New Forms of Diagrammatic Logic

Project: Research projectIndividual grant

Call title (Call ID)

Social Policy Grant 2018

Project Description

Logic is the ‘immune system of the mind’. It is the intellectual backbone of reasoning and decision-making of both the human mind and of the general intelligence assumed of computational machines. Theories of logic and reasoning developed since Aristotle have attempted to instruct us how to value arguments, how to weed out inferences that are ill, and how to improve our conduct and creative engagement when faced with problematic life situations. A good theory of logic could thus in this wide sense result in an improvement in intellectual abilities and in rational and ethically conscious decisions in life. As both a theory and an art, logic is expected to have a positive impact on the healthy operation of the mind, human and artificial.

Yet despite centuries of research, the function of logical thinking is not understood well, much like the precise response of immune system in human biology is not understood well. The problem is that current theories of logic are ill-suited to carry out such a wider job of instruction and conduct involved in matters of practical reasoning. The tradition has almost singularly taken the requisite theories to come in the form of a language – in the sense resembling those of natural languages – that we could read and write using certain external, largely symbolic and formal representations, rather than as forms that could directly be intuited in cognition.

But just as for our immune system to function well a complex balance between harmony and speed is essential, logical judgments that prove beneficial should occur in the mind without need of translating underlying descriptions into formal codes. To achieve this, a new notation that represents the basic concepts of logic and critical reasoning as a cognitive technique is needed.

New Forms of Diagrammatic Logic proposes such a new approach: it develops and works with certain graphical notation to represent the theory of logic and processes of inference. This method differs from all other approaches in that instead of using the language familiar from ordinary symbolic and formal notations, the subject matter indeed is a graphical, or in other words a diagrammatic language. We cannot speak or communicate Diagram in voce, but we can imagine the forms and relationships present in it, and develop its theory.

The main hypothesis of the present proposal is that diagrammatic languages open up a novel panorama to the nature of logic, inference and thought by which one could address the central questions that have bothered contemporary research in logic and its philosophy. Such questions concern the true nature of logical reasoning representation, logical consequence relation, logical constancy, as well as certain specific concepts such as quantification, identity (equality) and modality. The leading idea is that the proposed developments on graphs now provide a diagrammatic syntax which, unlike most other and ordinary approaches, is neither linear nor one-dimensional. Among the consequences of this proposal is that the notion of proof in such many-dimensional, diagrammatic syntax becomes of the nature of deep inference.

The history of the topic continues to surprise. The background of such diagrammatic modes of thinking and reasoning dates back to the theory of Existential Graphs of American polymath Charles S. Peirce (1839-1914). His massive and to date still largely unexplored logical material that we find in his manuscripts deposited at Houghton Library will in this project be investigated by contemporary tools of philosophical logic. These writings indeed play the conceptual and historical counterpoint to the proposed project.
Short titleNew DiaLog
StatusNot started