By "standard", I meant the one most people here use - let's call it Myers' model. There is no standard model, as such. If you are using Jung's, the tertiary is extroverted in nature (or some would say, it doesn't have a specific attitude).
INTP function orders under various schemes:
Myers
Ti/Ne/Si/Fe
Jung
Ti/Ne/S[e]/Fe
Beebe/Berens
Ti/Ne/Si/Fe/Te/Ni/Se/Fi
Thomson
Ti/Ne/Fi/Se/Ni/Te/Si/Fe
You have to state which scheme you are using for "tertiary" to mean anything as the order differs in each. For example, if you are talking about Thomson, I agree Fi is the way to develop the feeling function for INTPs and to reduce the potency of the inferior. If you are talking about Jung, Se is definitely a great stress-reliever for me, plus it pulls me out of myself to engage with the world on its terms, rather than mine, which is exactly what I need. But if you are talking about Beebe, (as you appear to be by stating the tertiary attitude mirrors the dom, despite also claiming Beebe is wrong...), then no, Si doesn't help develop a more rounded personality for INTPs and I don't know anyone who subscribes to this view.
The quote you used is misapplied. It doesn't refer to the tertiary function but to a "third way" in conflict resolution. This third way is more likely to be mediated by the auxiliary function (dom=thesis, inf=antithesis, aux=synthesis) than anything else (in Jung's thought too - as indicated by my previous quote.)
actually isabel myers briggs and katharine myers both thought that jung was saying that tert is in opposite attitude to dom, so what MBTI actually says that INTPs tert is Se, not Si. this is pretty common misconception about MBTI. but there are some authors in MBTI community who see tert being in same attitude as dom, for some reason this opinion has gained more popularity over internetbeings than what MBTI originally said.
from article 'Isabel Briggs Myers and type development' by Katharine Myers:
when it comes to jung, he isnt being too clear about the orientation of tert and there are multiple views on what jung meant, the MBTI view where tert is opposite to dom, the view where aux and tert has no orientation their own, the most common view where tert is same attitude to dom, the view where aux and tert has no orientation without being differentiated and them being able to be differentiated to either E or I, regardless of what dom is, view where dom and aux are in same attitude and tert and inferior are the opposite, the view where tert fluctuates between attitudes. usually when jungians talk about typology, they often make no reference to orientation of tert of aux, for example INTP is introverted thinking with intuition(not extraverted or introverted intuition).
also lenores model doesent say that INTP has Fi tert, she says that dom is Ti, aux Ne, tert Si and inferior Fe and refers to Fi and Se as right-brain alternatives(crows nest functions) and Ni and Te as left-brain alternatives(double agents).
this kinda eliminates your thought about my relation to beebes model, as its just one of many who assign I as tert to introvert types.
also when it comes to developing Si in my personal experiences, realizing the introverted attitude of my S was what allowed me to develop my Fe more. it was the realization of the subjectivity in my sense perceptions that allowed me to re-examine my views towards Ti and basically debunk shit loads of stuff that i had previously thought as simple objective facts and because i thought that they were objective facts, instead of subjective impressions of sensations i couldnt understand what the heck my Fe was doing and actually thought that it was Fi doing that stuff, when it was in reality just Fe guiding my introverted thinking. realizing this i could see more clearly how Fe was guiding my Ti and start guiding my Fe in more conscious ways. also i should mention that the realization about Si, i.e differentiation of it was instantly followed by realization of the correct path towards differentiating Fe as well.
you cant seriously think that the realization(for young INTP) about the subjectivity of his formerly thought "facts" wouldnt make an INTP more well rounded person. imo this realization is crucial in the development of INTP, as it kinda makes the INTP be more aware of the possibility that his logic might not the the ultimate truth of things, but just an theory of things that at least seemingly follows logic. also if an INTP realizes this, it will force him to do more comparison of his ideas to external world before accepting them as very very plausible theories(some might say facts, but i dont really like the word as it refers to something proven and nothing can be proven with 100% accuracy, because i can give counterargument for that by saying that you might be living in a matrix type of world and you would need to prove that and everything no matter how silly things i come up with in order to give 100% proof of the theory, and well, you cant really prove whether you live in matrix or not).
this jung quote that you talk about i assume is this "In order to cushion the impact of the unconscious, an irrational type needs a stronger development of the rational auxiliary function present in consciousness (and vice versa)."
actually this doesent debunk what i just said, you see jung saw both 2nd and 3rd functions as aux. also i dont disagree about the importance to developing 2nd function also in the individuation process. the general consensus is that you first develop dom, then aux, then tert, then inferior and trying to develop inferior straight away will only cause too much confusion for ego and that you need the auxiliary functions(2nd and 3rd) to "soften the blow".
when it comes to the quote i gave, this idea of tertium non datur applies to all conflicts between opposites of conscious and unconscious in jungs model of the psyche. you see the conflict between opposites is between ego and unconscious, dominant function is guided by the ego and it represses its opposite(inferior) to unconscious. by the principle of compensation, the inferior is pushed from the unconscious, but is repressed by the ego, so they need some mediator between the two in order to get over the repression of inferior.
http://www.nyaap.org/jung-lexicon/o said:
Opposites
Psychologically, the ego and the unconscious. (See also compensation, conflict, progression and transcendent function.)
Whatever attitude exists in the conscious mind, and whichever psychological function is dominant, the opposite is in the unconscious. This situation seldom precipitates a crisis in the first half of life. But for older people who reach an impasse, characterized by a one-sided conscious attitude and the blockage of energy, it is necessary to bring to light psychic contents that have been repressed.
The repressed content must be made conscious so as to produce a tension of opposites, without which no forward movement is possible. The conscious mind is on top, the shadow underneath, and just as high always longs for low and hot for cold, so all consciousness, perhaps without being aware of it, seeks its unconscious opposite, lacking which it is doomed to stagnation, congestion, and ossification. Life is born only of the spark of opposites.["The Problem of the Attitude-Type," CW 7, par. 78.]
This in turn activates the process of compensation, which leads to an irrational “third,†the transcendent function.
Out of [the] collision of opposites the unconscious psyche always creates a third thing of an irrational nature, which the conscious mind neither expects nor understands. It presents itself in a form that is neither a straight “yes†nor a straight “no.â€["The Psychology of the Child Archetype," CW 9i, par. 285."The Psychology of the Child Archetype," CW 9i, par. 285.]
Jung explained the potential renewal of the personality in terms of the principle of entropy in physics, according to which transformations of energy in a relatively closed system take place, and are only possible, as a result of differences in intensity.
Psychologically, we can see this process at work in the development of a lasting and relatively unchanging attitude. After violent oscillations at the beginning the opposites equalize one another, and gradually a new attitude develops, the final stability of which is the greater in proportion to the magnitude of the initial differences. The greater the tension between the pairs of opposites, the greater will be the energy that comes from them . . . [and] the less chance is there of subsequent disturbances which might arise from friction with material not previously constellated.["On Psychic Energy," CW 8, par. 49.]
Some degree of tension between consciousness and the unconsciousness is both unavoidable and necessary. The aim of analysis is therefore not to eliminate the tension but rather to understand the role it plays in the self-regulation of the psyche. Moreover, the assimilation of unconscious contents results in the ego becoming responsible for what was previously unconscious. There is thus no question of anyone ever being completely at peace.
you should note that this "third" is something that conscious mind does not really understand, nor expect, aux more often than not(and especially when trying to differentiate the inferior) is something that the conscious mind understands and tries to use.
then there is this thing called transcendent function(which comes out of tertium non datur), which is not a single function, but an combination of functions used together. there isnt any info about which functions are used there, but from personal experience and from following jungs model of the psyche its the tert/inferior working together, in somewhat similar fashion that dom Ti and aux Ne create intuitive thinking, you see intuitive thinking(or intuition and thinking separately) is something that INTP quite naturally understands as it is his ego point of view, however sensing feeling is something that INTP does not expect, not understand very well, at least before some level of differentiation being made first on the two.