Inspired by this question I am curious to know if Judaism has a concept of positive speech, i.e., turning a negative statement into a positive one.
The original example given above is, using a car with a flat tire as an example, to go from "the car has a flat tire" to "the tire is going to be fixed".
Is there a Jewish source for this?
You are referring to ברית כרותה לשפשים - "Covenent of the lips" which means not to mention a potential bad thing that can happen to oneself or others. See talmud-gemara Sanhedrin 102a where Yehu King of Israel spoke evil of himself and that evil befell him:
ויהוא לא שמר ללכת בתורת ה' אלהי ישראל בכל לבבו לא סר מעל חטאת ירבעם אשר החטיא את ישראל - "And Yehu wasn't carefull to go in the way of Hashem with all his heart, He did not stay away from the sin of Yerovom that he had caused Israel to sin (i.e worship the 2 golden calves as a replacement of the Beis hamikdash)" (Melachim 2 10 30), מאי גרמא ליה אמר אביי ברית כרותה לשפתים שנאמר What caused this sin? Says Abaye The covenant to the mouth. i.e not to say something bad about oneself as it says:. (Melachim 2, 10, 18) וַיִּקְבֹּץ יֵהוּא, אֶת-כָּל-הָעָם, וַיֹּאמֶר אֲלֵהֶם, אַחְאָב עָבַד אֶת-הַבַּעַל מְעָט; יֵהוּא יַעַבְדֶנּוּ הַרְבֵּה.- And Yehu gathered all the people and said to them "Achav served the Baal idol a bit, Yehu will serve it a lot"
See also talmud-bavli Moed Kattan where Shmuel also spoke ill of his brother Pinchas and was chastised for his words became fulfilled for the demise of Pinchas.
פנחס אחוה דמר שמואל איתרע ביה מילתא על שמואל למישאל טעמא מיניה חזנהו לטופרי דהוו נפישן אמר ליה אמאי לא שקלת להו אמר ליה אי בדידיה הוה מי מזלזלת ביה כולי האי הואי (קהלת י, ה) כשגגה שיוצא מלפני השליט ואיתרע ביה מילתא בשמואל על פנחס אחוה למישאל טעמא מיניה שקלינהו לטופריה חבטינהו לאפיה אמר ליה לית לך ברית כרותה לשפתים
The Gemara then further explains in the name of Rabbi Yochanan that the "Covenent of the Lips" can also benifit someone if he speaks of good tidings in the future which may be fulfilled Like when Avraham (Bereishit 22,5) said he would return with Yitzchak and it actually happened that they both survived and returned,even though Yitzchak was supposed to be sacrificed.
דאמר ר' יוחנן מנין שברית כרותה לשפתים שנאמר (בראשית כב, ה) ויאמר אברהם אל נעריו שבו לכם פה עם החמור ואני והנער נלכה עד כה ונשתחוה ונשובה אליכם ואיסתייעא מלתא דהדור תרוייהו
There is indeed a Torah source for this idea.
Of every clean animal you shall take seven pairs, males and their mates, and of every animal that is not clean, two, a male and its mate (Bereshit (Genesis) 7:2)
Why does the Torah write "every animal that is not clean" instead of "every unclean animal"? The question is even stronger when you know that many laws are derived from the addition or omission of a single letter - and here we find 8 extra Hebrew letters.
The Talmud (Pesachim 3a) answers
Rabbi Yehoshua ben Levi said: A person should never express a crude matter, as the formulation of a verse was distorted by the addition of eight letters rather than have it express a crude matter, as it is stated: “From the pure animals and from the animals that are not pure [asher einena tehora]” (Genesis 7:8)
A similar story is told (see here)
Someone once informed the Chazon Ish [a great 20th century rabbi] that a person was a liar. The Chazon Ish immediately rebuked the one who spoke to him: “That is no way to speak about someone. Say rather that his words are not true. The Torah tells us to distance ourselves from sheker [lies] – we should not allow ourselves near even the language of sheker. The very word “lie” is something we should avoid!”
