware that I hold three university degrees in four different subjects – almost certainly because I was unable to muster sufficient skill in any of those subjects to ‘go the whole way’. Still, I have made a useful career of transferring knowledge from experts in one discipline to those of another – making such translations of language and metaphor as were required by the circumstance.

I recall, that after I handed in the first written product of my Doctorate my supervisor pointed out of the window with a sigh. “Do you know what that building is?” He said.

“The library?” I hesitantly replied. For, after all, it was most familiar to me – had I not walked past it many times on my way to the Student Union bar during my three years at that university as an undergraduate?

“You and it need to become better acquainted.” he said, insightfully but rather hurtfully in my view.

I had not become terribly familiar with the inside of the Library as an undergraduate. On the first day of a Physics Bachelors Degree one may acquire a copy of some large tome containing hundreds of pages of impenetrable mathematics and diagrams. A good exemplar of this being Eisberg and Resnick’s “Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles”  (although I am now horrified to read one of its reviewers describes this as largely free of mathematics. Time may have taken its toll – but I do not recall it having been so). With diligence the more enthusiastic and able student might read most of such a book by the time they graduate (although comprehend rather less of it). You may understand why the thought that one’s fellow students in their studies of literature, philosophy and the arts might consume not just ‘some’ but ‘many’ books is a source of great consternation to us ‘hard scientists’.

Amongst the many benefits for my fellow students of consuming knowledge in such a voracious manner was not only their absorption of the facts of the matter, but also the process of reasoning by which such arguments are formed and communicated. That is, the development of the acuity of mind that would allow them to obtain some better understanding of truth in the face of partial, incomplete and occasionally erroneous premises.

In struggling up the rather Sisyphean intellectual ladder of writing my own PhD thesis, I finally myself gained some semblance of skill in making coherent arguments. Having experienced such torture myself, it is not then surprising that I now enjoy imposing the strictures of intellectual rigour on my own students. (I can do so with a clear conscious since I know it to be both for their benefit and certainly for that of their future employers and associates). That pleasure has been marred only occasionally by an incoherent, vacuous or spurious written arguments within an assignment submission. Still, I cheer myself in the long cold evenings of winter with the thought that if one could not fail student assessments then there would be little point, nor pleasure in setting and marking them.

My principle discipline is now Complex Systems Engineering. Thus, inevitably, my interest has turned to the tools, methods and processes by which we, who have not been blessed with an education in the arts, may better practice the disciplines of coherent argument. A primary source in the understanding of such methods is that of the work of Steven Toulmin, and in particular his 1958 work “The Uses of Argument”. In that treatise Toulmin introduces a model of defeasible argumentation which may be illustrated thus:

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Such diagrams intrigued me from the start. They have much in common with the semi-formal, diagrammatic ‘languages’ such as ‘UML’ and ‘sysML’ which I present as an element of the course on Systems Engineering I teach through the Department for Continuing Education. But in this case, they do not represent the structure or behaviour of a complex piece of technology, but the structure of an argument.

I first employed such diagrammatic models to address a problem we have in the development of large-scale, complex systems; that of explanation.  For, whilst engineers are normally skilled in documenting the design of a complex system, they often fall short in an explanation of why things are they way they are. This is important, since these large systems are often constructed by hundreds of people from different disciplines working in parallel. If these disparate individuals do not understand the ‘why’ they may easily undermine the solution through the course of the systems life.

The diagramming notation I invented (The ‘Essential Logic Model’ or ELM) uses a form of graphical argumentation to explain the design. An ELM ‘tells the story’ of why a system is the way it is.

More recently I set out to plough an adjacent field; the intersection between the modelling methods and tools of Systems Engineering and that of Business Strategy. The method developed as part of that work is called ‘PESTLEWeb’. PESTLEWeb is intended to help people understand and communicate the context for business strategy development. It uses a form of visual argumentation to explain how issues in the business environment have impacts on emerging business strategy. Such diagrams are most usefully created in a collaborative manner. Thus, in order to better understand how such collaboration might be facilitated I developed the website to enable users to create and share models. The theory and some of the research behind this work is available in my thesis on PESTLEWeb.

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The latest incarnation of this technology is called – which uses visual argumentation to help individuals and teams think-through their route to a specific objective.

Key research questions here revolve around how such tools should be designed. They have to be approachable and must require little learning to be effective. They must be ‘intuitive’ and yet they are intended to move the user towards more rigorous thinking through visual explanation and argument. Another important question is now ‘knowledge’ can be abstracted from any individual diagram to provide a library of reusable information. That is, how they can be used to mine ‘the wisdom of crowds’ – the collective intelligence of a group. In this, the research moves by a circuitous amble back into the fields of computation and statistics and the tools of what, in common parlance, is called ‘big data’. And so, I have been there and back again; from logic to defeasible argumentation and thence finally to return to computation.

Finally, I wonder if I should revisit my proposition to Professor Gibbons; that above our door we should not exhort our members towards logic but to coherent argument and explanation. After all, there is much to be had of both within Kellogg College.

Dr Rob Collins, February 2014

About the author:

Dr Robert Collins is a Visiting Fellow of Kellogg College and has been teaching on the MSc in Software Engineering at the University of Oxford for the past 10 years. He also teaches the Systems Engineering Fast-Track course through the Department for Continuing Education.

  • “A sufficiently smart person does not need the mathematical proof, since the truth or falsehood of the conclusion is entailed immediately from the premise: TRUE = TRUE.”

    We also need A ≠ not A 🙂

    I find logic a bit like chess. Formal rules define it but don’t tell you how to play.