Mathematics includes the study of such topics as quantity, structure, space, and change.
The multiverse, also known as an omniverse, is a hypothetical group of multiple universes including the universe in which we live. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, and the physical laws and constants that describe them. The different universes within the multiverse are called "parallel universes", "other universes", or "alternate universes".
A physical law or a law of physics is a statement "inferred from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present." Physical laws are typically conclusions based on repeated scientific experiments and observations over many years and which have become accepted universally within the scientific community. The production of a summary description of our environment in the form of such laws is a fundamental aim of science. These terms are not used the same way by all authors.
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist. Published in 2000, WMCF seeks to found a cognitive science of mathematics, a theory of embodied mathematics based on conceptual metaphor.
Reductionism is any of several related philosophical ideas regarding the associations between phenomena which can be described in terms of other simpler or more fundamental phenomena.
A law is a universal principle that describes the fundamental nature of something, the universal properties and the relationships between things, or a description that purports to explain these principles and relationships.
Quasi-empirical methods are methods applied in science and mathematics to achieve epistemology similar to that of empiricism when experience cannot falsify the ideas involved. Empirical research relies on empirical evidence, and its empirical methods involve experimentation and disclosure of apparatus for reproducibility, by which scientific findings are validated by other scientists. Empirical methods are studied extensively in the philosophy of science, but they cannot be used directly in fields whose hypotheses cannot be falsified by real experiment. Because of such empirical limits in science, the scientific method must rely not only on empirical methods but sometimes also on quasi-empirical ones. The prefix quasi- came to denote methods that are "almost" or "socially approximate" an ideal of truly empirical methods.
Mind–body dualism, or mind–body duality, is a view in the philosophy of mind that mental phenomena are, in some respects, non-physical, or that the mind and body are distinct and separable. Thus, it encompasses a set of views about the relationship between mind and matter, and between subject and object, and is contrasted with other positions, such as physicalism and enactivism, in the mind–body problem.
A scientific theory is an explanation of an aspect of the natural world that can be repeatedly tested and verified in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge.
Coherentism is the name given to a few philosophical theories in modern epistemology.
Experimental psychology refers to work done by those who apply experimental methods to psychological study and the processes that underlie it. Experimental psychologists employ human participants and animal subjects to study a great many topics, including sensation & perception, memory, cognition, learning, motivation, emotion; developmental processes, social psychology, and the neural substrates of all of these.
In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given observation. It was invented by Ray Solomonoff in the 1960s. It is used in inductive inference theory and analyses of algorithms. In his general theory of inductive inference, Solomonoff uses the prior obtained by this formula, in Bayes' rule for prediction.
Ray Solomonoff's theory of universal inductive inference is a theory of prediction based on logical observations, such as predicting the next symbol based upon a given series of symbols. The only assumption that the theory makes is that the environment follows some unknown but computable probability distribution. It is a mathematical formalization of Occam's razor and the Principle of Multiple Explanations.
The Kalām cosmological argument is a modern formulation of the cosmological argument for the existence of God; named for the kalam, it was popularized by William Lane Craig in his The Kalām Cosmological Argument (1979).
In the philosophy of science, underdetermination is the idea that evidence available to us at given time may be insufficient to determine what beliefs we should hold in response to it. Underdetermination says that all evidence necessarily underdetermines any scientific theory
In the philosophy of science, models of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at genuine knowledge.
The search for scientific knowledge ends far back into antiquity. At some point in the past, at least by the time of Aristotle, philosophers recognized that a fundamental distinction should be drawn between two kinds of scientific knowledge—roughly, knowledge that and knowledge why. It is one thing to know that each planet periodically reverses the direction of its motion with respect to the background of fixed stars; it is quite a different matter to know why. Knowledge of the former type is descriptive; knowledge of the latter type is explanatory. It is explanatory knowledge that provides scientific understanding of the world.
Indeterminacy, in philosophy, can refer both to common scientific and mathematical concepts of uncertainty and their implications and to another kind of indeterminacy deriving from the nature of definition or meaning. It is related to deconstructionism and to Nietzsche's criticism of the Kantian noumenon.
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena.
A hypothesis is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used synonymously, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a provisionally accepted hypothesis proposed for further research, in a process beginning with an educated guess or thought.
