Boethius' definition of "differentiae" is that they are "the Topics of arguments ... The Topics which are the Differentiae of [maximal] propositions are more universal than those propositions, just as rationality is more universal than man." This is the second part of Boethius' unique contribution to the field of rhetoric. Differentia operate under maximal propositions to "be of use in finding maximal propositions as well as intermediate terms," or the premises that follow maximal propositions.. Though Boethius is drawing from Aristotle's Topics, Differentiae are not the same as Topics in some ways. Boethius arranges differentiae through statements, instead of generalized groups as Aristotle does.
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Differentiae (distinction), 256–305 ::IX. Varietates (Varieties), 306–317 ::X. Synonyms (synonyms), 318–324 ::XI. Adumbrationes (description), 325–335 ::XII.
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His nomenclature differed from de Tournefort's in not using a diagnostic phrase with the first plant of a genus, adding differentiae only to the second and subsequent plant species. He corresponded with John Ray on matters of plant classification.
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According to Aristotle, the science of living things proceeds by gathering observations about each natural kind of animal, organizing them into genera and species (the differentiae in History of Animals) and then going on to study the causes (in Parts of Animals and Generation of Animals, his three main biological works).
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205 Gebhardt; Sopater Rhetor, vol 8, pp. 383-4 Walz; scholia to Aristophanes (Prolegomena on Comedy and on Birds 1297); Cyrus rhetor, Differentiae statuum vol. 8, p. 1 Walz to denote a witty personal attack made with total freedom against the most notable individuals (see Aristophanes' attacks on Cleon, Socrates, Euripides) in order to expose their wrongful conduct.
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"ii", follows the antiphon. The antiphons of the entrance (introits) have the gradual order of the mass as a rubric at the margin (on a verso page as here: left), i.e. the serial for the day with gradual (R), alleluia (All) or tractus (TR), offertorium (OF), and communio (CO). A conventional tonary with the list of differentiae was also attached to the beginning of the manuscript.
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James Franklin, "Aristotle on Species Variation", Philosophy, 61:236 (April 1986), pp. 245-252. The passage quoted here is from pp. 251-252. Thus, the notion of the Porphyrian tree as an actual diagram comes later than Porphyry himself. Still, scholars do speak of Porphyry's tree as in the Isagoge and they mean by this only that the idea of dividing genera into species via differentiae is found in the Isagoge.
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We are not told by the diagram what a term for irrational animal is, but the diagram indicates that a rational animal is a human. Thus, human is a rational species of the genus animal. Beneath human, however, there are no further species. "This" and "that" if they are considered differentiae, are of a special kind that map the species human not onto a new species but onto particular humans.
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After a review of his terms, Boethius spends BookV discussing Stoic logic and Aristotelian causation. BookVI relates the nature of the Topic to causes. In Topicis Differentiis has four books; BookI discusses the nature of rhetorical and dialectical Topics together, Boethius's overall purpose being "to show what the Topics are, what their differentiae are, and which are suited for what syllogisms." He distinguishes between argument (that which constitutes belief) and argumentation (that which demonstrates belief).
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As mention is made in it of the Baths of Diocletian, it cannot be earlier than the 4th century. It is possibly by a later Probus, whose existence is, however, problematical. #Appendix Probi, treating of the noun, the use of cases, rules of orthography (valuable in reference to the pronunciation of Latin at the time), and a table of Differentiae. As the author has evidently used the Institute, it also must be assigned to a late date.
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That, to be universal, the definition of "piety" must express the essence of the thing defined (piety), and be defined in terms of genus, species, and the differentiae. Hence, the Euthyphro dialogue is technically important for the dialectics of theology, ethics, epistemology, and metaphysics. Indeed, Plato's approach in this dialogue is anachronistic, because it is unlikely that Socrates was a master metaphysician; nonetheless, Aristotle's expositional treatment of metaphysics is rooted in the Platonic dialogues, especially in the Euthyphro.
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In Ciceronis Topica. 34 The other sort of Topic, the differentiae, are "Topics that contain and include the maximal propositions"; means of categorizing the Topics which Boethius credits to Cicero.Boethius. In Ciceronis Topica. 35 BookII covers two kinds of topics: those from related things and those from extrinsic topics. BookIII discusses the relationship among things studied through Topics, Topics themselves, and the nature of definition. BookIV analyzes partition, designation and relationships between things (such as pairing, numbering, genus, and species, etc.).
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In philosophy and second scholasticism, objective precision (Latin praecisio obiectiva) is the "objective" aspect of abstraction. Objective precision is the process by which certain features (the differentiae) of the real object of a formal concept are excluded from the comprehension of that concept; the object is thus being intentionally transformed into a universal objective concept. Objective precision is thus a process by which universal objective concepts arise. It is the "objective" aspect of the process of (total) abstraction or concept-formation.
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The deficit of such a bridge was first encountered in history by the Pre-Socratic philosophers during the process of evolving a classification of all beings (noun). Aristotle, who wrote after the Pre- Socratics, applies the term category (perhaps not originally) to ten highest- level classes. They comprise one category of substance (ousiae) existing independently (man, tree) and nine categories of accidents, which can only exist in something else (time, place). In Aristotle, substances are to be clarified by stating their definition: a note expressing a larger class (the genus) followed by further notes expressing specific differences (differentiae) within the class.
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The following Porphyrian tree consists of three columns of words; the middlemost (in boldface) contains the series of genera and species, and we can take as analogous to the trunk of a tree. The extremes (the terms that jut out to the left and right), containing the differentiae, we can take as analogous to the branches of a tree: This image is an illustration of the notion of a Porphyrian Tree as it comes down to us today through the European philosophical and logical tradition. The diagram shows the highest genus to be substance. (Whether substance is a highest genus, really, is not in question here: right now we are only going to discuss what the diagram shows, not whether what it shows is true or false.) The technical term for a highest substance is summum genus.
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