What is the relationship between the following two statements? 1. You may have heard this method called “proof by contradiction”. .. He is a member of the Department of Pure Mathematics and Mathematical Statistics at. for pure financial loss” under which reference was made to what “is reasonable reliance and a special relationship, has never been entirely clear,5 but up until. same-sex relationships, while Andrew and his partner epitomize Giddens' notion of the "pure relationship." Theirs is a partnership that is constantly negotiated.
It is just that they are surprised and impressed by what people do manage to do with inheritance. I am surprised and impressed by what they could be doing and largely try and prevent themselves doing.
Given the complexities of the modern family with multiple forms of parent-child relationship, given the increasing diversity of actual relationships as good and bad, close and far, rewarding and devastating, I choose to emphasis the degree to which people seem to try and find strategies for making these all equate with a relatively constant norm, based on the differentiation of family from non family, generation from transgeneration and the principle of fair and equal division.
Kinship lies in that highly formal and normative consistency, as well as in the flexible negotiations they have to use these days in order to achieve this consistency. In any case I will assume that Carsten's analysis is entirely correct and reasonable.
But once again I want to argue some caution in the embrace of the position on relationships it represents even in another part of South-East Asia.
For this purpose I want to refer to some preliminary reading I have conducted in preparation for a project I am carrying out with Dr Mirca Madianou of the University of Cambridge. We will study the operation of long distance relationships, specifically those of separated families and couples, and the ability of particular media to sustain those relationships over time. The core of this study will be a focus on Philippine and Caribbean relationships.
She notes there are approximately 9 million Filipino children under 18 with at least one parent abroad as migrant labour a: One might think that this situation starts with extraordinary acts of self-sacrifice. Particularly when we consider mothers who are choosing to work abroad.
Fathers spent rather more time back at home since their work allowed more time off. That means that the mothers in question basically did not see their children grow up. The mothers give their reasons for taking up this work largely in terms of the children's welfare, for example, education, medical bills and income generally. One expectation, which is the subject of my current research, is that the rise of regular and cheap communication would help to ameliorate the negative consequences of this separation, and enable to the children to feel close again to their mothers, and to come better to understand and appreciate their condition.
She also anticipated that they would be influenced by the more egalitarian and modernist forms of gender relations by which the father would take on more domestic roles in recognition of the mother taking on more of the traditionally male role of the breadwinner.
We might expect that this radical chance in actual relationships would change the normative formal order of the family. The reason for this becomes much clearer in terms of the same issue of relationships discovered in Finch and Mason.
Instead of kinship as a process that modernises with modern experiences, what tends to happen instead is that the period of separation simply exacerbates the distinction between the idealized norms represented by mother and child, and their actual relationship, which here is significantly diminished. These norms of mother child relationships are held both individually and collectively. As a result the process if anything reinforces the most conservative and traditional gender ideals about relationships and leads many of these children to concentrate less on the material benefits that accrue to them and more on the sense of abandonment by their mothers.
If anything these families tend to be stigmatized within the Philippines. It is generally assumed that a child growing up without their mother is more likely to be badly behaved and involved in crime and other misdemeanours than a child with the full support of a conventional family.
Children are often taunted about the behaviour of their mothers. There is a lack of support groups and lack of help from fathers a: In a similar fashion Pingol studied how the husbands who are left behind and who take on female associated activities of housecare and childrearing are taunted mercilessly by, for example, female students, for this potential loss of masculinity, and constantly try but fail to persuade their wives to return.
But equally problematic are the views of the children themselves a: In almost every case the children concentrate on the sense that they have been abandoned.
For example, phoning every morning to make sure they are getting ready for school b: Despite all this, the children regard the separation as irrevocable and say they will never again be really close to their mothers. You cannot hug her, kiss her, feel her, everything.
You cannot feel her presence. Its just words you have' a: So increasing the frequency of phone calls can have the opposite to the intended effect. To appreciate this failure of increased mobile phone use we have to note that even mothers who return more frequently are not necessarily thereby regarded as better mothers ibid: By contrast, it is perfectly possible for absent father's to be seen as behaving adequately just by keeping in touch by phone.
Because this more occasional or distant relationship is closer to the normative expectations of fathers. One of the reasons for this failure, is that by going away the mothers also threaten the traditional roles of parents. The fathers feel in danger of being seen as emasculated because their wives are now taking on so much of the traditional male role of bread winner, which is one of the reasons they often refuse to take over some of the female responsibilities for personal and emotional care of the children or turn to excessive drinking Pingol The children also tend to see their mothers as behaving inappropriately and therefore not as real mothers.
This is notwithstanding that the children are well aware of all the material benefits of their mothers being abroad, including often a better house, better schooling and money for such things as clothes and cinema and good food. So quite unlike my evidence from Jamaica, the person who acts as mother is not therefore regarded as one's mother. Her detailed and empathetic account, however, makes clear the contradictions that this situation has given rise to, which often comes across as poignant or indeed tragic.
But from a theoretical perspective what becomes clear is that where relationships in practice tend to be focused on discrepancies between actual and normative models of those relationships, then it is perhaps not surprising that a situation such as this, which exacerbates that distinction, results largely in increased anxiety about the relationship itself, and an overwhelming emphasis upon formal that is normative kinship, rather than the experience of the behaviour of those involved.
In my own study of shopping in north London, similar issues became very evident Miller b. To my surprise I found that generally mothers didn't like shopping with their children by their side.
The reason for this was that shopping was an act of love and care in which women gave considerable time and labour.
They naturally justified this in terms of their deserving and beloved children. The trouble was that when the children themselves came shopping they often got bored, behaved badly and demonstrated that they really didn't care very much about the level of choice their mother was making as an expression of her love for them. In other words it was much easier to fantasise about ones wonderful and fully deserving children when they were not actually with you.
You shopped more for the idealized relationship than the actual child. By studying consumption in London it was evident that the relationship between mother and child develops quite slowly in terms of its balance between this projected and actual behaviour, and which ultimately develops as a more mature and reciprocal relationship Miller This again shows why in the Philippine situation more frequent contact between mother and child by phone may have quite unexpected effects, for example, making the child seem less worthy as the deserving recipient of this abstract ideal of self-sacrifice.
My point is that there seems good evidence that in the Philippines what is striking is how relationships are not fluid and not responsive to the changing conditions of modernity, which have a tendency to reinforce rather than diminish the discrepancy between the normative and the experienced. I hope with that as my foundation I can then ratchet up the ambition of this review to tackle the larger question of what we mean by the term relationship itself.
For this purpose I will attempt two further brief reviews, both wildly over-ambitious for a more formal academic paper. The first asks what various disciplines mean when they use this word relationship, and the second asks what we mean, colloquially when we use the word relationship.
In the conclusion I hope to bring all these together to form a more general approach to relationships. In carrying out this investigation of what the word relationship means, it seemed essential to know if there was some consistency in the way it was used in various literatures. One method would be to trawl through various disciplines that make considerable use of the word relationship to see if one could locate at least some kind of underlying pattern.
What is a Relationship? Kinship as Negotiated Experience
In practice this means merely skimming the surface of these vast literatures which tend to be specific to a wide range of academic disciplines. Having discussed anthropology I now turn to two examples, philosophy and psychology.
To start from the top, as it were, with philosophy. On the one hand there is a long tradition of structuralist philosophy about the nature of the relation, which is not necessarily about relationships. Essentially it says in many different ways the same thing. Which is that entities do not exist in their own right, but are constituted by the totality of the relationships they possess with other entities.
A more useful alternative seemed to be the philosophical literature on specific kinds of relationships, such as lovers, family and friendship. To take the last as an example, Aristotle makes the issue of friendship central to his Nichomachian Ethics referring backwards to some Socratic dialogues, and the issue is taken up later in the classical literature by Cicero Each classical author has their own specific goals, Socrates gave more time to eros, while Cicero is more interested in the political dimension of friendship.
Taken as a group, however, what you find is a philosophical concern emerging during the classical period with friendship as an ideal state, and problems where this ideal state contradicts others, such as the obligations of the individual to the state or to oneself. This is summarised by Panglefor an anthropological perspective see Bell and Coleman Eds. Moving to later historical traditions, the same is largely true of the extensive religious literature that concerns itself both with the moral foundation of one's relationship to other persons and thence to the divine.
Writers such as Kierkegaard in the Christian tradition and Buber or Levinas in the Jewish tradition are again largely concerned with the ideals encapsulated by the term relationship. They differ from the classical assumption about the primary good as being that which applies to the self. So, for example, Aristotle is clear that the selflessness of family relationships such as parents to children are based on the perception that they represent another self, or extended self.
By contrast, later works influenced by Christianity, such as Kierkegaard, repudiate this in favour of a selfless love of others, found in many more theological works, or as in Montaigne's Essay on Friendship a transcendent value in the relationship itself Pangle Friendship is less prominent in more contemporary philosophy, but does feature. Sartre, for example, constructs a Marxist inspired investigation of how individuals may establish relationships to a larger group.
The overriding concern is still largely with the relationship as embodiment and expressive of an ideal. In short most philosophical writings are basically concerned, not to describe everyday relationships, but to create a normative base for discussing what relationships ideally should be. The disciplines with the most extensive literatures on relationships are psychology and psychoanalysis. I find both of these problematic, but there is only space here to give a brief illustration of each.
The academic psychological literature seems to me dominated by attempts to construct a science of relationships, defining the component parts of a relationship in universalistic terms. To take a paper extracted for nothing more than typicality, Moss and Schwebel try to locate the meaning of one element, intimacy within a particular category of relationships, the romantic.
Searching the psychology literature they find 61 definitions of intimacy as an aspect of relationships which they try and define in multidimensional as opposed to operational genres etc.
They then bravely march on to try and define what we mean by romantic, and then indeed love. A typical example of their definitions follows Hinde I would suggest that the only thing to emerge clearly from such studies is a measurement of consistency of terminology as used by psychologists.Lara Croft Tomb Raider: Pure Fantasy or Feminist Trailblazer?
For myself, as a qualitative and relativist academic, such papers show two things. First, that trying to define relationships by some component aspect such as intimacy will just lead us around in tautological circles, and second that semantic definition with its implied universals is only of limited value. More generally though the concern in psychology and psychoanalysis is not with definition but once again with normative issues.
To take just one example. For other reasons I have been undertaking a critical analysis of the work and impact of the psychoanalyst John Bowbly e.
Basic logic — relationships between statements — converses and contrapositives | Gowers's Weblog
Most psychologists and analysts are drawn into the practice of relationships in order to deal with the consequences of failed relationships - usually seen as pathological, inappropriate, or debilitating. This is because their main task is to help address such problems.
So it is not surprising that in general one tends to find an emphasis again on two ends of the spectrum. On the one hand an ideal of how relationships ought to be - such as the normative concept of the secure base, and on the other hand, the pathologies of relationships and how one helps people overcome or extricate themselves from these.
There is certainly a strong sense that relationships matter to people but the emphasis tends to be on how they relate to the needs of those people.
In summary the use of the term relationship in philosophy, psychology and psychoanalysis is by and large not directed to descriptions of relationships as part of day to day life, but are largely normative.
Social science used to concentrate more on the descriptive aspects of relationships, but recently they have been transformed by influences that incorporate an explicit moral or judgemental base. For example, it is not surprising that the extensive impact of feminist social science brings such disciplines closer to psychology as the main interest turns towards exposing and addressing what might be called the pathologies of the extant.
But there is a further consideration here. My initial concern was with how the word relationship was used. But one cannot examine the work of Bowlby, for example, without starting to become rather more concerned with the influence and consequence of that usage.
Bowlby clearly had a considerable impact through various forms of popular media on what mothers thought they were supposed to do as mothers - what a true mother is supposed to be like Riley Similarly with influences such as feminism we start to see that these academic literatures may play a major role in creating the normative formal expectations that people seem to have in their daily lives about how a relationship is supposed to be. The mediation between the academic literature and the everyday comes increasingly through popular media, which constantly inculcates such moral and idealized models of relationships.
Take, for example, television. Many countries relay what have become the classic US sitcoms as part of the daily fare of television over the last few decades, whether the Cosby Show, Rosanne, Malcolm in the Middle or cartoons such as the Simpsons.
All of these are set in family situations. All of them share a basic message which is that although the actual persons may be commonly dysfunctional, difficult and wrong, there is an underlying warmth and compassion that is based around a shared ideology about how, in the end, there is love and support based around the idealized normative roles expected of family relationships.
We are used to thinking about the normative as a discipline in Foucault's sense, mostly with respect to more formal institutionalised orders. For example I might have considered the work of Carol Smart and others e. Smart and Neale on how law acts as a similar source of normativity. But this idea of discipline is better appreciated through the constant flow between institutionalised orders such as law, popular media such as family sit-coms, and academic fashions such as psychoanalytical views on mothering, all of which seem to constantly influence each other.
Taken together it is not at all hard to explain why there remains such a consistent and normative position on formal relationships, in places as diffused and diverse as contemporary London, not just with respect to kin, but also relationships such as friendship, with strong normative expectations of each category of relationship.
Not what academics or various disciplines mean by the word but what it implies in daily usage in a place such as London where I live and work. Although there may be as many colloquial meanings of this term relationship as there are academic meanings, I think there is a dominant usage at present in everyday conversation. Today the word relationship is used increasingly as a kind of euphemism. If you ask a person whether they are in a relationship, it commonly tends to mean whether or not they are having, at least periodic, sex.
If this is used as a working definition of the term relationship, then we might ask what might be the consequence of this colloquial definition for what one might call colloquial practice, that is that actual variety of contemporary relationships. Discussing people's relationships is what I spend a good deal of my time doing when engaged in fieldwork, and at least in contemporary London I find that many people do seem prepared to ditch almost any kind of rule book or traditional expectations in favour of both creative and diverse practices.
To illustrate this I just want to list some of the varieties of relationships that I ended up listening to, sympathising with or gossiping about in the two weeks prior to writing this text. One was a couple who had been together for ten years where the man told his partner the relationship was over, has refused to give any reason except to confirm that he was not in another relationship.
But because they have a flat together and both are skint they have continued to co-occupy this flat for six months in this state of non-relationship. In another case a woman can't decide whether a relationship of four years is actually over even though she has told the man in question it is, mainly because, as a thirty year old, she just can't stand the idea of the sheer effort involved in finding a new relationship.
Another woman shares a flat with a man of her age who is a very old friend. They are both straight, but she is quite certain they will never sleep together and claims they don't fancy each other. Yet she tells me she still feels guilty when she goes out with another man and neither tells the other about their, as it were, real relationships. In that same week I also discussed a so called open relationship, and a largely internet based relationship.
Yet there are also generalisations. For example, I seem to talk to countless English men and women who admit to their problems in finding and having relationships, and in particular the problem of telling the potential partners what they are thinking.
This may be and they may be extraordinary liberal at one level, but they remain in these conversations just as incapacitated by a certain English anxiety as in the film Brief Encounter.
Its not that I was studying relationships per. All this information came as the by product of two research projects; one on how material culture helps people deal with the loss of relationships, and secondly some new fieldwork on the study of denim blue jeans. The most relevant materials, at least from the first project, seem to amount to an ethnography of dumping and being dumped. So at one level the degree to which the term relationship has become colloquially a referent for sex, is perhaps an understandable simplification at a time when it is really hard to know what consistency the semantics of the term relationship might even aspire to given the diversity of practice.
This conclusion seems to hark back to the writings of Finch and Mason who were also evidently impressed by the diversity and complexity of the contemporary family. I am impressed by the even greater complexity and diversity of contemporary relationships. In addition most observers of London life today emphasise the increasing importance of friendship as well as kinship and relationships defined in terms of sexual activity. The various contributors to Bell and Coleman show that friendship itself is varied in ethnographic encounters.
Most of the contributions contest the basic opposition between a specific Western form based on an autonomous self free to spontaneously gift friendship in an affective bond, as against a much more constrained self within a kinship dominated society. So again we have a similar range of practices. My concern here is with examples taken from specifically English contexts, which seems reasonable in the first instance since it is the English word relationship I am focusing upon. I would need others to comment upon the analogies and levels of generality that apply to other languages.
Finch and Mason used this evidence for diversity and complexity to support and integrate the contemporary anthropological approach to kinship as process. It was never my intention in this paper to repudiate or indeed detract from that contribution.
But I want to keep a balance between this consideration of the colloquial use of the term and the academic use of the term which took us in the opposite direction, towards firming up the idea of formal and normative relationships. I would argue that evidence for complexity and diversity does not preclude an equal and abiding emphasis upon normativity and formal ideals.
Consider, for example, the case of friendship as discussed by philosophers. When researching friendship in London there are still clear normative ideals of trust and reciprocity, even if they don't look much like the ideal types of Aristotle or Cicero. Failure to accord with these ideals may sometimes lead to a still greater sense of betrayal than failures of kin or even lovers. Similarly there are endless repetitions and reflections about whether, for example, one should first find a man who would make a good father and then fall in love with him, or have to wait till you fall in love first.
As well as a powerful normative dialogue about the state of being in love itself, which contrary to much modern sociology seems experienced more as a loss of agency than its expression. So somehow we have to contend with the simultaneous existence, even extension, of both of these trends, towards diversity and towards normative formality. I can see now, that this will have to await another paper. The statement claims that a certain inequality holds for every positive number.
But when In that argument, we started with the assumption in other words, we assumed that and ended up proving in other words, we proved that there is some positive number that is not greater than.
What makes it easier to prove the contrapositive in the cases when it is indeed easier? Instead, let me offer some stylistic advice, which is that you should always start by trying to prove a statement in the obvious direct way, turning to the contrapositive if i you get stuck and ii you can see why you will be less stuck if you try to prove the contrapositive.
We would have started trying to prove the statement directly. Hmm … but what number do I choose? At that point, feeling stuck, we wonder whether starting with the assumption that might help.
And we see that it does, since it provides us with a positive real number, namely the difference between and. So when we decide to try to prove the contrapositive instead, we are not doing so merely because we are stuck — there are plenty of times when we get stuck where turning to the contrapositive is clearly of no help whatsoever — but for the additional reason that gives us something that we needed in order to make progress.
There are two sorts of proof that make use of the negation of the conclusion. That is, you prove For every Another type of proof is this.