1. Defining Diagrams Austen Friesacher Conclusions Background
McGill University
Conclusions
Background
Simon & Larkin first proposed a simple definition: that diagrams are two-dimensional and sentences are one-dimensional
This has since been endorsed by Shin
This correctly classifies many familiar forms of representation such as Venn diagrams and written English
However it f ails to correctly classify one-dimensional diagrams
Obtaining a correct definition of diagrams is an important foundation for other projects in the philosophy of diagrams
The definitions of Stenning, Shimonima, and Simon & Larking don’t work
A definition shouldn’t treat diagrams as merely physical objects, as evidenced by the failure of definitions one and two
Definitions which rely on the specifics of formal semantics are at risk of classifying the same diagram in different ways
What is a diagram? What is not a diagram? At first glance it may seem easy to differentiate diagrammatic forms of representation from other forms of representation. Our intuitions are strong that Venn diagrams are an example of diagrammatic representation and that normal written English is not. But, providing a definition of diagrams is a problem that has busied and eluded many philosophers. This is problematic as many larger projects in the philosophy of diagrams hinge on the definition employed.
Here I present three prominent definitions of diagrams and reject them – in two cases offering a novel objection. From this some general lessons about the philosophy of diagrams can be drawn which may aid in obtaining a satisfactory definition.
Fig 1. A two-dimensional and one-dimensional representation.
Fig. 2 A one-dimensional flowchart is still a diagram.
Shimojima says that diagrams are defined by being subject to “nomic” constraints
A constraint is defined as the inability to realize one “state of affairs” in the representing world without realizing another state of affairs
Nomic constraints are constraints imposed by natural laws
This treats diagrams as physical objects and fails to account for differences in interpretations
Bibliography
Fig. 3 Whether this is a sentence or a diagram depends on how you interpret it.
Hammer, E. (1995). Logic and visual information.
Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words.
Shimojima, A. (2001). The graphic-linguistic distinction.
Shin, S.-J. (2015). The mystery of deduction and diagrammatic aspects of representation.
Stenning, K. (2002). Seeing reason: Image and language in learning to think.
Stenning claims that diagrams are defined by their lack of an ”abstract syntax”
A consequence of this is that if a physical relation is representative in a diagram, it always represents the sam4 thing
This is not the case for sentential systems
How narrowly are relations defined? Are they specified for specific types of graphical objects? Across all types of graphical objects? Is it up to the system’s creator?
Issues arise for each understanding of what constitutes a significant relation
Fig. 4 A diagram where the relationship of containment represents different things. However, by redefining the significant relations this can be considered as directly interpretable.