### What does **formal system** mean?

# Definitions for formal system

for·mal sys·tem

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **formal system**.

#### Did you actually mean formalisation or formalization?

### Wiktionary

formal systemnoun

The grouping of a formal language and a set of inference rules and/or axioms.

### Wikidata

Formal system

A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics. Euclid's Elements is often held to be the first formal system and displays the characteristic of a formal system. The entailment of the system by its logical foundation is what distinguishes a formal system from others which may have some basis in an abstract model. Often the formal system will be the basis for or even identified with a larger theory or field consistent with the usage in modern mathematics such as model theory. A formal system need not be mathematical as such, Spinoza's Ethics for example imitates the form of Euclid's Elements. Each formal system has a formal language, which is composed by primitive symbols. These symbols act on certain rules of formation and are developed by inference from a set of axioms. The system thus consists of any number of formulas built up through finite combinations of the primitive symbols—combinations that are formed from the axioms in accordance with the stated rules. Formal systems in mathematics consist of the following elements: ⁕A finite set of symbols, that can be used for constructing formulas.

### Numerology

Chaldean Numerology

The numerical value of formal system in Chaldean Numerology is:

**9**Pythagorean Numerology

The numerical value of formal system in Pythagorean Numerology is:

**4**

### Examples of formal system in a Sentence

He would refine his ideas through talking things out with people. I think one of the things he may have gotten disappointed with the Supreme Court was the lack of regular personal interaction among the justices. They have a very

**formal system**where they communicate with each other through memos.

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"formal system." *Definitions.net.* STANDS4 LLC, 2024. Web. 3 Oct. 2024. <https://www.definitions.net/definition/formal+system>.

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