Peter of Spain
Peter Hispanus is a significant logicians of the 13th century. He wrote in 1240 twelve tracts that were handed down under the title " Summulae logicales ". They represent the most popular medieval introduction is in the logic and are read to the 17th century.
Authorship
Often the logician Peter Hispanus is identified with the Portuguese physician Peter Hispanus (1205-1277), the XXI in his last year as Pope John. was appointed. This identification is not secured and controversial, as well as a Dominican named Peter Hispanus as a possible author of the Summulae logicales is discussed.
Importance
Peter Hispanus is by Dante in the Divine Comedy boasted wisdom among teachers in the canopy of the Paradiso (XII, 134-135 ) as Pietro Ispano lo qual già luce in dodici libelli ( Peter Hispanus whose light shines even in the twelve books ). His Summulae logicales was repeatedly reprinted and commented and were common until the 17th century at universities. They contain, among others, an early version of the Summary of the Aristotelian syllogistic. This is broadly in line with that of William of Sherwood. The dating of the logic fonts both logician is assessed differently so that their priority can not be determined unambiguously. But the memorable representation of Aristotelian logic for the scholastic education only reached popularity over Peter Hispanus. She is used to this day for the interpretation of Aristotle and is therefore meaningful.
Mnemonic syllogistic
The Summulae logicales Peter Hispanus speak in the first part of the Aristotelian logic and complement in the Tractatus IV mnemonics for syllogistic of Aristotle. They can also be found in Chapter III of Introductiones in Logicam of William of Sherwood. Both scholastics translated the Aristotelian sentences in an understandable language and shortened it from symbolically. Your translation can be reversed and the non-scanning the logical content of the original syllogism. Therefore, there is the logical advancement of scholastic representation only of symbolization with their mnemonic purpose. Last concentrated in a Wish poem which enumerates 19 Aristotelian syllogisms and identifies by name:
Encoding the statement forms and syllogisms
The scholastics replaced the difficult -to-understand statement forms that Aristotle in his Posterior Analytics used, by the immediately understandable expressions from earlier writings of Aristotle and shortened by the following vowel symbols from:
The mnemonic names to call after each statement occurring forms of the series in their first three vowels. The following table highlights the meaningful vowels in bold forth and transmits the names in syllogisms with two premises and a conclusion, is listed with a usually arrow → in the sense of " so ". The assignment of the syllogisms of the three figures of Aristotle presupposes the Wish poem. It should be noted that the scholastics swap the variables result in the statements of Originalsyllogismen. For example, would in direct abbreviation of the Aristotelian statement form "A is to B every " by AaB the syllogism Barbara the form of a Transitivgesetzes AaB, BaC → AaC. However, this original form disappears in scholastic presentation with interchanged variables. They also preferred instead of the Aristotelian if-then sentences with variables is an exemplary representation with three sets in a vertical arrangement:
Coding rules and evidence
The consonants of scholastic mnemonic names must also enter the evidence that began Aristotle in his evidence. A complete explanation of the consonants was only Peter Hispanus. He coded so that the Aristotelian syllogistic control system, which combines the following table:
The scholastic mnemonic names capture the syllogisms, together with proof. Excluded are the evidence of Darius and Ferio ( 1 figure), which Aristotle later nachreichte to reduce his axiom system. Even a trivial step in indirect evidence is not coded, namely that a and o or e and i to negate each other and contradict: The equations AaB = not ( AoB ) and AeB = not ( AUC ) can be applied there in silence. The following table highlights the meaningful consonant of the mnemonic names shown in bold and transfers the coding in the evidence of Aristotle. These are clear and precise understandable in scholastic symbolization:
Mnemonic name variants
The scholastic memory verse today is circulating in different variants. The core component includes the syllogisms of the 1st, 2nd and 3rd figure and remained unchanged up to orthographic variants in Camestres, Felapton, Baroco. The variation of the first figure was later replaced by a fourth character who only swapped the two premises. This, however, a change in the mnemonic names was necessary, notably Baralipton, Celantes, Dabitis, Fapesmo and Frisesomorum were converted into the following mnemonic names that use the code for the rules and provide the proof of the modified syllogism exactly:
Successor of Aristotle, completed the list of 19 Aristotelian syllogisms to all 24 possible syllogisms. They supplemented the missing in Aristotle decreases in syllogisms Barbara, Celarent, Camestres, Cesare, Calemes by a Subalteration the conclusion with the rules AaB → AuC or AeB → AoB. This provable, originating also from Aristotle rules have no consonant code; they will therefore not appear in the later modified common mnemonic names:
Porphyrianischer tree
Peter Hispanus coined in the Tractatus II, Chapter 11 of the Summulae logicales the concept of Porphyrianischen tree as a name for the tree, with the Boëthius the visualized based on the categories of Aristotle classification system of Porphyry.