1 Philosophy of science Jan Helm Technical University Berlin Email: [email protected] Abstract This is a concise presentation of important aspects of modern philosophy of science and humanities. It is based primarily on the Oxford Philosophy of science [1], and gives for every chapter in concise formulation the prevailing contemporary concepts and the concept of the author [JH], in some chapters only the latter. Contents 1 Basics 1.1 Theory and experiment 1.2 Theories of different sciences 1.3 General philosophy of science 1.4 Analogue and analytic human thinking 2 Philosophy of computational science 3 Philosophy of classical and non-classical physics 4 Philosophy of evolution 4.1 Distinguishable and non-distinguishable entities and evolution 4.2 Evolutionary hierarchy 4.3 Evolution of societies and ethics 5 Causation in science 5.1 Causation in science 5.2 Arrow of time in classical and quantum regime 5.3 Messaging and causation 5.4 Time and history 6 Induction in science 7 Determinism and indeterminism 7.1 Deterministic and prognostic systems 7.2 Regular, chaotic and non-causal classical and quantum systems 8 Consciousness 8.1 Concepts of brain functionality 8.2 Multi-layered personality 8.3 Maps as reality representations 8.4 Consciousness coordination 8.5 Classification of living beings based on feedback loops 8.6 Comparison animal- robot 8.7 Biological memory and concepts 9 Classification of human knowledge 9.1 Collection of data 9.2 Models 9.3 Biological data 9.4 Technology and tools 9.5 Actions and actors 9.6 Inner representation and language 9.7 Art 9.8 Symbols 10. Representations of reality, Kant & Popper , 4-worlds-theory 10.1 Popper and Kant 10.2 Four-world concept: extension of Popper’s concept 10.3 Metaphysical concepts: basic questions 11 Philosophy of language and intelligence 11.1 Human language 2 11.2 Evolution of human language 11.3 Other languages 11.4 Comparison natural language – program language 12 Philosophy of society and ethics 12.1 Societies as biological communities 12.2 Society models and ethics 12.3 Social dynamics in human societies 12.4 Individual action within a human society 12.5 Religion and society 13 Physical and neural world 13.1 World description 13.2 World context Literature 3 1 Basics 1.1 Theory and experiment The traditional approach to the notion of natural science is: The empirical content of theories, models, and data is a characteristic feature that distinguishes natural science from mathematics and other intellectual endeavors [1: 1.4] . Proposed concept [JH] 1 A natural science, e.g. physics is a collection of mathematical theories, which describe a set of real-world phenomena, where this set of real-world phenomena is a realization of the theory (in the mathematical sense. see below). 2 Experiments are verifications of a theory in a particular numerical setting, e.g. measuring the phase diagram p(T) of water and comparing it to the theoretical model in thermodynamics. An experiment yields a mapping of theory variables to measurable quantities, e.g. temperature T=E/kB into experimental temperature measured by a mercury thermometer. On the other hand, an experiment provides a real-world action-sequence for the measurement, e.g. build a mercury thermometer, fix the length scale (e.g. by water freezing point and water boiling point) and read the length of the mercury column. 3 A real-world phenomenon (phase diagram of water) is a realization of the theory, here the function p(T, material-parameters ξ), for water=H2O, a realization in the same sense as the group S3={permutations of 3 elements} is a realization of a non-commutative finite group. So in a theory there is a mathematical model -state function(of physical variables) (e.g. phase diagram) -partial differential equations (e.g. Maxwell equations) -Lagrangian (function of space-time, physical entity states like quarks ) of the minimal action (e.g. Lagrangian of the SU(3) quark color interaction) -statistical dynamical system with states, state transition probabilities, state probability distribution (e.g. ideal gas with Maxwell probability distribution of velocity, elastic collision as state transition) There is a mapping theory-> physical experiment, e.g. pressure p-> physical pressure in Pa , temperature T-> physical temperature in K, material parameter ξ-> physical quantity like density in g/cm3 . There is a geometric-physical experimental model , e.g. structure H2O of 2 hydrogen atoms and an oxygen atom as a model of the physical material water, with model parameters OH-bond length in angström, OH-bond energy in kJ/mol, molecule enthalpy in kJ/mol etc. [45]. 4 An experimental measurement is a statistical confidence test of N samples, in which the mean μ and the variance σ2 of a random variable x with the (approximately Gaussian) probability distribution P(x, μ, σ) are measured with a confidence of Pc(3 σ)= 0.9973. The object of a measurement can be a continuous function (like p(T) for water) or a discrete simulation mapping (like a weather simulation pressure p(ri, ti, bcond) on a lattice (ri, ti) of location and time depending on boundary conditions bcond). 5 As a summary, one can consider a natural science, e.g. physics, as a collection of triplets (mathematical theory, mapping functions, experimental models) in the sense of Nagel’s interpretation [44:2.2.1] . 6 On the other hand, an abstract science (e.g. various branches of mathematics) is a set of axioms with corresponding concepts (e.g. axioms of group theory with concepts {multiplication, unit element, ...}), a collection of models of this respective set of axioms (e.g. group S3={permutations of 3 elements}), and theorems formulated with these concepts of this respective set of axioms (e.g. theorems in group theory). 1.2 Theories of different sciences Fundamental physics A theory in fundamental physics consists of equations for physical objects (e.g. Dirac field equation of SU(3)- color-interaction for the wave-function Ψ[q](xμ) in space-time 4-vector xμ of a physical object q, e.g. u-quark q=u) and a structural model of these physical objects (e.g. quark model of color-interaction). The equations are derived from a minimum principle of the corresponding Lagrangian L(,) q x d4 x 4 In physics, there are two fundamental theories: the Standard Model of Particle Physics describing the small- scale quantum gauge field universe (microcosm) and the Lambda-CDM model describing the large-scale GR universe (macrocosm). The Standard Model of Particle Physics consists of the SU(1)elmxSU(2)weakSU(3)color Lagrangian (with the derived Dirac gauge field equations) and the structural quark-lepton-model with 28 parameters (masses, gauge field constants) [8]. The Lambda-CDM model is a pure equation with 2 Friedmann equations based on GR with 4 parameters ( D,,, K k ) [8]. Physics of species Species are typical large collection of objects with common properties. Classical species consist of non-identical components with parameters in a certain range: e.g. stellar systems, galaxies, or mesophysical structures like tectonic plates, mountain formations. They are described by a structural-evolutionary model, e.g. stellar models , and governed by statistical evolution laws (e.g. Hertz-Russel diagram for stars) and static structure laws (e.g. equation-of-state for a star). Quantum species consist of identical components: materials like water consist of molecules with fixed parameters (material parameters like density, boiling temperature etc.). They are governed by thermodynamic and chemical laws: the phase diagram p(,) T , the density (,)p T , chemical reaction rate E 1 A ( r k[][] AnAB B n k e RT ) of a molecular substance like water H2O, are precise, and their parameters can T0 be calculated from the molecular structure. Biology Biological species are described a structural model consisting of phenotype (typical structure), genotype (typical genetic code) and typical behavior. All these structural models have parameters, which have a Gaussian distribution among individuals with a relatively small variance. The description in time is the evolution history of the species. The governing laws in biology can be formulated as behavioral statistical Markov systems, resulting in statistical differential equations like the Lotka-Volterra equations for predator-prey-systems. Economy/sociology In human societies, the structural model has as its components the important agents in a society: labor unions, religious organizations, parties, powerful companies etc. The structural parameters (financial power, influence factor, cohesion of members etc.) are derived from statistical data. The governing laws in economy/sociology can be formulated, like in biology, as behavioral statistical Markov systems, resulting in statistical differential equations. 5 1.3 General philosophy of science The four dimensions of general philosophy of science (GPoS) [1: 1.7] The epistemic dimension deals with science as a mode of knowledge: science relies on theories, hypotheses, and principles that typically go beyond the observable aspects of the world. The metaphysical dimension deals with the way to explain and ground the regularity there is in the world. The conceptual dimension deals with ways to understand relation of physical theories to experience and experiment. The practical dimension deals with ethical and social implications of science. Proposed concept of four GPoS dimensions [JH] Epistemic: the generalization of observable experimental parameter range is accepted on the basis of Occam’s razor. Metaphysical: there is no need for explanation of the mathematical model: it is simply a way to know the past and to predict the future where it is possible. Conceptual: this is answered by the duality of theory and experiment as presented in 1.1. Practical: ethical and social implications do not belong to the area of natural science, they are dealt with by social science.