In analytic philosophy, anti-realism is the position that the truth of a statement rests on its demonstrability through internal logic mechanisms, such as the context principle or intuitionistic logic, in direct opposition to the realist notion that the truth of a statement rests on its correspondence to an external, independent reality. In anti-realism, this external reality is hypothetical and is not assumed.
In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are at least two main versions of nominalism. One version denies the existence of universals – things that can be instantiated or exemplified by many particular things. The other version specifically denies the existence of abstract objects – objects that do not exist in space and time.
The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: "Should the properties an object has in common with other objects, such as color and shape, be considered to exist beyond those objects? And if a property exists separately from objects, what is the nature of that existence?"
Reality is the sum or aggregate of all that is real or existent within the universe, as opposed to that which is only imaginary, nonexistent or nonactual. The term is also used to refer to the ontological status of things, indicating their existence. In physical terms, reality is the totality of a system, known and unknown.
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities.
Hilary Whitehall Putnam was an American philosopher, mathematician, computer scientist, and figure in analytic philosophy in the second half of the 20th century. He contributed to the studies of philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science. Outside philosophy, Putnam contributed to mathematics and computer science. Together with Martin Davis he developed the Davis–Putnam algorithm for the Boolean satisfiability problem and he helped demonstrate the unsolvability of Hilbert's tenth problem.
In philosophy, the philosophy of physics deals with conceptual and interpretational issues in physics, many of which overlap with research done by certain kinds of theoretical physicists. Historically, philosophers of physics have engaged with questions such as the nature of space, time, matter and the laws that govern their interactions, as well as the epistemological and ontological basis of the theories used by practicing physicists. The discipline draws upon insights from various areas of philosophy, including metaphysics, epistemology, and philosophy of science, while also engaging with the latest developments in theoretical and experimental physics.
Aristotelianism is a philosophical tradition inspired by the work of Aristotle, usually characterized by deductive logic and an analytic inductive method in the study of natural philosophy and metaphysics. It covers the treatment of the social sciences under a system of natural law. It answers why-questions by a scheme of four causes, including purpose or teleology, and emphasizes virtue ethics. Aristotle and his school wrote tractates on physics, biology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, and government. Any school of thought that takes one of Aristotle's distinctive positions as its starting point can be considered "Aristotelian" in the widest sense. This means that different Aristotelian theories may not have much in common as far as their actual content is concerned besides their shared reference to Aristotle.
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties.
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 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 entirely.
David Malet Armstrong, often D. M. Armstrong, was an Australian philosopher. He is well known for his work on metaphysics and the philosophy of mind, and for his defence of a factualist ontology, a functionalist theory of the mind, an externalist epistemology, and a necessitarian conception of the laws of nature.
The instantiation principle or principle of instantiation or principle of exemplification is the concept in metaphysics and logic that there can be no uninstantiated or unexemplified properties. In other words, it is impossible for a property to exist which is not had by some object.
James Franklin is an Australian philosopher, mathematician and historian of ideas.
Australian realism, also called Australian materialism, is a school of philosophy that flourished in the first half of the 20th century in several universities in Australia including the Australian National University, the University of Adelaide, and the University of Sydney, and whose central claim, as stated by leading theorist John Anderson, was that "whatever exists … is real, that is to say it is a spatial and temporal situation or occurrence that is on the same level of reality as anything else that exists". Coupled with this was Anderson's idea that "every fact is a complex situation: there are no simples, no atomic facts, no objects which cannot be, as it were, expanded into facts." Prominent players included Anderson, David Malet Armstrong, J. L. Mackie, Ullin Place, J. J. C. Smart, and David Stove. The label "Australian realist" was conferred on acolytes of Anderson by A. J. Baker in 1986, to mixed approval from those realist philosophers who happened to be Australian. David Malet Armstrong "suggested, half-seriously, that 'the strong sunlight and harsh brown landscape of Australia force reality upon us'".
Metaontology or meta-ontology is the study of the field of inquiry known as ontology. The goal of meta-ontology is to clarify what ontology is about and how to interpret the meaning of ontological claims. Different meta-ontological theories disagree on what the goal of ontology is and whether a given issue or theory lies within the scope of ontology. There is no universal agreement whether meta-ontology is a separate field of inquiry besides ontology or whether it is just one branch of ontology.
In philosophy and theology, infinity is explored in articles under headings such as the Absolute, God, and Zeno's paradoxes.
The following outline is provided as an overview of and topical guide to metaphysics:
Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All are controversial.
In the philosophy of science, structuralism asserts that all aspects of reality are best understood in terms of empirical scientific constructs of entities and their relations, rather than in terms of concrete entities in themselves.
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the number 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any natural number is defined by its respective place in that theory. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.
