What arguments support the idea that rational thinking requires language use?

Question

The idea that rationality has language as a necessary condition might be called, per Brandom, lingualism.

What are the most popular arguments for this position?

Why should we think that the way we think depends upon language as a necessary condition?

Answer 1

The topic is somewhat vast due to the vagueness of "language" and "language use", so the claim can be construed to implicate most of the analytic philosophy. As Dummet writes in The Logical Basis of Metaphysics

"It has until recently been a basic tenet of analytical philosophy, in its various manifestations, that the philosophy of thought can be approached only through the philosophy of language. That is to say, there can be no account of what thought is, independently of its means of expression..."

Before that some specific suggestions as to what (broadly linguistic) means thinking "requires" were made by Aristotle (phantasma), Kant (schemata) and Peirce (diagrams). Empirical studies over the last century made any such specialized "vehicle of thought" highly implausible. Brandom's is not that kind of claim, and I will focus on his. He allows that rational thinking may employ non-linguistic means, but for it to develop in the first place requires participation in what Wittgenstein called language games. More precisely, a particular type of language games, what Sellars called "giving and asking for reasons". Here is from Reason in Philosophy:

"The game of giving and asking for reasons is not just one game among others one can play with language. It is the game in virtue of the playing of which what one has qualifies as language (or thought) at all. I am here disagreeing with Wittgenstein, when he claims that language has no downtown. On my view, it does, and that downtown (the region around which all the rest of discourse is arrayed as dependent suburbs) is the practices of giving and asking for reasons."

In other words, the rationality is "parasitic", as Brandom puts it elsewhere, on "giving and asking for reasons". Let me try to flash out Brandom's "syllogism".

1) Rational thought is about imparting and understanding meaning.

2) Understanding meaning requires making inferences, meanings are inferential roles.

3) Learning inference requires norm-governed (hence communal) linguistic practice, "giving and asking for reasons".

Ergo. Let's say that 1) is vague enough to be relatively uncontroversial. 2) is the thesis of semantic inferentialism, which Brandom credits to Hegel (ultimately), although his own version is more reminiscent of late Wittgenstein and Sellars. What goes for inferentialism is that its traditional alternative, representationalism, ran into some intractable difficulties in semantics and epistemology, see What is the difference between expressivism and representationalism in modern philosophy of language? The best known are perhaps Wittgenstein's rule-following regress, especially as laid out by Kripke in Wittgenstein on Rules and Private Language, and Sellars's argument against the Myth of the Given touched on in How is the conflict between created by reason and external aspects of knowledge resolved? Brandom has a study guide for Sellars's Empiricism and Philosophy of Mind, where it was originally developed (some of its ideas were anticipated by Hegel, Peirce and Adorno, among others). Quine's indeterminacy of translation and Davidson's indeterminacy of interpretation also belong to this circle of arguments. Verheggen in How Social Must Language Be? gives an insightful commentary on Davidson's arguments in comparison to Wittgenstein's.

3) is a major theme of Wittgenstein's Philosophical Investigations, although, unlike Sellars, he talks of language as a "motley", and does not single out giving and asking for reasons. Still, Wittgenstein's private language argument suggests (vastly oversimplifying) that signposts can only point if there is a custom of following them, and hence that normativity requires communal practice. A language may be privately used but not privately developed and established, that "requires something independent". The argument is discussed under Did Wittgenstein consider the possibility of a private language with public content?

All three arguments are very complex and intricate, we can do them only so much justice in SE format. But I want to point out a peculiar feature. They are not so much arguments for Brandom's semantic pragmatism as against the existing alternatives. This is not accidental, and reflects a different approach to arguing a position, first championed by Peirce, see Do all epistemologies suffer from the "regress of justifications" problem? It is unlike that of classical rationalists, Descartes, Kant, Fichte or Husserl, who tried establishing positive claims from imaginary "ground zero". If Brandom manages to recover traditional semantics in its confines (established disciplines with well conceptualized domains), and give an attractive account of new concept formation and acquisition, which evades realist semantics and epistemology, his position will have to be accepted without any (traditionally) positive argument for it, as a better alternative. He names as much as his task since Making It Explicit.

Answer 2

I don't quite understand why you have only asked for arguments which support the proposition, it rather pre-supposes that such arguments exist which, as Philip Klocking pointed out in his first comment, I'm not sure they do. I'm going to give the question the benefit of the doubt, and presume it to be about the connection between language and rational thought in general.

Despite the persistence of philosophical speculation in this area, the question as asked is one which can be directly answered by scientists. Studies of language-less people such as those of Schaller (1995) have demonstrated by fMRI that language centres are not utilised in basic activities. Language-less people are capable of basic survival, even in relatively complex modern environments and so demonstrate actions which must result from rational thought.

What these studies do show, is that some elements of thinking seem to require language, such as time and number (see here for example), but that these elements have equivalents in those without such linguistic tools. Further, some elements of language even replace types of thought which were otherwise available to those without linguistic tools as the work of Hespos and Spelke (2004) demonstrates.

In support of the proposition some have shown that certain critical thinking tasks are disrupted by the use of language (Newton, Ashley M., and Jill G. de Villiers. 2007, for example), but some have even questioned the validity of these conclusions, pointing to Forder's experimental results which seem to show that the language centres of the brain may not be used explicitly for language.

In short;

1. The question you've asked should now be answered by properly designed experiments and case studies, there is little value in philosophical speculation on the matter now we have such investigative tools available to us. The philosophical questions in this field are more about what questions it would be instructive to ask, rather then answering them.
2. The answer to the question seems to be that the evidence indicates so far that language is not required for all rational thought, but that the structure of language may make some forms of critical thought easier, whilst simultaneously limiting other modes of thought which may have been available without it.