In regards to Montaigne's statement on page 23 in Apology for Raymond Sebond, I would deduce that he was using the metaphor of nature and natural tendencies in opposition to man's vain, self-seeking façade that displaces God the creator.
Montaigne's statement appears to (on the surface at least) value mans naturalistic tendencies and graces in a much better light than our own vain-striving presumptions that claim that our "competent utterances" hold the very answers to the "right" way in which to conduct oneself.
Montaigne constantly uses the contrast of animals and humans with the former representing a more pure, natural existence that I assume is to be more highly regarded because of it's proximity to the "original" way in which we were created by God. I think that Montaigne held in contempt his contemporaries and particular predecessors who he felt held themselves up above others and flaunted their intelligence and self-importance for all others to see.
In response to Montaigne's statement that posited the superiority of human nature over the practice of "owing our competence to our own powers", I believe that Augustine would firmly disagree and claim that in order for humans to truly come into communion with their creator, that they would need to transcend their natural urges and inclinations by way of prayer, confession, and piety.
In his Confessions, Augustine spoke of a drunkard who, through the procurement of a few begged coins, had seemingly obtained happiness (although, admittedly, it was not true happiness) due to the dulling of his senses and thus finding a temporary escape in his cognitive awareness and regressing to more of his natural or animal state.
Augustine later commented that he on more than one occasion felt like the drunkard in search of temporal happiness, but knew that the way was not to be gained by regressing or dulling ones intelligence and intellect to achieve release.
These qualities he equated with those who would never (unless miraculously) rise above the human condition and always seek pleasure according to earthly standards. Human nature was originally created faultless claims Augustine, but through original sin which was committed as an act of free will, we as humans and creations of God need to seek transcendence from this base human sin through God's grace (on Nature and Grace III,
3). Augustine constructed the concept of original sin and claimed that we as descendants of the first man and woman contained the fallen nature of the original transgression and thus had an inherently evil nature. This obviously would not mesh with Montaigne's statement touting human nature as the ultimate way to find favor with God.
I think that the true theological importance in choosing between Montaigne and Augustine lies in whether a person believes in the conception of original sin and what the actual nature of humanity as a whole is.
By admitting support of Montaigne in the matter, one is clearly saying "It is my belief that the creator made us as humans in His image and that in order to cleave to God, we must cast off the "unnatural" error's of vanity, reason, selfishness and let our natural tendencies decide our modes of conduct and also determine our paths in life that we may better come to "know" God.
An Augustinian perspective on the other hand would fully support the belief that we as humans are fallen creatures through the abuse of our God-given gift of free-will and that we have to transcend our "natural" inclinations to sin and seek vain-glory in order to begin to find peace and wholeness with God. Thus it matters greatly as to whom we side with for that decision is truly a reflection of how we see the human state to be; inherently good or inherently evil.
Through the eyes of Thomas Aquinas and Rene Descartes, we shall take in the landscape of Medieval and Renaissance philosophy in a micro/macro cosmic relationship that is, how their philosophies mirrored the thoughts and feelings of the given period.
On one hand, an aspect of medieval philosophy (generalization) focused on the extra-personal ways and modes in which a person's relationship with their creator ought to manifest them in daily life. Much of this was due to the pseudo-ecumenical reconciliation of the "new" Christian God to each individual person's belief system, traditions dogma, etc.
For example, from Augustine to Aquinas as well as through the multifaceted approaches by the Muslims (Avicenna, Averroes, and Al Farabi) and the Hebrews (Mamonides), medieval philosophy covered the gamut of cultures and thought and on how faith and reason might come to terms with one another.
One other aspect of this conflict could be seen as the collision of ancient thought and tradition, especially that of Plato and Aristotle with the introduction of a seemingly contradictory system of belief; Christianity.
Thomas's main chore of reconciliation began with melding Aristotelian thought to the church doctrine on the topic of universals in this way: Universals are neither autonomous forms nor mere mental states. They are "embedded" in particular objects as their essence, or more literally, their "whatness".
Through the power of abstraction, the human mind can recognize certain similarities that exist in nature. These become concepts and thus came about the view of Moderate Realism (similar to Abelard's conceptualism 120 years earlier). Aquinas' answer to the Faith vs. Reason dilemma relies heavily on the division between philosophy and theology in the sense that the philosopher uses reason alone while the theologian utilizes revelation as authoritative.
Thomas did claim however, that there was an area of overlap between the two, a conception that he called "natural theology". In support of natural theology Thomas invented what is now well known as the "five ways" which are a series of five proofs toward the existence of God which utilize another Aristotelian characteristic, that of a posterior knowledge.
The work of Thomas Aquinas is considered the apogee of the faith vs. reason debate that consumed so much of medieval philosophy, especially in terms of utilizing ancient Greek thought and synthesizing it with Christian theology.
It should be no surprise that at the very moment when the human intellect was articulated as the most excellent statement of the medieval period, that there were already powers that began to undermine the fragile synthesis that had been so sought after for so long. Thus the birth of the renaissance, with a focus on the physical instead of the metaphysical, began.
Although many philosophers laid the foundations of the Renaissance, none quite epitomized the embracing of secular science and empirical observation as that of Rene Descartes. Descartes was a top notch mathematician and scientist who also happened to be a Catholic (poor bastard).
Thus, Rene may not have purposely undermined the authority of the church in such a public way, but it is truly his humanistic endeavors that have been remembered unto the current day. It is in this way that Descartes epitomized the Renaissance i.e. the rebirth of individual accomplishment, on the individual's terms, and through the individuals own means.
The belief that human reason contained the answers became the norm, a seemingly watered down version of the Aristotelian teleological focus on potentiality and actuality in the sense that the human mind contained the potential (thoughts) to make the actual (Truth).
In regards to the shift in thought, ideas, etc. from medieval to renaissance, there are countless many social, political, and geographical reasons for the "rebirth", but king among these (in my opinion) was the drawing together of the world through various explorers (Marco Polo, Columbus, Magellan, to name a few) and the exchange of thoughts and ideas that ensued.
Also through the use of force in some cases and politics in others, peace became a platform upon which to a person had an opportunity for leisure time and creativity to study and contemplate the new exchange of ideas from different corners of the world. Not to mention the invention of the printing press and the ability to disperse thoughts and ideas through printed material.