We often hear expressions like “research proves…” or “clinical studies show…”
They reflect our reliance on the scientific method to give us valid data about conditions in and around us.
Invoking “research” is supposed to differentiate the subsequent statements from mere hearsay, opinion, or outright fraud.
We put our trust in the research, in the person doing the research and in the person reporting it.
In TaNaCh, there’s a phrase ” ’’כה אמר ה” — “Thus G-d says (or said).” It appears innumerable times, sometimes slightly varied.
It, too, means: “These words I say are valid because their source is unimpeachable.”
When a rabbi or other Jewish writer refers to a Biblical verse (“text”) to “prove” their point, that verse is called a “proof text.”
Certainly there can be intentionally or unintentionally invalid research.
Certainly there were “false prophets,” however convincing they might have seemed at the time.
This post isn’t about that.
In the Talmud, an argument, or decision, or statement, is validated by reference to a verse in Torah or elsewhere in TaNaCh.
“It is stated:
‘None of you shall approach to any that is near of kin to him.” 
Hence the Sages said:
“Let no man remain alone with a woman at an inn, even though she is his sister or daughter…” 
In this case, the Talmud gives a verse, then interprets or applies it to real-life circumstances.
“Mosheh only broke the tablets because he was commanded to do so by G-d, as it is stated:
‘With him do I speak mouth-to-mouth’ — 
By a mouth-to-mouth order I [G-d] commanded him to break the tablets’.” 
Here, the phrase “as it is stated” clearly indicates that the “proof” of the first statement is going to be found in the text that is about to be quoted.
In the “Perek Ha-Shalom,” (Rabbi) Bar Kappara uses proof texts from each of the three divisions of TaNaCh:
6. Bar Kappara  said:
“Great is peace,
for we find that Torah [*] modified a statement to maintain peace between Avraham and Sarah.
At first it’s stated:
‘Sarah laughed within herself, saying…my lord being old,’ 
but in the end it’s written,
‘I who am old’.” 
7. Bar Kappara  said,
“Great is peace,
for we find that ‘Prophets’ [**], too, modified a statement
to maintain peace between Manoah and Chanah (his wife).
At first it’s written:
‘Behold, now you are barren…but you shall conceive and bare a son,’ 
but in the end it’s written,
‘Behold you shall conceive and bare a son,’ 
and there’s no mention of the words ‘behold you are barren’.”
8. Bar Kappara  said:
“Great is Peace,
as among the angels there’s no [qualities of]
animosity, jealousy, hatred, commanding, or quarreling,
because the Blessed Holy One has made peace among them, as it’s written:
‘Dominion [משל] and dread [פחד] are with Him; He makes peace in His high places.’  [***]
‘Dominion’ is the angel Michael and ‘Dread’ is Gabriel,
one of whom is ‘fire’ and the other ‘water’.
Yet still they don’t injure each other,
for the Blessed Holy One has made peace between them.
How much more do human beings, in whom are all these qualities,
Because it’s an unfamiliar kind of reasoning and an equally unfamiliar style of writing to most modern readers, it can become a barrier to learning from traditional sources.
Sometimes, a “proof” is derived from the “proof-text” by stretching the meaning of a word, or by the relationship of the letters in one word with those in another, or by relating how a word is used in one context with how it’s used in another.
In Hebrew, it can also be derived by whether a word/verb is singular or plural. This doesn’t translate well into English, as our noun and verb forms don’t indicate “number.”
The principle underlying much of Talmudic interpretation in this form, is that Torah is perfect. There is absolutely nothing accidental in it. If a meaning can be derived, it’s implied that it was meant to be derived.
The rabbi who is providing the interpretation has simply uncovered something that was already there. He disavows that he “made up” the answer himself, without reference to Torah.
Quite a bit of time could be spent simply paying attention to how the rabbis of the Talmud (and later Jewish writings) derive or apply meaning, regardless of the meaning itself.
It would help break down some of the intellectual rigidity we incorporated in our education — especially in college.
 Vayikra/Lev. 18:6
 Avot d’Rabbi Natan, ch. 2; Soncino p. 18a (Hebrew)
 Dvarim/Deut. 5:27
 ibid. p. 18b
 see: en.wikipedia.org/wiki/Bar_Kappara
[*] Bar Kappara demonstrates the greatness of peace with reference to the entire TaNaCh. He begins with Torah.
 Ber./Gen. 18:12
 Ber./Gen. 18:13 G-d repeats Sarah’s statement, but conceals from Avraham that Sarah had referred to him as being “old.”
[**] Bar Kappara quotes from “N’vi’im/Prophets,” the second section of TaNaCh/Hebrew Scriptures. The book of “Shoftim/Judges” falls within the “N’vi’im/Prophets” section.
 Shoftim/Judges 13:3
 ibid. 13:7 In the text, Chana herself changes the angel’s wording.
 Ayov/Job 25: 2
[***] Bar Kappara quotes from Ayov/Job, which falls within the “Ketuvim/Writings” section of TaNaCh. Here he completes his reference to each of the three sections of TaNaCh, implying that the greatness of peace is found in the entire TaNaCh.