Meaning as Role in Question-Answer-Inferences: Beyond Robert Brandom’s inferential semantics

Meaning as Role in Question-Answer-Inferences: Beyond Robert Brandom’s inferential semantics 　　　　　　　　　　　　　Ｙｕｋｉｏ　ＩＲＩＥ SogangUniversity May 23, 2018

Contents of talk Part 1 QA inference 1 An inference presupposes a question 2 Wiśniewski’seroteticlogic 3 QA inference Part 2 QA inferential semantics 1 Concept of R. Brandom’sinferential semantics 2 Semantic QA inference 3 QAinferential semantics

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.

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. What shall I do to do X? The only measure of doing X is doing Y. ∴I shall do Y.

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. What shall I do to do X? The only measure of doing X is doing Y. ∴I shall do Y.

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.

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 presupposequestions.

Part 1 QA inference 2 Wiśniewski’s erotetic inference Andrzey Wiśniewskiclaimedthe 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 Wiśniewskiis one of leading researchers in this field.)

2.1 First kind of erotetic inference • The first kind of erotetic inference includesdeclarative 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? 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 Wiśniewskidefines 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.)

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).

(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 informativenessfrom ‘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 orMoscow. . ∴ 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? Ａndrewis yonger than Peter. ∴ How old is Peter?

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 presupposea question to select one sentence as its conclusion . In the Wiśniewski’serotetic 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 eroteticinferences. 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 JFK? 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 Q2are questions; Γis 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.

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.

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 theorycannot 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.

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 theorycannot 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

(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.

Meaning as Role in Question-Answer-Inferences: Beyond Robert Brandom’s inferential semantics