International disagreements Fabien Schang

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1 International disagreements Fabien Schang Laboratory for Philosophical Studies National Research University Higher School of Economics, Moscow EFAK X University of Tartu, September 2014

2 Introduction

3 Lord protect me from my friends, I can take care of my enemies. (Voltaire)

4 How to make sense of the above quotation? Why to protect from friends, by definition? An alternative definition of friendship? A case of blatant inconsistency: are friends equally enemies? Can friends be more dangerous than enemies? To what extent are they still friends?

5 Keywords - Allery - Balance - Enmity - Force - Friendship - Hegemony - Indifference - Neutrality - Ontology - Peace - Rivalty - Value - War

6 What is an enemy? Whoever threatens one of several states own security A gradation of danger/enmity

7 A state considers another state as an (actual or potential) enemy to the extent that it perceives the latter s intentions or actions as threatening the focal state s interests. (Kuperman, R. D. & Maoz, Z. & Talmud, I. & Terris, L. G (2001): 3)

8 What is an enemy? Whoever threatens one of several states interests A gradation of danger/enmity By opposition: What is a ally (international friend)? Whoever warrants one or several state s interests International bivalence? Are any two states either allies or enemies with each other (bipolar world)? They may be none: no relation between them (indifference) Neutrality: military indifference

9 A positive, conventional definition of international relations: - friendship F stands for a political agreement between states x,y: F(x,y) - enmity E stands for a political disagreement between states x,y: E(x,y) Agreements and disagreements are expressed by treatises, alliances, organizations, institutions, international regimes International indifference States may be indifferent to each other (neither friends nor enemies) if: - they have no influence on the other s political status - any two states have no international relations Balance: stable system of states Balance needn t entail peace (war may be the ultimate resort for balance preservation) (opposed coalitions in 1914: balanced relations)

10 An account of balance in social networks A model from social psychology: a set of implicit relations (by perception) Fritz Heider s theory of social balance: social networks - a network is a set of relations between objects (individuals, states) - relations are subject to dynamic changes for different purposes - balance is an intended state of psychological perception Heider s theory of balance: - balance is defined through triadic relations R(a,b,c) among the following FFF, FFE, FEF, EFF, EEF, EFE, FEE, EEE - any triad R(a,b,c) is said to be balanced as follows: FFF, EEF, EFE, FEE it is imbalanced, otherwise

11 How to assess the value of the aforementioned statement: (EEF) For every x,y,z: E(x,y) E(y,z)) F(x,z) Example: x = Poland, y = Russia, z = Ukraine (Donbass crisis, 2014) Counter-example: x = Syria, y = Israel, z = Jordania (Black September, 1970) A variant: (EFE) For every x,y,z: E(x,y) F(y,z)) E(x,z) An analogy with arithmetics: E for 1, F for -1 balance is a product of friendships (1) and enmities (-1) EEF (-1).(-1) = 1 EFE (-1).(1) = -1

12 Preliminary assumptions: - analogy in the social relations between individuals and states - related to similar entities (social ontology) within a given network - the actors aim at improving their inner perception - they need to combine several capacities within a field of relative forces Formal philosophy: formal methods to philosophical problems, including political philosophy Back to the roots of IRT (Schang 2014)

13 Several primary issues are in order to characterize the general relation R(a,b) between arbitrary agents a,b (1) The ontology: What is the nature of a and b in IRT? A state-centred reading of international relations: states are the main actors (2) The epistemology: What is the relation R holding between these? A set of various relations within a cooperative game (3) The logic: What are the logical properties of R, if any? A formal treatment of IRT: friendly, hostile,, motivated relations A more fine-grained analysis of E and F as structured opposite integers

14 1. Ontology of IRT

15 What is the international system? A set of relations between nodes (the states) in a social network (the World) For any states a,b in W: a W and b W iff R(a,b) (where R = F or R = E) Globalization: a maximization of the state interrelations in W From several to only one international system (hyper-power at the top) Global and local organization (sets of relations between states): networks Co-operation: a number of combined operations between related states, such that b turns into f(a) = b in W One network, one hegemon? A strategic game between interrelated networks

Economic networks ASEAN: Association of Southeast Asian Nations MERCOSUR: Mercado Comùn del Sur CARICOM: Caribbean Community IGAD: Intergovernmental Authority on Development CEMAC: Communauté

16 Economic networks ASEAN: Association of Southeast Asian Nations MERCOSUR: Mercado Comùn del Sur CARICOM: Caribbean Community IGAD: Intergovernmental Authority on Development CEMAC: Communauté Economique et Monétaire de l Afrique Centrale ECOWAS: Economic Community of Western African States EFTA: European Free Trade Association NAFTA: North American Free Trade Agreement GCC: Gulf Cooperation Council SADC: Southern African Development Community

17 Military networks NATO: North Atlantic Treaty Organization ESDP: European Security and Defence Policy SCO: Shanghai Cooperation Organization CSTO: Collective Security Treatise Organization AU PSC: Peace and Security Council SADC: Southern African Development Community

18 Cultural networks (Huntington s thesis)

19 A structural approach: the way states are related to each other depends upon the way the whole international system W is organized International system: a set of n states W = {w 1,, w n } within related networks (subsets w 1, w 2, ) Local (regional) ontologies: subsets of states in W = {w 1,,w n } Unipolar world: n = 1 Bipolar world: n = 2 Multipolar world: n > 2 or n = 3 (2 opposite subsets + the rest of the world)

20 Need any two states be enemies once they belong to different ontologies? Example: the political ontology of Europe from 1872 to Complete balance doesn t mean peace, but stability (status quo) - An overall interest is obtained through a set of alliances The European 1907 network is not unipolar, but multipolar - No leadership, but a set of two competing states with balanced forces Balance is to be investigated in the light of the whole network W - The more networks there are, the more complex relations are Pax Americana : one-sided leadership with regional delegations Multipolarity: several networks, several levels of relations

21 3 views of anarchic world (no pre-established order between the states): - Realism: universal enmity (Hobbes) - Liberalism: universal friendship (Kant) Fukuyama: towards a unipolar world from 1991 onwards? - Globalism: particular enmity/friendship, ordering (Locke) + Culturalism : Huntington s Thesis: a set of 9 clashing civilizations (sets of states)

22 3 main paradigms: how are states interests to be characterized? - realism (H. Morgenthau) Anarchic state of war between states, peace as provisory balance Military force is primary - liberalism (K. Waltz) Priority of trading over war Economic force is primary - constructivism (A. Wendt) No force is primary throughout the history of a state

23 Constructivism is a structural theory of the international system that makes the following core claims: (1) states are the principal units of analysis for international political theory; (2) the key structures in the states system are intersubjective rather than material; and (3) state identities and interests are in important part constructed by these social structures, rather than given exogenously to the system by human nature (as neorealists maintain) or domestic politics (as neoliberals favour). (Wendt 1994: 35)

24 2. Epistemology of IRT

25 Are there objective criteria of relevance? A state is to be defined within a unique referential network (that of the leader: the hegemon ) by a set of values (aims) and forces (potential) - military value (human resources, material equipment) - economic value (GDP, technology, subsoil resources) - social value (life level, group relations, religion, political regime) - cultural value (education level, mass culture, world-wide spread) Beyond agreement and disagreement: partnership as a constructive relation Are there official disagreements between different networks?

26 Cultural networks and their enmity degrees (Huntington)

27 Direct relations: relations between any 2 objects in a dyad: R(a,b) Indirect relations: relations between any 2 objects through a third one in a triad: R(a,b,c) = R(a,b).R(b,c,).R(a,c) For every set of n objects, there is a set of (n!/(m!(n-m)!)) m-adic relations Example: with n = 3 objects in m = 2-ary relations It results in a set of (3!/(2!(1!)) = 6/2 = 3 relations Example: alliances in Europe from 1872 to 1907: - a graph including 6 nodes (states), with (6!/3!3!) = 20 possible triads - not any two states are related to each other: gappy cases in W - a graph is composed of nodes related to at least one other nodes

28 Three Emperors League ( ) GB AH FR GE RU IT

29 Triple Alliance (1882) GB AH FR GE RU IT

30 German-Russian Lapse (1890) GB AH FR GE RU IT

31 French-Russian Alliance ( ) GB AH FR GE RU IT

32 Entente Cordiale (1904) GB AH FR GE RU IT

33 British Russian Alliance (1907) GB AH FR GE RU IT

34 Three Emperors League ( ) GB AH FR GE RU IT R(AH,FR) = -1 R(FR,GB) = -1 R(GB,GE) = R(GE,IT) = 1 R(IT,RU) = R(AH,GB) = -1 R(FR,GE) = -1 R(GB,IT) = R(GE,RU) =1 R(AH,GE) = 1 R(FR,IT) = R(GB,RU) = -1 Three Emperors League ( ) R(AH,IT) = R(FR,RU) = -1 R(AH,RU) = 1

35 Three Emperors League ( ) 7 triads: 5 balanced, 2 imbalanced R(AH,FR,GB) = -1 R(FR,GB,GE) = R(GB,GE,IT) = R(GE,IT,RU) = R(AH,FR,GE) = 1 R(FR,GB,IT) = R(GB,GE,RU) = R(AH,FR,IT) = R(FR,GB,RU) = -1 R(GB,IT,RU) = R(AH,FR,RU) = 1 R(FR,GE,IT) = R(AH,GB,GE) = R(FR,GE,RU) = 1 R(AH,GB,IT) = R(FR,IT,RU) = R(AH,GB,RU) = 1 R(AH,GE,IT) = R(AH,GE,RU) = 1 R(AH,IT,RU) =

36 British Russian Alliance (1907) GB AH FR GE RU IT R(AH,FR) = -1 R(FR,GB) = 1 R(GB,GE) = -1 R(GE,IT) = 1 R(IT,RU) = -1 R(AH,GB) = -1 R(FR,GE) = -1 R(GB,IT) = -1 R(GE,RU) = -1 R(AH,GE) = 1 R(FR,IT) = -1 R(GB,RU) = 1 R(AH,IT) = 1 R(FR,RU) = 1 R(AH,RU) = -1

37 British Russian Alliance (1907) 20 triads: 20 balanced, 0 imbalanced R(AH,FR,GB) = 1 R(FR,GB,GE) = 1 R(GB,GE,IT) = 1 R(GE,IT,RU) = 1 R(AH,FR,GE) = 1 R(FR,GB,IT) = 1 R(GB,GE,RU) = 1 R(AH,FR,IT) = 1 R(FR,GB,RU) = 1 R(GB,IT,RU) = 1 R(AH,FR,RU) = 1 R(FR,GE,IT) = 1 R(AH,GB,GE) = 1 R(FR,GE,RU) = 1 R(AH,GB,IT) = 1 R(FR,IT,RU) = 1 R(AH,GB,RU) = 1 R(AH,GE,IT) = 1 R(AH,GE,RU) = 1 R(AH,IT,RU) = 1

38 3. Logic of IRT

39 A logical analysis of friendship/enmity (truth-value in every model) Reflexivity (1) x F(x,x) (2) x E(x,x) Symmetry (3) x y F(x,y) F(y,x) (4) x y E(x,y) E(y,x) Transitivity (5) x y (F(x,y) F(y,z)) F(x,z) (6) x y (E(x,y) E(y,z)) E(x,z)

40 A logical analysis of friendship/enmity (truth-value in every model) Reflexivity (1) x F(x,x) (2) x E(x,x) Symmetry (3) x y F(x,y) F(y,x) (4) x y E(x,y) E(y,x) Transitivity (5) x y (F(x,y) F(y,z)) F(x,z) (6) x y (E(x,y) E(y,z)) E(x,z)

41 A logical analysis of friendship/enmity (truth-value in every model) Reflexivity (1) x F(x,x) (2) x E(x,x) Symmetry (3) x y F(x,y) F(y,x) (4) x y E(x,y) E(y,x) Transitivity (5) x y (F(x,y) F(y,z)) F(x,z) (6) x y (E(x,y) E(y,z)) E(x,z)

42 Heider s theorems of social psychology (truth-value in social models) FFF (5) x y z (F(x,y) F(y,x)) F(x,z) EEF (7) x y z (E(x,y) E(y,x)) F(x,z) EFE (8) x y z (E(x,y) F(y,x)) E(x,z) Corollary : FEE (9) x y z (E(x,y) F(y,x)) E(x,z) (by (3)) Goal: to find (counter-)models for (against) (1)-(9)

43 Heider s theorems of social psychology (truth-value in social models) FFF (5) x y z (F(x,y) F(y,x)) F(x,z) EEF (7) x y z (E(x,y) E(y,x)) F(x,z) EFE (8) x y z (E(x,y) F(y,x)) E(x,z) Corollary : FEE (9) x y z (E(x,y) F(y,x)) E(x,z) (by (3)) Goal: to find (counter-)models for (against) (1)-(9)

44 Heider s theorems of social psychology (truth-value in social models) FFF (5) x y z (F(x,y) F(y,x)) F(x,z) EEF (7) x y z (E(x,y) E(y,x)) F(x,z) EFE (8) x y z (E(x,y) F(y,x)) E(x,z) Corollary : FEE (9) x y z (E(x,y) F(y,x)) E(x,z) (by (3)) Goal: to find (counter-)models for (against) (1)-(9)

45 Heider s theorems of social psychology (truth-value in social models) FFF (5) x y z (F(x,y) F(y,x)) F(x,z) EEF (7) x y z (E(x,y) E(y,x)) F(x,z) EFE (8) x y z (E(x,y) F(y,x)) E(x,z) Corollary : FEE (9) x y z (E(x,y) F(y,x)) E(x,z) (by (3)) Goal: to find (counter-)models for (against) (1)-(9)

46 Heider s theorems of social psychology (truth-value in social models) FFF (5) x y z (F(x,y) F(y,x)) F(x,z) EEF (7) x y z (E(x,y) E(y,x)) F(x,z) EFE (8) x y z (E(x,y) F(y,x)) E(x,z) Corollary : FEE (9) x y z (E(x,y) F(y,x)) E(x,z) (by (3)) Goal: to find (counter-)models for (against) (1)-(9)

47 Heider s theorems of social psychology (truth-value in social models) FFF (5) x y z (F(x,y) F(y,x)) F(x,z) EEF (7) x y z (E(x,y) E(y,x)) F(x,z) EFE (8) x y z (E(x,y) F(y,x)) E(x,z) Corollary : FEE (9) x y z (E(x,y) F(y,x)) E(x,z) (by (3)) Goal: to find (counter-)models for (against) (1)-(9)

48 A more fine-grained account of IRT: OF (Opposition-Friendly) Logic FOL + non-fregean (but referential) semantics Direct relations are defined by means of a question-answer game (QAS) Incompatibility (symbols: INC): contrariety, contradiction (INC = {CT,CD}) Compatibility (symbols: C): subcontrariety, subalternation (C = {SCT,SB}) The logic of opposition (Aristotle) A generalization of sentential to abstract logic: OF (Opposition-Friendly) Logic A Boolean calculus of oppositions (Schang 2012) with opposite-forming operators: op = {cd,ct,sct,sb} Compare with relations/functions: E/e, F/f An application of OF Logic to IRT: states as meaningful objects in W

49 Each object (beyond sentences) in a finite domain W = {,, } is defined by a string of properties, to be accepted (1) or not (0) The sense of is a finite set of n relevant questions about : Q( ) = Q 1 ( ),, Q n ( ) The reference of is a finite set of corresponding answers: A( ) = A 1 ( ),, A n ( ) where A i ( ) maps from L to {1,0} (1: yes-answer; 0: no-answer) Example: A( ) = 1100, A( ) = 0110 with n = 4 For any objects (beyond sentences), defined by bitstrings (sequences of 0-1 single values):

50 1. is the contrary of iff whatever is asserted of is denied of ct( ) = iff {A( } A j ( ) = 1 A j ( ) = 0} 2. is the contradictory of iff whatever is asserted of is denied of, and conversely cd( ) = if {A( } A j ( ) = 1 A j ( ) = 0} 3. is the subcontrary of iff whatever is denied of is asserted of sct( ) = iff {A( } A j ( ) = 0 A j ( ) = 1} 4. is the subaltern of iff whatever is asserted of is also asserted of sb( ) = iff {A( } A j ( ) = 1 A j ( ) = 1} 5. An additional logical relation: independence (IND C) No constraint upon the related objects: freely accepted or rejected together

51 In IRT: enemies are incompatible with each other friends are compatible with each other (rivals are potential enemies: whatever may become an enemy) A calculus of intensional (one-many) opposite-forming operators: op(a) b inc: incompatibility-forming operators c: compatibility-forming operators e(e(a) = f(a), that is: inc(inc(a)) = c(a)? e(f(a)) = f(e(a)) = e(a), that is: inc(c(a)) = c(inc(a)) = inc(a)? Failure of EEF: contraries of contraries may be incompatible with each other (Schang 2012)

52 The questioning: a Question-Answer Game (QAS, Schang (2012)) Every object is individuated by an ordered set of n properties within a question-answer game: Q(s) = Q 1 (s),,q n (s) 4 features to define states throughout a hegemonic network w i W: Q(s) = Q 1 (s),q 2 (s),q 3 (s),q 4 (s) Which questions to characterize states? A 4-tuple of values Q 1 (s) = military agreement in w i? Q 2 (s) = economic agreement in w i? Q 3 (s) = social agreement in w i? Q 4 (s) = cultural agreement in w i?

53 Problems: (1) Oppositions in a globalized network - Only contrariety seems to make sense in a logic of IR - How to render contradiction, subcontrariety, subalternation in IRT? (2) Individuation and differentiation by questioning - What if any two states share all the same values (no qualitative difference)? (3) How to classify states in, according to their respective forces? - Quantitative data (forces), beyond qualitative properties (values)

54 Solution: an arithmetization of the logic of opposition (Schang 2011) 2 main amendments in the model: - No more absolute (yes-no) answers - Relative answers to compare the values of x,y in {w i x w i } A necessary appeal to quantities to define states s as a combination of: - collective coefficients A {2,4,8,16} (to discriminate the significance of any definitional criterion) - individual values v {-1,0,1} (in a multipolar world W with n = 3) - individual forces f {1,2,3,4,5} (1 = very weak; 2 = weak; 3 = average; 4 = strong; 5 = very strong) Av f (s) = A 1 v f (s) + A 2 v f (s) + A 3 v f (s) + A 4 v f (s)

55 Friendship as compatible, globally converging values x y E(x,y) = df Av f (x) + Av f (y) > Av f (x) Example: Av f (x) = Av f (y) = Enmity as incompatible, globally diverging values x y E(x,y) = df Av f (x) + Av f (y) < Av f (x) Example: Av f (x) = Av f (y) =

56 Global vs Local agreements - Two global friends (enemies) F(x,y) may be local enemies (friends) E i (x,y) Example: USA and Saudi Arabia are global friends Av f (USA) + Av f (SA) > Av f (USA), therefore F(USA,SA) local enemies (culturally): A 4 v f (USA) + A 4 v f (SA) < A 4 v f (USA), therefore E 4 (USA,SA) Subordination (political subalternation) as a total agreement - Any state x is subordinate to another state y iff, for every individual value a i : A i (y) + A i (x) > A i (y) A i v f (x) < A i v f (y)

57 Reflexivity (1) x F(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: (a + a) > a (2) x E(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: not (a + a) < a (Note: no schizophrenic state, no self-enemy such that a a)

58 Reflexivity (1) x F(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: (a + a) > a

59 Reflexivity (1) x F(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: (a + a) > a (2) x E(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: not (a + a) < a (Note: no schizophrenic state, no self-enemy such that a a)

60 Reflexivity (1) x F(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: (a + a) > a (2) x E(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: not (a + a) < a (Note: no schizophrenic state, no self-enemy such that a a)

61 Reflexivity (1) x F(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: (a + a) > a (2) x E(x,x) Proof: (Av f (x) + Av f (x) > Av f (x)) For any integer a: not (a + a) < a (Note: no schizophrenic state, no self-enemy such that a a)

62 Symmetry (3) x y F(x,y) F(y,x) Proof: (Av f (x) + Av f (y) > Av f (x)) (Av f (y) + Av f (x) > Av f (y)) For any integers a,b: (a + b) > a iff (b + a) > b (4) x y E(x,y) E(y,x) (Av f (x) + Av f (y) < Av f (x)) (Av f (y) + Av f (x) < Av f (y)) For any integers a,b: (a + b) < a iff (b + a) < b

63 Symmetry (3) x y F(x,y) F(y,x) Proof: (Av f (x) + Av f (y) > Av f (x)) (Av f (y) + Av f (x) > Av f (y)) For any integers a,b: (a + b) > a iff (b + a) > b (4) x y E(x,y) E(y,x) (Av f (x) + Av f (y) < Av f (x)) (Av f (y) + Av f (x) < Av f (y)) For any integers a,b: (a + b) < a iff (b + a) < b

64 Symmetry (3) x y F(x,y) F(y,x) Proof: (Av f (x) + Av f (y) > Av f (x)) (Av f (y) + Av f (x) > Av f (y)) For any integers a,b: (a + b) > a iff (b + a) > b (4) x y E(x,y) E(y,x) (Av f (x) + Av f (y) < Av f (x)) (Av f (y) + Av f (x) < Av f (y)) For any integers a,b: (a + b) < a iff (b + a) < b

65 Symmetry (3) x y F(x,y) F(y,x) Proof: (Av f (x) + Av f (y) > Av f (x)) (Av f (y) + Av f (x) > Av f (y)) For any integers a,b: (a + b) > a iff (b + a) > b (4) x y E(x,y) E(y,x) (Av f (x) + Av f (y) < Av f (x)) (Av f (y) + Av f (x) < Av f (y)) For any integers a,b: (a + b) < a iff (b + a) < b

66 Transitivity (5) x y z (F(x,y) F(y,z)) F(x,z) Proof: x y z F(x,y) F(y,z) F(y,z) Countermodel against (5): Av f (a) = Av f (b) = Av f (c) = Av f (a) + Av f (b) > Av f (a) Av f (b) + Av f (c) > Av f (b) Not Av f (a) + Av f (c) > Av f (a)

67 Transitivity (5) x y z (F(x,y) F(y,z)) F(x,z) Proof: x y z F(x,y) F(y,z) F(y,z) Countermodel against (5): Av f (a) = Av f (b) = Av f (c) = Av f (a) + Av f (b) > Av f (a) Av f (b) + Av f (c) > Av f (b) Not Av f (a) + Av f (c) > Av f (a)

68 Transitivity (6) x y z (E(x,y) E(y,z)) E(x,z) Proof: x y z E(x,y) E(y,z) E(y,z) Countermodel against (6): Av f (a) = Av f (b) = Av f (c) = Av f (a) + Av f (b) < Av f (a) Av f (b) + Av f (c) < Av f (b) Not Av f (a) + Av f (c) < Av f (a)

69 Transitivity (6) x y z (E(x,y) E(y,z)) E(x,z) Proof: x y z E(x,y) E(y,z) E(y,z) Countermodel against (6): Av f (a) = Av f (b) = Av f (c) = Av f (a) + Av f (b) < Av f (a) Av f (b) + Av f (c) < Av f (b) Not Av f (a) + Av f (c) < Av f (a)

70 Heider s theorems of social psychology FFF (5) x y z (F(x,y) F(y,x)) F(x,z) Proof: See above.

71 Heider s theorems of social psychology FFF (5) x y z (F(x,y) F(y,x)) F(x,z) Proof: See above.

72 Heider s theorems of social psychology EEF (7) x y z (E(x,y) E(y,x)) F(x,z) Proof: x y z E(x,y) E(y,z) F(x,z) Countermodel against (8): Av f (a) = Av f (b) = Av f (c) = Av f (a) + Av f (b) < Av f (a) Av f (b) + Av f (c) < Av f (b) Not Av f (a) + Av f (c) > Av f (a)

73 Heider s theorems of social psychology EEF (7) x y z (E(x,y) E(y,x)) F(x,z) Proof: x y z E(x,y) E(y,z) F(x,z) Countermodel against (8): Av f (a) = Av f (b) = Av f (c) = Av f (a) + Av f (b) < Av f (a) Av f (b) + Av f (c) < Av f (b) Not Av f (a) + Av f (c) > Av f (a)

74 Heider s theorems of social psychology EFE (8) x y z (E(x,y) F(y,x)) E(x,z) Proof: x y z E(x,y) F(y,z) E(x,z) Countermodel against (8): Av f (a) = Av f (b) = Av f (c) = Av f (a) + Av f (b) < Av f (a) Av f (b) + Av f (c) < Av f (b) Not Av f (a) + Av f (c) > Av f (a)

75 Heider s theorems of social psychology EFE (8) x y z (E(x,y) F(y,x)) E(x,z) Proof: x y z E(x,y) F(y,z) E(x,z) Countermodel against (8): Av f (a) = Av f (b) = Av f (c) = Av f (a) + Av f (b) < Av f (a) Av f (b) + Av f (c) < Av f (b) Not Av f (a) + Av f (c) > Av f (a)

76 Heider s theorems of social psychology FEE (9) x y z (F(x,y) E(y,x)) E(x,z) Proof: x y z E(x,y) F(y,z) E(x,z) Proof: by (8) and (3).

77 Heider s theorems of social psychology FEE (9) x y z (F(x,y) E(y,x)) E(x,z) Proof: x y z E(x,y) F(y,z) E(x,z) Proof: by (8) and (3).

78 Political interpretation #1: A hegemonic account of war and peace - Peace (War) results from (imb)alance between values (not only military!) Balance depends upon the values and forces in which related actors differ Relativity of ontology: state interests rely on their relation with the hegemon - Total, Global, Local (im)balance Total (im)balance: friendship (enmity) between any actors a,b in W Global balance: friendship (enmity) between most of the actors a,b in W Local balance: friendship (enmity) between some actors a,b in W - Balance needn t entail peace ( If you want peace, prepare the war ) Some global balances may entail local imbalances World wars occur for want of a strong hegemon beyond the local ontologies when most of the states find interest in imbalance

79 Political interpretation #2: a hegemon-dependent ontology The hegemon strives to maintain its leadership: - through its allies (against the states of opposite networks) - against its allies (by preventing them from augmenting their own capacities) H(x) = df x y Av f (x) > Av f (y) Any ally is a potential enemy: potential rivalty - subjection is a rational choice - any state strives to satisfy its own interest while playing collectively States don t share the same ontology (p) only if they share common values (q) - the converse holds: q p - hegemon proceeds as a Demiurge (ontology-maker)

80 Political interpretation #3: Friendship and Enmity in a Multipolar World? - In a multipolar world (without hegemon) W = {w 1,w 3 }: States cannot have opposed values any more: v = 0 or v = 1 (no more v = -1) - Enmity does not make sense any more: x y Av f (x) + Av f (y) > Av f (x) Can friendship still make sense without enmity, however? - Beyond friendship and enmity: actual rivalty Rivalty: any two states x,y are both cooperating and competing relata RIV(x,y) = df x y z (Av f (x) > Av f (y)) (Av f (y) + Av f (z) > Av f (x)) - A case against Fukuyama s end of history after the Cold War (W = {w 1,w 2 }): No hegemon standing peace, No hegemon = standing rivalty

81 We have not eternal allies and we have not perpetual enemies. Our interests are eternal and perpetual and those interests it is our duty to follow. (Lord Palmerston)

82 Conclusion

83 Summary (1) OF Logic deals with friendship/enmity as compatibility/incompatibility (2) Rivalry goes beyond friendship and enmity (3) Political paradigms lead to various valuations (4) The theorems (1)-(9) rely on the complex valuation of states (5) Back to the Great Debate, about the epistemological status of IRT - OF Logic does not overcome Dilthey s distinction natural/social sciences - both descriptive: values (v) and forces (f), in geopolitics prescriptive: the ordering of values A(x), in political philosophy - A plea for constructivism: dynamic, interdependent values A

84 IRT Science or art of agreement-making? A multi-player game of chess with (or without) one mastermind Who defines the rules of the game? If there is no common ruler, do states really play the same game together?

85 Anarchy is what the states make of it. (Wendt)

86 References Dilthey, W. Introduction to the Human Sciences, Princeton University Press, 1991 Heider, F. Attitudes and cognitive organization, The Journal of Psychology, Vol. 21, 1946: Kaplan, M. The New Great Debate: Traditionalism vs. Science in International Relations, World Politics, Vol. 19, N 1, 1966: 1-20 Kuperman, R. D. & Maoz, Z. & Talmud, I. & Terris, L. G.: What is the enemy of my enemy? Causes and consequences of imbalances international relations, , The Journal of Politics, Vol. 69, n 1, 2007: Schang, F. An arithmetization of the logic of oppositions, talk presented at the World Congress on Logic, Methodology and Philosophy of Sciences, Nancy, July 2011 Schang, F. Abstract logic of oppositions, Logic and Logical Philosophy, Vol. 21, 2012: Schang, F. Making sense of history? A formal theory of international relations, in in Globalistics and Globalization Studies (Aspects & Dimensions of Global Views), L. E. Grinin & I. V. Ilyin & A. V. Korotayev, Volgograd, 2014, Wendt, A. Collective Identity Formation and the International State, American Political Science Review, Vol. 88 (1994)

87 Merci! Thank you! Cпасибо! Aitäh!

Social Balance on Networks: The Dynamics of Friendship and Hatred

Social Balance on Networks: The Dynamics of Friendship and Hatred T. Antal, (Harvard), P. L. Krapivsky, and S.Redner (Boston University) PRE 72, 036121 (2005), Physica D 224, 130 (2006) Basic question: