How can the inferentialist make room for the distinction between factual and linguistic correctness?

Brandom (1994) made inferentialism an intensely debated idea in the philosophy of language in the last three decades. Inferentialism is a view that associates the meaning of linguistic expression with the role said expression plays in inferences. It seems rather uncontroversial that the correct theory of meaning should distinguish between linguistic correctness and factual correctness. For instance, speaker S can be wrong in saying ‘ I have arthritis ’ in two distinct ways: (i) S fails to apply a word correctly to make a true statement due to having made a factual error, and (ii) S uses an expression incorrectly because they are wrong about its meaning. In this paper, I show that properly understood normative inferentialism can make room for such a distinction. I propose that linguistic correctness is a structural issue : linguistic mistakes stem from the improper or insu ﬃ cient acquisition of an inferential role. Factual correctness, on the other hand, is a one-o ﬀ issue of the correct application of inferential rules to a particular situation. I argue that, by tying the issue of correctness to the game of giving and asking for reasons , inferentialism can establish a reliable method for distinguishing between two types of correctness (and mistakes).


Introduction
Brandom (1994, 2000a, 2000b, 2007, 2015) made inferentialism an intensely debated idea in the philosophy of language in the last three decades (see Weiss and Wanderer 2010 for an overview of related topics).Roughly speaking, inferentialism is a view that associates the meaning of linguistic expression with the role played by said expression in inferences.Therefore, inferentialism may be said to belong to a family of Conceptual Role Semantics (cf.Whiting 2006).
It is widely accepted across both philosophy and linguistics that there are two kinds of correctness/incorrectness in terms of which linguistic expressions can be evaluated: linguistic correctness and factual correctness.For instance, speaker S can be wrong in saying, 'I have arthritis' in two different ways: (i) S fails to apply a word correctly to make a true statement due to making a factual error, and (ii) S uses an expression incorrectly because they are wrong about its meaning.Importantly, it is not yet clear how normative inferentialism can account for this distinction.If linguistic meaning is a matter of inferential roles, then it would seem that any error in the use of an expression must come down to a mistake in drawing inferences.So, is it not the case that, for inferentialists, there is no real difference between factual and linguistic correctness?
In this paper, I examine how the inferentialist can make room for the distinction between factual correctness and linguistic correctness.First, I detail the distinction between linguistic and factual correctness.Second, I briefly outline the inferential approach to linguistic meaning.Finally, I demonstrate how the normative version of inferentialism can distinguish between linguistic and factual correctness.

Factual and linguistic correctness
The distinction between linguistic correctness and factual correctness is well established in the analytic philosophy of language.One of the first expressions of this idea comes from the following passage in Moore's (1954) Wittgenstein Lectures in 1930-33: It by no means follows, for instance, from the fact that you are using the word 'foot' 'correctly', i.e. for the length for which it is usually used in English, that when you make such an assertion as 'This rod is less than four feet long', your assertion is true; and, if you were to use it 'incorrectly' for the length which is properly called in English an 'inch' or for that which is properly called a 'yard', it would by no means follow that any assertion you made by this incorrect use of the word 'foot' was false.(308)(309) This distinction is notably prominent among Wittgenstein scholars.Consider the following excerpt from Hans-Johann Glock (2005): Some uses of words are mistaken solely because of what these words mean, irrespective of any other facts, of syntactical rules or of social expectations.
Conversely, one can apply a word in a way which is semantically correct, without applying it correctly in the sense of applying it to say something true.(229) The most common route to the conclusion that we need the distinct notion of linguistic correctness is through assumptions regarding the nature of understanding.Understanding the meaning of a term, it is claimed, involves using it in accordance with its meaning (see Wright 1980, 20;McDowell 1984;McGinn 1984, 109;Millar 2004;Schroeder 2008;Glock 2019).As recently noted by Reiland (2021): The notion of linguistic correctness as use in accordance with meaning makes sense if pursued from what I call the public language perspective.This is a common-sensical and entirely familiar point of view which clearly dominates contemporary philosophy of language and is common to philosophers otherwise as different as Burge, Brandom, Dummett, Evans, Kaplan, Lewis, Millikan, McDowell, Kripke, Perry, Recanati, Searle, Soames, Stalnaker etc., the main two outliers being Chomsky and later Davidson.Its essence can be captured with the following statement: linguistic meanings belong to expression-types in public languages like English, Estonian, or Esperanto.(Reiland 2021) Although there are no ideas in philosophy that cannot be disputed, the popularity of the public language perspective and its core featurethe distinction between factual and linguistic correctnessis very broad.Therefore, it would not be particularly controversial to claim that inferentialism would be better off if it distinguished between these two types of correctness (and two types of mistakes). 1he distinction between factual and linguistic correctness can be described as follows.The former, which can also be called semantic correctness in a narrow sense, is basically equivalent to the truth.To say that the use of an expression is semantically correct is to say that one's utterance did not result in a factual mistake or, in other words, that they did not say something false.Suppose that you apply a predicate, such as 'is red', to a typical double-decker bus.You are factually incorrect if and only if, you applied the predicate to an object to which it does not applyor, put differently, if you said something false.Suppose that you considered Ludwig to be German.To say that your judgement is incorrect is simply to say that it is false because Ludwig is actually Austrian.However, it has been argued that we need a further notion of correctness: the distinctively linguistic correctness.To say something linguistically correct is to use a linguistic expression in accordance with its meaning, or to use an expression according to its use-conditions.Some of the most obvious examples are 'Good morning' and 'Goodbye!'The former can be used correctly to greet a person in the morning, while the latter can be used correctly to bid someone farewell.If one were to use 'Good morning' to greet someone at 11PM or to say farewell to a friend, they would be using the expression linguistically incorrectly.The same would be true if one were to use 'Goodbye!' to greet someone.For another example, suppose a person sees a red animal and thinks that it is a female fox.They point to that animal and utter, 'That is a vixen!'The person knew the meaning of 'vixen' and applied it in accordance with its meaning: to talk about a female fox.However, the animal happened to be a deceptive-looking dognot a fox.Thus, factual and linguistic correctness diverged on this occasion: The utterance is false (thus, factually incorrect), but it appears to be linguistically correct (in accordance with its meaning).
Throughout the remainder of my paper, I investigate how an inferentialist can account for this distinction between factual and linguistic correctness (and mistakes).Most importantly, my aim is to determine whether inferentialism can effectively distinguish between these two types of correctness (and mistakes).Although Robert Brandom is the most prominent inferentialist, I will not speculate on how he would tackle this question.Inferentialism is not limited to Brandom; it can be found in Sellars' work, it can be traced back to proto-inferential theories developed prior to World War II (Ajdukiewicz 1934) and it is currently being developed independently of Brandom (e.g. Stovall 2019, 2022;Kaluziński 2022;Drobňák 2021).Consequently, I focus on whether inferentialismas a general viewpointcan distinguish between linguistic and factual correctness (and mistakes).I must make one more remark before I go further: When I discuss factual correctness, I am concerned with empirical facts (e.g. that certain object is red or that certain object a dog etc.), not with mathematical facts (e.g.2+2 = 4).

Inferentialist approach to linguistic meaning
As noted by Whiting (2008), Conceptual Role Semantics (a family of theories to which normative inferentialism belongs) 'can be profitably viewed as a refinement of the claim that the meaning of an expression is its use ' (2008).It is well known that later Wittgenstein identified meaning with use (1967Wittgenstein identified meaning with use ( : §43, 1969, 69), 69).However, there are some things that have use (e.g.hammers, 'abracadabra') but clearly lack linguistic meaning.A potential answer to this weakness of Wittgenstein's idea that 'meaning is use', may be the identification of meaning not with use in general but with use in inferences, as proposed by Wilfrid Sellars (2007).Robert Brandom (1994Brandom ( , 2000a)), the most prominent contemporary inferentialist, follows Sellars closely and claims that the meaning of a linguistic expression is identical with its inferential role.
An important source of inspiration for contemporary normative inferentialism lies in proof-theoretic semantics (see Prior 1960;Belnap 1962;Dummett 1973;Cozzo 1994;Peregrin 2006;Fouqueré & Quatrini 2013;Francez 2015;Warren 2015Warren , 2020Warren , 2022)): it is claimed that the meaning of logical connectives is determined not by their truth tables but by the rules for introducing and eliminating the connectives.Contemporary inferentialists do not restrict themselves to accounting only for logical vocabulary; they aim to account for linguistic meaning in general.Importantly, inferentialists use the notion of 'inference' 2 in a fairly broad sense, enabling us 'to talk about inferences from situations to utterances and from utterances to actions' (Peregrin 2014, 32).
Before I go any further, I would like to stress that, in this paper, I am focused exclusively on the normative version of inferentialism; I am ignoring entirely the naturalistic form of inferentialism (sometimes called 'inferential role semantics'), as discussed by Boghossian (1993Boghossian ( , 1994Boghossian ( , 2012)).
According to normative inferentialism, the meaning of linguistic expression is its inferential role as determined by the rules pertaining to the following kinds of inferences (moves, transitions): α From situations to sentences: For example, there is a rule within the linguistic community that tells us that we are allowed to say 'This is a lion' when pointing to a lion.
β From sentences to sentences: For example, there are rules within the linguistic community that allow us to infer that, if 'x is a lion', then (i) 'x is an animal', (ii) 'x is not a fish' and (iii) 'x is a carnivore', among other things.
γ From sentences to actions: For example, there are rules within the linguistic community that allow us to infer that, if 'x is a lion', then (i) 'one should keep a distance from x' and (ii) 'one should not irritate x', among other things.
2 Normally, an inference is a transition from one meaningful statement to another meaningful statement.
So, talking about inferences-from situations to utterances and from utterances to actions-may seem strange.Such transitions are not, strictly speaking, inferences; they may be considered inferences only in a metaphorical sense.If one feels uncomfortable with the use of 'inferences from situations to sentences' or 'inferences from sentences to actions', they may stick to the terminology used by Sellars (1974), who distinguished between 'language entry transitions', 'intra-linguistic moves' and 'language exit transitions'.
Hence, the meaning of a linguistic expression is determined by the rules that tell us what inferences of the types α, β and γ we are allowed or forbidden to make.Normative inferentialism understands linguistic meaning as a role that the expression plays within the practice of speaking the language.It should not be surprising that such a role is normally understood by inferentialists as analogous to the role that pieces of wood play in a chess match.Consider the role of a pawn, which is specified by the set of rules telling us how we can and cannot move the piece: (R1) A pawn can move one square forward.(R2) If it is the pawn's first move, it can move two squares forward.(R3) A pawn can capture one of the opponent's pieces by moving diagonally forward one square to the left or right.(R4) A pawn on its fifth rank may capture an enemy pawn on an adjacent file that has just moved two squares in a single move, as if the pawn had only moved forward one square.The pawn can only do this on the turn immediately following the enemy pawn moving forward (en passant).(R5) A pawn cannot jump over any other piece.(R6) When reaching its final rank, a pawn is promoted to another piece (knight, bishop, rook, or queen).
According to normative inferentialism, there is a deep analogy between language and games.There are rules similar to (R1-6) that tell us what inferences of the type α, β and γ we are allowed or forbidden to make and, thus, determine the role of a sentence within the practice of speaking a language.
Although inferentialists like to claim that there is an analogy between language and games, there are also key differences.The most striking one is that the rules of games such as chess, football and basketball are explicit rules that are formally established by official authorities.Rules of language are not explicit, so how, then, are they understood?Essentially, these rules are brought to life by the normative attitudes of people.These attitudes manifest in people recognising certain behaviours as conforming to the rules (and, in turn, as correct) and recognising other behaviours as breaching the rules (and, in turn, as incorrect).Second-order attitudes are crucial: Correct behaviour is not properly subject to reprimand, correction, punishment, but incorrect behaviour is.As noted by Peregrin (2014), 'In sum […] the existence of a rule may be documented by three kinds of behavioral regularities: (1) complying with the rule (e.g.avoiding chief's food); (2) correcting those who do not comply (e.g.beating those who do not avoid chief's food); (3) explicitly endorsing the rule (e.g.saying that one should avoid chief's food)' (74-75).

Inferentialism and factual/linguistic correctness
In this section, I analyse how normative inferentialism can make room for the distinction between linguistic correctness and factual correctness.Allow me to sketch two scenarios concerning the distinction between linguistic and factual correctness that will serve as a test for an inferentialist theory of meaning.To be considered satisfactory, the theory must correctly distinguish between the two types of mistakes attributed to speakers (factual and linguistic).The difference between the two cases seems aptly characterised by saying that the subject is wrong about two different thingsonce about the non-linguistic facts and once about the meaning facts.Consider the following scenarios, which are a modified thought experiment of Burge (1979): A. Suppose that a patient named John feels pain in his joints.He goes to his doctor, Kate, and undergoes a series of diagnostic tests (e.g.blood, urine, some scans).After obtaining the results of these tests, she states, 'You have arthritis'.However, the patient does not suffer from arthritis.In this case, the test results are wrong.One of the machines with which the tests were performed malfunctioned and gave the doctor wrong results.Thus, in a sense, Kate applied the term 'arthritis' incorrectly, as the patient does not have arthritis.
Importantly, however, one cannot deny that she knows the meaning of the term 'arthritis', as she is a well-trained doctor.B. Suppose that a patient named John feels pain in his joints.He actually suffers from arthritis.However, he does not know the proper meaning of the term 'arthritis'; he simply takes the term to mean any disease that manifests with pain in one's limbs.He pays a visit to his doctor and says, 'I have arthritis'.Following a series of tests, the results come back with the following diagnosis: arthritis.
In Scenario A, Kate appears to make a factual mistake: she makes a false statement, but she intends to speak the truth.Her mistake stems from a malfunctioning diagnostic machine.She certainly knows the proper meaning of the term 'arthritis'; after all, she is an expert in the relevant field.In Scenario B, John does not appear to make a factual mistake.He intends to speak the truth and somehow succeeds in making a true assertion.It must be a linguistic mistake, since he does not differentiate among arthritis, a fractured ankle, tennis elbow, a torn Achilles tendon, and many other medical issues.He does not know the proper meaning of the term 'arthritis'.Thus, the fact that his assertion ('I have arthritis') is true is more a matter of luck than of his competence of any sort.Here, I would like to remind you of the basic intuition concerning linguistic correctness: it entails using an expression in accordance with its meaning.The term 'arthritis' is used to talk about arthritis.However, John uses the term 'arthritis' to talk about everything that can manifest as pain in the limbs, meaning that he is doing something linguistically incorrect.Note that, in order to do something linguistically correct, one must first acquire a basic understanding of the meaning of the relevant expression.While they do not need a full understanding of its meaningwhich may be beyond the capacity of any individual (Drobňák 2021)a basic degree of competence is required, and John appears to lack that competence.
The starting point of my further investigation is the idea that linguistic correctness is a structural issue: linguistic mistakes stem from the improper or insufficient acquisition of an inferential role.Factual correctness, on the other hand, is a one-off issue of the correct application of inferential rules to a particular situation.Returning to the language and games analogy, linguistic correctness assumes that one grasps the meaning of an expression.Thus, linguistic correctness is analogous to grasping the role of, say, a pawn as stipulated by the rules of chess (when one grasps the role of a pawn, one can knowingly move it correctly during the game); factual correctness is analogous to an individual move within the game of chess, such as a player moving a pawn that had not yet been moved from square d2 to d3.
This characterisation of linguistic and factual correctness may not be very controversial, but it is also not particularly illuminating.What we need is some sort of criterion or method of actually determining if a linguistic or factual mistake occurs.Inferentialism can appeal to the game of giving and asking for reasons in pursuit of such a method.As Peregrin puts it: No empirical word is meaningful in the distinctively human way (particularly none expresses a concept) unless it is capable of taking part in complex linguistic games (and especially the game of giving and asking for reasons).A word does not express the concept of dog unless it can be used as part of sentences that can in turn be used for reasoning, i.e. from which other sentences can be inferred and which themselves can be inferred from other sentences.The English word dog would not express our concept of dog if it could not be used to reason from This is a dog to This is an animal, This is not a cat etc. (2014,31) Consider the meaning of the term 'horse'.Its meaning is its inferential role in the game of giving and asking for reasons.So, it is correct to infer from 'x is a horse' that 'x is an animal', 'x has hooves', 'x eats grass' and 'A person can ride on x's back', among other things.It is not correct to infer from 'x is a horse' that 'x is a bird', 'x has gills' or 'x can play the violin'.If a person were to say 'x is a horse', we could assess their grasp of the inferential role of the term 'horse' by asking a series of diagnostic questions, such as the following: . Does a horse have gills?
. Is a horse a carnivore? .Is a horse an animal? .Can a person ride on a horse's back? .Can a horse fly?
The better they answer such questions, the better they grasp the meaning of the term 'horse'.Importantly, grasping the meaning of a term is not binary; one does not simply either grasp or not grasp the meaning of a term.It is a matter of degree (Drobňák 2021).Seasoned zoologists, for example, would have far greater knowledge of the inferential rules concerning the term 'horse' than most people, including myself.However, it is safe to assume that there is a minimum threshold that one must meet to be qualified as a competent language speaker; it should be quite uncontroversial to say that correctly answering the questions listed above regarding the meaning of the term 'horse' is necessary to meet that threshold.In other words, one is not likely to be viewed as understanding the term 'horse' if they are unable to answer these questions.Thus, if one says that horses have gills, are carnivores or can fly, they are not using the term 'horse' in line with its use-conditions; they are using the term to talk about something other than horseslikely nothing in the real world.Put succinctly, during the game of giving and asking for reasons, we can determine if one is using a term like 'horse' according to its use-conditions.
Here, allow me to say a few words about factual correctness and the game of giving and asking for reasons.Roughly speaking, an utterance is factually correct if it 'hits the target'.There is an α-type inferential rule that allows us to utter 'This is a horse' when pointing to a horse, and our assertion is factually correct when it 'matches' that rulewhen the object that we are pointing to is actually a horse.But how can we determine the success of our application of an α-type inferential rule in any particular situation?Is it possible for normative inferentialists to provide any criterion for such a success?Once again, inferentialism can provide us with a method of delimitation by appealing to the game of giving and asking for reasons.An inferential rule is not an entity in 'Platonic heaven'; it must manifest in speakers' dispositions and behaviour.First, such a rule manifests as first-order behaviour.In this case, it manifests as seasoned zoologists referring to that animal as a 'horse'.Second, it manifests as second-order dispositions to correct improper behaviour, such as people applying the term 'horse' to things that are not horses and being corrected in some way.In other words, the application of an α-type inferential rule is correct if: (i) it matches the application that would have been made by relevant competent speakers in optimal cognitive conditions, or (ii) one is making an assertion (e.g.'This is a horse'), and members of the relevant 'jury' (e.g.seasoned zoologists) are not disposed in optimal cognitive conditions to make a genuine correction of that assertion (perhaps after conducting some sort of tests, e.g.genetic, morphological).
It is important to note that being a member of the relevant 'jury' may require a sufficient level of competence from peers observing our linguistic behaviour.When we say 'This is green' about fresh grass in normal lighting conditions, the required level of competence is relatively basic: it suffices that our peers know English on a fundamental level.As discourse becomes increasingly specialised, however, more qualifications are required.For instance, when assessing the correctness of Kate the doctor's assertion -'John has arthritis'the relevant peers who can make a judgement on that assertion are not laypeople who just know English but other doctors: people who have undergone multiple years of medical training and passed all of the exams necessary to practise medicine.Additionally, it is important to note that we can face correction for multiple reasons.For example, a surgical resident's inferences may be challenged by their mentor just to check their level of confidence.This would not count as a genuine correction.Other times, a correction may not occur even when it should.This could be the case if, for example, somebody is very sleepy or distracted, so they failed to notice an incorrect inference.When I mention optimal cognitive condition, I mean no factors that may disturb perception, memory, reasoning (e.g.hangover, sleepiness, intoxication, deceptive lighting) or the proper functioning of the devices used by the jury.What really counts is not the fact that some expert actually made a correction but the fact that a correction is appropriate.Once again, think about games: What really matters are the rules, not the individual decisions of a referee; the former constitutes the game, while the latter is either in accordance with the rules or not; and can be challenged by Video Assistant Referee).
The inferentialist, in accounting for the distinction between factual and linguistic correctness, can appeal to the game of giving and asking for reasons and inferential rules that govern that game.Sometimes, however, there are no such rules resonating among relevant members of the linguistic community.This can occur, for instance, when there are disagreements about a novel topic among experts on a subject matter (e.g. the severity of each individual SARS-CoV-2 variant during the COVID-19 pandemic), and they have yet to reach a consensus.The other possibility is that some applications of the predicate are essentially 'in the grey zone'.For instance, we would all agree that a typical London double-decker bus is red, but we may disagree regarding whether object X is sufficiently similar in colour to a double-decker bus to be considered red rather than pink.Importantly, however, this kind of disagreement is fine; a small amount of imprecision and vagueness in natural language is something we may have to live with.
Additionally, inferential rules can change over time.Consequently, assessments of our grasp of meaning can also change.Suppose that, in 1970, disease X was considered to be inflammatory, caused by factor A and it was assumed that it should be treated with drug B. However, as science developed, it came to be considered a genetic disease that is caused by mutation C and can be treated with drug D. Today, if one were to answer diagnostic questions concerning disease X based on the state of knowledge in 1970, their grasp of the meaning of 'X' would be assessed as poor and outdated.
Before going any further, I must resolve one issue.One may wonder if it would not suffice to grasp the rules concerning the α-type of inference (in other words, to grasp a term's reference) to be considered a competent language speaker who has adequately acquired the term's meaning.The α-type inferences are simply not enough.Why?Consider a cat emitting a peculiar kind of hiss when it sees a dog: the hiss, in the mouth of the cat, appears to be tied to the same situations to which the sentence 'This is a dog' is in the mouth of a speaker of English.So why do we say that the latter is a meaningful sentence, a description of the situation, whereas the former is a mere reaction to the situation?(Peregrin 2014, 30) The answer is because the cat cannot know how the meaning of 'This is a dog' is interconnected with the meanings of other expressions, such as 'This is an animal', 'This is a mammal' and 'This is not a fish'.It is an inferentialist orthodoxy that meaning should be understood in holistic terms. 3 Allow me to use the term 'meaning holism' here in opposition to 'meaning atomism', which is the view that each word's meaning is independent of every other word's meaning (see Jackman 2020).Meaning holism exists in both radical and modest forms (Quine 1951;Dummett 1976).The former claims that the meanings of all words in any given language are interconnected; the latter (sometimes known as 'molecularism') is the weaker claim that a word's meaning is closely tied to the meanings of some other words in the language.While I do not extensively discuss the issue of meaning holism in this paper, I must briefly state that inferentialism requires some form of holism.Notably, its modest form is probably more promising.
It is time to demonstrate how the ideas concerning linguistic and factual correctness outlined above can work in practice.In order to do this, allow me to present how they deal with Scenarios A and B. In analysing Scenario A, inferentialism appears to give an account that passes the test presented at the beginning of this section.Kate, the doctor, knows perfectly well from what types of situations one is allowed to infer that 'S has arthritis'.She knows that one can infer that 'S has arthritis' from certain symptoms and test results.She also knows that, from 'S has arthritis', one can infer that 'S has inflammation in his joints' but not that 'S has a tapeworm'.Finally, she knows that it is correct to infer from 'S has arthritis' that 'S should take ibuprofen' but not correct to infer that 'S should take penicillin'.She knows well the inferential rules concerning the term 3 Consider the following passage from Reiland's (2021) discussion of linguistic correctness: 'a declarative sentence like 'Bertrand is British' is for using when one is doing the above acts and further predicating the property of the person, resulting in your entertaining the proposition that Bertrand is British.[…] To take a different sort of example, the expressive interjection 'Ouch!' is for using while you're in pain whereas 'Oops!' is for using when you've just observed a minor mishap […] Finally, situational terms like 'Hello!' or 'Goodbye!' might be for using while you're meeting someone or parting from them'.Now, ask yourself if one can use, for instance, 'Bertrand is British' to entertain the proposition that Bertrand is British without, say, the knowledge that being British is a nationality.Consider if one can use 'The grass is green' to entertain the proposition that the grass is green without knowing that 'green' is a colour.Once again, inferentialism tends to answer such questions negatively; it is committed to some form of meaning holism.
'arthritis'.If other doctors were to ask her multiple questions about arthritis, she would be disposed to answer them correctly; in turn, it would not be appropriate for the 'jury' to correct her statements.Rather, it would be appropriate for it to approve her actions.Hence, it appears that she is doing something linguistically correct because she has a solid grasp of the meaning of the term 'arthritis'; she is using it in accordance with its meaning (i.e.she uses the term 'arthritis' to talk about arthritis).However, she fails in making a factually correct statement.Her assertion 'You have arthritis' does not match the inference that would have been made by seasoned doctors in optimal cognitive conditions.If the jury were to re-run all of the same tests on different, properly functioning machines, they would come to the conclusion that the patient does not suffer from arthritis.Thus, she knows the meaning of the term but fails to make a true assertion.Now, let's move to Scenario B. John appears to have no knowledge of what 'arthritis' actually means.In contrast to Kate, he does not know the inferential rules concerning the term.He never went to medical school, never read medical textbooks, etc.So, if seasoned doctors were to ask him questions about arthritis, he would struggle to answer them correctly.Even if he did answer some questions correctly, he would struggle with the follow-up questions.For instance, even if he could guess the correct answer to the question 'Is arthritis an inflammatory disease?', he would fail to provide answers on the details of inflammatory diseases.In a nutshell, he would 'lose' in the game of giving and asking for reasons, and that is a clear sign that he has not acquired the inferential role of the term 'arthritis'.It appears that he does not use the term 'arthritis' to talk about arthritis; rather, he uses it to talk about a wide range of medical conditions that manifest as pain in one's limbs.However, his assertion 'I have arthritis' is factually correct: If a team of seasoned doctors were to run all of the necessary tests in optimal cognitive conditions, they would come to the conclusion that he does, in fact, suffer from arthritis.So, his inference matches the inference that would have been made by experts in optimal conditions.Before I conclude, allow me to emphasise one feature of the inferentialist distinction between factual and linguistic correctness as presented in this paper.In the case of factual correctness, we can determine whether one's assertion is factually correct by checking if their inference matches the inferential rule, and this match can manifest in three ways, as presented at the end of Section 2. In the case of linguistic correctness, we can determine whether one's utterance is linguistically correct by asking several diagnostic questions during the game of giving and asking for reasons.Hence, it may not be possible to instantly determine correctness or incorrectness.In the case of both factual and linguistic correctness, time and effort may be required to determine whether an utterance is correct.Some tests and/or consultations with relevant experts may be necessary.Participating in the game of giving and asking for reasons can be a laborious process!However, this seems fine, as what matters in this case is not time or effort but a reliable method of determining correctness.Moreover, by tying the issue of correctness to the game of giving and asking for reasons, we can actually distinguish between cases in which one uses a term in accordance with its meaning and cases in which an assertion appears linguistically correct on the surface but in fact the use of the expression in question is not correct.This was the case with John's assertion 'I have arthritis'.At first glance, that statement appears to be correct.However, once he needs to answer diagnostic questions, the process reveals that he is not using the term in accordance with its meaning: he is wrong about the meaning facts, hence his assertion is not linguistically correct.Importantly, such a mistake may not impact communication.When John says 'I have arthritis' incorrectly, he may be well understood by his doctor Kate, though she would think that he is referring to arthritis.If she were to ask him some questions about arthritis, she would realise that he is using the term incorrectly.

Conclusion
One may think that inferentialist theories of meaning are focused on inferences and, as such, may struggle to make room for the distinction between linguistic and factual correctness.This distinction is closely associated with the public language perspective, which is very popular in contemporary philosophy of language, two notable exceptions being Chomsky and Davidson.In this paper, I have shown that properly understood normative inferentialism can make room for this distinction.One must remember that normative inferentialism understands the term 'inference' in a broad sense that includes 'moves' from situations to sentences, sentences to sentences and sentences to actions.Linguistic correctness should be understood as a structural issue: linguistic mistakes stem from the improper or insufficient acquisition of an inferential role.Factual correctness should be understood in terms of correctly applying inferential rules to a particular situation.By tying the issue of correctness to the game of giving and asking for reasons, we gain a method of delimiting linguistically and factually correct utterances.The distinction between linguistic and factual correctness presented in this paper seems to offer intuitive results when it comes to differentiating between various types of mistakes.