It may be that Eysenck's personality trait of Psychoticism is the primary dimension of personality in humans - that which underlies and explains (and valuably-reconceptualizes) other personality traits such as Agreeableness, Conscientiousness, Extraversion-Introversion, Schizotypy and Self-esteem.
Here, as a reminder, is a summary of some of the defining characteristics of Psychoticism as they appear in self-reported personality evaluations:
High Psychoticism is in bold font; Low Psychoticism is normal font.
1. Cold - versus warm, charming
2. Aggressive - versus submissive
3. Egocentric - versus follows groups expectations
4. Unempathic - versus sympathetic, feels the emotions of others
5. Tough-minded (i.e. impervious to events) - versus tender-minded, strongly affected by experience
6. Antisocial - versus gregarious, needs other people
7. Impersonal - versus life consists of intense, direct relationships
8. Impulsive (behaviour dominated by current emotions) - versus behaviour dominated by predictions or weaker emotions.
9. Creative - versus applies peer-approved, learned rules and traditions
[Note added 18 July 2013: I don't find the characterization of emotionally-cold to be quite correct. Indeed, it is probably misleading. High Psychoticism is more likely to be interpersonally spontaneous and natural - which could be engaging and pleasant or, in another person, selfish and cruel; while low Pychoticism would be lacking in these qualities - more conventional, polite, careful, 'diplomatic'...]
The underlying distinction here is, I suggest, related to the orientation-of, or domination-of, Short Term Memory (STM)
(STM includes explicit memory, awareness, attention, conscious will and deliberation - our 'self' as we perceive and know it directly.).
High Psychoticism (P) is the orientation of STM toward Long Term Memory (LTM), and the subordination of STM to the associative processes of LTM.
Low Psychoticism is the suppression of this natural state of domination of the STM by the LTM - and instead an 'outward looking' orientation of STM towards the external perceptual (sensory) environment.
So, high P is about inner/ memory worlds, while low P is about outer/ sensory worlds - and the cognitive difference between them relates to the contrasted associative logic of long term and short term memory.
The natural (more evolutionarily ancient) state is high Psychoticism (see second link above about evolution of creative genius) - this is characterized by
1. A dream-like/ psychosis-like mode of highly associative thinking reflective of the functioning of LTM (i.e. high schizotypy, dream/psychosis-like mentation).
This happens because STM (and awareness) is orientated towards memories, and dominated by the way that memories are processed; rather than the external environment.
It is this mode of high Psychoticism thinking which is creative, due to its exceptionally wide field of association/ connection-making; and which - when combined with high intelligence, drive and luck, leads to that rare but vital phenomenon of Genius (see HJ Eysenck's 1995 book Genius).
2. A relatively inner-dominated, hence inward-looking disposition which is seen as being:
a. Low in Agreebleness/ Empathy - because less orientated-towards and concerned-by other people feelings.
b. High in self-esteem - due to autonomy-from, indifference-to, the evaluations of other people.
c. Low in Conscientiousness - since C. is about subordination to an understanding of what 'other people' say is important, instead of what you personally feel to be important.
d. Introverted - because not very interested by other people, hence not reliant upon other people for psychological stimulation, hence likely to be less compulsively sociable.
Introversion may also be seen as a kind of self-sufficiency, autonomy, lack of need for external stimulus - which fits with the above conceptualization of Psychoticism.
(Note: Eysenck, of course, had Introversion as a separate dimension from Psychoticism - but J Philippe Rushton's work on the General Factor Personality (GFP) showed that there is an underlying association between most of the main personality variables. Furthermore, I consider the Extraversion-Introversion dimension to be somewhat ill-formed by the excessive emphasis in questionnaires on social interactions as if these were the primary characteristic of Extraversion - which misses out the important sub-group of Autistic-Extraverts. This idea I am presenting about Psychoticism is therefore, to a considerable extent, a re-framing of Rushton's GFP as the inverse of Psychoticism, but with Psychoticism regarded as primary and high GFP as a more recently, and variously, evolved disposition.)
However, low Psychoticism is the commonest-personality type among the indigenous population in Western and East Asian Societies (especially in East Asia).
The person of low Psychoticism experiences life via Short Term Memory that has become, to a considerable extent, cut-off from (oriented-away from, independent of) the dream- or psychosis-like inner world of LTM; and instead is oreintated to the external environment as revealed from the senses and as evaluated by the explicitly experienced and narrowly 'rational' processes of STM.
The person of low Psychoticism is focused on the surrounding world, the world of vision (especially), and - due to selection pressures - the social world of other people. Hence a person of low Psychoticism is Empathic/ Agreeable (sensitive to the feelings of others), Conscientious and gaining the greatest satisfaction in performing socially-valued tasks, and low in impulsivity in the sense of suppressing actions that derive from unconscious long-term memory associations.
A person of low Psychoticism is extraverted, in the sense that they require strong external (and usually social) inputs in order to maintain arousal.
However, the picture is muddied by 'autistic' extraverts,
who require external stimulus, but of a non-social kind.
(This is in contrast to the low P introvert, whose stimulus comes interacting with the powerful associations deriving from their own LTM.)
A person of low Psychoticism is un-creative, because they perceive reality at 'face value' of whatever comes to them via perception and social norms as analyzed by the relatively simple and limited 'rational' and 'explicit' processing of Short Term Memory.
By contrast, the high Psychoticism person deals has a greater tendency to deploy the much greater capacity system of Long Term Memory - with its vastly greater range of stored information, and the ability to consider associations among these memories, going beyond those of the narrow 'rationality' of STM.
Hence the positive association between high Psychoticism and creativity
So, Psychoticism can be seen as the major general personality trait, underlying many of the other more specific traits for fundamental reasons to do with the nature of cognitive processing.