This second episode of the talk on Aristotle tries, and I do not know what happened as possible, to develop further the concept of boundaries statute, starting with the Aristotelian theory of places and moving between mathematics, physics and neurophysiology, in the direction of establishing a basis for analysis of human perception (in general, animal ) of the outside world, properly defined, and then to discuss the activities of scientific investigation in terms of mental operations.
Aristotle did not invent the word place , τóπος, he found existing in the Greek language with its sense of place, physical place. If you look at the modern use of the word place, placed, you realize that they generally require the association to a resident who makes his residence. It 's rare that we use the word site with a genitive inanimate. Examples. The site of a rock? The site of a house? In the philosophical connotation, the word place brings an existential meaning, and to indicate the location of the geometric space is used rather than the word place or site constructs and their derivatives, such as location, inherent located. Assuming, of course all be discussed, that the word implies a place to stay there, we call this being Lord of the place, be it human or animal. Each animal forge a place for its activities. Every living being is the center of a three-dimensional geometric domain, its τóπος, where he practices his reproductive activities, hunting, etc.. A domain is a volume that has a center of gravity, from which the Lord gives life and family ramifications. It is important to emphasize that such a geometric domain exists only in the mind of the Lord. The raids, or rather the external excursions are limited by boundaries, fixed objects that mark the end , the εσχατα Aristotle (τω δε τι κεξωρισμενον, which is separated ) that the individual for her own choices and cultural life will not exceed (boundaries that are clearly time-varying). In a simplified manner, we can say that Aristotle imagined that every living thing with this is his territory mental, inner projection of outer space in which to be lies. What I would like to discuss is how this is related to the mental territory physical territory in which the animal is submerged.
Initially, we attribute this to be a mobility within this domain (in the mathematics of topology, is called a connected open set) of the ordinary Euclidean space. The need for a place to have the εσχατα is a locally owned, which characterizes the ' be the ουσια. The site is defined by its external border. But what should be surprising is that this local property is actually set up as a double border. In terms of geometry, topology, and a convex hull replacing the place of extremes. This is the very nature of the concept of topological edge, border.
With Parmenides appears for the first time the concept of συνεκησις, usually translated as continuous (referring to the continuity of space). Translation partially misleading, according to René Thom (author of the famous essay on Aristotle as "the first topology of the history of mathematics" that inspired these reflections), which emphasizes that the sunékesis , which flows along , rather evokes the concept of domain continuously connected (without breaks) as tracing a perimeter of an object without lifting the pen from the paper. How would the sailors, who can test the connection geometry to complete the circumnavigation of an island. In fact, at the time of the late Plato and Aristotle, surveyors experienced a certain repugnance to the idea that two points were coincident, the notion that lacked even a proper term. Later, however, the time of Euclid, it will not hesitate before the operation concept of sliding two geometric figures in space, to bring them to match and verify the equivalence, for example by moving a team spirit on one line (the verb Euclid επιαρμωζειν indicates this). Thom noted that an immediate reading of the formula Εν ταυτωι γαρ τα εσχατα του περιεξοντος και του περιεξομενου (for the little 'I remember greek would translate as wholesale are together the edges of the perimeter of the perimeter and above underlying ) Aristotle seems to think of an identity boundaries, where the adverb is used instead in ταυτωι sense of proximity, what today we would call internal identity of two sets.
This discourse leads us to explore the idea of \u200b\u200bcoincidence of two points, as designated in the enigmatic Aristotle says: "The entelechy generates separation." Consider an infinite straight line at both ends. If we place a point source O on this line, the entelechy the cut made by the arbitrary choice of origin, creates two half-half for any segment AB that passes through the origin, and the line itself. The intersection of the two half-segments, X'-AX and B, are distinct, X and X ', although coincident. As in the case of the two geometric figures translated to make it match the perimeter, the boundaries are overlapping but distinct .
This Aristotelian theory of the site has historically suffered from a profound ambiguity, even defined the locus horribilis Aristotelianism, seen as an outdated monolith of more primitive conceptions of the teacher accused Stagira. Ambiguity is a theory of inspiration strictly geometric in the modern sense of the term or, conversely, a theory based sull'etologia, ie employment of space from the living? The second view seems more relevant to the tradition "biologistic" of Aristotle, and would make it the cornerstone of modern ethology of central questions: How does an animal to organize their living space within a certain area? For example, birds have the natural barrier of the nest, which is a key element in the education of children, the subject of many ethological studies. There is an activity in animals
projection on the inner eschata eschata outer boundaries reproduce the map of the territory that borders the soul, which is determined simultaneously, over the movements of the Lord's place within its territory. Build a continuum of mental spaces involved in moving the physical places that are a match while remaining distinct, which is also an external mapping 's own inner world. The structure ενταυτα, coincident, the εσχατα εσχατα on external affairs. A double edge, empty, which again according to Thom, an analogy in the mathematical formulation of topological edge for two sets overlap, d ⊗ d '= 0, a non-place-place, a no coincidence size.
E 'need for this identification of bidirectional coincidence without identity between external and internal borders, or just a new artificial language devoid of any substance? We
to a body that atraverso the border of the body contact the outside world (the representation that makes the brain) and the inner world projected in imagery, such as the eye. The vision of an external object is to construct a virtual image on the retina, a form enclosed by a boundary. This boundary is projected in the mind as a real board , not at all virtual, some receptors of the retina receive the full, others vacuum, and the brain identifies the transition region between solid and void with a sequence of signals on / off the receptors. This board is propagated backwards in sequence, until the visual cortex, where it is mapped topologically unchanged (with geometric distortion, no doubt, but keeping the connection properties and dimensional relationships) in the neurons of the nucleus visual perception. This seems a plausible modern interpretation of Aristotle's description of the perceptual process, with the union of form and feeling in the generation dell'ειδος, the image imprinted in the soul, which in modern terms is obviously to be identified with the definition of mind that occurs in neuroscience.
The perception is the result of a process of mental impression of forms drawn from outside through the interaction with the boundaries of the body and, conversely, the projection of mental borders on external objects by recognizing the elements of τóπος, scope vital place.
The rejection of the Aristotelian theory of Platonic forms, presented in the "Nicomachean Ethics" is explained in this sophisticated analysis of the perceptual process, so much next to the conceptions of modern neurophysiology. According to Aristotle, Plato's error was the assumption that, since the mind can separate an object and its abstract form, both have exist separately (and as we know, Plato arrives then to attribute reality only to the abstract forms). Aristotle says the other hand, with a very modern look, that the human mind is naturally capable of doing the abstract thought, and the fact that a person is able to abstract the mental image the shape object that generates it, does not necessarily mean that the form has a life of its own. The form, in conclusion, it is purely a mental image, their perception of the process of every being, human or animal, not intrinsic to the object.
This analysis, as only the beginning, still primitive and sketchy, incomplete and totally reprehensible, and all you want, make out, in my opinion, Aristotle's theory places its state of locus horribilis philosophiae the function of a statute boundaries.
That is, the definition of perceptual sensitivity by specifying the boundaries: first, the boundary between inside and outside of the body, what happens inside the life and what happens outside it, and secondly, the boundary that demarcates and sets out the substance of the external world, expressed geometrically as perimeter or area, and temporally as the interval between the beginning and end, and thirdly, the boundary that represents the mental images of external substances, ideally comparable to the real substance in the process of formal recognition, possibly coincident with those, but still distinct, the author of "double border" vanishing zero length that characterizes the methodology of representation.
One might argue that Aristotle in these my speculations longer seems to be used as an excuse methodology, not as a true subject of philosophical reflection. Maybe. But I said from the beginning. And nevertheless, the status of the borders will be used to correlate the activity of mental representation with the scientific activities ... but also linguistic or musical.
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