Abstract:
First, the numerous claims that the theory of natural selection would be a tautology, just empty circular reasoning, are shown to be erroneous, and that they follow from an essentialistic and deterministic way of thinking, which is not consistent with the dynamic theory of evolution. Secondly, it is proposed that a careful analysis applying Fisher’s Fundamental Theorem of Natural Selection of the seemingly tautologous sentence in question: “those who reproduce most, reproduce most” shows that in actual fact it is a predictive statement. Consequently, the analysis presented reduces the essence of the theory of natural selection to that one single statement.

Abstract:
Some scholars have pointed out the phenomenological character of the theory of natural selection, in the sense that it does not propose new theoretical terms. Since others have held that one of the characteristics of explanatory theories is that they conceptually enrich their field of application, it could be said that the theory in question is lacking with respect to its explanatory capacity. The article addresses this issue by proposing an informal reconstruction of the Darwinian theory of natural selection using structuralist meta-theoretical tools. The objective is to show that the theory suggests at least one explanatory concept, which could be called “aptitude”, although all of its concepts are non-theoretical in the structuralist sense.

Abstract:
Kin selection theory is a kind of causal analysis. The initial form of kin selection ascribed cause to costs, benefits, and genetic relatedness. The theory then slowly developed a deeper and more sophisticated approach to partitioning the causes of social evolution. Controversy followed because causal analysis inevitably attracts opposing views. It is always possible to separate total effects into different component causes. Alternative causal schemes emphasize different aspects of a problem, reflecting the distinct goals, interests, and biases of different perspectives. For example, group selection is a particular causal scheme with certain advantages and significant limitations. Ultimately, to use kin selection theory to analyze natural patterns and to understand the history of debates over different approaches, one must follow the underlying history of causal analysis. This article describes the history of kin selection theory, with emphasis on how the causal perspective improved through the study of key patterns of natural history, such as dispersal and sex ratio, and through a unified approach to demographic and social processes. Independent historical developments in the multivariate analysis of quantitative traits merged with the causal analysis of social evolution by kin selection.

Abstract:
Species coexistence is one of the central themes in modern ecology. Coexistence is a prerequisite of biological diversity. However, the question arises how biodiversity can be reconciled with the statement of competition theory, which asserts that competing species cannot coexist. To solve this problem natural selection theory is rejected because it contradicts kinetic models of interacting populations. Biological evolution is presented as a process equivalent to a chemical reaction. The main point is that interactions occur between self-replicating units. Under these assumptions biodiversity is possible if and only if species are identical with respect to the patterns of energy flow in which individuals are involved.

Abstract:
The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and regressions. Population genetic equations depend on genetic variances. How can we read those statistical expressions with respect to the meaning of natural selection? One possibility is to relate the statistical expressions to the amount of information that populations accumulate by selection. However, the connection between selection and information theory has never been compelling. Here, I show the correct relations between statistical expressions for selection and information theory expressions for selection. Those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics, and communication. We can now read the equations of selection in terms of their natural meaning. Selection causes populations to accumulate information about the environment.

Abstract:
Standard evolutionary theories of aging and mortality, implicitly based on assumptions of spatial averaging, hold that natural selection cannot favor shorter lifespan without direct compensating benefit to individual reproductive success. Here we show that both theory and phenomenology are consistent with programmed death. Spatial evolutionary models show that self-limited lifespan robustly results in long-term benefit to a lineage; longer-lived variants may have a reproductive advantage for many generations, but shorter lifespan ultimately confers long-term reproductive advantage through environmental feedback acting on much longer time scales. Numerous model variations produce the same qualitative result, demonstrating insensitivity to detailed assumptions; the key conditions under which self-limited lifespan is favored are spatial extent and locally exhaustible resources. Numerous empirical observations can parsimoniously be explained in terms of long-term selective advantage for intrinsic mortality. Classically anomalous empirical data on natural lifespans and intrinsic mortality, including observations of longer lifespan associated with increased predation, and evidence of programmed death in both unicellular and multicellular organisms, are consistent with specific model predictions. The generic nature of the spatial model conditions under which intrinsic mortality is favored suggests a firm theoretical basis for the idea that evolution can quite generally select for shorter lifespan directly.

Abstract:
Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type theory as well as a computational approach to algebraic topology via type theory-based proof assistants such as Coq. The present work investigates inductive types in this setting. Modified rules for inductive types, including types of well-founded trees, or W-types, are presented, and the basic homotopical semantics of such types are determined. Proofs of all results have been formally verified by the Coq proof assistant, and the proof scripts for this verification form an essential component of this research.

Abstract:
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal with conceptual and mathematical problems of quantum theory without any appeal to frameworks of Hilbert spaces and measure spaces.

Abstract:
For Lee Smolin, our universe is only one in a much larger cosmos (the Multiverse) - a member of a growing community of universes, each one being born in a bounce following the formation of a black hole. In the course of this, the values of the free parameters of the physical laws are reprocessed and slightly changed. This leads to an evolutionary picture of the Multiverse, where universes with more black holes have more descendants. Smolin concludes, that due to this kind of Cosmological Natural Selection our own universe is the way it is. The hospitality for life of our universe is seen as an offshot of this self-organized process. - This paper outlines Smolin's hypothesis, its strength, weakness and limits, its relationship to the anthropic principle and evolutionary biology, and comments on the hypothesis from different points of view: physics, biology, philosophy of science, philosophy of nature, and metaphysics. Some of the main points are: (1) There is no necessary connection between black holes and life. In principle, life and Cosmological Natural Selection could be independent of each other. Smolin might explain the so-called fine-tuning of physical constants, but life remains an epiphenomenon. (2) The Darwinian analogy is an inadequate model transfer. The fitness of Smolin's universes is not constrained by its environment, but by only one internal factor: the numbers of black holes. Furthermore, although Smolin's universes have different reproduction rates, they are not competing against each other. (3) Smolin's central claim cannot be falsified.

Abstract:
Formal synthesis is the process of generating a program satisfying a high-level specification. In recent times, effective formal synthesis methods have been proposed based on the use of inductive learning. We refer to this class of methods that learn programs from examples as formal inductive synthesis. In this paper, we present a theoretical framework for formal inductive synthesis. We discuss how formal inductive synthesis differs from traditional machine learning. We then describe oracle-guided inductive synthesis (OGIS), a class of synthesizers that operate by iteratively querying an oracle. An instance of OGIS that has had much practical impact is counterexample-guided inductive synthesis (CEGIS). We present a theoretical characterization of CEGIS for learning any program that computes a recursive language. In particular, we analyze the relative power of CEGIS variants where the types of counterexamples generated by the oracle varies. We also consider the impact of bounded versus unbounded memory available to the learning algorithm. In the special case where the universe of candidate programs is finite, we relate the speed of convergence to the notion of teaching dimension studied in machine learning theory. Altogether, the results of the paper take a first step towards a theoretical foundation for the emerging field of formal inductive synthesis.