'מתני MISHNA: Everyone slaughters - Everywhere that [the tanna] teaches "everyone," in each instance he brings the halacha from the beginning of tractate Arakhin and explains (Arakh. 2a:4), "Everyone [makes valuations], to include whom?" And "everyone slaughters," which is taught in the Mishna, the amoraim argue about it in the Gemara to [ultimately] say, "to include an impure person [slaughtering an animal] for mundane use," and to say, "to include a Samaritan or a heretic."

וכולן And all of them - In the Gemara it is explained who are "and all of them."

GEMARA: 'And their slaughter is valid' after the fact - This [should be read as] a question [rather than a statement] (i.e., "And [is the Mishna saying that] their slaughter is valid after the fact?"). And the opening clause ("Everyone may slaughter") is difficult, for it implies that whoever is included in "everyone" is included ab initio. But if the latter clause ("and their slaughter is valid") implies that it is extending [the same meaning of] "everyone," then it would be extending [the same] to [encompass] an after-the-fact [slaughter], but we do not extend [the authorization to perform an act] ab initio [to encompass what is only acceptable] after the fact. And thus we cannot say that our Mishnah withholds something ab initio and that [only] one [thing] is taught. For since it is taught "Everyone may slaughter," it would be obvious that [their slaughter is] valid! [This would render the latter clause redundant.]

וכל And does every [use of the word] "everyone" (הכל) indicate [that the action may be performed] ab initio? - [For if you take that position,] it would be difficult for you [to explain all similar instances where הכל is used]. Nor would you be able to say that every [instance indicates that the action is valid] after the fact. And this is what the tanna means to say: "Everyone as to whom the laws of slaughter apply [may slaughter]." For [otherwise], if those who were disqualified from slaughtering [nonetheless] slaughtered, it would come out that their slaughter was valid [after the fact]. [This result would be unacceptable.]

אלא Rather, "Everyone (הכל) may substitute [an unconsecrated animal for a consecrated animal]" (Tem. 1:1) - Can it be [seriously] claimed that this statement is [intended to authorize that] ab initio, one may bring an unconsecrated animal in place of a consecrated animal, and say, "This one is a substitute for that one"?! [Certainly not! Rather,] the "everyone" in [the tractate of] Temurah is explained over there (Tem. 2a:6-8) to include an heir who substitutes the offering of his [deceased] father, and it is taught over there, that one may not substitute with the offering of another.

טוב Good - Unblemished.

רע Bad - Blemished.

התם Over there, the tanna means to say - To uproot the "everyone" stated in the first clause (i.e., of Temurah 1:1), so as not to say that it means "ab initio." But "everyone slaughters" remains in its place, since as long as he does not uproot it, and teaches that disqualified individuals should not be permitted to slaughter, [then he can argue by analogy that] in the same way that it is uprooted over there from the implication [that the rule of substitutions applies] ab initio, he extends it, and thereafter he teaches "and their slaughter is valid," so that it implies [validity] after the fact.

לא שהאדם רשאי Not that a person is permitted - It is written (Lev. 27:10), "He shall not substitute for it [and he shall not exchange it]," and the first clause [of Tem. 1:1] means to say the following: "Everyone as to whom the laws of substitution apply..." And thus it is taught that the first clause, "Everyone substitutes," is necessary (see Tem. 2b:5). Also, [the clause is necessary] to explain "not that a person is permitted [ab initio], etc.," and he did not state in the first clause [due to the] abbreviated phrasing [of the Mishna], "Everyone who substituted, their substitutions are [valid] substitutions." This is the wording of the tannaim, such as "Everyone slaughters," "Everyone leans [their hands on an offering]," "Everyone is obligated." Therefore, here, even though [the tanna] had a need to lengthen [his wording], the tanna did not wish to alter his wording.

מומר It is a [valid] exchange - Liability is incurred for the second [animal], and both of them (i.e., both animals involved in the substitution) are [deemed] consecrated.

וסופג He incurs forty lashes - On account of the negative commandment of, "he shall not exchange it" (Lev. 27:10).

הכל מעריכין Everyone may make valuations - Over there (Arakh. 2a:4), it is explained to include a [minor] of uncertain ability to discriminate [in matters of valuations], who is close in age to adulthood; a child who knows how to clearly utter [a vow of valuation] in the name of those who are consecrating; and if he is next to his parent, he is [considered to be] like one who is twelve years and one day old, [and] his words are established [as binding] even though they know that he is a minor, until he is thirteen years and one day old.

מעריכין May make valuations - The laws of valuations apply to them, for if he said, "It is incumbent upon me to donate my valuation," or "The valuation of so-and-so is incumbent upon me," his vow is established. And even though he is a minor, the person who took the vow is liable to give double the valuation, and amount is fixed on the portion [of valuations in the Torah (Lev. 27:3-7)].

הכל נערכין All are valuated - They have a valuation, and even one who is afflicted with boils [to the extent] that he would be worth nothing if he were sold in the marketplace, his valuation is [fixed by] the portion [of valuations in the Torah], and if he said concerning himself, "It is incumbent upon me to donate my valuation," or he said about another, "The valuation of that one who is afflicted with boils is incumbent upon me," they do not say [to him], "Since he has no market value, he also has no valuation." [Rather, his valuation is set by the Torah irrespective of his true market value, and the one who vowed is liable to fulfill his obligation.]

הכל נודרים All may vow - "My market-value is incumbent upon me" or "The market-value of so-and-so is incumbent upon me." And over there (Arakh. 2a:4) it is explained, that since [the tanna] wanted to teach "All may be the subject of a vow," he also taught "All may vow."

הכל נידרין All may be the subject of a vow - Every person who has no worth [nevertheless] has a market-value, and if he said "My market-value is incumbent upon me," or another said about him, "The market-value of so-and-so is incumbent upon me," he gives according to what he is sold for in the marketplace, and even if he was vowed for less than a one-month old, and he said "The market-value of this infant is incumbent upon me," he gives his market-value, and even though there is no assessment-value [under Torah law] less than that of a one-month old. Or if he said [regarding the newborn infant], "His assessment-value is incumbent upon me," he is exempt from everything, for the law of assessment-values was not given for him, as it is written (Lev. 27:6), "And if from the age of one month up to the age of five years...."

לא There shall not be any sin in it - Here, if you were to vow, there would be [an element of] sin it.

טוב אשר Better than one who did not vow - Before that (i.e., that which was quoted) it is written "...one who vows [and] pays, and even the best of all is one who does not vow [in the first place], lest he vows and does not pay." This is how Rabbi Meir explains it.

טוב מזה Better than this one and that one - Than one who vows and pays and who vows and does not pay.

שאינו Who does not vow whatsoever - For one who accustoms himself to making vows comes to eventually not fulfill his words.

רבי יהודה Rabbi Yehuda says, better than this one and that one is one who vows and pays - The implication here is that it is better not to vow than to vow and not pay, but one who vows and pays -- is he not better than all of them?

ואפילו And even Rabbi Yehuda only said so in relation to one who says, "Behold, this [animal is hereby consecrated]" - For if it dies or is stolen, he is not liable for it responsibility. Alternatively, since it can be brought out to pasture [until it develops a blemish], he can go back on it (i.e., a that point he may treat the animal as chullin without having broken his vow).