Staffan Angere has a wonderfully lucid paper titled 'Identity and intensionality in Univalent Foundations and philosophy' which can be found here.
Perhaps to pique the interest of the generalist, he quotes the following paragraph by, the Number Theorist, Michael Harris from the marvellously idiosyncratic book
he has recently published-
It’s impossible to overstate the consequences for philosophy, especially the philosophy of Mathematics, if Voevodsky’s proposed new Foundations were adopted. By replacing the principle of identity by a more flexible account modeled on space, the new approach poses a clear challenge, on which I cannot elaborate here, to the philosophy underlying “identity politics”; it also undermines the case for analytic philosophy to seek guidance in the metaphysics of set theory, as in W.V.O Quine’s slogan “to be is to be the value of a variable.” (Harris 2015, p. 219)
This puts us in mind of Sam Harris, the nueroscientist and professional atheist's, view that Identity Politics has become a political religion. By this he means that people, on the basis of identity, have ready made preferences, or prejudices, across a range of unconnected issues- e.g. abortion, gun-control, immigration etc.
The problem with this view is that all
political coalitions display a similar structure under 'first past the post' voting systems. This explains why, to Sam Harris's dismay, people mention their Identity (whose own most salient 'single issue' would be known to others in the coalition) when voicing their opinions. Thus, when I stand up at my local Labour Party meeting, I might say 'as a Hindu, who like most Hindus in West London, is highly dependent on Public Transportation, I oppose Brexit because it will inevitably lead to higher fares, cutbacks on routine maintenance, and the God Shiva opening his third eye and destroying the Universe.' Clearly, there is a large tactical element in what I have said and very little alethic content. Nevertheless it conveys a lot of information and would have a far bigger impact than anything else I could say.
Mention of one's religion or other predominating 'identity class' adds imperative force to one's signal. It serves as a proxy for preference intensity. Moreover, particular identity classes may be 'swing voters'- i.e. have a high Banzhaf power index- and thus we should expect, under an imperfect voting rule, a hypertrophy of identitarian statements.
Nevertheless, it may be, some people would find my mention of my religion somewhat jarring.
Amartya Sen, who won a Nobel Prize for applying set theory to Social Choice, voiced an unease that Harris shares, when he wrote in 'Identity and Violence'-
‘a major source of potential conflict in the contemporary world is the presumption that people can be uniquely categorized based on religion or culture’.
Sen presumes that the set of agents can be neatly partitioned into two disjoint subsets- in one of which are people who make stupid presumptions- this box would contain Sen, if he really believed what he was saying rather than just writing in a facile and sententious manner- while the rest of us who hold no such view would belong in the other box.
The truth is, the opposite proposition to Sen's has some justification- viz. if people can be uniquely categorised, with respect to a motive, by religion or culture, then an irenic movement within that culture or religion could greatly reduce conflict and promote peace. Since such irenic movements could create incentives and penalties of a novel kind for their own members in a way which no outside arbiter could- we might say they internalise the creation of positional goods or a currency of a certain kind so as to permit the Revelation Principle to incarnate in a 'Vickrey Clarke Groves' mechanism- it follows that neither the motive of Justice nor that of conflict resolution should reject unique, intensional, definitions of identity out of hand.
Indeed, both would in fact show a homotopy of their own to that of irenic religion or 'civilizational' culture, or even ethnicity. Thus, as has often been remarked Harris & his fellow 'four horsemen', preside over what looks very much like a cult.
What endogenous, not purely circumstantial, factors would determine whether it is an irenic or a violent motive which reconfigures an identity class?
Well, violence is a learned skill. One may wish to fight an external enemy so as to learn how to be better at fighting or to gain a reputation for bellicosity. This might feed into the differential determination of economic or political outcomes within one's identity class.
By contrast, if a reputation for peacefully resolving conflicts and abiding by contracts boosts one's status or life-chances within one's in-group, then the identity class as a whole may be intensionally reconstituted by an irenic motive. However, in the latter case, it is also likely that the community will be able to devote resources to collective defence- or profitable aggression. If this sort of professionalised violence is more effective than the thymotic sort, then Identity will still correlate to, not open, but delegated and disguised Violence- except, paradoxically, some members of the class being coerced would be voluntarily, if more or less unconsciously, contributing to this outcome.
Much actual 'identity politics' is about challenging this manifestly unjust situation. Why should women pay taxes or otherwise support a machinery of Law and Justice which blames the victim for rape? Why should African Americans support a system which incarcerates a large proportion of their own rising generation?
This raises the further question- what is to be done? Whither our next step? Clearly if this step- whatever it might be- is taken in a coordinated, or otherwise unanimous, manner, it will speed the desired outcome. Is there some way in which Identity politics can have a compelling logical expression such that one particular step become Schelling focal for everybody almost simultaneously without the need for any hysterical propaganda or dubious 'moral entrepreneurship' based on telling stupid, paranoid, lies? This seems a tough call. It is invidious, but seemingly necessary, to distinguish between strategy from tactics and methods from objectives and so forth. However, this can split the movement before it gets off the ground so all one ends up with is more and more internecine conflict and name calling.
is an approach whose motive is to make mathematics much more productive. It may be that. by using it to clarify our notion of identity, identity politics too can be rendered utile rather than antagonomic.
Angere's paper begins thus-
Abstract The Univalent Foundations project constitutes what is arguably the most
serious challenge to set-theoretic foundations of mathematics since intuitionism. Like
intuitionism, it differs both in its philosophical motivations and its mathematicallogical
apparatus. In this paper we will focus on one such difference: Univalent
Foundations’ reliance on an intensional rather than extensional logic, through its use of
intensional Martin-Löf type theory. To this, UF adds what may be regarded as certain
extensionality principles, although it is not immediately clear how these principles are
to be interpreted philosophically. In fact, this framework gives an interesting example
of a kind of border case between intensional and extensional mathematics. Our
main purpose will be the philosophical investigation of this system, and the relation
of the concepts of intensionality it satisfies to more traditional philosophical or logical
concepts such as those of Carnap and Quine.
Identity- even self-identity- isn't unproblematic. It requires the sort of close analysis that Hohfeld gave to jural relationships. Consider the following passage from Amartya Sen-
Some years ago when I was returning to England from a short trip abroad (I was then Master of Trinity
College in Cambridge), the immigration officer at Heathrow, who scrutinized my Indian passport rather
thoroughly, posed a philosophical question of some intricacy. Looking at my home address on the
immigration form (Master’s Lodge, Trinity College, Cambridge), he asked me whether the Master, whose
hospitality I evidently enjoyed, was a close friend of mine.
Why did the immigration officer (many such are of Indian origin) ask this particular question? The answer is that Sen had not stated that his occupation was 'Master of Trinity' but used some more modest description. Obviously, the Master resides in the Master's Lodge.
Sen, being an economist, was of course blissfully unaware of the nature of the exchange between him and the immigration officer.
This gave me pause since it was not altogether
clear to me whether I could claim to be a friend of myself. On some reflection, I came to the conclusion
that the answer must be yes, since I often treat myself in a fairly friendly way, and furthermore, when I say
silly things, I can immediately see that with friends like me, I do not need any enemies. Since all this took
some time to work out, the immigration officer wanted to know why exactly did I hesitate, and in
particular whether there was some irregularity in my being in Britain.
Well, that practical issue was eventually resolved, but the conversation was a reminder, if one were
needed, that identity can be a complicated matter.
This is bizarre. The immigration officer had a job to do which involved pouncing on anyone who appeared nervous or was acting suspiciously.
Sen failed to see what aspect of his identity was relevant to the immigration official. It may be that the official could have expedited matters by putting a different question to Sen. He couldn't ask 'is that your own house?' because that would defeat the purpose. He needed to hear Sen say something to that effect in his own words. Why? Most people hesitate or have a quaver in their voice when telling a lie.
Still, the immigration officer could have asked another question, one less ambiguous- instead of 'is that your friend's house?'- so as to elicit the substantive assertion 'no, it is my house'- he could have said 'is that your boyfriend's house?' However, in that case, the officer may himself have found himself roped into the Dungeon Master of Trinity's hi-jinks up to at his 'Lodge'.
There is, of course, no great difficulty in persuading
ourselves that an object is identical to itself.
Nonsense. Some things can be identical with themselves according to one or more criteria of identity, others can't at all. There is no way of determining in advance, or independently of pragmatics, why and when this will happen.
That chair there is not wholly and verifiably
identical with itself because of the Uncertainty principle. No physical object is. It may be identical with itself for some purposes- e.g. certification as the antique chair Dr, Johnson sat upon- even if every part of it had been repaired or replaced. Something similar is true even of purely mental objects.
Sen is aware of this- he writes
Wittgenstein, the great philosopher, once remarked that
“there is no finer example of a useless proposition” than saying that something is identical to itself, but he
went on to argue that the proposition, though completely useless, is nevertheless “connected with a certain
play of the imagination.”
More than in the realms of imagination, it is in juristic, economic or chrematistic, or 'buck stopped', protocol bound discourse that identity relations have salience. They are highly utile. What matters is the motive behind the seeking of a cohomology or identity relationship.
It seems to be a common assumption in analytic (but of course not continental) philosophy
that identity is a fairly simple concept. A forerunner here is Frege, who in
the afterword to the second volume of the Grundgesetze—the one in which he reacts
to Russell’s paradox—argues against taking classes to be improper objects since this
would require them to have their own notion of identity. Identity, he says, “is a relation
given in so determinate a way that it is inconceivable that different kinds of it could
occur” (2013, p. 254). More recently, we find David Lewis expressing quite similar
Identity is utterly simple and unproblematic. Everything is identical to itself;
nothing is ever identical to anything except itself. There is never any problem
about what makes something identical to itself; nothing can ever fail to be. (1986,
Making a distinction with the notion of reference, McGinn rather matter-of-factly
writes in his book Logical Properties that “one could not write a good book entitled
The Varieties of Identity” (2000, p. 1).
But such a view can only be defended if one has already decided that the concept of
identity of, say, classical predicate logic, is the correct one, in which case the simplicity
and lack of problems that Lewis alludes to naturally spring from the fact that a decision
has already been made, even if unconsciously. As soon as we leave classical logic’s
safe confines, the conceptual landscape opens up. In the classical presentation of his
type theory Martin-Löf (1984) distinguishes four forms of identity
(i) The definitional equality a ≡d.f b. This is “the equivalence relation generated by
abbreviatory definitions, changes of bound variables and the principle of substituting
equals for equals” (Martin-Löf 1984, p. 31). It is a purely syntactic notion, and
is therefore not strictly the same as the identity judgment a ≡ b : X, which—
to start with—also makes reference to a specific type. In Martin-Löf (1984), it is
the only form of identity that the author holds to be intensional.
Definitional identity, thus, is motivated by a potential gain from substitutabilty. This can either be licit or illicit. If it is licit, it is possible that our knowledge base will expand. If it is illicit, noise will drown out signal. Thus, in Ambedkar's view, Gandhi dressing up as a peasant or cleaning toilets like a bhangi
was an illicit type of claim to definitional identity- Gandhi was substituting himself for large sections of society so as to gain a salience and obligatory passage point status, during a transition to Democracy, much larger than would accrue to him as a lawyer from a mercantile caste.
Of course, the same point might be made about Ambedkarite identity politics. Highly educated people rely upon a hereditary definition of themselves as 'Dalit' 'broken people' so as to gain an advantage in the higher echelons of the administration without concerning themselves any further with the plight of that particular class from which, at least notionally, they themselves have sprung.
(ii) The equality of elements a ≡ b : X, where X is a type of which a and b are
elements. This is perhaps the version most like classical identity in that it allows
replacing equals for equals arbitrarily, subject only to type restrictions. This is
what we have referred to as the judgmental equality.
The Law does create judgemental identity and such 'identity politics' as is concerned with changing the Law or improving access to judicial remedies may have some utility- or, as too often happens, disutility, if the underlying vinculum juris
is incentive incompatible.
(iii) The equality of types X ≡ Y , which consists in them having judgmentally equal
This permits different separating equilibriums to form a pooling equilibrium thus rendering different types equivalent or grossly substitutable. Thus, according to prevailing exchange rates, I- as a working class Hindu from Hammersmith who is heavily reliant on Public Transport- have a judgmental identity perfectly expressed by the term 'Fat Bastid'.
(iv) The identity type family IdC(x, y)through which every pair of elements a, b of C
is assigned a specific type IdC(a, b). Using the Curry–Howard correspondence,
the elements of this type are interpretable as proofs of the proposition a = b, and
this form of identity is therefore also referred to as propositional. Furthermore,
if a : C, there is a postulated element reflC(a) of IdC(a, a) called a’s reflexivity
proof, which corresponds to a canonical proof that a = a; e.g. the one obtained
by a single application of equality introduction
Propositional identity, then, can motivate canonical solutions to coordination problems which are independent of what is focal to a particular identity. Because of Girard's paradox, we know, Identities won't dissolve into an undifferentiated mass because then every truth would be provable. Thus you get a rational 'representative agent' theory- or to put it another way you can work with 'centre's of gravity' rather than unwieldly shapes. This one reason why definitional identity is always worth sticking with rather than dissolving because to do so would be to reduce degrees of freedom. Rather every intensional identity should be admitted to achieve Hannan Consistency. This means equilibria have robust defences against suddenly becoming 'anything goes'.
This is the Holy Grail of Economics in which Preference diversity displays a Goldilocks condition, there is no chrematistic hedging nor do any significant 'Income effects' obtain and so the Revelation Principle is univocal with its Mechanism.
Granted, the above is impressionistic, if not wholly incoherent, still, it seems to me, there is an obvious link between motivic cohomology, univalent foundations, and redeeming 'identity politics' from its Gadarening trajectory on such campuses as we read about or see represented on Netflix.
A more modest claim would be that a proper analysis of the notion of identity can make such Public Discourse as it motivates, at least marginally, useful to the commonweal.
As a first step, perhaps we can agree to distinguish between
1) intensional identity- whereby the fulfilment of all necessary and sufficient conditions establishes identity. Amartya Sen fulfilled the conditions for admission to the UK because he had both a legal right of abode as well as sufficient means and suitable accommodation- and thus was unlikely to become a charge on public funds. Had he been a British citizen, the economic criteria would not have been a necessary condition for his admission.
2) extensional identity- i.e. as arising from membership in a list of a certain sort. Prior to Sen's immigration to the UK there was a time when his holding an Indian passport would have been sufficient for him to be admitted to the country. However, the law was changed. It is likely that Sen's granted permanent residency in the UK on the basis, not of his identity as an Indian, but rather because of some skills he possessed which initially made him worthy of a work permit on the basis of which he would have been granted indefinite leave to remain. However, this could have been revoked for criminal misconduct. His name would have been struck off a list.
Intensional identity, in socio-political contexts, naturally arises wherever there is a monopoly or monopsony or where unconscionable contracts may arise by reason of great differences in market power.
Things like the colour of one's skin or one's gender are difficult and costly to disguise. Mother tongue, ethnicity, Religion, Sexuality, too may become easier to detect over the course of an incomplete contract and may become the basis of price, wage or service provision discrimination.
The relevant economic theory here predicts that the establishment of a countervailing power by a discriminated against identity class may increase allocative and dynamic efficiency.
We all benefit, even if we don't all acknowledge it, when merit rises to the top regardless of historic prejudices or the vested interests of rent-seeking cabals.
How can this countervailing power arise? The answer is that some people have to send a 'costly signal'- they have to sacrifice something or undergo some suffering for the collective good- such that a new 'separating equilibrium' is established. One way to sabotage this is to pretend that the original was a 'pooling equilibrium'- everyone was treated equally- and this will generate some worthless pi-jaw or 'cheap talk'. Some 'activists' may get misled by this availability cascade and start babbling about Total Revolution or Universal Human Rights or some such shite- i.e. postpone fixing things till everything is fixed once and for all.
One way of looking at what is going on is to speak of discriminated against people, or those with lower market or institutional power, as needing to enter a 'discoordination game' so as to get 'judgmental identity' or 'process equality' with respect to the hegemonic 'coordination game'.
Extensional identity, too, has significance though it corresponds to a widening 'pooling equilibrium' under a cheap talk regime. However, at the margin, we can expect dramatic saltation events. Thus, when Prof. Ranajit Guha, the great Marxist, emigrated to the UK, his being an Indian citizen was a sufficient condition for his being admitted to the country. By the time, the far less Left wing, Professor Sen emigrated, this was no longer the case. However, at that time, there seemed little prospect that immigration officers would bar the re-entry of people of Commonwealth origin who had established domicile in England and who were neither criminals nor a charge on public funds. Thus many Commonwealth citizens of Sen's generation did not bother to acquire British nationality. Going forward, this is unlikely to be the case.
Economic, Political and Juristic processes often have a nomothetic framework with idiographic contents. There is a subtle interplay between intensional and extensional notions of identity. This can confuse the hell out of elderly Professors like Dr. Sen who jump to the conclusion that most people have adopted an absurd view of the world- probably because they didn't read some particular footnote in a book by a long dead White Dude- and who thus become ready to play the Chomsky to the Media's Ali G.
This is by no means inevitable. If Economists and Philosophers give up a silly, supposedly set theoretic, notion of identity, and embrace recent advances- like 'univalent foundations'- they need not talk worthless shite so incessantly. Campuses can purge themselves of antagonomic culture warriors whose antics have provoked a Trumpian backlash.
How? The answer is that they must focus on the motive behind the identity being claimed. Motivic cohomology allows us to go beyond puerile name-calling. Consider the following tweet by Dr. Priyamvada Gopal who thinks the porters at Kings College are racist. She says they refused to call her 'Dr. Gopal' instead of 'madam' and one actually said 'I don't care who you are'.
Kings is standing by its porters and Dr. Gopal is refusing to teach there.
Racism does not have a univocal trigger. The fact that those same porters treated me deferentially does not mean they might not have mistreated Gopal simply because of her colour. In my case, it may be that the friend I was visiting was an old fashioned, gentlemanly, 'wog'- i.e. a liberal tipper. and even more liberal toper, who was wont to engage the porters in maudlin conversation when of strong drink taken. They may have mentally pigeonholed me as some sort of declasse
Accountant or Solicitor who had been dispatched by the Family to rake the young prodigal over the coals.
What is interesting here is that Gopal says that she is making a decision on behalf of 'other people of colour'. Presumably she means 'other people of colour whom the porters were racist towards'. The problem here is that it may be that there is no racism here at all- even if it is shown that the Porters use terms like 'nigger' or 'Paki' amongst themselves. After all, plenty of people who don't like me call be 'Fat bastid'. They may be portly themselves or enjoy close friendships with people more obese than myself but they use this pejorative term in referring to me so as to express their animus against me and relieve their feelings a little.
Gopal, however, takes a different view, in a subsequent tweet she says-
This may be a reasonable claim. Perhaps Kings College has been taken over by a racist cabal who are creating a 'hostile environment' for coloured people so that they will stop teaching or studying there.
Colleges are themselves a sort of gatekeeper. They admit some- perhaps to liweves of erudition or affluence- and reject others- it may be to lives impoverished of intellectual, aesthetic or financial rewards.
If Gopal really believes that Kings is a racially discriminatory gatekeeper- in other words, it is breaking the Law- then. surely, something more is demanded of her than a couple of tweets and the decision not to teach at a place where the custodial staff are rude?
To answer this question, we need to consider what Gopal's identity might be. We normally think it incumbent on the subject of a tort, or crime, to report the matter or otherwise set the wheels of justice in motion. Failure to take such action does not however mean that the issue is de minimis
or otherwise not justiciable. It may be that the victim is of diminished capacity or that there is some necessary aspect of her identity which both militated towards her being victimized as well as prevents her securing justice in proprio persona.
The problem here is that there may be evidence that Gopal has been quick to secure her rights in the past where the facts of the case permitted her to do so. This does not however wholly invalidate her assertion that she is the victim of systemic top-down racism at Kings. It may be that she has multiple identities arising out of being subject to different regimes of power. Thus, in some other context, say if I steal her bicycle, she may be able to go to the Police because her identity as victim of a theft is not problematic for the Constabulary. Even in that situation, however, it may be that she will be unable to bring to book the true motive force behind my stealing her bicycle- viz. the nexus between comprador neoliberalism and alt right misogynistic White Nationalism orchestrated by David Attenborough and the sneezing Baby Panda on You Tube.
This represents a scandal for Sen's notion of multiple identities. Why should we subscribe to a theory which says Gopal, for a priori reasons, can get justice when I steal her bike but not when Kings constructively dismisses her purely because of her colour? Is it not better to admit that she has identical litigation capacity in both instances? By doing so, identity can give rise to a useful political action- Gopal could file a class action suit which would have a demonstration effect and perhaps lead to a clarification by way of an amendment to existing statute law. After all one of her multiple identities, as Sen might say, is that of an educated person. Why should this identity not function even in the context of her supposed abject status?
The answer is that Priyamvada Gopal specialises in Feminist Post Colonial literary theory. Its univalent foundations are not in identity but counterfeiting a dispossessed alterity so as to justify fraudulently cashing the pension cheques of Dead White Men.