The Rights of Zombies

February 10, 2014 – 12:11 am

An article by Peter at Conscious Entities considers the question of whether philosophical zombies have rights. It seems to me that under most forms of ethical theory that have been attractive to philosophers they would do. Let’s consider them systematically:

(a) Teleological theories

a.1 – Consequences are Utilities

A consequentialist theory – if it grants rights to any moral agents at all – does so because the consequences of that grant are better than the consequences of not doing so. Obviously, the most important of these are the members of the class of Rule Utilitarian ethical theories, in which it is claimed that rights are rules of social interaction that, if everyone follows them, together with the other rules that are in force and observed, will lead to greater utility than would be the case if any other rules were followed.  

a.1.1 – Utilities are Felicities

If utility is understood to be some kind of happiness or pleasure, then the moral agent in question, being a zombie, does not contribute to the result of the felicific calculation. What difference would this make to the result of the calculation? Suppose we got a different result by zeroing out all the contributions to the final sums made by the happiness (positive or negative) of the moral agent. Is this equivalent to considering the case of the calculation for the society as if that agent was simply not a member? Well, not quite, because the agent, operating according to the various rules imagined to be in force, will produce felicific effects in other members of the society. We can say, however, that unless the felicific significance of the zombie agent is greater than that of random other members, there is no reason to believe that it will affect the final outcomes.

a.1.1.1 – proportion of zombies

We might also wonder whether it makes a difference how many zombies there are. In the penultimately extreme case that there is just one non-zombie in the society, it is still likely that the happiness of that one member would be maximised by the calculations that justified the grant of rights in the zero-zombies situation. In the case of a society entirely constituted of zombies, there is no felicific consequence to be considered and no such thing as a distinction between right and wrong or good and bad.

a.1.1.2 – determinability of zombiehood

We might also note at this point that it makes a difference for these kinds of theories whether we are able to determine the fact of zombie-nature and the ease and accuracy with which this determination can be made. If it were possible to make this determination easily and accurately then clearly rules might include conditional statements of application relating to the zombie-status of the agents and patients involved. Such a rule might very well be the rule that came top in the appropriate felicific calculation, and such a rule might very well exclude zombies from the possession of rights. Counting against that possibility, we would have to consider that the philosophical zombies are likely to behave just as non-zombies would behave if systematically discounted in ethical calculations; which is to say, they would likely behave as if they saw themselves as alienated from the moral system in force and this might plausibly lead to more unpleasantness for the non-zombies than if they were all treated identically.

a.1.2 – decision theory vs. definitional theory

At this point the merely notional nature of the calculations involved prevents any further specificity, which is usually the case with this sort of thing. These calculations are never performed – they are impossible in principle; but from Bentham on utilitarians have been quite clear that their systems are not intended to be decision procedures, but they are intended to demonstrate that there really are precise conditions that distinguish in fact between right and wrong. Our inability, even in principle, to discover these conditions in any particular case, makes no difference to its rightness or wrongness, which is an objective fact of the world. Of course, this may mean that the proper rule to be followed might be a rule containing conditional statements of application relating to the zombie-status of the agents and patients involved – even if it was in principle impossible to make the determination. We would then be systematically prevented from knowing the right thing to do by yet another of the epistemological blocks to using the felicific calculus as a decision procedure.

(b) Deontological Theories

b.1 – Kantian theories

The standard alternative to the utilitarian theory is some form of deontological theory, usually derived from Kant. Rights in this case derive from the application of the Categorical Imperative. But this has several forms and is justified accordingly in several different ways. The justifications are related, of course, and the classes of good or bad actions determined by each form are supposed by Kant to coincide, so that it should not matter which of these we consider. Since this is not universally accepted, let’s look at the two most important forms of the CI: the universal law form and the principle of ends form.

b.1.1 – Universal Law

Kant’s justification for this form, though tricky in details, and missing important parts, is fairly easy to apply to the zombie case. We are told that one follows the rule:

Always act so that the maxim of your action can rationally be taken to be a universal law.

Any rational being will follow a categorical imperative, because it is only in that way that it demonstrates that it is operating with a Free Will. If it is to distinguish amongst all the things that might be covered by categorical imperatives but are not, it will apply The Categorical Imperative. All of the reasoning behind this refers only to the rationality of the moral agent. In this case the universal law form of the categorical imperative should apply to any rational being – and the zombie would be included amongst those along with robots and Martians and smart squid.

b.1.1 – Principle of Ends

According to the PE form of the CI:

Treat humanity, whether in your own person or in that of another, always as an end and never as a means only.

This is somewhat trickier. Let’s agree to ignore an objection that worries that zombies lack humanity and therefore are not covered by the CI:PE. This would be defining the zombies out of the question. For convenience we might rephrase it as

Treat yourself and others, always as ends and never as means only.

In any case the argument for treating oneself and others (moral agents) as ends is that one and they are unconditionally valuable: they are not valuable just because they are necessary to the achievement of some other end which has value. That would make them merely conditionally valuable. What makes them unconditionally valuable is that they are value-giving. And they are value-giving because they are rational and are able to formulate plans in which some things are conditionally valuable.

In so far as that goes, the philosophical zombies may be stipulated to be rational and therefore value-giving in just the same way that non-zombies are. The only objection might be that in the case of a zombie it is hard for us to imagine that value really is given to the necessary elements of a plan that it forms. Note that something which is conditionally valuable for the agent X is something for which it can be said that it is valued by X because it is a means to an end which X desires. If we are able to give a definition of desiring that does not exclude zombies then we‘ve got no problem, otherwise we do.

b.2 – God’s Law

Much less popular these days, but still important because the philosophical shape of our rights talk preserves the imprint of its origins therein, is the idea that rights are given to us as amongst the regulations instituted by God for the proper running of the World, His creation. The general picture of is most accessibly put forward by Aquinas, but the consequence in Human Rights is developed by Locke. According to this view, God has so ordained the world that it operates according to certain rules that He has promulgated, whose effect is to make the world perform that function for which God has designed it. (God being rational always has a reason for what He does, and thus had a reason for creating the world and man in it.) Some of these rules we do not have the choice to disobey: these are the Laws of Nature. With regard to others we may exercise our Free Will. These are the Natural Laws. Amongst the Natural Laws are our Human Rights. God has given us a certain number of rights that, if we acknowledge and respect them will lead to the proper functioning of the world.

Moreover, God has made it the case that we can identify these Natural Laws by the use of reason. Roughly speaking, we can say that, if we assume that God wants us to achieve X in the world, and it seems reasonable to the wisest amongst us that this purpose would best be achieved by organising the world thus and so, then we are justified in claiming that the world is in fact so arranged. The wisest amongst us have determined that God’s purpose is human flourishing in this world, and that this would be best achieved if we all had certain unalienable rights, therefore we do have such rights.

We could simply stop at this point and just point out that this is essentially the position that we had in the case of the rule utilitarians, except that now we have the claim that utility equal flourishing. For utilitarians the obligation to obey the utilitarian rule comes from the idea that obligations are always conditional on delivering our preferences, and this principle will best deliver our preferences. For Natural Law theorists, the obligation to follow the Law comes from the authority of the creator to organise His creation. (Yes, that’s a moral notion. No I don’t know how it’s justifiable.) But this difference applies only to the originating source of all moral normativity, and we are here concerned with the particular rules which partake of that normative force.

b.2.1 – Zombie flourishing

Let’s assume that human flourishing is in fact the worldly function. The questions relating to rights for zombies in this case are pretty obvious, and the first question would have to be: does God’s plan include the flourishing of (human) zombies? We can make some headway on this if we can establish what normal human (non-zombie) flourishing would be. If this flourishing essentially required something like ‘Joy’ or the experience of the love of God or some other such internalia, then this would be something that a zombie could not achieve, and therefore the flourishing of zombies could not include it. This being the case, zombies would be in the position of beings incapable of participating in God’s plan for the world, and therefore the world was not designed for the flourishing of zombies. Zombies are here to be considered as incidental parts of God’s plan, like animals and plants and the landscape.

If, on the other hand, human flourishing was something like the development of souls able to know God, then whether or not zombies could flourish would depend on unanswerable questions like whether they had souls (they were not stipulated to lack them) or whether it was possible to ‘know’ God in the proper way without an experiential capability. And on the answer to such questions would hang the possibility of zombie flourishing. We don’t seem to be getting very far in these theological speculations.

b.2.2 – Zombie rules

But happily, none of that may be necessary. It may be sufficient to consider that since zombies behave in exactly the same way that non-zombies do, we could say that the flourishing of the non-zombies under the regulations that would be proposed to allow the flourishing of a population without zombies would be completely unchanged. Unless there was the possibility of some form of regulation that would preferentially encourage the flourishing of non-zombies, there is no reason to modify the Natural Laws that would have been derived for the non-zombie case; and therefore we conclude that zombies would be attributed all the same rights and duties as non-zombies. And so, they do have all our rights and duties.

b.2.2.1 – discriminating Zombies

In the alternative case that we are able to discriminate zombie from non-zombie, and this discrimination may be achieved practicably, the possibility might well arise that we could conditionalise the Natural Law so that some rules would apply differently according to zombie-status. If that were the case, we would again have to refer to the kind and possibility of zombie flourishing before we could know what God would have us so.

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The Evolutes of Prakriti

January 19, 2014 – 10:51 pm


In the course of researching the Samkhya cosmogony, I noticed that the diagrams indicate a great variety of interpretations. I thought it would be interesting to display them here.

 

 

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Yoga Links from ‘Sacred Texts’

January 9, 2014 – 12:33 pm


THE YOGA SUTRAS OF PATANJALI by Charles Johnston [1912]
THIS CONCISE WORK DESCRIBES AN EARLY STAGE IN THE PHILOSOPHY AND PRACTISE OF YOGA.
Dating from about 150 B.C., the work shows dualist and Buddhist influences. Required reading if you are interested in Yoga or meditation.

THE YOGA SUTRAS OF PATANJALI
ANOTHER TRANSLATION OF THIS CLASSIC TEXT OF YOGA.

THE HATHA YOGA PRADIPIKAtranslated by Pancham Sinh [1914]
THE OLDEST EXTANT WORK ABOUT HATHA YOGA, INCLUDING THE FULL SANSKRIT TEXT.

GREAT SYSTEMS OF YOGA by Ernest Wood [1954]
A REVIEW OF THE YOGIC SYSTEMS.

RELAX WITH YOGA by Arthur Liebers [1960]
AN INTRODUCTION TO MODERN RAJA YOGA, WITH PHOTOS OF ASANAS.

HOW TO BE A YOGI by Swâmi Abhedânanda [1902]
A ROAD-MAP OF THE YOGIC SCHOOLS.

KARMA-YOGA by Swami Vivekananda [1921]
CAN WORK BE HOLY?

HINDU MYSTICISM by S.N. Dasgupta [1927]

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Short Reading List on Sociological Identity

January 8, 2014 – 12:16 am

A Conceptual Model of Multiple Dimensions of Identity by Susan R. Jones, Marylu K. McEwen, Journal of College Student Development, V 41, No. 4, July/August 2000

A conceptual model of multiple dimensions of identity depicts a core sense of self or one’s personal identity. Intersecting circles surrounding the core identity represent significant identity dimensions 

IDENTITY CONSTRUCTION: New Issues, New Directions by Karen A. Cerulo, Annu. Rev. Sociol. 1997. 23:385–409

Many works refocus attention from the individual to the collective; others prioritize discourse over the systematic scrutiny of behavior; some researchers approach identity as a source of mobilization rather than a product of it; and the analysis of virtual identities now competes with research on identities established in the copresent world. This essay explores all such agenda. 

Theorizing Identity, Nationality and Citizenship: Implication for European Citizenship Identity by Lynn Jamieson,

This paper reviews theoretical approaches to the key concepts of ‘identity’ and ‘citizenship’ exploring their implications for the possibility of ‘European’ identity and ‘European’ citizenship.

Types of Groups in Openstax collection ‘Introduction to Sociology’

Summary:

  • Understand primary and secondary groups as the two sociological groups
  • Recognize in-groups and out-groups as subtypes of primary and secondary groups
  • Define reference groups

Identity Theory and Social Identity Theory by Jan E. Stets, Peter Burke. Social Psychology Quarterly 2000, Vol 63, No. 3, 224-237

In social psychology, we  need to establish a general theory of the self, which can attend to both macro and micro processes, and which avoids the redundancies of separate theories on different aspects of the self.

Sociology: How are Identities Formed?

A mind map

Class Identities and the Identity of Class by Wendy Bottero, Sociology, 2004; 38; 985

The uneasy relationship between older and newer aspects of ‘class’ within renewed class theory means the wider implications of inequality considered as individualized hierarchy (rather than as ‘class’) have not been fully explored.The debate on class identities (an important example of this new form of class analysis) illustrates these dif?culties.

A Sociological Approach to Self and Identity by Jan E. Stets, Peter J. Burke; Chapter for Handbook of Self and Identity, edited by Mark Leary and June Tangney, Guilford Press

Because the self emerges in and is reflective of society, the sociological approach to understanding the self and its parts (identities) means that we must also understand the society in which the self is acting, and keep in mind that the self is always acting in a social context in which other selves exist (Stryker, 1980). 

Introducing Identity by David Buckingham; Youth, Identity, and Digital Media. Edited by David Buckingham. The John D. and Catherine T. MacArthur Foundation Series on Digital Media and Learning. Cambridge, MA: The MIT Press, 2008. 1–24. doi:10.1162/dmal.9780262524834.001 

There are some diverse assumptions about what identity is, and about its relevance to our understanding of young people’s engagements with digital media.  

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Identity

January 4, 2014 – 10:33 am


Let X be an ensemble and x an individual. This individual may or may not be aware of their membership status wrt X, and may or may not correctly understand their status

Bx[ xX ] Bx[ xX ]
xX Identity False Alienity
xX False Identity Alienity

~Bx[ xX ] ~Bx[ xX ]
x ∈ X Latent Identity Pre-Identity
xX Pre-Alienity Latent Alienity

Let X be an ensemble.
We say x is a Conscious Member of X if xX & Bx[ xX ]
X is a Conscious Ensemble if (∀xX) Bx[ xX ]

  • Note that it is widely accepted that groups are necessarily conscious ensembles; i.e.:
    γ(G) → (∀xG) Bx[ xG ]

The conscious memberships of an individual define its Identity wrt society. Thus for the individual x who is a conscious member of ensembles X1, …, Xn, the identity of x is that collection, and we write:
ID(x) = {X1, …, Xn} iff xX1 ∩ … ∩ Xn & Bx[ xX1 ∩ … ∩ Xn ]

Some sets of ensembles are mutually exclusive wrt membership. A collection of such ensembles δ = {X1, …, Xn}, that minimally covers another ensemble, X, is a Division of that ensemble and we write δ|X. Thus,
{X1, …, Xn} is a division of X iff:

  1. X1, …, Xn are relatively disjoint, and
  2. X ⊂ ∪i=1,…,n Xi, and
  3. For i = 1, …, n, XXi ≠ ∅.

Where δ is a division of X and xX, ID(x|δ) is the element of δ of which x is a conscious member. Read it as the Identity of x wrt δ. Thus: For δ = {X1, …, Xn}, δ|X, ID(x|δ) = Xj iff xXj & Bx[ xXj ]

  • Where δ1, …, δn are divisions of X, we can call A = {δ1, …, δn} an Identity Analysis of X.
  • Let A = {δ1, …, δn} be an analysis of X. Then the identity of x wrt that analysis is:
    ID(x|A) = {ID(x1), …, ID(xn)}

Example:

A person may be a male, Christian, labourer, for which we write: let ξ1 = {‘Male’}, ξ2 = {‘Christian’}, ξ3 = {‘Labourer’}, xX1, X2, X3 such that ξ1(X1), ξ2(X2), ξ1(X3).
If these are all conscious ensemble memberships their identity wrt society is male, Christian, labourer.

A set of ensembles defined by religious affiliation is typically mutually exclusive – especially if they are conscious ensembles – since if one is a Christian one can’t be a Buddhist or a Hindu, and if one is a Hindu then one is not Buddhist or Christian, and, of course, if one is Buddhist then one is not Christian or Hindu. Similarly for socio-economically defined ensembles, or educational, or residential ensembles, etc.

An example of a division might be the confessional allegiances in a nation. If the citizens are one only of Buddhist or Hindu – as in Sri Lanka – then {Buddhists, Hindus} is a division of Sri Lanka. Since there are no Christians (we’ll pretend), {Buddhists, Hindus, Christians} is not a division of Sri Lanka, though it contains one.

Suppose we have X = Sri Lanka, δ = {Buddhists, Hindus}, then it might be that ID(Bob|δ) = Buddhist (if Bob is a Buddhist.)

An identity analysis of Sri Lanka might include divisions according to religious and racial and linguistic criteria. Thus we might have X = Sri Lanka, δ1 = {Buddhists, Hindus}, δ2 = {monolingual Tamil, monolingual Singhala, bilingual}, δ3 = {Tamil, Singhala}. Then A = {δ1, δ2, δ3} would be an analysis of Sri Lanka.

So far as this analysis goes ID(Bob|A) = {Hindu, monolingual Tamil, Tamil}

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Agent Based Modelling Material

January 1, 2014 – 11:19 pm


The Ascape Model Developer’s Manual
Individual-Based Models:an annotated list of links by Craig Reynolds
Introduction to Stochastic Actor-Based Models for Network Dynamics (pdf) by Tom A.B. Snijdersy, Gerhard G. van de Buntz, Christian E.G. Steglichx

This paper gives an introduction to stochastic actor-based models for dynamics of directed networks, using only a minimum of mathematics. The focus is on understanding the basic principles of the model, understanding the results, and on sensible rules for model selection.

TUTORIAL ON AGENT-BASED MODELING AND SIMULATION PART 2: HOW TO MODEL WITH AGENTS (pdf) by Charles M. Macal, Michael J. North

This tutorial describes the foundations of ABMS, identifies ABMS toolkits and development methods illustrated through a supply chain example, and provides thoughts on the appropriate contexts for ABMS versus conventional modeling techniques.

AGENT-BASED MODELS (pdf) by Nigel Gilbert

This ?rst chapter begins with a brief overview of agent-based modeling before contrasting it with other, perhaps more familiar forms of modeling and describing several examples of current agent-based modeling research.

Modeling Social Mechanisms: Mechanism-Based Explanations and Agent-Based Modeling in the Social Sciences (pdf) by Cyril Hédoin

This article evaluates the relevance of ABM to representing (social) mechanisms. It emphasizes the difficulties surrounding the representation of a particular form of social mechanisms I call “institutional mechanisms”, where the behavior of the social system and of its components (the social agents) are determined by institutional objects such as norms or conventions.

Some Links to Simulation Resources on the Web. Materials supporting sociology 242G by Robert Hanneman of the Department of Sociology at the University of California, Riverside.
From Factors to Actors: Computational Sociology and Agent-Based Modeling (pdf) by Michael W. Mac, Robert Willer

Like flocks of birds, human group processes are highly complex, nonlinear, path dependent, and self-organizing. We may be able to understand these dynamics much better not by trying to model them at the global level but instead as emergent properties of local interaction among adaptive agents who influence one another in response to the influence they receive.

Why Sociology Should Use Agent Based Modelling by Edmund Chattoe-Brown

Although Agent Based Models (hereafter ABM) are now regularly reported in sociology journals, explaining the approach, describing models and reporting results leaves little opportunity to examine wider implications of ABM for sociological practice. This article uses an established ABM (the Schelling model) for this.

From micro to macro and back again: Agent-based models for sociology (pdf) by Federico Bianchi

In this paper the importance of agent-based simulation is advocated for mechanism-based sociology [1]. The main epistemological reasons are to be found in the analogies between mechanism-based sociological theory [1.1], the study of complexity and emergent properties [1.2] and the generative explanatory power of computer simulations [1.3].

Finally, an Amazon wish: Agent-Based Computational Sociology [Hardcover] by Flaminio Squazzoni

This book looks at a new research stream that makes use of advanced computer simulation modelling techniques to spotlight agent interaction that allows us to explain the emergence of social patterns. It presents a method to pursue analytical sociology investigations that look at relevant social mechanisms in various empirical situations, such as markets, urban cities, and organisations.

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Norms

July 6, 2012 – 12:38 pm

Amongst the beliefs that are important in the subjective determination of interest-maximising behaviour are some that impose restrictions on the kinds of actions that the agent believes are permissible in certain circumstances. Such beliefs are beliefs about norms of action. Actions which fall outside the range permitted by the appropriate norms are not taken even where taking them would lead to greater total satisfactions than any other action.

A Norm is an action-directing rule, n, for which

(∃Cx,applies ⊂ Cx) (∃αbad(x) ⊂ α(x)) (∀cx,0 ∈ Cx,applies) (∀ax ∈ αbad(x)) [n & ax |– ⊥ ]

  • An equivalent condition might be written positively as
    (∃Cx,applies ⊂ Cx) (∃αgood(x) ⊂ α(x)) (∀cx,0 ∈ Cx,applies) (∀ax ∉ αgood(x)) [n & ax |– ⊥ ]

  • Cx,applies and Cx are sets of contexts for x. Cx is the set of all possible contexts for x.
  • The condition that makes n normatively prescriptive is a logical condition: the forbidden action is logically inconsistent with the norm. Accurate logical reasoning is at least a part of the process by which x goes about determining his action in the circumstances, though we cannot depend upon it being a main part or that it will be very accurate.
Example:

The reason for the indirect nature of the previous description of norms is that it is likely that the norms occur in a variety of forms. An example of the form of a simple norm might be:

(∀cx ∉ Cx,war ∪ Cx,self-defense) (∀ax ∈ αkill(x)) [~ax]

which would be the form of the general statement that ‘Except in war or in self-defence, thou shalt not kill.’

Consider the case that might apply if x has been insulted. The reasoning could include

  1. cx,0 ∈ Cx,insult
  2. (∃ax ∈ αkill(x))(∀ax’ ≠ ax) [T(C(ax, cx,0, x), I(x), x) > T(C(ax’, cx,0, x), I(x), x)]
  3. ∴ ax (by i., ii.)

which is to say that the decision would be made to kill. But if the reasoning included the norm as sketched above, we would have

  1. cx,0 ∈ Cx,insult
  2. (∃ax ∈ αkill(x))(∀ax’ ≠ ax) [T(C(ax, cx,0, x), I(x), x) > T(C(ax’, cx,0, x), I(x), x)]
  3. ∴ ax (by i., ii.)
  4. (∀cx ∉ Cx,war ∪ Cx,self-defense) (∀ax ∈ αkill(x)) [~ax]
  5. Cx,insult ∩ (Cx,war ∪ Cx,self-defense) = ∅
  6. cx,0 ∉ Cx,war ∪ Cx,self-defense
  7. ∴ ~ax (by iv. & vi.)
  8. ∴ ⊥ (by iii. & vii.)

Meaning that the decision to kill is impermissible

An agent x is an Acceptant of the norm n iff x accepts the rule n. We will write

K(n) = {x: B(x)[ n ]}

  • In this case, there is a condition for accepting that B(x)[ n ] based on the notion that we can discover whether x really accepts a norm by observation of his behaviour. Thus
    B(x)[ n ] → (∃Cx,applies ⊂ Cx) (∃αbad(x) ⊂ α(x)) (∀cx,applies ∈ Cx,applies) (∀ax,bad ∈ αbad(x))
    [n & ax |– ⊥ → A(x, cx,0) ≠ ax]
    which is to say that, if x produces an action in a circumstance in which the norm determines that that action is impermissible, then x cannot be said to accept that norm.
  • The reasons why x might fail this test are many. It might just be that x is not very clever and fails to reason logically accurately; perhaps the norm is too complex for any human; perhaps information is lacking; etc. We do not need to assume that x is actually dishonest.
  • It would seem, on the face of it anyway, that it’s quite possible that ~B(x)[ n ] & B(x)[ B(x)[ n ]]; and other curiosities of epistemic logic may also apply. It will be necessary eventually to decide which axiomatization of epistemic logic is most appropriate for the operator B. We can ignore the question for now.
  • The condition given for x being an acceptant of n may not adequately reflect the fuzziness of our belief states, or the degrees to which we believe something. Assuming that we wish to do so, and that this cannot be done by massaging the context variable of the action function as it applies to the conditions under which we will apply the norm, we may propose the following refinement:

    B(x)[ n ] → (∃Cx,applies ⊂ Cx) (∃αbad(x) ⊂ α(x)) (∀cx,applies ∈ Cx,applies) (∀ax,bad ∈ αbad(x))
    [((n & ax |– ⊥) &
    (&forall>ax,alt ≠ ax)~B(x)[ (T(C(ax,alt, cx,0, x), I(x), x) ] >> T(C(ax, cx,0, x), I(x), x)) ]))
    → A(x, cx,0) ≠ ax]

    Which is simply stating that x will not contravene n unless he estimates that the total satisfaction to be gained by doing so is sufficiently greater than the satisfaction to gained by abiding by n.

  • The degree of excess expressed by ‘>>’ is left deliberately vague – as in other uses of it. (To be set, perhaps, by empirical research.)

A Norm Formation is a set of norms, N = {n1, …, nn}.

  • an agent x is an acceptant of the norm formation N iff x accepts the rules in n.
    K(N) = {x: B(x)[ N ]}
  • Standard classes of norm formations are conventions, traditions, etc. (which may be analysed later.)

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Norms and Institutions

July 1, 2012 – 11:49 am

A Norm is an action-directing rule, n.

  • an agent x is an Acceptant of the norm n iff x accepts the rule n.

    K(n) = {x: B(x)[ n ]}

  • We can discover whether x accepts a norm by observation of his behaviour

A Norm Formation is a set of norms, N = {n1, …, nn}.

  • an agent x is an acceptant of the norm formation N iff x accepts the rules in n.

    K(N) = {x: B(x)[ N ]}

  • Standard classes of norm formations are conventions, traditions, etc. (which may be analysed later.)

An Institution may be formalized as a norm formation which imposes a group structure on K(N)

  • This definition results in a particular selection of social structures being called institutions which may differ from the selections made by other theoretical views. This is no great difficulty, since we have the theoretical machinery to deal with all reasonable extensions or restrictions of this concept.
  1. An institution imposes an (Institutional) Organization on K(N)
    • N → (∃Q ={r1, …, rn} ⊂ 2K(N))

      [((∀x ∈ K(N))(∃ri ∈ Q) [x ∈ ri]) &
      ((∀x ∈ K(N))(∀ri, rj ∈ Q) [x ∈ ri & x ∈ rj → ri = rj])]

    • We call the elements of Q the (Institutional) Roles of the organization of N
  2. An institution imposes a relation of (Institutional) Dominance on K(N)
    • x institutionally dominates y in N iff

      (∃αresponse(x) ∈ B(y)[ α(x) ])
      (∃αneutral(x) ∈ B(y)[ α(x) ] – αresponse(x))
      (∃αchallenge(y) ∈ B(y)[ α(y) ])
      the following conditions are satisfied:

      1. (∀achallenge ∈ αchallenge(y)) (∀aresponse ∈ αresponse(x)) B(y)[ P(αneutral(x) | A(y)=achallenge & A(x)≠aresponse ] ≈ 1
      2. (∀achallenge ∈ αchallenge(y)) (∃aresponse ∈ αresponse(x)) (∃N’ ⊂ N) [(B(y)[ N’ → (A(y)=achallenge → A(x)=aresponse )]]
      3. (∀aresponse ∈ αresponse(x)) (∀achallenge ∈ αchallenge(y)) (∃N’ ⊂ N)[(B(y)[ (A(x)=aresponse → A(y)=achallenge) → N’]
      4. (∀cresponse ∈ B(y)[ C(αresponse, cx,0, x) ]) (∀cneutral ∈ B(y)[ C(αneutral, cx,0, x) ])[B(y)[ T(cresponse, I(y), y) ] << B(y)[ T(cneutral, I(y), y) ]
    • This condition differs from the condition for (non-institutional) dominance in parts 2 and 3, which express y’s belief that his action together with the rules of the institution will produce x’s response, and that without those rules there would be no such response. This is, therefore, a special case of the previous definition.
    • Note that since N creates the conditions under which T is degraded for noncompliant agents, N provides the mechanism of enforcing compliance.
    • Express x institutionally dominates y as x/Ny
  3. Let the Group determined by the institution N be denoted GN = < K(N), R >, where R contains at least
    • O(GN), the institutional organization as defined on |GN|,
    • ADD(GN) = {< x, y >: x, y ∈ |GN|, x/Ny}, the (Institutional) Agent Dominance Diagram of GN, and
    • RDD(GN) = {< ri, rj >: ri, rj ∈ O(GN), ri/Nrj}, the (Institutional) Role Dominance Diagram of GN, where, for disjoint sets X and Y, Y institutionally dominates X iff (∀x ∈ X) (∀y ∈ Y) [y /N x].

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Group Function: Preliminaries

June 24, 2012 – 8:55 pm

Groups may be viewed as operators on the social world. They take a context and modify it. This context modification includes that which is responsible for the advantaging of intentional interests of the members, but is not limited to that. We can write this quickly as

F(G): C → C

But to understand what it entails we will have to further modify the context function we have been using. Previously, we considered:

  1. The function C(b, x) = c, for b a behaviour of x and c the social context parameters that feature in the partial satisfaction functions S for x.
  2. The refinement C(B(x), x) = {C(b1, x), …, C(bm, x)} = {c1, …, cm}, where B(x) = {b1, …, bm} refers to the range of x’s possible behaviours

Now we can build up a further series of refinements;

  1. Make the substitutions for the new notation to get C(A(x), x) = {C(a1, x), …, C(am, x)} = {c1, …, cm}, where A(x) = {a1, …, am} refers to the range of x’s possible actions
  2. Note that we need to index the output contexts for the agent whose partial satisfactions they are taken to determine. Thus the function C(ax, y) = cy, for ax a behaviour of x and cy the context parameters that feature in the partial satisfaction functions S for y.
  3. C(A(x), y) = {C(ax,1, y), …, C(ax,m, y)} = {cy,1, …, cy,m}, where A(x) = {ax,1, …, ax,m} refers to the range of x’s possible actions
  4. C(A(x), cx,0, y) = {C(ax,1, cx,0, y), …, C(ax,m, cx,0, y)} = {cy,1, …, cy,m}, where cx,0 refers to the context in which x acts.
  5. C(A(X), CX,0, y) = {C(A(x), CX,0, y): x ∈ X} = {cy,1, …, cy,n}, (note the index change from m to n,) where
    • X is a set of agents
    • A(X) is the range of possible actions for each x in X
    • CX,0 refers to the context in which each x in X acts. It is the complete set of social parameters that feature in the partial satisfaction functions S for x in X
  6. C(A(X), CX,0, Y) = {C(A(x), CX,0, Y): x ∈ X } = {CY,1, …, CY,n}, where CY,i are the complete sets of social parameters that feature in the partial satisfaction functions S for y in Y.

We can now observe that the group function described means that G is so organized that

F(G) (Cin) = Cout

Which, in fact, means that

C(A(|G|), C|G|,in, |G|) = C|G|,out

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Notation Revision

June 23, 2012 – 6:06 pm

Revise the notation to be suggestive of the standard terminology in intentional psychology – which is to say BDA psychology. The least disruptive change I judge to be as follows:

B(x)[ argument ] is the ‘belief’ of x about ‘argument’, which replaces E(x)[ argument ]
D(x)[ argument ] is the ‘desire’ of x about ‘argument’, which replaces D(x)
A(x) is the ‘action’ by x, which replaces A(x) and B(x). It yields the range of possible actions for x.

Previous terminology using ‘intensional’ will now use ‘believed’

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