**Limitations**

Although first-order logic is sufficient for formalizing much of mathematics, and is commonly used in computer science and other fields, it has certain limitations. These include limitations on its expressiveness and limitations of the fragments of natural languages that it can describe.

For instance, first-order logic is undecidable, meaning a sound, complete and terminating decision algorithm is impossible. This has led to the study of interesting decidable fragments such as C_{2}, first-order logic with two variables and the counting quantifiers and (these quantifiers are, respectively, "there exists at least *n*" and "there exists at most *n*") (Horrocks 2010).

Read more about this topic: First-order Logic

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—William Howard Taft (1857–1930)