Multiple readability in principle and practice: Existential Graphs and complex symbol
Bibliographic record
Abstract
Since Sun-Joo Shin's groundbreaking study (2002), Peirce's existential graphs have attracted much attention as a way of writing logic that seems profoundly different from our usual logical calculi.In particular, Shin argued that existential graphs enjoy a distinctive property that marks them out as "diagrammatic": they are "multiply readable," in the sense that there are several different, equally legitimate ways to translate one and the same graph into a standard logical language.Stenning (2000) and Bellucci and Pietarinen (2016) have retorted that similar phenomena of multiple readability can arise for sentential notations as well.Focusing on the simplest kinds of existential graphs, called alpha graphs (AGs), this paper argues that multiple readability does point to important features of AGs, but that both Shin and her critics have misdiagnosed its source.As a preliminary, and because the existing literature often glosses over such issues, we show that despite their non-linearity, AGs are uniquely parsable and allow for inductive definitions.Extending earlier discussions, we then show that that in principle, all propositional calculi are multiply readable, just like AGs: contrary to what has been suggested in the literature, multiple readability is linked neither to nonlinearity nor to AGs' dearth of connectives.However, we argue that in practice, AGs are more amenable to multiple readability than our usual notations, because the patterns that one needs to recognize to multiply translate an AG form what we call complex symbols, whose structural properties make it easy to perceive and process them as units.Nevertheless, we show that such complex symbols, though largely absent from our usual notations, are not inherently diagrammatic and can be found in seemingly sentential languages.Hence, while ultimately vindicating Shin's idea of multiple readability, our analysis traces it to a different source and thus severs its link with diagrammaticity.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.026 |
| Scholarly communication | 0.009 | 0.028 |
| Open science | 0.002 | 0.007 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".