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In (Givón, 2013), the author makes the two following groupings:

Functionalism: rationalism, naturalness, universality, mentalism, innateness, emergence, evolution

Structuralism: empiricism, arbitrariness, diversity, externalism, input-dependence

Is it correct?

Also, it the grouping of "functionalism" also true for the Cognitive Linguistics framework (i.e. Lakoff, Langacker, Goldberg, Croft, Talmy)

Terminology

Rationalism :

Rationalism is the philosophical view that knowledge is acquired through reason, without the aid of the senses. Mathematical knowledge is the best example of this, since through rational thought alone we can plumb the depths of numerical relations, construct proofs, and deduce ever more complex mathematical concepts. We can even envision that someone locked in a room with no sensory experience whatsoever might still arrive at a sophisticated level of mathematical knowledge. Several ancient and medieval writers held to rationalism, most notably Plato and philosophers who followed in the Platonist tradition. In the mid seventeenth-century, though, rationalism was given a unique twist by philosophers who held that our most important mental concepts are innate, or inborn, and from these we deduce other truths with absolute certainty. Advocates of this position were largely from the continental European countries of France, the Netherlands, and Germany, hence this new breed of rationalism is often called “Continental Rationalism.” The main philosophers associated with this movement, which we will explore in this chapter, are René Descartes, Nicholas Malebranche, Baruch Spinoza, and Gottfried Wilhelm Leibniz. (Definition by Professor James Fieser, from the article "Continental rationalism", The History of Philosophy: A Short Survey)

Empiricism:

During the seventeenth and eighteenth-centuries, Britain certainly had its fair share of rationalist philosophers, particularly of the Platonist variety. However, Britain’s philosophy was soon dominated by an alternative and more scientific view that knowledge is gained primarily or mainly through the five senses. We see this presumption in Francis Bacon’s statement that in our efforts to understand nature we can “can act and understand no further than [we have] ... observed in either the operation or the contemplation of the method and order of nature” (New Organon, 1.1). Direct experience is foundational for obtaining knowledge, and this position is known as empiricism. During the first half of the 18th century, three great philosophers—Locke, Berkeley and Hume—argued for this approach, thus forming a philosophical movement known as British empiricism. Contrary to the 17th century rationalist philosophers in Continental Europe, these British empiricists largely denied the role of innate ideas and deduction in the quest for knowledge. Instead, they argued, knowledge comes from sensory experience and inductive reasoning. (Definition by Professor James Fieser, from the article "British Empiricism", The History of Philosophy: A Short Survey)

Direct comparison between empiricism and rationalism:

The empiricists solve [the problem of the origin of ideas] in a very different way than Descartes and his successors like Spinoza, Malbranche or Leibniz. Empiricists are interested in the how and not the why. Because the latter is, in their eyes, unattainable. (Jean-Michel Dufays, "L'empirisme dans les îles britanniques aux XVIIe et XVIIIe siècles", around 3rd minute, Translated from French)

As I understand it, this quote states that rationalists are motivated to find the why of phenomena, while the empiricists are motivated to find the how of phenomena.

I am not sure about the definition of mentalism and externalism. And I am not sure why to oppose naturalness to arbitrariness.

References:

Givón, T. (2013). On the Intellectual Roots of Functionalism in Linguistics. In Shannon Bischoff & Carmen Jany (eds.), Functional Approaches to Language, 9–28. Berlin, Boston: De Gruyter.

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I presume your question is about the above clustering, and you are not asking for a critical analysis of Givon's article. The implication of that clustering is that linguistic practice tends to fall into two well-characterize types where there is a strong correlation between other independently chacterizable beliefs. And furthermore, that the dichotomy exists in the self-labels adopted by practitioners, so that if you gather all of the linguists into one room, you could easily separate the "functionalists" from the "structuralists". But most linguists are not comfortable with this particular package deal.

The extreme version of rationalism holds that all knowledge and cognitive abilities are implicit in the mind, and does not require any external input. The extreme version of empiricism holds that no knowledge or cognitive ability is implicit, and everything must be learned. No linguist that I know believe that. Every two linguists that I know differ somewhat in the extent to which they believe in innate mental structures, and the extent to which they allow that some language fact can or must be learned.

The division between "natural" and "arbitrary" may be seen to be about what is in the language faculty (however you conceive of that faculty). There is a camp which holds that the mind has facts of the real world baked in, so that a child comes to the task of language learning knowing what is "out there" in nature, for instance knows that the sound "t" is more natural than "ɢ". However, another view of "naturalness" is that the language faulty is more "arbitrary", that it is an ability to analyze, and that "natural" facts (the stuff that we use to learn language) are influenced by the mind-external. So saying that language works this way because we have built-in knowledge of what is best for language can end up being observationally indistinguishable from the claim that humans have general learning abilities and that raw data filtered through Mother Nature influences what we learn – therefore, one way or the other we have the same tendency towards "naturalness".

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  • "No linguist that I know believe that." Believe what? The extreme rationalism, or the extreme empiricism? Or both? In regard to the final claims in this paragraph, so there is no such extreme views, but still some linguists pointing to one view (rationalism), or the other (empiricism)
    – Starckman
    Jan 28, 2023 at 7:15
  • Concerning the third paragraph on naturalness and arbitrariness, I feel it describes more the mentalism/externalism dichotomy put forward by Givón in his table. (Although I am not 100% clear about what he means by mentalism)
    – Starckman
    Jan 28, 2023 at 7:18
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There are three main schools of linguistics: structuralism, functionalism and formalism. Below, the first two paragraphs are taken from an article from a German academic.

The most influential school in linguistics of the twentieth century is of course structuralism. This theory, founded by Ferdinand de Saussure, has been posthumously published in Cours de linguistique generale (1916). In this essay, only the conclusions which are considered as Saussurean structuralism are described whereas other approaches like Prague school or American structuralism are left out. It is important to note that both functionalism and formalism developed from the basis of this linguistic school. A hallmark of structuralism is that linguistic phenomena are regarded “as systems or the product of systems” and not as “collections of isolated items or in terms of their history”1. [...]

While structural linguistics rather deals with langue, functionalism wants to explain how the concrete usage of a language in a given context shapes its structure, and tries to describe the communicative aspects of a language[4]. Therefore, language is considered to be a “tool”[5] with external functions (usage in communication) and internal functions (various set of communicative functions).

An Overview of Three Linguistic Theories

Formalism:

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.[3][4] Such formalisms include different methodologies of generative grammar which are especially designed to produce grammatically correct strings of words;[5] or the likes of Functional Discourse Grammar which builds on predicate logic.[6]**

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.[7]

Formalism in Linguistics from Wikipedia

[The foregoing is merely the tip of the iceberg.]

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  • "functionalism wants to explain how the concrete usage of a language in a given context shapes its structure", I added a section "Terminology", in which I put a quote concerning the different motivation (why vs. how) underlying empiricists and rationalists investigation
    – Starckman
    Jan 28, 2023 at 7:34
  • To me, "structuralists" are more descriptive, and so more empiricists in the sense of the quote
    – Starckman
    Jan 28, 2023 at 7:35
  • @starckman I think that Ferdinand de Saussure and Hjelmslev would balk at the term "empiricist". In general, Anglos (including Americans) are known for being more empirical and the Europeans more rationalist, philosophically speaking.
    – Lambie
    Jan 28, 2023 at 18:10
  • Those definitions are meaningless and don’t supply any argumentation for the assertions therein! Seriously, this is abhorrent quality “theory” or “scholarship”. “The most influential school in linguistics of the twentieth century is of course structuralism.” … Why? This can be categorically dismissed until they can make watertight and certain what a “school” of linguistics is, and how one can be “influential”, and how this author adduced that school A had “influentialness”-amount B. This is patent, airy word-salad as well as bloviation. Mar 1, 2023 at 15:06
  • “A hallmark of structuralism is that linguistic phenomena are regarded “as systems“”.. That is practically insufferable from a theoretical vantage. Can you imagine, the revelatory 20th century notion put forward by Saussure that language was a “system”? Who would have thought? And shortly thereafter came Albert Einstein with his theory of relativity, in which he attested that physics, too, could be viewed as a “system”. This is egregious intellectual banality and mediocrity, glitzed up as deep. Mar 1, 2023 at 15:06
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I know this is not a definitive answer but it's worth saying that there is a recurrent phenomenon where people try to analyse concepts that have emerged internal to a field to describe ideas within that field itself (the exact same thing happens in literary studies). It's slippery and honestly deeply theoretically dissatisfying because one is trying to observe how a term has been used while at the same time assert the hidden connections in the various uses, effectively claiming what it is at the same time. It's a problem because they have not justified why the concept should exist at all in the first place, but are seeking definitions for words they heard somebody else use: like "a solution in search of a problem".

It is inherently unanswerable to ask what the correct definition of a term is. Someone can refer you to a scholarly reference work. That doesn't bottom out the recursion. We just delegated the problem to somebody else, who has the same problem that you cannot authoritatively define a word that human beings will continue using however it befalls them to, wherever their inspiration leads them.

It looks like the author is claiming that those are general paradigms associated with what they consider a school of thought in linguistics. This is valid, but it's somewhat imprecise. This list on its own does not help someone feel absolutely clear and confident, when coming across a theory, if it's this type or that (maybe the rest of the article does help create that distinction, but I wouldn't know).

I personally would adopt your own understanding of those words. "Structuralism" means nothing to me because I see everything in language as being about "structure", but maybe it distinguishes that mentality from a very humanistic approach to language that is not thinking at all about language as a heavily rule-based system, like literary studies. "Functionalism" to me means analysing very accurately why a certain structure is used in a certain way. It basically just means understand the rules, not just the forms or patterns.

I personally think seeking a reputable definition of what is inherently an unanchored word bouncing around an intellectual community isn't a satisfying intellectual goal because it starts with the false premise that there is one. It's a non-topic because it fails to acknowledge from the outset that there is no answer to the question. It leads to confusion and doesn't generate hard knowledge. Yet, it is the only too common fallacy of reification, in which people cannot imagine that something simply does not exist, just because it's a word they've heard time and time again, so given human's common automatic thinking processes, it is too counterintuitive to think that there is no such thing; rather that there is surely such a thing, and we just need to find a definition for it.

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    Both structure and function are important words in linguistics. In some theories, they're considered to be opposed. There are many varieties of structural linguistics, and of functional linguistics, and ways of using both concepts together. In general, I agree with Givon's summary. BTW, that's not what generative grammar means; Chomsky's intuitions are not universally admired.
    – jlawler
    Jan 27, 2023 at 16:08

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