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[ x ∈ X ] | Bx[ x ∉ X ] | |
| x ∈ X | Identity | False Alienity |
| x ∉ X | False Identity | Alienity |
| ~Bx[ x ∈ X ] | ~Bx[ x ∉ X ] | |
| x ∈ X | Latent Identity | Pre-Identity |
| x ∉ X | Pre-Alienity | Latent Alienity |
Let X be an ensemble.
We say x is a Conscious Member of X if x ∈ X & Bx[ x ∈ X ]
X is a Conscious Ensemble if (∀x ∈ X) Bx[ x ∈ X ]
- Note that it is widely accepted that groups are necessarily conscious ensembles; i.e.:
γ(G) → (∀x ∈ G) Bx[ x ∈ G ]
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 x ∈ X1 ∩ … ∩ Xn & Bx[ x ∈ X1 ∩ … ∩ 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:
- X1, …, Xn are relatively disjoint, and
- X ⊂ ∪i=1,…,n Xi, and
- For i = 1, …, n, X ∩ Xi ≠ ∅.
Where δ is a division of X and x ∈ X, 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 x ∈ Xj & Bx[ x ∈ Xj ]
- 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(x|δ1), …, ID(x|δn)}
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Example:
A person may be a male, Christian, labourer, for which we write: let ξ1 = {‘Male’}, ξ2 = {‘Christian’}, ξ3 = {‘Labourer’}, x ∈ X1, X2, X3 such that ξ1(X1), ξ2(X2), ξ1(X3). 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} |
One Response to “Identity”
Change ‘conscious’ to ‘acceptive’, since we are not interested in self-image or self-awareness, except in so far as there is a sociological consequence.
With this change note that If x can sincerely be said to believe (in the common sense meaning of the term) that he is a member of X, then Bx[ x ∈ X ] is true, but the converse will not necessarily follow.
By SteveGW on Jan 6, 2014