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Aristotle’s Apprehension of Reality I. Antoniou

School of Mathematics Aristotle University

Thessaloniki Greece 54124

iantonio@math.auth.gr

XIIth Quark Confinement and the Hadron Spectrum 28 August 2016 to 4 September 2016

Thessaloniki, Greece https://indico.cern.ch/event/353906/overview

mailto:iantonio@math.auth.grhttps://indico.cern.ch/event/353906/overviewhttps://indico.cern.ch/event/353906/overview

[0] PLATO's Definition of Knowledge 3 CONTRIBUTIONS of ARISTOTLE

[1] METHODOLOGY of SCIENTIFIC ENQUIRY

[2] MODEL of REALITY based on (including) Man-Woman Relation with REALITY

[3] APPLICATION to All Known Human Activities of his Time Key Discrimination between a Congregation (Συναθροιση) and a Collective Whole (System)

Π Superhighway to Knowledge

[0] Knowledge PLATO's Definition

KNOWLEDGE is JUSTIFIED TRUE BELIEF (JTB) «Την μετα λόγου αληθή δόξαν επιστήμη είναι, την δε άλογον εκτός επιστήμης» [Θεαιτητος, 201d] Knowledge (επιστήμη) is: • A Belief (δόξα) expressed as a Statement SYNTACTIC ASPECT • The Belief is justified (μετα λόγου) acquires Meaning of in the Context of some specific Ontology network of concepts linked according to depth (genus) and width (species) SEMANTIC ASPECT • The Belief is Verified as True (αληθή) by Observation-Experiment PRAGMATIC ASPECT A Belief without justification (άλογον) is outside (εκτός) knowledge JTB in Modern Management

Plato was Happy but Not Satisfied He missed a Method of Direct Apprehension of Reality [Plato Theaetetus 210b] • οὔτε ἄρα αἴσθησις, • οὔτε δόξα ἀληθὴς • οὔτε μετ' ἀληθοῦς δόξης λόγος προσγιγνόμενος ἐπιστήμη ἂν εἴη Knowledge is • neither Sense Observation • Nor True Belief • Nor Logos attached-supported by True Beliefs

METHODOLOGY of SCIENTIFIC ENQUIRY Observation Verification Processing by Reasoning Classification-Categorization

Aristotle Recommendation: • Identify the Rules of Reasoning [Organon] • Use the Rules of Reasoning to obtain Knowledge of (Accessible-Observable) Facts Mathematics Pythagorean Theorem Eudoxus Axiom of Continuity to understand Time • Define Concepts and Identify their Relation

with respect to Genus-Species [Organon] Classification, Categorization

Semantic Networks Ontologies

Networks History Peirce’s Existential Graphs, followed and extended G. Boole’s work on:

• The transformation of Aristotle’s Logic into Algebra Boolean Algebra • The Universe of Discourse

• Statistical Reasoning Boole George 1854, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. Macmillan. Reprinted with corrections, Dover Publications, New York, NY, 1958. Corcoran J. 2003, Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, vol. 24, pp. 261–288.

Boole and Pierce provided the foundations of: Causal Graphs Decision Graphs Mind Networks Ontologies = Semantic Networks + Reasoning OWL Ontology Web Language Semantic Web

Semantic Network

Aristotle Ontology 330 BC Την κατά µηδεµίαν συµπλοκή λεγοµένων έκαστον ήτοι ουσίαν σηµαίνει ή ποσόν ή ποιόν τι ή πού ή ποτέ ή κείσθαι ή έχειν ή ποιείν ή πάσχειν. 'Εστι δε ουσία µεν ως τύπω ειπείν οίον άνθρωπος ίππος, ποσόν δε οίον δίπηχυ, τρίπηχυ- ποιόν δε οίον λευκόν γραµµατικόν προς τι δε οίον διπλάσιον, ήµισυ, µείζον' πού δε οίον εν Λυκείω, εν αγορά' ποτέ δε οίον χθές, πέρισυν: κείσθαι δε οίον ανάκειται, κάθηται‘ έχειν δε οίον δε υποδέδεται, ώπλισται: ποιείν δε οίον τέµνειν, καίειν πάσχειν δε οίον τέµνεσθαι, καίεσθαι [Aristotle Organon Categories 1,4]

Aristotle Ontology ΚΑΤΗΓΟΡΙΑ CATEGORY ΠΑΡΑΔΕΙΓΜΑ Ουσια Substance άνθρωπος, ίππος, Θεμελιωδεις Γενικες Εννοιες Ποσόν (ποσότητα) Quality δύο πήχεις τρείς πήχεις Ποιόν (ποιότητα) Quantity λευκός, µορφωµένος Ως προς τι (σχέση) Relation διπλάσιος, µισός µεγαλύτερος Πού (τόπος) Where στο Λυκειο, στην αγορά Πότε (χρόνος) When χθες, πέρυσι Κεισθαι = Ανηκειν = Ενθεση Placement ξαπλώνω, κάθοµαι Εχειν Having υποδύοµαι, οπλισµένος Ποιειν, Πραττειν, Ενεργειν Action τεμνω, καίω Πάσχειν Passion κόβοµαι, καίγοµαι

Σημασιολογικο Δικτυο Semantic Network

Οντολογια Μποστανζογλου 1962 Eννοιες Γενικες

Υπαρξις Σχεση Ενοτης Ταξη Ποσοτης Αριθμος Χρονος Xωρος Διαστασις Σχημα Ενεργεια Κινησις

Οντα Υλικα Αβια Εμβια

Οντα Αυλα

Νους Βουλησις Δρασις Αξιες Συναισθημα Ηθος Θεος

Ontology Roget Thesaurus 2004 WORDS EXPRESSING ABSTRACT RELATIONS

Existence Relation Quantity Order Number Time Change Causation

WORDS RELATING TO SPACE

Space Dimensions Form Motion

WORDS RELATING TO MATTER

Matter Matter Inorganic Matter Organic

WORDS RELATING TO THE INTELLECT

Ideas Ideas Formation Ideas Communication

WORDS RELATING TO VOLITION

Individual Volition Intersocial Volition

WORDS RELATING TO AFFECTIONS

Affections Personal Affections Sympathetic Affections Moral Affections Religious Affections

Networks History Isaac Newton 1700 constructed The first Semantic Network representing the Links of Concepts from Aristotle’s “Organon” Newton's Handwritten Notes on Aristotle's «Organon» Trinity College, Πανεπιστημιο Cambridge, 32TUhttp://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5U32T

http://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5

Hadron Spectra

Search Engines

Basis of PRESENT Semantic Web of Linked Data

Brain-Web Analogy Brain as Web and Web ως Global Mind Π Last Lecture

MODEL of REALITY based on (including) Man-Woman Relation with REALITY Potential-Actual-Entelechy

ἔτι ἡ ὕλη ἔστι δυνάμει ὅτι ἔλθοι ἂν εἰς τὸ εἶδος· ὅταν δέ γε ἐνεργείᾳ ᾖ, τότε ἐν τῷ εἴδει ἐστίν. Ethica Nicomachea 1050 α 15 matter (ὕλη) exists potentially (δυνάμει), because it may attain to species (εἰς τὸ εἶδος); but when it exists actually (ἐνεργείᾳ), it is then in species (ἐν τῷ εἴδει) δυνάμει οἷον ἐν τῷ ξύλῳ Ἑρμῆν καὶ ἐν τῇ ὅλῃ τὴν ἡμίσειαν Ethica Nicomachea 1048 α 29 Hermes exists potentially (δυνάμει) in the (unprocessed, raw) wood and that the Half-line exists potentially in the whole line

Adapt Mathematical Models to Observations Select the Actual-Relevant among the Mathematical Potentialities EXAMPLES: • Electrodynamics • Thermodynamics • Statistical Mechanics, Chaos • Quantum Mechanics, QFT • Equilibrium Phase Transitions • Non-Equilibrium Phase Transitions. Self-Organization • Networks

Potential Δυναμει

Entelechy Εντελεχεια

Actuality Ενεργεια

Mechanism Structure Net Defining the Possibilities available

The Goal-Scope underlying the Realization of the Possibilities available Policy = Decide on: Filters (Feasibility, Constraints) Embedding Enviroment Selection Rules Order of Application

Actual Manifested Function

Electrodynamics ENDELECHY: Radiation Condition added to the Potential Solutions of Helmholtz's Equation, Maxwell's Equation as a Selection Rule "the sources must be sources, not sinks of energy. The energy which is radiated from the sources must scatter to infinity; no energy may be radiated from infinity into ... the field." A. Sommerfeld, Partial Differential Equations in Physics, Academic Press, New York, New York, 1949

POTENTIAL: Every convex combination of Outgoing and Incoming Waves

ACTUAL: The Outgoing Waves

Thermodynamics: Diffusion ENDELECHY: Outgoing Condition Selects Diffusion in the Future Entropy Increases in the Future (Selection Rule)

Statistical Mechanics: Entropy Increases in the Future (Selection Rule) k=8.6173324 ×10−5 eV⋅K−1 the Boltzmann's Constant

Intrinsically Irreversible Dynamical Systems Baker’s Map Chaos Hopf 1932

Chaotic Dynamical Systems Baker’s Map

Baker’s Map: Deterministic Diffusion in the Future

Quantum Mechanics: Scattering ENDELECHY: The Asymptotic Condition Heisenberg 1943 necessary to construct the Wave Operators Moller 1946 "long before and long after scattering, dynamics is indistinguishable from the "non-Interacting Dynamics" POTENTIAL: All possible scenaria ACTUAL: Incoming Solutions in the Past, Outgoing Solutions in the Future

Quantum Mechanics: Measurement ENDELECHY: The Projection Postulate Von Neumann J. 1932, Mathematical Foundation of Quantum Mechanics, Princeton Univ. Press, New Jersey 1955, p212-214 Abstraction from the Compton –Simons (1925) scattering of Light by Electrons POTENTIAL:

𝜓 >< ψ = � < 𝑎|ψ|a > 2 α >< α𝑎

+ � < 𝑎|𝑎≠𝛼�

ψ|α� >< 𝑎�|ψ|α > α >< α�

ACTUAL: 𝜚� = ∑ < 𝑎|ψ|a > 2 α >< α𝑎 Wave-packet Reduction (Correlations are Not Observed)

Phase Transitions Diagrams indicate Possibilities Brookhaven National Laboratory 2014

Phase Transitions far from Equilibrium ΔS = ΔSINTRINSIC + ΔSFLOW Δ SINTRINSIC ≥ 0

Phase Transitions Far From Equilibrium Bifurcations. Structural Instability. New Geometry

Phase Transitions Far From Equilibrium Bifurcations. Structural Instability. New Geometry

Phase Transitions Far From Equilibrium Bifurcations. Structural Instability. New Geometry Observable Variable Control Parameter

Bénard instability is a classic example of complexity in hydrodynamics . If we heat a liquid from below, we will at first have only thermic conductivity from the lower, hotter

layer to the upper colder layer. But if we increase the difference of temperatures we will see the formation of vortices. This

formation corresponds to billions of particles whose motion is correlated to the motion of surrounding particles, producing large-scale organized flows.

Knowledge Networks Nodes: Agents Links: Communication Channels for Knowledge Exchange

Knowledge Networks Knowledge Attainment in time [Ioannidis, Antoniou 2015] Knowledge Attainment Curve in an Organizational Network of a Real “Consulting Company” The horizontal axis marks the time steps The vertical axis marks the knowledge attained. Blue curve: Knowledge evolution first Filtering, then Selecting Black curve: Knowledge evolution first Selecting, then Filtering Both scenaria are Potential

Key Discrimination between a Congregation (Συναθροιση) and a Collective Whole (System)

System “ἀνάγκη γὰρ τό γε τοσοῦτον φράζειν: πᾶν διάγραμμα ἀριθμοῦ τε σύστημα καὶ ἁρμονίας σύστασιν ἅπασαν τῆς τε τῶν ἄστρων περιφορᾶς τὴν ὁμολογίαν οὖσαν μίαν ἁπάντων ἀναφανῆναι δεῖ τῷ κατὰ τρόπον μανθάνοντι, φανήσεται δέ, ἄν, ὃ λέγομεν, ὀρθῶς τις εἰς ἓν βλέπων μανθάνῃ δεσμὸς γὰρ πεφυκὼς πάντων τούτων εἷς ἀναφανήσεται διανοουμένοις” [Plato Epanomis 991ε] “for it is necessary to explain it thus far: every diagram, and system of number, and every combination of harmony, and the agreement of the revolution of the stars must be made manifest as one through all to him who learns in the proper way, and will be made manifest if, as we say, a man learns aright by keeping his gaze on unity”

What is the cause of unity? τί αἴτιον τοῦ ἓν εἶναι; πάντων γὰρ ὅσα πλείω μέρη ἔχει καὶ μὴ ἔστιν οἷον σωρὸς τὸ πᾶν ἀλλ' ἔστι τι τὸ ὅλον παρὰ τὰ μόρια, ἔστι τι αἴτιον, ἐπεὶ καὶ ἐν τοῖς σώμασι τοῖς μὲν ἁφὴ αἰτία τοῦ ἓν εἶναι τοῖς δὲ γλισχρότης ἤ τι πάθος ἕτερον τοιοῦτον. What is the cause of being one? There exists some cause underlying those Beings consisting of many parts and they are not like a pile. The cause of such unity is contact or some gluing property or some other similar interation Aristotle Metaphysics 1045α 9-19.

the whole is more than the sum of its parts.

Collectivity Quantum Mirages Quantum Chaos IBM The Well Quantum Corral (2009) by J. Voss-Andreae, Created by Lutz et al., (1993) Pictured in a 2009 review of the art exhibition "Quantum Objects" [Nature]

EPILOGUE ΕΠΙΛΟΓΟΣ

Was Aristotle Right in His Results-Conclusions? He was specific and precise to initiate serious (falsifiable) Dialogue Compare the Statements: "Proved to be Wrong" "Not Even Wrong!" [Pauli]

Aristotle's MIND Realize the Created-Anticipated Potentialities According to: Vision-Policy Interest Boundary conditions Feasibility Aleksander I., Morton H. 2012, Aristotle's Laptop: The Discovery of our Informational Mind Aristotle's convincing philosophy is likely to have shaped (even indirectly) many of our current beliefs, prejudices and attitudes to life. This includes the way in which our mind (our capacity to have private thoughts) appears to elude a scientific description.

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