Metaphysics could be defined as the public expression (i.e. in language or other symbols) of an understanding of the most fundamental nature of reality.
This means that metaphysics is the most fundamental, basic, deepest of all discourses - but also that there may, in principle, be a deeper level below metaphysics, i.e. the assumptions of pure consciousness and the pure thought; that of which 'consciousness is conscious'!
Such might be expressed by analogy in a (metaphysical!) model; that we are living beings that have a kind of ultimate 'life' (with motivations) which Just Is; and this being also necessarily includes a (very variable) degree of consciousness of itself.
But the evaluation of our own metaphysics by (as Bonald says) 'not conflicting with experience', doesn't happen often; because metaphysics shapes what counts as experience and how we interpret it; such that apparent 'conflicts of metaphysics with experience' tend to be dealt with by denying or distorting the reality of experience - not vice versa.
(This is why and how people can believe metaphysical assertions that appear to be conflicting with experienced reality; such as the mandatory current assumptions that there is 'no such thing' as race, and men can really be turned into women.)
And the criterion of 'internal checks' to ensure that a metaphysics must be coherent with itself, while true, depends upon another set of metaphysical assumptions as to 'what counts as coherent'; plus both the ability and the motivation to carry out these checks with sustained concentration and rigour. Yet it seems that neither the ability nor the rigour for such checking are very common.
For such reasons; I would emphasize that in practice the motivation to embark on metaphysical analysis probably has different roots than the detection of incoherence.
Insofar as we can purely (without translation into words) be conscious of our own being, then we can become aware of a discrepancy between this inner awareness, and the public expression and discourse which is metaphysics.
This is a conflict between our innermost understanding of reality, and the way we talk or think about ultimate reality.
However, I think this is primarily 'negatively' experienced as a kind of 'existential uneasiness', a nagging dissatisfaction, rather than anything as exact as a comparison between two conflicting descriptions. That is we are negatively aware of what is Not working - hence not-true, rather than of what is true.
Perhaps a personal example will help. Up until the middle 2000s I had a metaphysical description of reality that ruled-out any possibility of a person's soul or spirit surviving after biological death. The furthest this would take me towards 'life after death' was a quasi-biological notion that the essence of a person's nature might be transmitted genetically to descendants...
So that it might be observed that a grandmother was 'reborn' in her grand-daughter - in that the grand-daughter was essentially the same nature as her grandmother. But that this genetic inheritance was Not Mendelian - so that such sameness of nature could skip several or many generations and appear in rather remote relatives.
Another (fictional) example would be Tolkien's idea that the Numenorean nature - with its special wisdom and elvish/ magical aspects - 'ran true ' in Aragorn (and, to a somewhat lesser degree; in Denethor and Faramir) despite many intervening generations in which this was not the case.
I still regard the above as broadly true; but I still experienced a sense of dishonesty whenever I asserted (mostly to myself) that there was no survival of a particular Man's soul or spirit after death. I became aware that - at this deepest and wordless level - I actually believed that personal survival actually happened, in some way.
In other words; I became aware that (at this deepest level) I apparently assumed that at least some people who had died biologically, were still alive in some way.
I also became aware that I - again deep down and without being put into words - apparently regarded the universe as purposive, not 'random'; and that the universe had preferences about me and what I thought, said and did.
Why, then, did I become negatively aware of such (seemingly) life-long assumptions at this particular point in my life?
I think it was related to the public/ social collapse of my previous metaphysics which was rooted in science and scholarship, and in particular the way that science and scholarship had all-but abandoned a belief in real truth.
Of course, this abandonment of truth became apparent in the 1960s and was gaining ground rapidly through the 1980s; but for a while I assumed that this was just a societal 'blip'; and that it would soon become normal again for scientists and academics to believe that there was a real truth, and that it was their duty to seek and speak this truth.
In trying to justify such assumptions to my 'colleagues', and to myself; I became aware of this serious mismatch between my innermost assumptions and awareness of them; and the public discourse into which I had formulated what was supposedly my ultimate metaphysics.
This eventually led to my conversion to Christianity, and later to a similarly-motivated rejection of the standard/ classical/ traditional public discourse of metaphysics that was used to explain Christianity.
The point I wish to make here is that events in the public and social world can bring-metaphysics-to-the-surface; where some kind of existential and chronic dissatisfaction and unease may become evident.
Such unease may provide a strong motivation to embark on the difficult task of metaphysical self-examination - in search of a way of alleviating this unpleasant insecurity at the heart of one's sense of being.
And, in principle, I think this kind of motivation is sufficient for anybody to escape a metaphysics that is causing such feelings.
To take a step further back; I would suggest that God (as creator) is behind the situations that tend to lead to awareness of dissatisfaction and unease; and the Holy Ghost is behind such feelings of existential unease - and this is a very fundamental way in which God and the Holy Ghost guide us through this mortal life.
And, although metaphysics may seem terribly difficult (because so abstract) I think that anybody can - if motivated to address this feeling, reach a basis of positive deep metaphysical assumptions that is sufficient for his salvation and theosis.
All systems of metaphysics will ultimately be wrong; to the extent that we cannot capture in explicit language the innate reality of our true selves; but several possible metaphysical 'systems' (some of them simple enough for a child to hold) will work well-enough for the divine and creative, yet temporary, purposes of this mortal life.
Therefore, we may at any time become negatively aware that our explicit metaphysical system is 'not working' well-enough. But we can (by personal effort and with divine help) always find something positively better-enough sufficiently to resolve the unease that we are motivated and guided enough to reach salvation (resurrection to eternal Heavenly life) and to learn from our experiences of mortal life (i.e. theosis).
In sum; once identified, negative dissatisfaction will be helped to positive motivations.
And this, everyone can know - in accordance with his nature and capacities - by means of the guidance provided (directly and to each individual): by God and the Holy Ghost.
NOTE ADDED: It strikes me that the 'ultimate' pure consciousness of life in the above scheme is able to account for the fact that atheists (of which I was one for most of my life) are able honestly and indignantly to claim that they believe in truth and objective morality and beauty:
Metaphysics is the most fundamental, basic, deepest of all discourses - but also that there may, in principle, be a deeper level below metaphysics, i.e. the assumptions of pure consciousness and the pure thought; that of which 'consciousness is conscious'! Such might be expressed by analogy in a (metaphysical!) model; that we are living beings that have a kind of ultimate 'life' (with motivations) which Just Is; and this being also necessarily includes a (very variable) degree of consciousness of itself.
What is happening is that the atheist is introspectively aware of his own belief in a purposeful and meaningful universe, and the reality of truth/ beauty/ virtue, at the most fundamental level of pure consciousness; but is not aware that such deeper-than-metaphysical assumptions are in stark contradiction to his explicit, expressed-in-language metaphysical discourse.
To be aware of pure consciousness, and then to be aware of one's own metaphysical model of reality, are two different experiences; and the analytic comparison of the coherence of these two experiences is a third thing.
Not many people have (apparently) done this third thing, and actually made this analytic comparison between metaphysical discourse and wordless intuition - and so they are not aware that their inmost intuition are actually in stark and ineradicable conflict with their expressed metaphysics.
Once the comparison has been made; then something will 'have to give'.
Either the metaphysics must be brought into harmony with intuition; or else some additional metaphysical assumption (or obfuscation) will need to be inserted between metaphysics and intuition - to bridge the gap.
(Such obfuscations include 'it's a mystery', 'the human mind cannot comprehend this' and the introduction of reason-stunning abstractions and paradoxes such as infinitudes and assumptions of timelessness.)
