In linguistics, the term formalism is used in a variety of meanings which relate to formal linguistics in different ways. In common usage, it is merely synonymous with a grammatical model or a syntactic model: a method for analyzing sentence structures. Such formalisms include different methodologies of generative grammar which are especially designed to produce grammatically correct strings of words; or the likes of Functional Discourse Grammar which builds on predicate logic. Additionally, formalism can be thought of as a theory of language. This is most commonly a reference to mathematical formalism which argues that syntax is purely axiomatic being based on sequences generated by mathematical operations. This idea stands in contradistinction to psychologism and logicism which, respectively, argue that syntax is based on human psychology; or on semantic a priori structures which exist independently of humans. Definitions Rudolph Carnap defined the meaning of the adjective formal in 1934 as follows:"A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for example, the words) or to the sense of the expressions (e.g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are constructed."Martin Kusch defines linguistic formalism as "a purely syntactical treatment of language". History The term 'formalism' originally pertains to late-nineteenth-century debates in the philosophy of mathematics, but these discussions would also lead to the development of formal syntax and formal semantics. In such debates, advocates of psychologism argued that arithmetic arises from human psychology, claiming that there are no absolute mathematical truths. Thus, in principle, an equation like 1 + 1 = 2 depends on a human way of thinking and therefore cannot have objective value. So was argued by psychologist Wilhelm Wundt among others. Many mathematicians disagreed and proposed "formalism" which considered mathematical sequences and operations as purely axiomatic with no mental content and thus disconnected from human psychology. Edmund Husserl disagreed with both claims. He argued that both cardinal numbers and arithmetic operations are fundamentally meaningful, and that our ability to carry out complex mathematical tasks is based on the extension of simple concepts such as low non-imaginary numbers, addition, subtraction, and so on. Based on mathematical logic, Husserl also created a "formal semantics" arguing that linguistic meaning is composed of series of logical propositions. Additionally, he argued on