We want to explore axiomatic foundations, and test the hypothesis that there is something fragmenting and perhaps blind about axiomatic approaches

Computer science Placeholder | Back Computer science is the study of algorithmic processes, computational machines and computation itself. Sun, Apr 4, 2021 Reference Computer science is the study of algorithmic processes, computational machines and computation itself.[1] As a discipline, computer science spans a range of topics from theoretical studies of algorithms, computation and information to the practical issues of implementing computational systems in hardware and software.[2][3] Its fields can be divided into theoretical and practical disciplines. For example, the theory of computation concerns abstract models of computation and general classes of problems that can be solved using them, while computer graphics or computational geometry emphasize more specific applications. Algorithms and data structures have been called the heart of computer science.[4] Programming language theory considers approaches to the description of computational processes, while computer programming involves the use of them to create complex systems. Computer architecture describes construction of computer components and computer-operated equipment. Artificial intelligence aims to synthesize goal-orientated processes such as problem-solving, decision-making, environmental adaptation, planning and learning found in humans and animals. A digital computer is capable of simulating various information processes.[5] The fundamental concern of computer science is determining what can and cannot be automated.[6] Computer scientists usually focus on academic research. The Turing Award is generally recognized as the highest distinction in computer sciences. ********** Discoveries The philosopher of computing Bill Rapaport noted three Great Insights of Computer Science:[52] Gottfried Wilhelm Leibniz's, George Boole's, Alan Turing's, Claude Shannon's, and Samuel Morse's insight: there are only two objects that a computer has to deal with in order to represent "anything".[note 4] All the information about any computable problem can be represented using only 0 and 1 (or any other bistable pair that can flip-flop between two easily distinguishable states, such as "on/off", "magnetized/de-magnetized", "high-voltage/low-voltage", etc.). See also: Digital physics Alan Turing's insight: there are only five actions that a computer has to perform in order to do "anything". Every algorithm can be expressed in a language for a computer consisting of only five basic instructions:[53] move left one location; move right one location; read symbol at current location; print 0 at current location; print 1 at current location. See also: Turing machine Corrado Böhm and Giuseppe Jacopini's insight: there are only three ways of combining these actions (into more complex ones) that are needed in order for a computer to do "anything".[54] Only three rules are needed to combine any set of basic instructions into more complex ones: sequence: first do this, then do that; selection: IF such-and-such is the case, THEN do this, ELSE do that; repetition: WHILE such-and-such is the case, DO this. Note that the three rules of Boehm's and Jacopini's insight can be further simplified with the use of goto (which means it is more elementary than structured programming). URL https://en.wikipedia.org/wiki/Computer_science Collaborative ontology Everything derived from the continuum Cognitive science Axiomatic systems Taxonomy and dimensionality

What is an axiom? Placeholder | Back The Wikipedia reference makes a couple of important distinctions Logical axioms Thu, Apr 8, 2021 Reference An axiom, postulate or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíma, 'that which is thought worthy or fit' or 'that which commends itself as evident.' The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning. As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom", "postulate", and "assumption" may be used interchangeably. In most cases, a non-logical axiom is simply a formal logical expression used in deduction to build a mathematical theory, and might or might not be self-evident in nature (e.g., parallel postulate in Euclidean geometry). To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms), and there may be multiple ways to axiomatize a given mathematical domain. Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be "true" is a subject of debate in the philosophy of mathematics. URL https://en.wikipedia.org/wiki/Axiom Formal systematic definitions Axiomatic systems Equality