Extended Call for Papers

What is a logical diagram? What can we say is truly distinctive of diagrammatic notations for logical reasoning, relative to equivalently expressive non-diagrammatic forms? Several responses have been given in the literature – logical diagrams are visual (Shin 2002), they have multiple, equivalent “readings” (Shin 2002, Macbeth 2005, Schlimm 2018), they are directly interpreted (Lemon 1996, Stenning 2000) – that have attempted to overcome the old difficulty of defining a logical diagram in terms of isomorphism. However, none of these responses has gained universal acceptance.

Intuitively we should be able to answer this: the Euler circles for the universal affirmative proposition is a diagram, while the corresponding formula in FOL is not:

The aim of this workshop is to subject this idea to analysis by seeking contributions that explore the notions of operational iconicity and observational advantages from different perspectives: the formal semantics of diagrammatic languages, the philosophy of language and logic, studies on mathematical and logical cognition, the philosophy of mathematical practice, and the psychology of reasoning. We envision a multidisciplinary collaborative workshop that will enable us to identify common questions and goals, and to share findings across these areas of research. The workshop will follow on from the success of the first International Workshop on the Philosophy of Notation in Tallinn, 2015.

The more general question of the notational difference among expressively equivalent languages has never really been posed, not even by the inventor of a “theory of notation” (Goodman 1973). With a few exceptions (French 2017), scholars have preferred to devote their energies to research around the more particular question of what is a logical diagram. The mere notion of isomorphism is insufficiently specific: “∀xAx ⟿ Bx” is no less isomorphic to the logical content it represents than is the corresponding formula in Euler circles.

The matter is roughly as follows: when one depicts, according to the conventions of Euler diagrams, the premises of a syllogism in BARBARA one thereby depicts the conclusion of that syllogism, though no specific step for the depiction of the conclusion has been taken; this clearly does not happen in FOL: writing “∀xAx⟿Bx” and “∀xBx⟿Cx” is not thereby to be write “∀xAx⟿Cx”. Recently, the notions of content specificity and free rides have been generalized into that of observational advantage (Stapleton, Jamnik, Shimojima 2017, 2018). In a nutshell, the contrast is between inferring a statement from a given representation of information, and observing that statement without inferring it, and it is said that a given representation of information is observationally advantageous over another if the former allows us to observe something that can only be inferred from the latter.

Is operational iconicity an universal feature of those logical languages that we intuitively characterize as diagrammatic, or are there forms of it that are also found in languages that we intuitively characterize as non-diagrammatic? Is the piece of information obtained "for free” always a logical consequence of the information displayed or there are other kinds of “observational advantages”? Is operational iconicity a sufficiently safe and general parameter against which to evaluate, and even categorize, logical notations? What is the mathematical or geometrical background of operational iconicity? What features of space (symmetry, isotropy, etc.) or of the abstract syntax (linearity, prefixness, infixness, etc.) of logical languages lie behind this phenomenon?

The situation becomes more complex when it comes to the diagrammatic representation of polyadic quantificational theory. Euler circles and Venn diagrams cannot do this; existential graphs and the Begriffsschrift can. In what sense are these languages to be regarded as logical diagrams, and in what sense are they operationally iconic or observationally advantageous over the standard language of FOL? A useful distinction by Stenning (2000) can be so reformulated as to account for the notational variety of languages for quantificational logic: we may distinguish type-referential languages as those in which the identity of the individuals is represented by the identity of the variable-type, each occurrence of the type referring to the same individual, and occurrence-referential languages as those in which the identity of individuals is represented by the identity of the variable-occurrences, each occurrence referring to a distinct individual. This distinction seems to capture sufficiently well the difference between Peirce’s Beta graphs and the Begriffsschrift: both are two-dimensional and thus non-linear, but Beta graphs are occurrence-referential, while Frege’s notation (just as FOL) is type-referential. How is the occurrence/type referentiality of the notation to be understood in terms of operational iconicity and observational advantages? Is there any specific observational advantage that directly derives from occurrence- or type-referentiality?

We seek contributions that explore these connections and attempt to answer these questions from two core perspectives: the philosophy of language and logic, and the mathematics and formal theory of diagrammatic languages. We believe that it will be only through the close cooperation of these two perspectives that a satisfactorily general explanation of operational iconicity and observational advantage can be provided.