Norms and Games as Integrating Components of Social Organizations

Nakayama, Yasuo

doi:10.1007/978-4-431-54598-9_12

Yasuo Nakayama⁶

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Abstract

Previous chapters in this book mainly discuss individual humans from the viewpoint of psychology or neuroscience. In this chapter, we discuss how mental states and attitudes of individuals are related to the society from a philosophical viewpoint. In this discussion, we are particularly concerned with the question of what kinds of roles norms play when individuals establish social connections. Then, we discuss how various kinds of human capacities are related to each other and how people build and maintain social organizations. In the end, we see that humans are beings that have cognitive capacities to form their own lives by behaving in accordance with the accepted norms and changing the norms for better lives.

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Notes

1.
Different kinds of speech acts may be distinguished (Seale 1979). Our view is that the distinction between assertive and normative sentences is fundamental, and speech acts can be expressed in terms of this distinction. See Nakayama (2014).
2.
These normative modalities are also called deontic modalities.
3.
These two conditional propositions are expressed as P p → ¬F p and F p → O¬p in the standard deontic logic (SDL). SDL is a modal logic proposed by von Wright. In SDL, prohibition and permission are definable through obligation: F p ⇔_def O¬p and P p ⇔_def ¬O¬p, where ¬ is the sign of negation. See Åqvist (2002).
4.
We use not, &, ⇒, and ⇔ as meta-semantic abbreviation for not, and, if … then, and if and only if. For more precise definition and characterization of LNS, see Appendix of this chapter. The reader may consult Nakayama (2013, 2014) as well.
5.
Formally, we can avoid the use of PER, because what is permitted is uniquely determined when we determine T and OB. However, in this chapter, we include PER into the structure of normative systems, because we allow information updates of normative systems with respect to permission, in order to take ordinary language practices into consideration.
6.
First-Order Logic is the standard logic that is usually used for proving mathematical theorems.
7.
Actually, we should translate sentences (7a), (7b), (7c) into sentences of First-Order Logic. For simplicity, we omit this translation step.
8.
bel(CUS) means the belief base of CUS.
9.
For this derivation, please consult theorems in Appendix of this chapter.
10.
In LNS, once a Congress of the USA is built, it is no longer obligatory to construct the Congress, and its existence becomes a (social) fact.
11.
DNL is a framework for logical analysis of social interactions. Dynamic epistemic logic is a well-known framework developed for the same purpose. See van Benthem (2011). However, his description is restricted on propositional logic and does not discuss about quantification. In Sects. 12.7 and 12.8, we will see that typical games can be defined in DNL. A game is a kind of normative system that includes information update (Nakayama 2013). A move in a play changes the previous information state.
12.
We say sometimes normative state instead of normative system , when information update plays a role. In other words, a normative state is a normative system that an agent has for a period of time. The index 2 in ns ²(a, t) indicates that ns ² is a function with two arguments. Generally, we use ns ²(a, τ), when term τ involves a temporal component.
13.
∅ denotes the empty set, i.e., the set that contains no element.
14.
In such a case, for every time t and for every G’s member a, ob ²(a, t) = ob ²(G, t) & per ²(a, t) = per ²(G, t).
15.
A command is a speech act that creates an obligation for the addressee. See Searle (1979), Yamada (2008), and Nakayama (2014).
16.
int _A(α) means A’s interpretation of word α.
17.
This problem of finding the right interpretation for an uttered expression seems closely related to the symbol grounding problem. The latter problem is explained as follows: “abstract, arbitrary symbols such as words need to be grounded in something other than relations to more abstract arbitrary symbols if any of those symbols are to be meaningful” (Glenberg and Robertson 2000, p. 381). See also Shapiro (2011, pp. 95–98).
18.
et(PI§2) contains axioms of linear order for ≤ and ≤ _t as well.
19.
The consistency of union(ns ²({A, B},0)) ∪{A calls out “block” in t _f(1)} can be shown by constructing a finite model.
20.
For the derivation of this sentence, you use theorem (A2e1) in Appendix.
21.
Nakayama (2013) describes a small part of a restaurant scene in full detail in DNL.
22.
For four-dimensionalism and mereology, see Sider (2001) and Nakayama (2009).
23.
There are discussions on norms, roles, and plays in sociology. See Mead (1934), Parsons (1937), Merton (1949), Goffman (1959), and Habermas (1981).
24.
This kind of social dilemmas is discussed in Nakayama (2011) chap. 7 sect. 3.

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Authors and Affiliations

Graduate School of Human Sciences, Osaka University, Suita, Osaka, Japan
Yasuo Nakayama

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Editors and Affiliations

Graduate School of Letters, Kyoto University, Kyoto, Japan, Osaka University, Osaka, Japan
Masashi Kasaki
Graduate School of Engineering Science, Osaka University, Osaka, Japan
Hiroshi Ishiguro
Graduate School of Engineering, Osaka University, Osaka, Japan
Minoru Asada
Division of Cognitive Neuroscience Robotics, Institute for Academic Initiatives, Osaka University, Osaka, Japan
Mariko Osaka
Graduate School of Medicine, Osaka University, Osaka, Japan
Takashi Fujikado

Appendices

Appendix

In this appendix, we describe the definitions and theorems mentioned in the main text in more exact manners.

The definitions (8a) to (8f) of LNS can be expressed more rigorously as follows:

(A1a) When each of T, OB, and PER is a set of sentences in First-Order Logic, NS = 〈T, 〈OB, PER〉〉 is a normative system.
(A1b) A normative system NS is consistent ⇔ union(NS) is consistent, where union(NS) = T∪OB∪PER.
(A1c) B _NS q ⇔ T ├ q.
(A1d) O _NS q ⇔ (consistent(union(NS)) & T∪OB ├ q & not B _NS q).
(A1e) F _NS q ⇔ O _NS ¬q.
(A1f) P _NS q ⇔ (consistent(union(NS) ∪{q}) & not B _NS q).

Based on these definitions, we can easily prove the main theorems of LNS, where NS (NS = 〈T, 〈OB, PER〉〉) indicates a normative system .

(A2a) (B _NS (p → q) & B _NS p) ⇒ B _NS q.
(A2b1) (O _NS (p → q) & O _NS p) ⇒ O _NS q.
(A2b2) F _NS p ⇔ O _NS ¬p.
(A2b3) O _NS p ⇒ P _NS p.
(A2b4) F _NS p ⇒ not P _NS p.
(A2c1) P _NS p ⇒ not B _NS p.
(A2c2) B _NS p ⇒ (not O _NS p & not F _NS p & not P _NS p).
(A2d1) (O _NS (p → q) & B _NS p) ⇒ O _NS q.
(A2d2) (O _NS (p ∧ q) & not B _NS p) ⇒ O _NS p.
(A2d3) (O _NS (p ∧ q) & B _NS p) ⇒ O _NS q.
(A2d4) (O _NS (p ∨ q) & B _NS ¬p) ⇒ O _NS q.
(A2d5) (O _NS (p ∨ q) & F _NS p) ⇒ O _NS q.
(A2d6) (O _NS p & not B _NS q) ⇒ O _NS (p ∨ q).
(A2d7) (B _NS (p → q) & O _NS p & P _NS q) ⇒ O _NS q.
(A2e1) (O _NS ∀x _1… ∀x _n (P(x ₁, …, x _n) → Q(x ₁, …, x _n)) & B _NS P(a ₁, …, a _n) & not B _NS Q(a ₁, …, a _n)) ⇒ O _NS Q(a ₁, …, a _n).
(A2e2) (F _NS ∃x _1… ∃x _n (P(x ₁, …, x _n) ∧ Q(x ₁, …, x _n)) & B _NS P(a ₁, …, a _n) & not B _NS ¬Q(a ₁, …, a _n)) ⇒ F _NS Q(a ₁, …, a _n).

Two theorems express the relationship between the normative states of a group and those of its members:

[T1] If all members of G share the normative system ns(G), then the following sentences hold:
- (A3a) For all a∈G, (B _ns(G) p ⇒ B _ns(a) p).
- (A3b) For all a∈G, ((O _ns(G) p & consistent(ns(a)) & not B _ns(a) p) ⇒ O _ns(a) p).
- (A3c) For all a∈G, ((F _ns(G) p & consistent(ns(a)) & not B _ns(a) p) ⇒ F _ns(a) p).
- (A3d) For all a∈G, ((P _ns(G) p & consistent(ns(a)) & not B _ns(a) p) ⇒ P _ns(a) p).

[T2] If all members of G share the normative state ns ²(G, t) at t, then the following sentences hold:
- (A4a) For all time t and for all a∈G, (B _ns2(G,t) p ⇒ B _ns2(a,t) p).
- (A4b) For all time t and for all a∈G, ((O _ns2(G,t) p & consistent(ns ²(a, t)) & not B _{ns2(a, t)} p) ⇒ O _{ns2(a, t)} p).
- (A4b) For all time t and for all a∈G, ((F _ns2(G,t) p & consistent(ns ²(a, t)) & not B _{ns2(a, t)} p) ⇒ F _{ns2(a, t)} p).
- (A4b) For all time t and for all a∈G, ((P _ns2(G,t) p & consistent(ns ²(a, t)) & not B _{ns2(a, t)} p) ⇒ P _{ns2(a, t)} p).

T1 and T2 indicate the problem of consistency for a personal normative system . This problem is quite interesting in view of our real life experience. Suppose that you belong to groups G ₁ and G ₂ whose normative systems are mutually inconsistent, and that all members of G ₁ and all members of G ₂ share their normative systems ns(G ₁) and ns(G ₂). Then, your normative system becomes inconsistent, and, according to (A1d), (A1e), and (A1f), all of your normative requirements disappear. This is a case of social dilemma that many of us face in the real life.^{Footnote 24}

Exercises

Discuss the following problems:

1.
What is a normative system?
2.
What is Logic for Normative Systems?
3.
What is Dynamic Normative Logic?
4.
How can normative powers be explained?
5.
How can roles be explained?
6.
How are individuals and social organizations related?

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Nakayama, Y. (2016). Norms and Games as Integrating Components of Social Organizations. In: Kasaki, M., Ishiguro, H., Asada, M., Osaka, M., Fujikado, T. (eds) Cognitive Neuroscience Robotics B. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54598-9_12

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