Abstract

 [full article, abstract in English; only abstract in Lithuanian]
 The paper deals with the problem of the “two Barbaras” in the Aristotelian modal syllogistic. The problem consists in Aristotle’s differing views on two at a first sight similar in nature syllogisms of mixed assertoric (X) and necessary (L) premises: Barbara LXL and Barbara XLL. The fact that Aristotle believed the first syllogism to be valid and the second one – not, has been received either 1) negatively, because both Barbaras have been held to be invalid, or 2) negatively, because both Barbaras have been held to be valid, or 3) positively, by giving a reason why the two Barbaras differ. We commit ourselves to the position (3) by proving that modal propositions for Aristotle have their modalities de dicto and that Aristotelian modal operators act according to their own separate rules where only the type of the modality of a major premise is relevant for the modal status of the conclusion.
Highlights
Aristotelian modal syllogistic has been considered to be a highly controversial matter ever since its origination in the 4th century BC
Unlike the “basic” assertoric syllogistic, which has had the status of a finished project and remained almost unquestioned until the rise of modern logic, its modal counterpart represented in the chapters 8–23 of Analytica priora has been generally seen as suffering from serious internal inconsistencies by both Aristotle’s contemporaries and his modern interpreters
One of the best known de dicto readings of Aristotle was suggested by his contemporaries Theophrastus and Eudemus, who offered a radical elimination of all mixed syllogisms where the conclusion is necessary and at least one of the premises is not
Summary
We have named different drawbacks of each of our mentioned de re interpretations, and two major reasons why it is very unlikely that Aristotle endorsed something like a de re understanding of a modal syllogism: namely (1) the inability to make conversions possible, and, more importantly, (2) the fact that, when interpreted de re, Barbara XLL obviously yields no conclusion, while for Aristotle it does give an assertoric one Those reasons encourage us to see if there is a tenable reconstruction of Aristotelian modal syllogistic by using de dicto modality. One of the best known de dicto readings of Aristotle was suggested by his contemporaries Theophrastus and Eudemus, who offered a radical elimination of all mixed syllogisms where the conclusion is necessary and at least one of the premises is not In their opinion, both Barbaras violated the modal principle, later known as the peiorem rule. A syllogism used by Theophrastus to show the invalidity of Barbara LXL is: All that walks is necessarily in movement
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