(In a comment to a previous post, Rabbi David Mescheloff suggested that the commentary of Nachmanides — Rabbi Mosheh ben Nachman; the “Ramban” — addressed similar themes. I’ve excerpted it below. The full text can be seen at: http://www.mesora.org/Ramban-Exod-13-16.htm. My reasons for posting this can also be explained by reading my two preceding posts. I thank Rabbi Mescheloff for directing my attention to this commentary.)
And it shall be as a sign on your hand
and as a symbol between your eyes
that with a mighty hand
the Eternal brought us out from Egypt. 
(The Ramban begins his commentary on this verse by teaching about the proper understanding and performance of this mitzvah/commandment, then goes on to a more general discussion of its meaning.)
And now I shall declare to you a general principle in the reason of many commandments. Beginning with the days of Enosh when idol-worship came into existence, opinions in the matter of faith fell into error. Some people denied the root of faith by saying that the world is eternal; they denied the Eternal, and said, ‘It is not He [Who called forth the world into existence].’ Others denied His knowledge of individual matters, and they say, ‘How does G-d know?’ and ‘Is there knowledge in the Most High?’ Some admit His knowledge but deny the principle of providence and make men as the fishes of the sea, [believing] that G-d does not watch over them and that there is no punishment or reward for their deeds, for they say ‘The Eternal hath forsaken the land.’
Now when G-d is pleased to bring about a change in the customary and natural order of the world for the sake of a people or an individual, then the voiding of all these [false beliefs] becomes clear to all people, since a wondrous miracle shows that the world has a G-d Who created it, and Who knows and supervises it, and Who has the power to change it.
And when that wonder is previously prophesied by a prophet, another principle is further established, namely that of the truth of prophecy, that G-d speaks with man, and that He reveals His counsel to His servants, the prophets, and thereby the whole Torah is confirmed.
This is why Scripture says in connection with the wonders [in Egypt]: ‘That you [Pharaoh] may know that I am the Eternal in the midst of the earth,’  which teaches us the principle of [Divine] providence, i.e., that G-d has not abandoned the world to chance, as they [the heretics] would have it; ‘That you may know that the earth is the Eternal’s,’  which informs us of the principle of creation, for everything is His since He created all out of nothing; ‘That you may know that there is none like Me in all the earth,’  which indicates His might, i.e., that He rules over everything and that there is nothing to limit Him.
The Egyptians either denied or doubted all of these [three] principles, [and the miracles confirmed their truth]. Accordingly, it follows that the great signs and wonders constitute faithful witnesses to the truth of the belief in the existence of the Creator and the truth of the whole Torah.
And because the Holy One, blessed be He, will not make signs and wonders in every generation for the eyes of some wicked man or heretic, He therefore commanded us that we should always make a memorial or sign of that which we have seen with our eyes, and that we should transmit the matter to our children, and their children to their children, to the generations to come, and He placed great emphasis on it, as is indicated by the fact that one is liable to extinction for eating leavened bread on the Passover, and for abandoning the Passover offering, [i.e., for not taking part in the slaughtering thereof].
He has further required of us that we inscribe upon our arms and between our eyes all that we have seen in the way of signs and wonders, and to inscribe it yet upon the doorposts of the houses, and that we remember it by recital in the morning and evening – just as the Rabbis have said: ‘The recital of the benediction ‘True and firm,’ [‘Emet v’emunah,’ which follows the Sh’ma in the morning and which terminates with a blessing to G-d for the redemption from Egypt], is obligatory as a matter of scriptural law because it is written, ‘…that you may remember the day when you came forth out of the land of Egypt all the days of thy life.’  [He further required] that we make a booth every year, and many other commandments like them, which are a memorial to the exodus from Egypt.
All these commandments are designed for the purpose that in all generations we should have testimonies to the wonders so that they should not be forgotten and so that the heretic should not be able to open his lips to deny the belief in [the existence of] G-d. He who buys a Mezuzah for one zuz [a silver coin] and affixes it to his doorpost and has the proper intent of heart on its content, has already admitted the creation of the world, the Creator’s knowledge and His providence, and also his belief in prophecy as well as in all fundamental principles of the Torah, besides admitting that the mercy of the creator is very great upon them that do His Will, since He brought us forth from that bondage to freedom and to great honor on account of the merit of our fathers who delighted in…His Name.
It is for this reason that the Rabbis have said: ‘Be as heedful of a light commandment, as of a weighty one…,’  for they are all exceedingly precious and beloved, because through them, a person always expresses thankfulness to his G-d.
And the purpose of an the commandments is that we believe in our G-d and be thankful to Him for having created us. We know of no other reason for the creation, and G-d the Most High has no demand on the lower creatures, except that man should know and be thankful to G-d for having created him…”
 Shemot/Ex. 13:16
 Shemot/Ex. 8:18
 Shemot/Ex. 9:29
 Shemot/Ex. 9:14
 Devarim/Deut. 16:3
 Pirkei Avot 2:1