Bottomline:
(i) The reason as to why, “[If he vows to bring] a small one and brings a large one, he fulfills his obligation,” is neither only because the person had but in mind ‘nothing less,’ nor, because ‘within the big there is the small.’
(ii) Maimonides in his opening to his Laws of Vows writes, “(They contain 3 mitzvot: two positive commandments and one negative commandment. They are: 1.) To heed the utterances of one’s mouth and to fulfill one’s vow,” because there are two concepts here: (i) “To heed the utterances of one’s mouth”, and (ii) “to fulfill one’s vow”.
(iii) Rebbi holds that the primary issue is that, “To heed the utterances of one’s mouth,” the actual words that he said, while the Rabbis hold that the primary issue here is, “to fulfill one’s vow,” the context of his promise. --And this aligns with the ongoing disputes between Rebbi and the Rabbis, in which Rebbi holds that the primary is the simple meaning of the words said (of the verse, teaching, or of people), and all its details, while the Rabbis hold that the primary is the context. And this explains the dispute here concerning, “[If he vows to bring] a small one and brings a large one:” Rebbi holds that he did not fulfill his words, “the utterances of one’s mouth,” and thus did not fulfill his obligation, while the Rabbis hold that the content of his promise, “one’s vow,” he fulfilled.
(iv) This is the meaning behind Maimonides (-Laws of Vows 1:4), “It is a positive commandment of Scriptural origin for a person to fulfill his oath or vow, whether it be a vow involving prohibitions or a vow of sanctification, as it is stated (-Deuteronomy 23:24), ‘That which your lips give out (utter) heed, and do as you have promised.’ And it is stated (-Numbers 30:3), ‘As all that he gives out from his mouth (utters) he shall do.’”
“That which your lips give out (utter) heed, and do as you have promised,” speaks of “vows involving the consecration of articles.” This articles of consecration, only that they befall is through the word of man, that there befall upon him the obligation to bring this offering of charity. However, the offering’s becoming an “Object of Mitzvah” an existing “Biblical Mitzvah” is not through the word of man.
