A Kantian Platonist view of mathematics

What does Kant say about mathematics?

Kant argues that mathematical reasoning cannot be employed outside the domain of mathematics proper for such reasoning, as he understands it, is necessarily directed at objects that are “determinately given in pure intuition a priori and without any empirical data” (A724/B752).

What is the Platonist view?

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.

Is mathematics a priori or a posteriori?

A priori knowledge is independent from current experience (e.g., as part of a new study). Examples include mathematics, tautologies, and deduction from pure reason. A posteriori knowledge depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge.

What is nominalism math?

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.

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Was Aristotle a Platonist?

“The title of this work indicates quite clearly where the author stands regarding the relationship of these two ancient philosophers: Aristotle, contrary to the usual thinking in the philosophical literature, is a Platonist.

Was Cicero a Platonist?

Cicero was not a Platonist. He was not a Stoic, either. He hardly ever described himself as a philosopher at all. But Plato, the writer and thinker himself, was a presence of the greatest importance in Cicero’s own writing and thinking; and Stoic ethics mattered a good deal to him too.

What is nominalism theory?

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 is nominalism and realism?

Realism is the philosophical position that posits that universals are just as real as physical, measurable material. Nominalism is the philosophical position that promotes that universal or abstract concepts do not exist in the same way as physical, tangible material.

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.

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.

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What is nominalism in history?

nominalism, in philosophy, position taken in the dispute over universals—words that can be applied to individual things having something in common—that flourished especially in late medieval times.

Was Kant A nominalist?

I have heard it said that Kant was a nominalist and that the basic points of his transcendental idealism are epistemic in nature–that Kant believes the human mind is limited by the sense-data of the body and is therefore unable to directly apprehend reality.

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.

Who is the father of nominalism?


Philosophically, Abelard is best known as the father of nominalism. For contemporary philosophers, nominalism is most closely associated with the problem of universals but is actually a much broader metaphysical system.