Sciences as Categorical Closures

There was a problem providing the content you requested

---

From then onwards, Bueno and a number of authors have developed this philosophy through specific applications to fields as diverse as classic chemistry, quantum mechanics, chaos theory, cybernetics, Darwinism, ethology, geology, plate tectonics, anthropology, sociology, economics and psychology.

Andreas Baudisch, Closures in ℵ0-categorical bilinear maps - PhilPapers

This has resulted in a number of doctoral dissertations, books and articles. Unfortunately, that wealth of literature is for the most part only available in Spanish, although some of it has been produced in English and French or has been later translated into German and Chinese. Therefore, this translation is a welcome step towards an overdue effort. Gustavo Bueno is known as the main developer of philosophical materialism, one of the few last efforts to construe a comprehensive and coherent philosophical system in direct conversation with the natural and social sciences.

His founding book Ensayos materialistas dates from There, he finds bodies of knowledge composed not of ready- made theories about nature but of bodily movements, apparatuses, formulae, conversations and theorems. Bueno takes specific scientific fields as his units of analysis and traces the ways in which they attain the individuality that makes them different from one another. His main thesis, the one which gives title to this book, is that each science resembles what topologists call a categorical closure, that is, a set of objects and relationships the operations with which render new objects and relationships belonging to that same set.

A categorical study of compactness via closure

A set together with a closure operator on it is sometimes called a closure space. In topology, the closure operators are topological closure operators , which must satisfy. In algebra and logic , many closure operators are finitary closure operators , i.

In universal logic , closure operators are also known as consequence operators. In the theory of partially ordered sets , which are important in theoretical computer science , closure operators have an alternative definition.

The topological closure of a subset X of a topological space consists of all points y of the space, such that every neighbourhood of y contains a point of X. The function that associates to every subset X its closure is a topological closure operator. Conversely, every topological closure operator on a set gives rise to a topological space whose closed sets are exactly the closed sets with respect to the closure operator.

My Account

Finitary closure operators play a relatively prominent role in universal algebra , and in this context they are traditionally called algebraic closure operators. Every subset of an algebra generates a subalgebra: This gives rise to a finitary closure operator.

Perhaps the best known example for this is the function that associates to every subset of a given vector space its linear span. Similarly, the function that associates to every subset of a given group the subgroup generated by it, and similarly for fields and all other types of algebraic structures.

The linear span in a vector space and the similar algebraic closure in a field both satisfy the exchange property: A finitary closure operator with this property is called a matroid. The dimension of a vector space, or the transcendence degree of a field over its prime field is exactly the rank of the corresponding matroid.

Similar books and articles

The function that maps every subset of a given field to its algebraic closure is also a finitary closure operator, and in general it is different from the operator mentioned before. Finitary closure operators that generalize these two operators are studied in model theory as dcl for definable closure and acl for algebraic closure.

The convex hull in n -dimensional Euclidean space is another example of a finitary closure operator. It satisfies the anti-exchange property: Finitary closure operators with this property give rise to antimatroids. Suppose you have some logical formalism that contains certain rules allowing you to derive new formulas from given ones.

DIGITAL - Sciences as categorical closures

For a set X of formulas, let cl X be the set of all formulas that can be derived from X. Then cl is a closure operator on P. Unfortunately, that wealth of literature is for the most part only available in Spanish, although some of it has been produced in English and French or has been later translated into German and Chinese. Therefore, this translation is a welcome step towards an overdue effort.

Navigation menu

Gustavo Bueno is known as the main developer of philosophical materialism, one of the few last efforts to construe a comprehensive and coherent philosophical system in direct conversation with the natural and social sciences. His founding book Ensayos materialistas dates from There, he finds bodies of knowledge composed not of ready- made theories about nature but of bodily movements, apparatuses, formulae, conversations and theorems. Bueno takes specific scientific fields as his units of analysis and traces the ways in which they attain the individuality that makes them different from one another.

His main thesis, the one which gives title to this book, is that each science resembles what topologists call a categorical closure, that is, a set of objects and relationships the operations with which render new objects and relationships belonging to that same set.

As such, summing operations with natural numbers produce new natural numbers. But what makes each of these fields scientific?

Account Options

• Howler
• Follow The Honey Bird
• Think Good Thoughts: Affirmations for Depression and Bipolar Disorder / Cyclothymia
• El Grimorio del Papa Honorio (Spanish Edition)
• One Week Left
• Brorotica Vol. 1: Five Stories of Straight Men and Gay Sex