Physical world in the context of "Sciences"

Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into two – or three – major branches: the natural sciences, which study the physical world, and the social sciences, which study individuals and societies. While referred to as the formal sciences, the study of logic, mathematics, and theoretical computer science are typically regarded as separate because they rely on deductive reasoning instead of the scientific method as their main methodology. Meanwhile, applied sciences are disciplines that use scientific knowledge for practical purposes, such as engineering and medicine.

The history of science spans the majority of the historical record, with the earliest identifiable predecessors to modern science dating to the Bronze Age in Egypt and Mesopotamia (c. 3000–1200 BCE). Their contributions to mathematics, astronomy, and medicine entered and shaped the Greek natural philosophy of classical antiquity and later medieval scholarship, whereby formal attempts were made to provide explanations of events in the physical world based on natural causes; while further advancements, including the introduction of the Hindu–Arabic numeral system, were made during the Golden Age of India and Islamic Golden Age. The recovery and assimilation of Greek works and Islamic inquiries into Western Europe during the Renaissance revived natural philosophy, which was later transformed by the Scientific Revolution that began in the 16th century as new ideas and discoveries departed from previous Greek conceptions and traditions. The scientific method soon played a greater role in the acquisition of knowledge, and in the 19th century, many of the institutional and professional features of science began to take shape, along with the changing of "natural philosophy" to "natural science".

A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex; for example, theorems, proofs, and even formal theories are considered as mathematical objects in proof theory.

In philosophy of mathematics, the concept of "mathematical objects" touches on topics of existence, identity, and the nature of reality. In metaphysics, objects are often considered entities that possess properties and can stand in various relations to one another. Philosophers debate whether mathematical objects have an independent existence outside of human thought (realism), or if their existence is dependent on mental constructs or language (idealism and nominalism). Objects can range from the concrete: such as physical objects usually studied in applied mathematics, to the abstract, studied in pure mathematics. What constitutes an "object" is foundational to many areas of philosophy, from ontology (the study of being) to epistemology (the study of knowledge). In mathematics, objects are often seen as entities that exist independently of the physical world, raising questions about their ontological status. There are varying schools of thought which offer different perspectives on the matter, and many famous mathematicians and philosophers each have differing opinions on which is more correct.

The doctrine or theory of immanence holds that the divine encompasses or is manifested in the material world. It is held by some philosophical and metaphysical theories of divine presence. Immanence is usually applied in monotheistic, pantheistic, pandeistic, or panentheistic faiths to suggest that the spiritual world permeates the mundane. It is often contrasted with theories of transcendence, in which the divine is seen to be outside the material world.

Major faiths commonly devote significant philosophical efforts to explaining the relationship between immanence and transcendence but do so in different ways, such as:

Philosophical realism—usually not treated as a position of its own but as a stance towards other subject matters—is the view that a certain kind of thing (ranging widely from abstract objects like numbers to moral statements to the physical world itself) has mind-independent existence, i.e. that it exists even in the absence of any mind perceiving it or that its existence is not just a mere appearance in the eye of the beholder. This includes a number of positions within epistemology and metaphysics which express that a given thing instead exists independently of knowledge, thought, or understanding. This can apply to items such as the physical world, the past and future, other minds, and the self, though may also apply less directly to things such as universals, mathematical truths, moral truths, and thought itself. However, realism may also include various positions which instead reject metaphysical treatments of reality altogether.

Realism can also be a view about the properties of reality in general, holding that reality exists independent of the mind, as opposed to non-realist views (like some forms of skepticism and solipsism) which question the certainty of anything beyond one's own mind. Philosophers who profess realism often claim that truth consists in a correspondence between cognitive representations and reality.

Physical art, as contrasted with conceptual art, refers to art that entirely exists in physical reality, in space and time. Its ontological status is that it is a physical object. The art is concretely realized but may be abstract in nature. For example, a painting, sculpture, or performance exists in the physical world. This is contrasted to conceptual art, some but not all kinds of performance art, computer software, or objects of mathematical beauty, such as a mathematical proof, which do not exist in the mental world or in physical world, but have other ontological status, such as in Plato's world of ideals. Here, the art may be realized in the physical world, such as a mathematical proof written on a chalkboard, but refer to objects that exists in the mind as concepts, not physical objects. A music performance is physical, while the composition, like computer software, is not.