Meaning as Role in Question-Answer-Inferences:

Meaning as Role in Question-Answer-Inferences:
at Sogan University 5/24/2018 Meaning as Role in Question-Answer-Inferences: 　　Beyond Robert Brandom’s inferential semantics 　　　　　　　　　　　　　　Ｙｕｋｉｏ　ＩＲＩＥ Sogang University May 23, 2018 The use of single and double quotations marks is inconsistent.

3 QA inferential semantics
Contents of talk Part 1 QA inference 1 An inference presupposes a question 2 Wiśniewski’s erotetic logic 3 QA inference Part 2 QA inferential semantics 1 Concept of R. Brandom’s inferential semantics 2 Semantic QA inference 3 QA inferential semantics

Part 1 QA inference 1 An inference presupposes a question. 1
Part 1 QA inference 1 An inference presupposes a question. 1.1 A theoretical inference presupposes a theoretical question. Validity of a theoretical inference： If the premises of a theoretical inference are true, then the conclusion is also necessarily true. All penguins are birds. All birds are oviparous. ∴All penguins are oviparous.

In such an inference, if the premises are true, not one but many sentences are logically true, as follows: 　　 All penguins are birds. All birds are oviparous. ∴All penguins are oviparous. All that are oviparous are not penguins. Some penguins are oviparous. There is no penguin that is oviparous. In above example, only one sentence “All penguins are oviparous” serves as the logical conclusion; why is this?

To answer this question, we must bear in mind that an inference is drawn to answer a certain question, and the conclusion is an answer to that question. The above inference is drawn to answer the following question: 　　 Are all penguins oviparous? All penguins are birds. All birds are oviparous. ∴All penguins are oviparous.

Are there penguins that are not oviparous? All penguins are birds.
Thus, the same premises could have produced a different conclusion if the answer to a different question were sought. 　　Are there penguins that are not oviparous? All penguins are birds. All birds are oviparous. ∴There is no penguin that does not lay eggs. Thus, we can claim that the theoretical inference presupposes* a theoretical question. (This presupposition is, to be precise, different from presupposition in an ordinary inference).

1.2 A practical inference presupposes a practical question
Also in practical inferences, many sentences are deduced as conclusions from same premises. 　　 I shall do X. The only measure of doing X is doing Y. 　∴　I shall do Y. If I cannot do Y, I give up doing X. If I do not want to do Y, I must give up doing X. If I intend to do X, I need to intend to do Y. Why “I shall do Y” was selected as the conclusion from among many candidates?

We could consider that the inference is performed in response to a practical question. For example, I shall do X. What shall I do to do X? The only measure of doing X is doing Y. ∴ I shall do Y. A practical inference is therefore the process of answering a practical question. Thus, we can explain why the utterance of the intention “I shall do Y” follows from the initial two premises. In this case the question ‘What shall I do to do X? ’ entails the intention ‘I shall do X’. Therefore, we could omit it as follows.

Ｔhe same premises would produce a different conclusion if we were answering a different practical question. 　　　 I shall do X. In what case will I be unable to do X? The only measure of doing X is doing Y. 　 ∴　I cannot do X if I cannot do Y. Therefore, both theoretical and practical inferences presuppose questions.

2 Wiśniewski’s erotetic inference
Part 1 QA inference 2　 Wiśniewski’s erotetic inference Andrzey Wiśniewski claimed the possibility of the inferences that has a question as its conclusion. He call it ‘erotetic inferences’ and divides it into two kinds, the first kind and the second kind. (Cf. Wiśniewski, Questions, Inferences, and Scenarios, College Publications, 2013. The logical research of questions is very common in Poland, and Andrej Wiśniewski is one of leading researchers in this field.)

2.1 First kind of erotetic inference
The first kind of erotetic inference includes declarative sentences with truth values as presuppositions and a question as their conclusion. For example, 　　She always arrives on time, but now she is late. 　∴ What happened to her?

Then what is the validity of this inference
Then what is the validity of this inference? He claimed two conditions for the validity of the first kind of erotetic inference. The usual definition of a valid inference is that if all presuppositions are true, then the conclusion is necessarily true. But a question cannot be true or false. So Wiśniewski defines the soundness of a question as to admit at least one true answer. The first condition for the validity is (C1) (C1) (Transmission of truth into soundness) If the premises are all true, then the question that is the conclusion must be sound. (Ibid. p. 51.)

at Sogan University 5/24/2018 But (C1) is insufficient, because the following inference that meets with (C1) is not a good inference: 　 She is rich. 　 She is happy. 　　　∴　Is she happy? In this inference, the answer to the question is already given in a premise. Therefore, the question is redundant. For this reason, Wiśniewski adds the following condition (C2). The meaning of “meet” is not clear; please clarify here and elsewhere as needed.

(C2) (Informativeness) The question that is a conclusion must be informative relative to the premises. He defines informativeness as the lack of entailment of any direct answer from the premises. (Cf. bid. p. 51.) “Direct answer” is defined as a possible just-sufficient answer, where “just-sufficient” means “satisfies the request of a question by providing neither less nor more information than is requested”. (Ibid. p. 18)

Wiśniewski rejects the following inference by this definition of informativeness.
　　　If Andrew is rich, then Andrew is happy. 　　　Andrew is rich. 　∴ Ｉｓ　Ａｎｄｒｅｗ　happy? This restriction seems too strong because, in many cases, answers of logical or mathematical questions are logically or mathematically entailed. So I would like to weaken the definition of the informativeness from ‘the lack of entailment of any direct answer from the premises’ to ‘the lack of any direct answer in the premises’.

2.2 Second kind of erotetic inference
The second kind of erotetic inference has a question and declarative sentences as premises and a question as a conclusion, as in the following inference: 　　Where did she go? 　　If she took her famous umbrella, then she 　　　　　 went to London; otherwise, she went to 　　 Paris or Moscow 　 ∴ Did she take her famous umbrella?

Two necessary conditions for the validity of the second type of erotetic inference.
(C3) (Transmission of soundness/truth into soundness) If the initial question is sound and all the declarative premises are true, then the question that is the conclusion must be sound. (C3) is an extended version of (C1) for the first kind of erotetic inference. (Ibid. p. 52.)

However, (C3) is not sufficient because the following inference that meets with (C3) is problematic. Is she a logician? Some philosophers are logicians, and some are not. ∴ Is she a philosopher? In this case, even if we do arrive at an answer to the question in the conclusion, we do not necessarily have an answer to the initial question. So the question as coclusion is not useful for answering the question as premise.

Wiśniewski formalizes the second condition as follows.
(C4) (Open-minded cognitive usefulness) For each direct answer B to a question that is a conclusion, there exists a non-empty proper subset Y of the set of direct answers to the initial question, such that the following condition holds: (♣) if B and all the declarative premises are true, then at least one direct answer A∊Y to the initial question. For example, the following inference meets with (C4) 　 How old is Andrew? 　　Ａndrew is yonger than Peter.　　 ∴ How old is Peter?

In the Wiśniewski’s erotetic inference a question is a conclusion.
Part 1 QA inference 3 QA Inference Here, I will combine Wiśniewski’s argument of erotetic inference with the argument in the first section. (Ibid. p. 53.) In the first section, I argued that an inference can have many sentences as candidates for its conclusion. Therefore, we must presuppose a question to select one sentence as its conclusion . In the Wiśniewski’s erotetic inference a question is a conclusion. Then, can a erotetic inference has many questions as candidates for its conclusion?

3.1 The first kind of erotetic inference presupposes a question.
The following is one of the first kind of erotetic inferences. 　　　An organization carried out the assassination of JFK. 　　　∴ Which organization carried out the assassination of JFK? This inference can also have many questions as its conclusion, as follows.

　　　An organization carried out the assassination of JFK. 　　
　∴ Which organization carried out the assassination of JFK? How did the organization carry out the assassination of Why has this not become public knowledge?

Why does the question “Which organization carried out the assassination of JFK?” become the conclusion in this case? We can explain this by presupposing a question, such as the following: Who carried out the assassination of JFK? 　　An organization carried out the assassination of JFK. 　　 ∴ Which organization carried out the assassination of JFK? The question ‘Which organization carried out the assassination of JFK?’ is selected, because it is cognitively useful to answer the question as a premise. The first kind of erotetic inference presupposes a question at least implicitly .

3.2 Does the second kind of erotetic inference also have a superordinate question?
The first kind of erotetic inference at least implicitly presupposes a question. When we explicitly express such implicit presupposition, we get a second type of erotetic inference. Then, does the second kind of erotetic inference also have a superordinate question?

Suppose that Q3→Q2→Q1 and this means that Q3 posits Q2 to get the answer to Q3, and Q2 posits Q1 to get the answer to Q2. The answer to Q2 is cognitively useful for answering Q3. However this does not depend on what Q1 is. Therefore, Q3 cannot select the subordinate question Q1 for Q2. Q2 might have a superordinate question like Q3, but it is not for selecting a subordinate question Q1 to answer to Q2.

3.3 Conclusion: Four types of QA inference
As a result, we have identified an inference that can have questions as a premise and a conclusion. I call all such types of inference a question–answer inference(QA inference). This is classified into following four types. 1) Complete type: Q, Γ┣　P 2) Implicit complete type (= normal declarative inference): Γ┣　P 3) Incomplete type: Q2, Γ┣　Q1 4) Implicit incomplete type: Γ┣Q (Q, Q1, and Q2 are questions; Γ is a set of declarative sentences; and P is a declarative sentence)

As to 1), two conditions for the validity of a complete type: Q, Γ┣ P (C5) (Transmission of soundness/truth into truth) If the initial question is sound and all the declarative premises are true, then the conclusion must be true. (C6)（Direct answer condition) P is a member of the set of direct answers to Q.

Part 2 Toward QA inferential semantics
2.1 Concept of Brandom’s inferential semantics 2.2 Semantic version of QA inference 2.3 QA inferential semantics Here I would like to apply QA inference to semantics. In 2.1 I will explain the basic concept of Brandom’s inferential semantics. In 2.2 I will refine QA inference to apply it to inferential semantics. In 2.3 I will apply QA inference to semantics and try to show the significance of the application.

(1) Inferential semantics as a kind of use theory of meaning
2.1 Concept of Brandom’s inferential semantics (1) Inferential semantics as a kind of use theory of meaning The truth functional theory, the assertibility theory, and the use theory of meaning are the main theories of meaning. Ｔhe truth functional theory and the assertibility theory cannot effectively address sentences without truth value. Thus, the use theory of meaning has an advantage over these alternatives as it is able to explain the meaning of sentences without truth value. Inferential semantics is a kind of use theory. Inferential semantics is the theory proposed by Robert Brandom, who considered the meaning of an expression to be equivalent to its inferential roles. Inferential semantics can explain the meaning of sentences or utterances without truth value, like an order, a promise, or a declaration. They have inferential relationships with other sentences or utterances.

(1) Inferential semantics as a kind of use theory of meaning
2.1 Concept of Brandom’s inferential semantics (1) Inferential semantics as a kind of use theory of meaning The truth functional theory, the assertibility theory, and the use theory of meaning are the main theories of meaning. Ｔhe truth functional theory and the assertibility theory cannot effectively address sentences without truth value. Thus, the use theory of meaning has an advantage over these alternatives as it is able to explain the meaning of sentences without truth value. Inferential semantics is a kind of use theory. Inferential semantics is the theory proposed by Robert Brandom, who considered the meaning of an expression to be equivalent to its inferential roles. Inferential semantics can explain the meaning of sentences or utterances without truth value, like an order, a promise, or a declaration, because they have no truth values but inferential relationships with other sentences or utterances.

(2) Basic idea of inferential semantics “Understanding the conceptual content […] is a kind of practical mastery: a bit of know-how that consists in being able to discriminate what does and does not follow from the claim, what would be evidence for and against it, and so on.” (Brandom, Articulating Reason, 2001, p. 19) To understand P is to be able to discriminate what does and does not follow from P, i.e., to distinguish between a correct inference and an incorrect inference from P as a premise. I will call such inference an ‘downstream inference” of P； P, Γ┣ R To understand P is also to be able to discriminate what would be evidence for and against P, i.e. to distinguish between a correct and an incorrect inference that has P as a conclusion. I will call such inference a ‘upstream inference” of P； Γ┣ P

(3) Upstream and downstream inference
According to Brandom, the assertibility theory of meaning, and reliabilism are efforts to understand the meaning of expressions from the perspective of upstream inference. In contrast, classical pragmatism is an effort to explain it from the perspective of downstream inference. However, Brandom claims that we need both upstream and downstream inferences.

(4) Material inference Brandom refers to an inference understood in the standard way as a ‘formal inference’. If the premises of a formal inference are true, then the conclusion is true. The validity of an inference is explained by the truth of sentences. If we accept the basic idea of the foregoing, to understand a sentence is to understand the correct upstream and downstream inferences; therefore, the correctness of an inference cannot depend on the meaning or truth values of sentences. In contrast, inferentialism explains the truth as that which is preserved in a correct inference. Brandom refers to such correct inferences as “material inferences”. “The kind of inference whose correctness determines the conceptual contents of its premises and conclusions may be called, following Sellars, material inferences”. (AR. p. 52)

The example of material inference offered by Brandom is the following inference:
　from “Pittsburgh is to the west of Princeton” 　to “Princeton is to the east of Pittsburgh.” The meanings of “to the west of ” and “to the east of ” are made explicit by this material inference. We understand the meanings of “west” and “east” by accepting this material inference. (Cf. Brandom, Articulating Reasons, p. 52).

The example of material inference offered by Brandom is the following inference:
　from “Pittsburgh is to the west of Princeton” 　to “Princeton is to the east of Pittsburgh.” The meanings of “to the west of ” and “to the east of ” are determined by this material inference. We understand the meanings of “west” and “east” by accepting this material inference. (Cf. Brandom, Articulating Reasons, p. 52).

Part 2 QA inferential semantics
2 Semantic Version of QA inference 2.1 Cognitive and expressive tasks of logic It would be helpful to expand the inferential relationships identified by Brandom to the QA inferential relationship. However, we cannot directly apply QA inference to inferential semantics because inferential semantics focuses on the expressive tasks of logic rather than on the cognitive or practical tasks.

Brandom identifies two tasks performed by logic
Brandom identifies two tasks performed by logic. (Articulating Reason, p. 19) ・The epistemological task of logic: to establish the truth of certain kinds of claims by proving them. ・The expressive task of logic: to make explicit the sematic relationships among linguistic expressions. Inferential semantics focuses on the expressive task. ‘According to the inferentialist account of concept use, in making claim one is implicitly endorsing a set of inferences, which articulate its conceptual content’. AR. 19

The QA inference in Part 1 focuses on the cognitive and practical task of logic, which is necessary for analysis of cognition and action.　　　　　 However, in order to apply the QA inference to semantics, it is required to cut down it to the expressive relationships in the QA inferences. I will call this the ‘semantic version of QA inference’.

2.2 Semantic version of QA inference
# Semantic version of Wisniewski’s ‘erotetic inference’ He identifies the following two conditions, (C1) and (C2), for the first kind of erotetic inference. (C2) is the condition of informativeness. (C2) is not necessary here because we are focused on only the sematic relationships. He raises the two conditions, (C3) and (C4), for the second kind of erotetic inference. (C4) is the condition of cognitive usefulness. Therefore, it is not necessary here. However, we can keep (C1) , (C3), (C5), and (C6) here.

We classified the four types of QA inference as follows
We classified the four types of QA inference as follows. We can keep this classification here. 1) Complete type: Q, Γ┣　P 2) Implicit complete type (= normal declarative inference): Γ┣　P 3) Incomplete type: Q2, Γ┣　Q1 4) Implicit incomplete type: D1, …Dm┣Q

Part 2 QA inferential semantics
I will discuss the expansion of inferential semantics by semantic version of QA inference. I will first focus on declarative sentences and then move on to interrogative sentences.

3.1 Meaning of declarative sentences
Brandom’s basic idea of inferential semantics is as follows: To understand a proposition is to be able to discriminate ‘what does and does not follow from the claim’, ‘what would be evidence for and against it’. (AR. p. 19) Let me analyze this in a bit more detail. To answer the first question, ‘What does and does not follow from the claim P ?’, is to answer ‘If the claim P is true, then what can we and can we not claim?’ or ‘If the claim P is true, then can we or can we not claim R ?’ These questions result from the claim P. So QA inference P┣Q is holding here.

Brandom’s basic idea of inferential semantics is as follows: To understand a proposition is to be able to discriminate ‘what does and does not follow from the claim’, ‘what would be evidence for and against it’. (AR. p. 19) This means, as above explained, to understand P is to understand the correct upstream and downstream inferences. Let me here analyze this in a bit more detail. To answer the first question, ‘What does and does not follow from the claim P ?’, is to answer ‘If the claim P is true, then what can we and can we not claim?’ or ‘If the claim P is true, then can we or can we not claim R ?’ These questions result from the claim P. So QA inference P┣Q is holding here.

Brandom’s basic idea of inferential semantics is as follows: To understand a proposition is to be able to discriminate ‘what does and does not follow from the claim’, ‘what would be evidence for and against it’. (AR. p. 19) This means, ass above explained, to understand P is to understand the correct upstream and downstream inferences. Let me here analyze this in a bit more detail. To answer the first question, ‘What does and does not follow from the claim P ?’, is to answer ‘If the claim P is true, then what can we and can we not claim?’ or ‘If the claim P is true, then can we or can we not claim R ?’ These questions result from the claim P. So QA inference P┣Q is holding here.

（ａ）Downstream QA inferences of a declarative sentence P
There are four types of downstream QA inference of P 1) Complete type: Q, P, Γ┣ R 2) Implicit complete type (= normal declarative inference): P, Γ┣　R 3) Incomplete type: Q2, P, Γ┣ Q1 4) Implicit incomplete type: P, Γ┣ Q Brandom’s inferential semantics has already considered type 2). I will refer to 1) and 3) later. The aforementioned P┣ Q belongs to type 4).

（ｂ）Upstream QA inferences of a declarative sentence P
There are two types of downstream QA inference of P. 1) Complete type: Q, Γ┣　P 2) Implicit complete type (= normal declarative inference): Γ┣　P As to 1), if understanding p entails to be able to discriminate which question P can be an justified answer to, then understanding P entails to understand the QA inference of this type. As to 2), Brandom’s inferential semantics has already considered it.

3.2 Meaning of an interrogative sentence
Brandom’s inferential semantics unfortunately cannot explain the meaning of interrogative sentences because they have no inferential relationships with other sentences in ordinary inference. Thus, if we expand the normal inference to the QA inference, we could explain the meaning of interrogative sentences in terms of QA inferential roles. A question can have both upstream and downstream inferences in QA inferences .

#Basic idea of semantics of question
#Basic idea of semantics of question. Understanding a question is to be able to discriminate (a) what is and is not requested as an answer to the question and (b) what is and is not a condition for the question having a true answer. To discriminate (a) is to discriminate a correct and incorrect inference in the type of Q, Γ┣ P. To discriminate (b) is to discriminate a correct and incorrect inference in the type of P┣ Q. Thus to understand a question is to understand QA inferential relations of Q.

（ａ）Downstream QA inferences of a interrogative sentence Q or Q2
There are two types of this kind of sentence. 1) Complete type: Q, Γ┣ P 3) Incomplete type: Q2, Γ┣ Q1 As to 1), P Is an answer to Q and P is justified by Γ. To understand Q is to understand what is the justified answer to Q. Therefore to understand Q is to understand the correct QA inference of this type. As to 3), the sound Q2 and the true Γ makes Q1 sound. If to understand Q2 entails to understand which question becomes possible by Q2, then to understand Q2 is to understand the correct QA inference of this type.

（ａ）Downstream QA inferences of a interrogative sentence Q or Q2
There are two types of this kind of sentence. 1) Complete type: Q, Γ┣ P 3) Incomplete type: Q2, Γ┣ Q1 As to 1), P is an answer to Q and P is justified by Γ. To understand Q is to understand what is the justified answer to Q. Therefore to understand Q is to understand the correct QA inference of this type. As to 3), the sound Q2 and the true Γ makes Q1 sound. If to understand Q2 entails to be able to discriminate which question becomes possible by Q2, then to understand Q2 is to understand the correct QA inference of this type.

（b）Upstream QA inferences of a interrogative sentence Q1 or Q
There are four types of this kind of sentence. 3) Incomplete type: Q2, Γ┣ Q1 4) Implicit incomplete type: Γ┣ Q As to 3), to understand Q1 is to be able to discriminate which question and declarative sentences can or cannot make the question Q1 sound. Therefore to understand Q1 is to understand the correct QA inference of this type. As to 4, Γ makes Q sound. Therefore Γ is sufficient condition for the soundness of Q. To understand Q is to be able to discriminate what is the sufficient condition for the soundness of Q. Therefore to understand Q is to understand the correct QA inference of this type.

Conclusion Brandom’s basic idea of inferential semantics about the meaning of a declarative sentence could be be further explicated in terms of QA inference. In addition, the meaning of an interrogative sentence can also be explained in terms of QA inference. In today’s talk I used only the semantic version of QA inference. However when I explain the perceptual report and practical inference, I will need to use the original version of QA inference, because in such a context we need to consider the cognitive and practical effectiveness.

Ｔｈａｎｋｙｏｕ for listening.
감사합니다

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