On Aristotelian genus ( το γένος ) notion and natural science after Cartesian revolution.

1. On Aristotelian genus (το γένος) notion and natural science after Cartesian revolution. Johannes Scholasticus ὁ Ιωάννης Σχολαστικός (Galatasaray University, Constantinople)

2. Outline • 1. Aristotelian notion of genus (pl. genera). • 2. Cartesian concepts of mathematics and the physical world. • 3. Consequential influence of Cartesian concepts to physics and medicine.

3. Definition of genus (Metaphysica I,8) • That what constitutes the unity and the identity (ᾧ ἄμφω ἕν ταὐτο λέγεται ) of two things possessing non-accidental difference (μὴ συμβεβηκὸςἔχον διαφοράν ) with respect to material (ἡ ὕλη ) or otherwise.

4. Example of genus: genus of animals contains species of both human being and horse (differentiated not by chance, not accidentally).  • Species partakes of genus. • But not genera of species. • Genus is an equivalence class of species=causa formalis=eidos (το εἶδος) (Heusser “Formative cause” 2011). Tautologically speaking, one species is equivalent to another if both of them belong to the same genus (non-axiomatic definition of the equivalence relation).

5. Accidental difference : • Accidental difference: a. A musician’s skin can be white or black (non inest in musico inquantum huijusmodi). –Not a necessary consequence. An attribute without determined cause. • b. A triangle may have accidentally three equal angles. While the sum of three angles must be always 1800 • After Descartes, even hardness, colour, heaviness, cold and hot are accidental and non-essential to the nature of a stone .

6. Indivisibility of soul and body • An animal is visible and sensible as a body, but it is neither visible nor sensible as a soul. Therefore “animated body” (τὸ σῶμα ἔμψυχον) cannot be genus of animal. Because the body is only a part (of what makes animal as a whole). (Topica IV, 126a20) • Opposite to the Cartesian dualism.

7. “Genus” etymologically comes from the verb γίγνομαι (to be born) > ἡ γένεσις=genesis. • Small surface can generate large surface -> they belong to the same genus. • A line cannot generate surface. (Metaphysica A 9, 992a) • -> genus of lines (one dimensional) ≠ genus of surfaces (two dimensional) ≠ genus of bodies • This echoes his basic anti-Platonic position: not to recognize the genus of “being”(το εἶναι) neither that of geometric object of any dimension. Why the revival of Platonism in Renaissance was necessary to prepare the scientific revolution after XVI-th century.

8. Genus of numbers ≠ genus of geometric magnitudes. Arithmetic proof cannot be transferred to the geometric proof (Anal.Post.75b). Continuous magnitudes are not “numbers” ! Arithmetic and geometry treat objects of different genera. And the passage from one genus to another (ἡ μετάβασις εἰς ἄλλο γένος) is impossible. Scientific knowledge treating one genus cannot be applied to that for another genus.

9. Plato vs. Aristotle on the role of “Being”. • Plato: the material Universe and the world of “Ideas” as a hierarchy of genera and species subordinate to the supreme genus = the Being or the One (Plotinus : το ἕν, Greek Patristic: το ὄντως ὄν) . To this hierarchy every being, until that of the lowest order, is participating. • Aristotle: the Being is decomposed into a multiplicity of irreducible categories that are incommunicable one another. The first genera (the highest of genera: Nature= ἡ φύσις, One, Substance=ἡ οὐσία) are absolutely heterogeneous.

10. Ghost of genera distinction in XIX-th century medicine. • Vitalism(with obscurantism flavour): Specific feature of life is characterized by its vital power that cannot be explained by laws of materials (physics, chemistry etc.). • Science on life shall be neatly distinguished from sciences on inanimate materials. Nondeterministic aspects are decisive in the behaviours of a living organism. • The simple “physical phenomena of life” make only tiny and insignificant parts of the life. • Criticised by Claude Bernard (Introduction à l’étude de la médicine expérimentale, 1865. Deterministic & non-mechanistic, hippocratic point of view ).

11. Descartes –The exclusive concern of mathematics is with questions of order or measure and that it is irrelevant whether the measure in question involves numbers, shapes, stars, sounds or any other object whatever (“Rules for the Direction of the Mind”, Rule IV). • Mathematics = mathesis universalis. It covers all subordinate sciences = astronomy, music, optics, mechanics. • After abstraction of accidental (cf. Aristotelian συμβεβηκὸς) circumstances, every measurable properties of any physical body are subject to mathematical rules. Part 2. Cartesian concepts on mathematics and the physical world.

12. Cartesian concept:Body and Extension Nothing belongs to the nature of the body if it has no extension with length, width and depth (extreme form of materialism). Extension per se is a product of pure imagination. Body possesses extension and extension is not a body. If corporeal substance is distinguished from its quantity, it is conceived in a confused manner as something incorporeal. (Reduction of a substance to its quantity. Total identification of two heterogeneous notions= belonging to different genera.)

13. 3. Consequential influence of Cartesian concepts to physics and medicine . • 1. Fock space. (Vladimir A.Fock 1932) All particles are created from the vacuum state after application of creation (resp. annihilation) operator (resp. ) Physical states (in a Hilbert space) with arbitrarily many particles are algebraically constructed. Limited but efficient ways to realise certain physical states i.e. in quantum encryption.

14. 2. Lobotomy • Neurosurgical procedure cutting the connections to and from the prefrontal cortex (Antonio Egas Moniz 1936). • Try to improve mental disorder symptoms (depression, schizophrenia, mania, panic disorder etc.) by means of a treatment consists in annihilation of the neural pass ways that allow “aberrant and fixed pathological brain circuits.” (mental disorder “localised” in the prefrontal cortex. Mental disorder as Brain disease.)

15. Background: Faith in a purely physico-physiological characterisation of the mental disease. (cf. Dementia, Alzheimer's disease: loss of neurons and synapses in the cerebral cortex etc.) ↔Modern neuroscience & psychiatry Aberrant activity in the components of distribu distributed circuits in prefrontal cortex, hippocampus & subcortical . &su structures. Functional abnormalities in neural connectivity (new eidos =causa formalis& genus?).

16. Concluding Remarks: Aristotle vs. Descartes • Descartes‘ axiomatic world construction has quite limited applications (mathematics, Fock space etc.) • Aristotle‘s non-axiomatic world view based on „genera“ hierarchy can be reexamined. Refining adjustment to the Cartesian abstraction e.g. Walking (ὁ βαδισμός) ≠Ιmpulsion(ἡ φορά ) • Cartesian geometric world view yields localization in space and time of the scientific investigation. • Aristotle‘s „genus“ makes us to think on the necessity of global scientific setting (e.g. neural connectivity in the entire body. Well-functioning↔abnormality: two genera).