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Critical mathematics pedagogy is an approach to mathematics education that includes a practical and philosophical commitment to liberation. [1] Approaches that involve critical mathematics pedagogy give special attention to the social, political, cultural and economic contexts of oppression, as they can be understood through mathematics. [2]
'The problem of demarcation' is an expression introduced by Karl Popper to refer to 'the problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as "metaphysical" systems on the other'.
Cognitive closure (philosophy) – Proposition in philosophy of mind; Critical rationalism – Epistemological philosophy advanced by Karl Popper; Duhem–Quine thesis – Principle in the philosophy of science; Problem of the criterion – Philosophical problem about the starting point of knowledge; Rational fideism
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship ...
Critical thinking is the process of analyzing available facts, evidence, observations, and arguments to make sound conclusions or informed choices. It involves recognizing underlying assumptions, providing justifications for ideas and actions, evaluating these justifications through comparisons with varying perspectives, and assessing their rationality and potential consequences. [1]
Nevertheless, it is an open philosophical problem to explain why the axiom systems that lead to rich and useful theories are those resulting from abstraction from the physical reality or other mathematical theory. In summary, the foundational crisis is essentially resolved, and this opens new philosophical problems.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science.Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language.
Philosophy – The study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. Branches of philosophy. Aesthetics – The study of the nature of beauty, art, and taste, and with the creation and appreciation of beauty. Epistemology – The study of knowledge and belief.