Looking for a reference on a kind of mathematical platonism

What is platonic math?

Platonic solid, any of the five geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles. Also known as the five regular polyhedra, they consist of the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron.

Is mathematical Platonism true?

Mathematical Platonism, formally defined, is the view that (a) there exist abstract objects—objects that are wholly nonspatiotemporal, nonphysical, and nonmental—and (b) there are true mathematical sentences that provide true descriptions of such objects.

What is an example of platonism?

For example, a platonist might assert that the number pi exists outside of space and time and has the characteristics it does regardless of any mental or physical activities of human beings.

Who invented Fictionalism?

(We will return to this issue below, in section 2.4.) Finally, it should also be noted at the start that fictionalism is a version of mathematical nominalism, the view that there are no such things as mathematical objects. Fictionalism was first introduced by Field (1980, 1989, 1998, 2016).

Why is platonism important?

Platonism had a profound effect on Western thought. Platonism at least affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism.

See also  According to Hasker's emergent dualism, why does the mind have to be spatial?

What is the difference between platonism and aristotelianism?

In Philosophy

Plato believed that concepts had a universal form, an ideal form, which leads to his idealistic philosophy. Aristotle believed that universal forms were not necessarily attached to each object or concept, and that each instance of an object or a concept had to be analyzed on its own.

What is mathematical nominalism?

Nominalism is the view that mathematical objects such as numbers and sets and circles do not really exist. Nominalists do admit that there are such things as piles of three eggs and ideas of the number 3 in people’s heads, but they do not think that any of these things is the number 3.

What type of philosophy is platonism?

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and non-mental. Platonism in this sense is a contemporary view.

Which philosophy is represented by aristotelianism?

In metaphysics, or the theory of the ultimate nature of reality, Aristotelianism involves belief in the primacy of the individual in the realm of existence; in the applicability to reality of a certain set of explanatory concepts (e.g., 10 categories; genus-species-individual, matter-form, potentiality-actuality, …

What is fictionalism theory?

Fictionalism is the view in philosophy according to which statements that appear to be descriptions of the world should not be construed as such, but should instead be understood as cases of “make believe”, of pretending to treat something as literally true (a “useful fiction”).

See also  Natural sociality in Rousseau and Aristotle

What is revolutionary fictionalism?

2.2 Hermeneutic and revolutionary fictionalism

Revolutionary fictionalism, by contrast, insists that when engaging in D we ought only to make such pretend-assertions; the point of engaging in D would be achieved by pretend-assertions.

What is the opposite of nominalism?

Opposite of a doctrine that universals do not have an existence except as names for classes of concrete objects. realism. pragmatism. practicality. level-headedness.

What is an example of nominalism?

Nominalism arose in reaction to the problem of universals, specifically accounting for the fact that some things are of the same type. For example, Fluffy and Kitzler are both cats, or, the fact that certain properties are repeatable, such as: the grass, the shirt, and Kermit the Frog are green.

Is nominalism a heresy?

In the Middle Ages, when Platonic and Aristotelian realisms were associated with orthodox religious belief, nominalism could be interpreted as heresy.

What do nominalists believe?

Nominalism, coming from the Latin word nominalis meaning “of or pertaining to names”, is the ontological theory that reality is only made up of particular items. It denies the real existence of any general entities such as properties, species, universals, sets, or other categories.

What does nominalism teach?

nominalism in philosophy, the doctrine that universals or general ideas are mere names without any corresponding reality. Only particular objects exist, and properties, numbers, and sets are merely features of the way of considering the things that exist.

What is wrong with nominalism?

According to Class Nominalism properties are classes of things, and so the property of being scarlet is the class of all and only scarlet things. One problem with this theory is that no two classes can have the same members, while it does not seem that properties with the same instances need be the same.

See also  What justifies Russell's Law of Identity?