Antimodularity and the deductive-nomological model

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Table of contents

I Introduction 
1 Modularity, Antimodularity, Explanation: an Introductory Tour 
1.1 Modularity
1.1.1 Modularity in complex systems
1.1.2 Modularity, decomposability, and economy of description
1.1.3 Modules as repeated similar high-level parts
1.1.4 Structural and dynamical modularity
1.1.5 Near-decomposability and Aggregability
1.1.6 Modularity in discrete dynamical systems
1.1.7 Modularity in computational systems
1.1.8 Hierarchical modularity, levels, robustness and validity
1.1.9 Modularity and explanation
1.1.10 Some example applications of modularity in real-life scientific research .
1.2 Algorithmic detection of modularity
1.2.1 Modularity detection In networks and computational complexity
1.2.2 Modularity detection In discrete dynamical systems and computational systems
1.2.3 Some Applications of modularity detection in real-life researches
1.3 Computational hardness
1.4 Antimodularity
1.4.1 Antimodular emergence
1.4.2 Antimodularity and models of explanation
1.4.3 Antimodularity and functional or mechanistic explanations
1.4.4 Antimodularity and the deductive-nomological model
1.4.5 Antimodularity and topological explanations
1.4.6 Explanation and prediction
1.4.7 Computation and computational explanation
1.4.8 Antimodularity, cellular automata and computational explanations
1.4.9 High-level modularity as a condition for programming and scientific research
1.4.10 Explanatory emergence
1.4.11 Is it likely to encounter antimodular systems in science?
1.5 Some additional reflections on modularity, metaphysics, computing, history of science
1.5.1 A metaphysical attempt: Modularity as ontology? Constrained antirealism
1.5.2 Computational methods in scientific research: a possible historical turning point?
II Modularity 
2 A first look at modularity
2.1 An informal definition of modularity
2.2 Early concepts related to modularity
2.2.1 Aggregation in dynamical systems
2.2.1.1 Approximate aggregation
2.2.1.2 Aggregation is computationally hard
2.2.2 Decomposability
2.2.3 Simon-Ando near-decomposability
2.2.4 Timescales and decomposition in nearly-decomposable systems
2.3 Hierarchical modularity
2.4 Generic near-decomposability
2.5 Modularity is relative to the choice of a metric
2.6 Summary of the chapter and outlook
3 Modularity and networks 
3.1 Networks and network science
3.1.1 Random and regular networks
3.1.2 Small-world networks
3.1.3 Scale-free networks
3.2 Modularity in networks
3.2.1 Community and hierarchical structure detection
3.2.1.1 The Modularity measure Q
3.2.1.2 Reliability of the detected modular structure and computational hardness of Q optimization
3.2.1.3 Modularity detection in weighted networks
3.2.1.4 The problem of overlapping communities
3.2.1.5 community structure and scale-free networks
3.2.2 Network motifs and network themes
3.2.3 Network roles
3.2.4 Functional typology of hubs: party hubs and date hubs
3.2.4.1 Timescale decoupling and dynamical methods for community detection
3.2.5 Coarse-graining of networks with community structure or recurring modules
3.2.6 Modularity, small-world networks and information processing
3.2.7 Differences between modularity in networks and general modularity .
3.3 Limitations of algorithmic detection of modularity in networks
3.3.1 Time complexity of community structure and hierarchy detection .
3.3.1.1 Accuracy of community structure detection
3.3.1.2 Trade-off between accuracy and speed in community structure detection
3.3.2 Time complexity of network motifs detection
3.3.3 Time complexity of network roles detection
3.4 Summary of the survey on modularity detection algorithms
4 Modularity of computer programs 
4.1 Computer programming
4.1.1 Computer programs
4.1.2 The Von neumann architecture
4.1.3 What a program is
4.1.4 Programming languages
4.1.4.1 Low-level languages
4.1.4.2 High-level languages
4.1.4.3 Syntax and semantics of programming languages
4.1.4.4 Program semantics and flow charts
4.1.5 Program specification and program implementation
4.1.5.1 Specification, abstraction and naming
4.1.5.2 Kinds of specification
4.1.5.2.1 Kind B: bare specification
4.1.5.2.2 Kind A: the aggregate kind
4.1.5.2.3 Kind M: the modular kind
4.1.5.2.4 Kind C: the kind by convention
4.1.6 A common definition of computer program
4.2 Program modularity
4.2.1 Subroutines
4.2.2 Structured programming
4.2.3 Object-oriented programming
4.2.4 Program modularity, coupling and cohesion
4.3 Reverse Engineering and modularity detection in computer programs
4.3.1 Reverse-engineering of program specifications in modular programs
4.3.1.1 Specification mining
4.3.2 Program modularity favors program development
4.3.3 Inherently antimodular programs
4.3.4 Modularization of computer programs by program slicing
5 Modularity in discrete dynamical systems 
5.1 Discrete Dynamical Systems
5.1.1 Modular/digital and DDSs
5.1.2 A general definition of DDS
5.2 Cellular automata
5.2.1 Stephen Wolfram’s classification of CAs
5.2.2 Process modularity in CAs
5.2.3 Self-organization in CAs
5.2.4 Higher-level modularity in CAs
6 Thinking about modularity 
6.1 Modularity and its properties: summing up
6.2 Structural and dynamical modularity
6.2.1 Structure and process
6.3 Modularity is relative
6.4 Forms of functional modularity
6.5 Modularity of the dynamical model and prediction
6.6 Hierarchical levels of descriptions
6.6.1 Abstractions
6.6.2 Preferred languages
6.6.3 Abstraction, aggregation and multiple realizability
6.6.4 Transformation of languages by abstraction
6.6.5 Descriptions and simulations
6.6.6 Languages and levels of description
6.6.7 Redescriptions
6.6.8 Validity of a redescription
6.6.9 Preferred descriptions
6.6.10 Modular redescriptions, aggregated redescriptions, explanatory redescriptions, robustness and validity
6.6.11 High-level modularity and macrodescriptions
6.6.12 Macro level and Micro level
6.6.13 Levels and the specification/implementation relation
6.6.14 A meta-consideration on levels of description
6.7 Temporal decoupling of hierarchical levels
6.8 Modularity, economy of description, explanation
6.9 High-level modularity conditions experimental research and computer programming
6.10 Summary
7 Some issues about modularity in biology 
7.1 Evolution and modularity
7.1.1 Evolution of modularity in Herbert Simon’s view
7.1.2 Modularity as emergent self-organization in complex systems and the role of natural selection
7.1.3 Evolution and modularity of the genotype-phenotype map
7.1.4 Modularity as due to natural selection
7.2 A modular functional view of biological systems
7.3 A computational view of biological processes
III Models of explanation 
8 The deductive-nomological model of explanation 
8.1 Known problems of the DN model
9 Functions and functional explanation 
9.1 Functions
9.2 Functional analysis
9.3 Functional explanation of computational systems
10 Mechanistic explanation 
11 The new mechanistic school 
11.1 Machamer, Darden and Craver’s account of mechanistic explanation
11.1.1 Mechanisms and functions
11.1.2 Activities, causes and laws
11.1.3 Diagrams
11.1.4 The working cycle of a mechanism
11.1.5 Hierarchies and Bottoming Out
11.1.6 Mechanism schemata, mechanism sketches, explanation, and scientific theories
11.1.7 Intelligibility and multi-level mechanistic explanation
11.2 Becthel and Abrahamsen’s view of mechanistic explanation
11.2.1 Main differences between BA and MDC accounts
11.2.2 BA’s definition of mechanism
11.2.3 Hierarchical organization of mechanisms
11.2.4 Diagrams and simulation in mechanistic explanation
11.2.5 Discovering mechanisms: decomposition and localization
11.2.6 Testing mechanistic explanations
11.2.7 Generalizing without laws
11.3 Functional analysis and mechanistic explanation
12 Philippe Huneman’s topological kind of explanation 
IV Antimodularity 
13 The notion of antimodularity
13.1 Problems with the detection of modularity
13.2 A definition of antimodularity
13.3 Antimodular emergence
14 Consequences of antimodularity on explanation 
14.1 Antimodularity and functional or mechanistic explanations
14.2 Antimodularity and the deductive-nomological model
14.2.1 Antimodularity and weak emergence hamper DN explanation
14.3 Antimodularity and topological explanations
14.4 Explanation and prediction
14.5 Antimodularity and computational explanation
14.5.1 Computation and computational explanation
14.5.2 Antimodularity, cellular automata and computational explanations
14.6 Explanatory emergence
15 Are there antimodular systems in science? 
17 Computer science basics 
17.1 General notions
17.2 Automata theory
17.2.1 Finite automata
17.2.2 Nondeterministic finite automata
17.2.3 Probabilistic finite automata
17.2.4 Pushdown automata
17.2.5 Turing machines
17.2.6 The halting problem and the Entscheidungsproblem
17.2.7 Nondeterministic Turing machines
17.2.8 Linear bounded automata
17.2.9 The Chomsky hierarchy
17.2.10Grammars
17.2.10.1 Context-free grammars
17.2.10.2 Relationships between the expressive power of grammars
17.3 The Church-Turing thesis
17.4 Computational complexity
17.4.1 Time complexity
17.4.1.1 The TIME complexity classes
17.4.1.2 The EXPTIME complexity class
17.4.1.3 P, NP and complexity classes
17.4.1.3.1 The class P
17.4.1.3.2 The class NP and the P = NP problem
17.4.1.3.3 NP-completeness
17.4.1.3.4 NP-hardness
17.4.2 Space complexity
17.4.2.1 The SPACE complexity classes
17.4.2.2 The class PSPACE
17.4.2.3 The EXPSPACE complexity class
17.4.2.4 PSPACE-completeness
17.4.3 Relationships between space and time complexity classes and open problems
17.4.3.1 Existence of intractability
References