Chapter 5 · פרק ה

Now, up to this point we have spoken of what is conceived in our intellect from the statements that we read or hear.

However, it is further engraved in our nature to reflect, from within what is heard, upon what was not heard, because it is necessarily joined to what is heard.

For example, when the Torah said, "These are the living things that you may eat" [Leviticus 11:2] — now, this statement we understand at first according to the understanding of these words of it: that these species mentioned in the passage — it is permitted for us to eat them;

however, it is impossible for us not to understand from this as well that the other species besides these are not permitted to us.

Likewise, when it said, "These are the last words of David" [2 Samuel 23:1], we reflect from this that, by implication, there are first ones — for it is impossible to understand "last" without "first."

But everything that we understand from within a statement, which it did not make explicit, we call an "inference."

And now we shall explain its rules.

Now, likewise, when a statement is uttered, all its words ought to preserve the proportion and measure fitting to them;

that is, one should not confine a predicate to a single subject if it is fitting for many, nor assert of many subjects a predicate that is fitting for only one of them.

Likewise, in the same way, one should not confine a subject to a single predicate if more befit it, nor should many predicates be asserted of a subject if only one of them befits it.

Now, on the basis of this principle, when one of the statements comes before us, our intellect looks to its parts and to their measure, and according to what it sees, such will be the conception it receives from them;

and whatever lies outside that limit, it will judge to be rejected.

For example, we have learned [Mishnah Shabbat 13:5]: "R. Yehudah says: one who traps a bird into a cupboard or a deer into a house is liable."

And they inferred in the Talmud: "It is [for trapping] into a house that he is liable, but into enclosures — no."

The foundation of this inference is this: R. Yehudah confined the liability to the limited subject of one who traps a deer into a house, and it is fitting that we judge from his words that whoever is not included in this subject that he limited will not have this predicate — that is, one who does not trap into a house;

for if the liability were indeed upon every trapper, absolutely, he would not have mentioned in his subject "one who traps into a limited [place]," namely "one who traps into a house".

And likewise for everything of the like.

However, you must know that there are two kinds of inferences: the necessary and the non-necessary.

The non-necessary inference is the one that depends on precision as to the order of the words and their relation; for although reflection at the outset gives grounds for us to draw it precisely, a reason may yet be found on account of which we concede the statement and deny the inference.

For example, when we learned, "If the majority are Jews — he recites the blessing" [over a light seen outside a town; Berachot 53a] [ed. Berachot 53a: the inference drawn there, הא מחצה על מחצה אינו מברך, "hence half and half he does not bless," is not printed in 1742], and afterward they said: "By right, even [for] half and half [he should bless]; but since the first clause taught 'majority,' the latter clause taught 'majority' as well" (ואידי דתנן רישא רב תנא סיפא נמי רב) —

now, the inference is deflected by what was said, that the Tanna did not intend to exclude half and half, but only to follow the wording of the first clause.

But the necessary inference is the one that depends on the essence of the statement, such that it is impossible for us to acknowledge the statement and deny that inference, for in truth it is not separable from it.

For example, once we know the statement "Any wool that is clean along with its mother rises" [i.e., wool kept clean while still on the ewe turns out well], it is necessary that we also know that whatever did not rise was not clean along with its mother.

However, the necessary inferences as a whole are these.

From every categorical affirmative statement two inferences are drawn;

for example, "Whatever is clean along with its mother rises" — from it is inferred: whatever did not rise was not clean along with its mother — and this is called the contrapositive;

and from it is inferred that one of those that rise well is the one "clean along with its mother," and this is called the limited converse.

And from every categorical negative statement only one inference is drawn;

for example: "No evil descends from above [Bereshit Rabbah 51:3]; nothing that descends from above is evil." And this is called the complete converse.

And from every partial affirmative statement three inferences are drawn.

For example: "There is one who is diligent and gains" [Pesachim 50b]; from it is inferred: "there is one who is diligent and does not gain" — and this is called the absolute opposite;

and from it is inferred: "there is one who does not gain and is diligent" — and this is called the limited contrapositive;

and from it is inferred: "one of those who gain is the diligent one," and this is called the limited converse.

Likewise, from every partial negative statement these three inferences are drawn.

For example: "There are consecrated things that have redemption"; you will infer from this (there are consecrated things that have redemption): there are things that have redemption and they are consecrated; there are things that have no redemption and they are consecrated.