What Follows from the Impossible
Everything or Nothing? (An Interpretation of the ‘Avranches Text’ and the Ars Meliduna )
Bibliographic Data
| ID | 21451388 |
|---|---|
| Authors | Wolfgang Lenzen (0000-0002-5456-1685, Department of Philosophy, University of Osnabrück, Osnabrück, Germany, corresponding author) |
| Year | 2022 |
| Volume | 43 |
| Issue | 4 |
| Pages | 309-331 |
| Publication date | 2022-10-02 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | History and Philosophy of Logic (JOURNAL) |
| Journal identifiers | ISSN: 0144-5340 • E-ISSN: 1464-5149 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/01445340.2021.2008222 |
| OpenAlex | W4200314677 |
| Language | EN |
| Citations received | 2 |
| References cited | 8 |
One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the Parvipontani defended the view that from an impossible proposition everything follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition B can be logically derived from a pair of contradictory propositions A and Not-A. The author of the Ars Meliduna instead argued that nothing follows from an impossible proposition (‘ex falso nihil sequitur’). This view is supported by various counterexamples which aimed to show that the admission of impossible premises would give rise to inconsistent conclusions. Upon closer analysis these inconsistencies do not, however, have the formal structure of a real contradiction like A and Not-A, but rather the structure of two rivalling conditionals like ‘If B then A’ and ‘If B then Not-A’. Hence these counterexamples rather have to be considered as refutations of the basic principles of ‘connexive logic’
Contradiction · Counterexample · Discrete mathematics · Epistemology · Interpretation (philosophy) · Linguistics · Mathematical economics · Nothing · Property (philosophy) · Proposition · Syllogism · Classical Philosophy and Thought · Mathematics · Medieval and Classical Philosophy · Medieval Philosophy and Theology · Philosophy
| Unique citing works | 2 |
|---|---|
| Citations per year | 1 |
| Citation span | 2024 - 2026 (3) |
| Citation velocity | current |
| Highly cited | No |
| Citation types | Neutral: 2 |