sandygautam

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Sandeep Gautam is a psychology and cognitive neuroscience enthusiast, whose basic grounding is in computer science.

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The ABCD of Personality Structure

Regular readers of The Mouse Trap would be aware of my ABCD model of psychology whereby all psychological phenomena are explained in terms of Affective, Behavioral, Cognitive and Dynamic/Desire dimensions.

Personality Traits from SignalPatterns.com

Personality Traits from SignalPatterns.com (Photo credit: Wikipedia)

The affective dimensions is also related to sensory processes; the behavioral dimension to motor processes; the cognitive dimension to associative processes and the desire/dynamic/motives dimension to social processes.

We are increasingly focusing on brain as a means to study psychological phenomena and thus four major divisions of neurosciences are affective neurosciences, behavioral neurosciences, social neurosciences and cognitive neurosciences.

Now, I have written extensively about personality, especially in relation to emotions, and have written a series of posts about the structure of personality traits and the underlying basic emotions. I have also tangentially touched upon or used ABCD and the fundamental four model while coming up with those previous posts; but today’s post is exclusively focused on the ABCD model and its utility for delineating personality traits.

Before we move onto personality traits, lets refresh our knowledge of brain structure. As per a controversial theory of brain structure, by Paul McLean, brain can be divided into a reptilian brain,a paleomammalian brain/ limbic brain and a neomammilain brain/neocortex; for our purpose the details of the model need not be true. However, one thing that McLean postulated was that older brain regions are in control of newer regions and if newer brain regions malfunction/ do not exercise control the behavior due to older system may get activated. Hughlings Jackson had surmised the same earlier and this is the part I will be focusing on.

Consider an earlier brain part that controls movement; (this may be mostly instinctual responding or impulsive initiation) ; a later brain part may inhibit and lead to better response/ proactive action that is well considered/ planned. I will call these two instances bottom-up effects and top-down effects on movement respectively.

With this in mind lets start a deeper look at the ABCD.

  1. Affective/sensory: This would be related to detecting unexpected stimuli or looking out for expected stimuli.
    1. The bottom up process of detecting incoming stimuli is enhanced by level of arousal. High arousal leads to better detection and low arousal to lesser detection; people may differ in their natural arousal levels and I guess you know where I am going with this-the introversion- eXtraversion dimension.
    2. The top down process of looking out for (potentially harmful) stimuli may lead to worry or anxiety. High Anxiety may help in vigilant detection, while lower anxiety to lapses in detecting harmful stimuli; the natural variation in this may be the trait Emotionally stable-Neuroticism( Emotionality). Anxiety remember was one of the dimensions discovered by Gray as relevant to personality.
  2. Behavioral/Motor:   This would be related to initiating action or responding to stimuli.
    1. The bottom up process here would lead to Impulsivity , another dimension elaborated on by Gray. The personality trait relevant here would be Impulsive Sensation Seeking as defined by Zuckerman.
    2. The top down process here would lead to Inhibition; when that process does not work, the low pole would be disinhibition (which is distinct from impulsivity). In FFM/HEXACO , this trait may be labeled as Conscientiousness and is related to strength of self-regulation.
  3. Drives/Social:  This would be related to interactions with others and the motives behind them – either to help others or the reciprocate a previous help.
    1. The bottom up process here is reactive reciprocation; or aggression in case of deception/defection by the other. The one end of this pole will be characterized by Aggression and hostility while the other pole by nice and reciprocal behavior and this leads us right on to Agreeableness dimension.
    2. The top down or expectation driven process here would be trusting and helping others on the one pole (in hope of reciprocation) and manipulating, hurting or exploiting people on the other. this naturally leads us to Honesty-humility dimension of HEXACO and the opposite pole that I believe is the dark tetrad of sadism, Machiavellianism, narcissism and sadism.
  4. Cognitive/ associative : This would be related to the tendency to make and use broad vis–vis narrow associations while doing information processing.
    1. The bottom up process here could be related to distractibility vis-a-vis focus. Some people may be easily distracted/ form loose associations and this may lead to Openness to experience in them; others may be more closed to new information. I think of this as the encoding process.
    2. The top down process here could be related to imagining novel associations between concepts etc. I would say this is a new dimension called Imagination dimension (Scott Barry Kaufman would be happy to hear:-)) .  At one end would be daydreamers and creative folks , at the other end more pragmatic/ reality oriented folks. I relate this to retrieval process. As this trait may still be evolving, we see psychosis related to this- imaginations/ top down processes overpowering reality orientation. this may also explain the association of creativity and mental illness.

 

I am happy with this personality structure organization with eight traits, instead of the usual five, that I have come up with. It has a solid theoretical rationale and a lot of thinking has gone into it; of course empirical work will prove whether its true or not and whether it stands the test of time!!

The Evolution of Altruism And Its Relationship to Personality

Altruism, put simply, is helping others or cooperating with others, even if it is costly to self. Of course, something like that cannot evolve, unless there are benefits too, associated with such acts of apparent selflessness.

Evolutionary theory mandates that there be some genetic payoffs in terms of either inclusive fitness or future benefits to self (reciprocity) for any kind of altruism/ cooperation to evolve.

I recommend reading Wikipedia articles on reciprocity, kin selection, and evolution of cooperation if they are not familiar to you or you need a refresher.

Cooperation, to start with, can evolve based on three forms of reciprocity: direct, indirect and network. All are based on the fact that there re repeated interactions between group of people- dyads, triads or many more. Reciprocity can typically be measured in the lab using the repeated Dictator/ Trust game.

Direct reciprocity was proposed by Robert Trivers as a mechanism for the evolution of cooperation. If there are repeated encounters between the same two players in an evolutionary game in which each of them can choose either to “cooperate” or “defect”, then a strategy of mutual cooperation may be favoured even if it pays each player, in the short term, to defect when the other cooperates.

Here, in direct reciprocity A trusts/helps B and hopes that when time comes B will reciprocate/help A. The top-of-the-mind factor is whether or not to trust somebody and whether or not to reciprocate someone’s trust. Trust and exploitation may be relevant issues here. In the Dictator/ Trust game this trust/exploitation manifests as the amount that is split and given to the other person vs kept with oneself.

In the standard framework of indirect reciprocity, there are randomly chosen pairwise encounters between members of a population; the same two individuals need not meet again. One individual acts as donor, the other as recipient. The donor can decide whether or not to cooperate. The interaction is observed by a subset of the population who might inform others. Reputation allows evolution of cooperation by indirect reciprocity.

This is partially correct that reputation for being trustworthy helps in indirect reciprocity; however that is only true for the downstream version; for the upstream version feelings of gratitude/happiness/awe/elevation in persons receiving the help/ witnessing the act also lead to more pro-social behavior by those receiving help/ witnessing. Thus feelings of gratitude/ awe/elevation mediate this kind of upstream indirect reciprocity. See below for upstream and downstream variants.

Individual acts of indirect reciprocity may be classified as “upstream” or “downstream”:

  • Upstream reciprocity occurs when an act of altruism causes the recipient to perform a later act of altruism in the benefit of a third party. In other words: A helps B, which then motivates B to help C.

  • Downstream reciprocity occurs when the performer of an act of altruism is more likely to be the recipient of a later act of altruism. In other words: A helps B, making it more likely that C will later help A.

Before touching upon network reciprocity, I will take a quick detour about kin selection. I believe kin selection or inclusive fitness is also a type of reciprocity (that between related individuals sharing genes) and may be rechristened genetic reciprocity. After all if A is likely to help B because they share x % of genes, the reverse is equally true and applicable. And of course this is mediated by emotional attachment to the kid/kin.

As per one definition of kin selection:

A biological theory stating that a gene that causes an organism to exhibit behavior detrimental to its survival will increase in frequency in a population if that behavior benefits the organism’s relatives, which will pass the gene on to subsequent generations.

If I slightly change words form above definition, I can now define a neighbor selection process as a cultural theory stating that a meme that causes an organism to exhibit behavior detrimental to its survival will increase in frequency in a population if that behavior benefits the organism’s neighbors, which will pass the meme on to subsequent neighbors.

We are now ready to look at network reciprocity:

Real populations are not well mixed, but have spatial structures or social networks which imply that some individuals interact more often than others. One approach of capturing this effect is evolutionary graph theory, in which individuals occupy the vertices of a graph. The edges determine who interacts with whom. If a cooperator pays a cost, c, for each neighbor to receive a benefit, b, and defectors have no costs, and their neighbors receive no benefits, network reciprocity can favor cooperation.

Basically, what I understand from the above is that if you help your neighbors sometimes such that the cost is not too high but benefits to neighbors are high and if  cost to benefit compares favorably with average number of neighbors/ neighborly interactions you have, then in the long run you will benefit and this form of cooperation can evolve.  To me the effects are mediated by the number of neighbors or sociability of a person.

Of course, even if you have all these mechanisms in place, cooperation may not evolve, as you may have free-riders. One important mechanism that has evolved to keep the free-riders in check is that of punishment. And once punishment is part of the picture you don’t even need repeated interactions, one-off games may be sufficient. I call this phenomenon Direct Punishment. One way it has been measured is with the Ultimatum game.

In the Ultimatum game, the second player can inflict costly punishment on first player by refusing to accept the division; this costly punishment is dyadic in nature and the aggression/hostility/vengefulness of the second player ensures that cooperation in even one-off encounters happens.

Basically instead of trusting and helping B, A starts by exploiting B and B retaliates by punishing A at cost to oneself.

Of course one can then surmise that there can be a phenomena of indirect punishment. This again may happen in two ways:

  1. Indirect punishment upstream: A is exploitative in nature; A exploits B; B punishes A, who then feels guilt/ gets reformed and stops exploiting C or even starts helping C.
  2. Indirect punishment downstream: A is exploitative in nature: A exploits B, B punishes A; B gets a reputation for being tough/competent and stops getting exploited by others say C or C may now even help B.

The Indirect reciprocity effects can be seen in Public goods/ trust game.

I will now take a detour and introduce the HEXACO model of personality which set me thinking about this in the first place.

HEXACO is an alternate personality model that is based on the same principles as the Big Five/FFM; i.e. it uses factor analysis of lexical terms in various languages to arrive at major personality traits.

The six factors are generally named Honesty-Humility (H), Emotionality (E), Extraversion (X), Agreeableness (A), Conscientiousness (C), and Openness to Experience (O). The personality-descriptive adjectives that typically belong to these six groups are as follows:

  • Honesty-Humility (H): sincere, honest, faithful, loyal, modest/unassuming versus sly, deceitful, greedy, pretentious, hypocritical, boastful, pompous

  • Emotionality (E): emotional, oversensitive, sentimental, fearful, anxious, vulnerable versus brave, tough, independent, self-assured, stable

  • Extraversion (X): outgoing, lively, extraverted, sociable, talkative, cheerful, active versus shy, passive, withdrawn, introverted, quiet, reserved

  • Agreeableness (A): patient, tolerant, peaceful, mild, agreeable, lenient, gentle versus ill-tempered, quarrelsome, stubborn, choleric

  • Conscientiousness (C): organized, disciplined, diligent, careful, thorough, precise versus sloppy, negligent, reckless, lazy, irresponsible, absent-minded

  • Openness to Experience (O): intellectual, creative, unconventional, innovative, ironic versus shallow, unimaginative, conventional

The factor H is a new factor not present in Big Five/FFM. The E though looking similar to N of big Five, is conceptually different; it no longer contains anger/hostility which are instead present in HEXACO A. similalrly there are important differences between HEXACO A and Big Five A. the other 3, C, O and X (extarversion) are similarly conceptualized and defined in both systems and have same loadings when tested together.

Ashton and Lee, the proponents of the HEXACO model, have themselves related evolution of altruism to these traits [pdf] and I am building on their work.

Basically as per them,

To begin, we have proposed that the Honesty- Humility and Agreeableness factors represent two complementary aspects of the construct of reciprocal altruism (Trivers, 1971). Honesty-Humility represents the tendency to be fair and genuine in dealing with others, in the sense of cooperating with others even when one might exploit them without suffering retaliation. Agreeableness represents the tendency to be forgiving and tolerant of others, in the sense of cooperating with others even when one might be suffering exploitation by them. (For a discussion of two broadly similar, although not identical, constructs, see Perugini, Gallucci, Presaghi, & Ercolani, 2003.) Presumably, high levels of Honesty- Humility are associated with decreased opportunities for personal gains from the exploitation of others but also with decreased risks of losses from withdrawal of cooperation by others. In a similar manner, high levels of Agreeableness are associated with increased opportunities for personal gains from long-run reciprocal cooperation with others, as well as with increased risks of losses from exploitation by others. (Note that we use the term altruism in terms of a dimension of altruistic versus antagonistic tendency, which involves both a willingness to help or provide benefits to others and an unwillingness to harm or impose costs on others.)
In addition, we have proposed that Emotionality represents tendencies relevant to the construct of kin altruism (Hamilton, 1964), including not only empathic concern and emotional attachment toward close others (who tend to be one’s kin) but also the harm-avoidant and help-seeking behaviors that are associated with investment in kin (see also Lee & Ashton, 2004). Presumably, high levels of Emotionality are associated with increased likelihood of personal and kin survival, as well as with decreased opportunities for gains that are often associated with risks to personal and kin survival.
To me, this looks like equating direct reciprocity with H and direct punishment with A.  With this in mind I now list the personality trait (HEXACO)/ evolution of altruism linkages.
1. Kin Selection/ Genetic Reciprocity : mediated by emotional attachments etc and related to Emotioanlity.
2. Neighbor Selection / Network Reciprocity: mediated by sociability and related to sociability aspects of Extrarversion.
3. Direct Reciprocity : mediated by trusting others and being honest and related to Honesty-humility.
4. Direct Punishment:  mediated by punishing others and being aggressive/ hostile when needed and related to Agreeablness.
5. Indirect Reciprocity upstream:  mediated by feelings of gratitude/ awe/ elevation and possibly related to Openness to Experience
6. Indirect Punishment upstream: mediated by feelings of guilt/responsibility and related to Conscientiousness.
 7. Indirect Reciprocity downstream: mediated by signaling and being trustworthy; need a new personality dimension for this.
8. Indirect Punishment downstream: mediated by signaling and being competent/ tough and possibly related to Surgency dimension of Extarversion.
I am more and more convinced, looking at the above model that we evolved to be cooperative/ altruistic rather than otherwise.

The Four Sub-Types of ADHD

Recently, I wrote a post about the four neural sub-types of depression. That classification was based on resting stage fMRI comparing depressive patients with controls; I hope someone does similar studies for other psychiatric conditions.

English: Symptoms of ADHD described by the lit...

English: Symptoms of ADHD described by the literature (Photo credit: Wikipedia)

The current post is an attempt to delineate what may come out in such a study if done for ADHD. I will be focusing on ADHD as it manifests in children, adolescents as well as adults.

I will be mostly relying on factor analytical studies of ADHD that have typically revealed 3 to 4 underlying factors.

ADHD has typically been diagnosed by looking at symptoms from inattentive or hyperactive-impulsive domains. You can find the DSM-5 criteria here. And its sub-types are combined presentation, predominantly inattentive presentation and predominantly hyperactive-impulsive presentation.

As per some studies, a majority (as much as 90 %) of ADHD subjects have inattentive symptoms while a few have hyperactive-impulsive symptoms. This is analogous to the depression findings that predominately depressive patients have a core pathology marked by low mood ; and subtypes marked by say anergia, anhedonia and anxiety.

However, factor analytical studies have presented a more nuanced picture. As per this study [pdf] there are four underlying factors of ADHD.

  1. Inattentive/ cognitive problems
  2. Hyperactivity/restlessness
  3. Impulsivity/ emotional lability
  4. Problems with self-concept

The first there factors are well established and quite apparent. To impulsivity description I may just add sensation-seeking too. The problems with self concept is something like low self-confidence/ self esteem, possibly due to continued underachievement and problems at school/ work. I would like to add another dimension to this fourth problems with self concept factor – that of disruptive/ defiant behavior possibly due to self-concept issues.

And I am sure in future, in future, when brain basis and neutral subtypes are more easily available for ADHD, we will find these four subtypes.

Before we leave, its important to note that ADHD lies on a continuum and its a matter of degree than a matter of kind .

Also, ADHD confers benefits too like enhanced creativity and some work has shown that creativity can be mistaken for ADHD in kids.

The above four sub-types may then be classified by their positive poles too:

  1. Daydreaming/broadened attention
  2. High energy and enthusiasm
  3. risk-taking and emotional sensitivity
  4. independent and idiosyncratic

All the above are also traits associated with the creative person. ADHD & creativity are indeed very closely related and its time we stopped seeing differences like ADHD in purely pathological terms.

Do Cultures Have Personality?

When people talk about culture and personality, the normal top-of-the-mind concern is whether cultures affect personality and if so to what extent?

English: An Inglehart-Welzel Cultural Map of t...

English: An Inglehart-Welzel Cultural Map of the World: World Secular-Rational and Self Expression Values as a map of world cultures based on World Values Survey data. Svenska: En Världskulturkarta av Inglehart-Welzel typ. (Photo credit: Wikipedia)

Personality, or enduring individual differences in thinking, feeling, motivations and behavior among have been shown to be partly heritable and under genetic effect; they are partly shaped by the culture and early life experiences also.

However, this post is not about the culture’s effect on personality; rather just like individuals differ from each other on certain universal traits (say the Big Five) and this individual difference is what typically comes to mind when one talks of personality of an individual (i.e. so-and-so is extarverted as compared to population mean etc) , so too cultures show differences from each other and one may conceive of these differences as enduring and differentiating aspect of that culture vis-a-vis other cultures, in essence its personality.

A name that is quite well-known in this context is that of Geert Hofstede. He, initially, in the 1970s, analyzed values data from IBM employees, from over 50 countries to arrive at four dimensions on which the cultures differed. He later extended this work and analyzed data from World Values Survey and work by him and others later led to addition of two more dimensions. The six dimensions, on which cultures differ, in his own words [pdf] are:

1. Power Distance, related to the different solutions to the basic problem of human inequality;
2. Uncertainty Avoidance, related to the level of stress in a society in the face of an unknown future;
3. Individualism versus Collectivism, related to the integration of individuals into primary groups;
4. Masculinity versus Femininity, related to the division of emotional roles between women and men;
5. Long Term versus Short Term Orientation, related to the choice of focus for people’s efforts: the future or the present and past.
6. Indulgence versus Restraint, related to the gratification versus control of basic human desires related to enjoying life.

Lets analyze this a bit further.

Power Distance has been defined as the extent to which the less powerful members of organizations and institutions (like the family) accept and expect that power is distributed unequally.

To me it seems all about relationships among people- whether the hierarchical relationships are accepted or resisted. If one could extend an analogy to individual differences in personality, this may be analogous to the trait of Agreeableness in individuals- whether you are kind and nice or aggressive towards others.

Uncertainty Avoidance is not the same as risk avoidance; it deals with a society’s tolerance for ambiguity. It indicates to what extent a culture programs its members to feel either uncomfortable or comfortable in unstructured situations. Unstructured situations are novel, unknown, surprising, and different from usual.

To my mind it is absolutely clear that is a cognitive dimension and analogous to Openness to Experience in individual variation. Both share the underlying theme of being open and exploratory and tolerant of ambiguity.

Individualism on the one side versus its opposite, Collectivism, as a societal, not an individual characteristic, is the degree to which people in a society are integrated into groups. On the individualist side we find cultures in which the ties between individuals are loose: everyone is expected to look after him/herself and his/her immediate family. On the
collectivist side we find cultures in which people from birth onwards are integrated into strong, cohesive in-groups, often extended families (with uncles, aunts and grandparents) that continue protecting them in exchange for unquestioning loyalty, and oppose other ingroups.

To me this looks like an analog of Extraversion-introversion in individuals. One end is quite while the other is quite engaged with outside activities. In cultural terms, one end is characterized by close knit families while the other with more individualistic pursuits.

Masculinity versus its opposite, Femininity, again as a societal, not as an individual characteristic, refers to the distribution of values between the genders which is another fundamental issue for any society, to which a range of solutions can be found.

I cannot find a ready analogue of this in individual differences in personality in terms of the Big Five. In cultural terms this is related to whether gender roles are heavily differentiated (masculine cultures) or less so (feminine cultures).

Values found at this pole (long term orientation) were perseverance, thrift, ordering relationships by status, and having a sense of shame; values at the opposite, short term pole were reciprocating social obligations, respect for tradition, protecting one’s ‘face’, and personal steadiness and stability.

This can be equated easily with the Conscientiousness individual difference, one pole of which is associated with self-control etc.

Indulgence stands for a society that allows relatively free gratification of basic and natural human desires related to enjoying life and having fun. Restraint stands for a society that controls gratification of needs and regulates it by means of strict social norms.

This focus on happiness/ well-being versus constraint and repression of desires may be the analogous of neuroticism and emotional stability, where one end may have repressed desires at individual level while other exhibits more stability.

I know this is a far conjecture, and by no means am I suggesting that if a culture is high in Uncertainty avoidance, the individuals within it will have low openness to experience; the relationship between cultures and personality is more complex than that; but it is a good way to think about cultures that they too have a unique personality and its structure may be on the same lines as individual differences personality.

The Four Neural Sub-Types of Depression

Regular readers of The Mouse Trap will be familiar with my obsession with knowing how nature is carved at its joints or in other words what are the natural categories or basic kinds.

Anhedonia (The Graduate album)

Anhedonia (The Graduate album) (Photo credit: Wikipedia)

This translates into thinking a lot about what are the fundamental drives, basic emotions and personalty traits and what taxonomic system of mental illness is most reflective of underlying fundamental nosological differences.

While synthesizing the work of others, has great value, and one derives many valuable theoretical insights based on such musings; there is nothing better than finding empirical studies that shed some light on such matters.

For example, I have argued that one set of disorders that arise form emotional polarity of fear/interest is Anxiety disorders and Obsession disorders. When fear is disproportional/ inappropriate  to circumstances, it leads to anxiety; when interest is disproportional/ inappropriate it leads to Obsession. Fear and interest though opposed are two separate constructs as per the first tenet of positive psychology that good is not the absence of bad.

Similarly, the set of disorders that arise form sadness/ Joy polarity is depressive disorders and manic disorders. I am deliberately using plural form while defining depressive/ manic disorders as they contain sub-types – as we  will soon see in the case of depression.

Now while depression is characterized by excessive low affect (sadness), one way to conceive Mania is as having excessive energy; the opposite of manic symptoms thus might be conceived of as fatigue or anergia. Anxiety is of course marked by excess anxiety while Obsession is too much interest; a possible opposite of obsession may be anhedonia– a sort of disinterest or apathy.

Now, its common to find depression and anxiety disorders comorbid with each other and just like treating bipolar as well as schizophrenia under one umbrella of psychosis, one may conceivably treat depression/ anxiety / anergia and anhedonia under a common nomenclature- in this case that of depression.

But we are perhaps getting ahead of ourselves. Lets backtrack a bit and go straight to this new study that found four neural subtypes of depression.

Basically, Liston and colleagues, used resting state fMRI to look at the functional connectivity of depressed patients and developed an algorithm to predict who has depression and who does not have in a sample consisting of both depressed patients and healthy controls. They found abnormal functional connectivity in frontostraital and limbic systems in teh depressive patients.

They also used clustering techniques to find that their depressive subset of patients clustered around two dimensions- one of which they called anxiety dimension and the other anhedonia. When one takes into account that there could be 2×2 = 4 combinations of anxiety and anhedoinia they found that their patients neatly clustered in those four quadrants.

If you note in the figure 1f accompanying the article,

  • cluster 1 subjects have low scores on anhedonia and high scores on anxiety
  • cluster 2 subjects have neither anxiety nor anhedonia
  • cluster 3 have high anhedonia but low anxiety
  • cluster 4 have both high anxiety and high anhedonia

The authors note that all subjects had low mood (sadness, hoplessness, helplessness) and that is why they were classified as depressed patients in the first place. The core depressive signature was also associetd with anergia and anhedonia with majority of patients showing these symptoms across all subtypes.

They also found slightly different neural signatures for all the four subtypes. For eg. cluster 1 & 4 characterized by high anxiety had reduced frontoamygdalar connectivity, linking it with fear circuit. Cluster 3 & 4 were associated with hyper connectivity between thalamic and frontostriatal networks and had high anhedonia and psychomotor retardation associated with them. And cluster 1 & 2 had reduced connectivity between anterior cingulate and orbitofrontal coretx involved in reward and incentive salience and guess what they showed anergia or fatigue.

To me it seems apparent that what we are seeing here are different effects of low mood, anxiety, anhedonia and anergia playing out as four clusters.

Cluster 3 I would classify as primarily anehdoina related; cluster 4 as primarily anxiety related; cluster 1 may be thought of as  anergia related and clusetr 2 as pure depression or low mood related.

If my hunches are true we should find similar subdivisions in diagnosed anxiety disorders, obsessive disorders , manic disorders too. Of  course that is an empirical fact to be proved.

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