Whenever the term "disqualified" is used with regard to foods, the intent is that the food itself is considered as impure, but it does not impart impurity to other similar foods. Instead, if it touches another food, it is pure.
אכָּל מָקוֹם שֶׁנֶּאֱמַר בָּאֳכָלִין פָּסוּל הוּא שֶׁיִּהְיֶה הָאֹכֶל עַצְמוֹ טָמֵא וְלֹא יְטַמֵּא אֹכֶל אַחֵר. אֶלָּא אִם נָגַע בְּאֹכֶל אַחֵר הֲרֵי הוּא טָהוֹר:
With regard to ordinary foods, a primary derivative of impurity contracts impurity and imparts impurity to others. A secondary derivative is disqualified, but does not impart impurity, for a secondary derivative does not create a tertiary derivative with regard to ordinary food.
What is the source that teaches that ordinary food which is a secondary derivative is disqualified? Leviticus 11:33 states: "Whenever one of them falls into its inner space, everything in its inner space contracts impurity." Now, a carcass of a crawling animal is a primary source of impurity. The earthenware container into whose inner space it falls is a primary derivative of impurity. Thus the food in the container is a secondary derivative and yet Scripture calls it impure.
Similarly, if the carcass of a crawling animal falls into an oven, bread in the oven is a secondary derivative, for the oven is a primary derivative.
בהָרִאשׁוֹן שֶׁבְּחֻלִּין טָמֵא וּמְטַמֵּא. הַשֵּׁנִי פָּסוּל וְלֹא מְטַמֵּא וְאֵין שֵׁנִי עוֹשֶׂה שְׁלִישִׁי בְּחֻלִּין. וּמִנַּיִן לְאֹכֶל שֵׁנִי שֶׁהוּא פָּסוּל בְּחֻלִּין שֶׁנֶּאֱמַר (ויקרא יא לג) "וּכְלִי חֶרֶשׂ אֲשֶׁר יִפּל מֵהֶן אֶל תּוֹכוֹ כּל אֲשֶׁר בְּתוֹכוֹ יִטְמָא". נִמְצָא הַשֶּׁרֶץ אָב וּכְלִי חֶרֶס שֶׁנָּפַל הַשֶּׁרֶץ לַאֲוִירוֹ רִאשׁוֹן וְהָאֹכֶל שֶׁבַּכְּלִי שֵׁנִי וַהֲרֵי הוּא אוֹמֵר יִטְמָא. וְכֵן שֶׁרֶץ שֶׁנָּפַל לַאֲוִיר הַתַּנּוּר הַפַּת שְׁנִיָּה שֶׁהַתַּנּוּר רִאשׁוֹן:
With regard to terumah, primary and secondary derivatives of impurity contract impurity and impart impurity. A tertiary derivative is disqualified, but does not impart impurity, for a tertiary derivative does not create a derivative of the fourth degree with regard to terumah.
What is the source that teaches that food that is terumah which is a tertiary derivative is disqualified? Leviticus 22:7 states: "And the sun will set and he will become pure. Afterwards, he shall partake of consecrated food." Thus a person who immersed that day is forbidden to partake of terumah until nightfall. If he touches it, he disqualifies it. A person who immerses is like a secondary derivative. Thus one can conclude a secondary derivative makes a tertiary derivative with regard to terumah.
גהָרִאשׁוֹן וְהַשֵּׁנִי שֶׁבַּתְּרוּמָה טְמֵאִים וּמְטַמְּאִים. הַשְּׁלִישִׁי פָּסוּל וְלֹא מְטַמֵּא וְאֵין שְׁלִישִׁי עוֹשֶׂה רְבִיעִי בִּתְרוּמָה. מִנַּיִן לְאוֹכֵל שְׁלִישִׁי שֶׁהוּא פּוֹסֵל בִּתְרוּמָה שֶׁנֶּאֱמַר (ויקרא כב ז) "וּבָא הַשֶּׁמֶשׁ וְטָהֵר וְאַחַר יֹאכַל מִן הַקֳדָשִׁים" נִמְצָא טְבוּל יוֹם אָסוּר בִּתְרוּמָה עַד שֶׁיַּעֲרִיב שִׁמְשׁוֹ וְאִם נָגַע בָּהּ פְּסָלָהּ וּטְבוּל יוֹם כְּשֵׁנִי לְטֻמְאָה הוּא. הָא לָמַדְתָּ שֶׁהַשֵּׁנִי עוֹשֶׂה שְׁלִישִׁי בִּתְרוּמָה:
With regard to consecrated food, primary, secondary, and tertiary derivatives contract impurity and impart impurity. A derivative to the fourth degree is disqualified, but does not impart impurity, for a derivative to the fourth degree does not ever create a derivative to the fifth degree.
What is the source that teaches that a tertiary derivative is impure with regard to consecrated foods? Leviticus 7:19 states: "Meat that touches anything that is impure shall not be eaten." And Scripture has already referred to a secondary derivative of impurity as "impure," as stated: "Everything in its inner space contracts impurity." Thus one can conclude that consecrated meat that touches a secondary derivative contracts impurity and must be burnt.
What is the source that teaches that a fourth degree derivative disqualifies consecrated foods? It is derived through an inference from a more lenient matter to a more stringent one: A person who is lacking atonement is permitted to partake of terumah, but is forbidden to partake of sacrificial food until he brings the offerings that secure atonement for him. If so, should not a tertiary derivative of impurity which disqualifies terumah cause a derivative to the fourth degree to become impure? Nevertheless, a fifth degree derivative is pure.
דהָרִאשׁוֹן וְהַשֵּׁנִי וְהַשְּׁלִישִׁי בַּקֹּדֶשׁ טְמֵאִין וּמְטַמְּאִין. הָרְבִיעִי פָּסוּל וְאֵינוֹ מְטַמֵּא וְאֵין רְבִיעִי עוֹשֶׂה חֲמִישִׁי לְעוֹלָם. וּמִנַּיִן לַשְּׁלִישִׁי בַּקֹּדֶשׁ שֶׁהוּא טָמֵא שֶׁנֶּאֱמַר (ויקרא ז יט) "וְהַבָּשָׂר אֲשֶׁר יִגַּע בְּכָל טָמֵא לֹא יֵאָכֵל" וּכְבָר קָרָא הַכָּתוּב לַשֵּׁנִי טָמֵא שֶׁנֶּאֱמַר (ויקרא יא לג) "כּל אֲשֶׁר בְּתוֹכוֹ יִטְמָא" הָא לָמַדְתָּ שֶׁבְּשַׂר הַקֹּדֶשׁ שֶׁנָּגַע בְּשֵׁנִי נִטְמָא וְיִשָּׂרֵף. וּמִנַּיִן לָרְבִיעִי בַּקֹּדֶשׁ שֶׁהוּא פָּסוּל מִקַּל וָחֹמֶר. וּמַה מְחֻסַּר כִּפּוּרִים שֶׁהוּא מֻתָּר בִּתְרוּמָה אָסוּר בְּקֹדֶשׁ עַד שֶׁיָּבִיא כַּפָּרָתוֹ. הַשְּׁלִישִׁי שֶׁהוּא פָּסוּל בִּתְרוּמָה אֵינוֹ דִּין שֶׁיַּעֲשֶׂה רְבִיעִי בְּקֹדֶשׁ. אֲבָל הַחֲמִישִׁי טָהוֹר:
Even though ordinary meat is pure, our Sages decreed that it should be considered as a tertiary derivative of impurity and convey impurity to sacrificial food. It does not impart impurity to terumah. It appears to me that the Sages enforced their decree against it solely so that ordinary meat not become mixed with sacrificial meat. Were that to happen, an error could be made and inadvertently, one might think that the meat is ordinary and eat it while he is impure, although in truth it is consecrated.
הבְּשַׂר תַּאֲוָה אַף עַל פִּי שֶׁהוּא טָהוֹר גָּזְרוּ עָלָיו שֶׁיִּהְיֶה כִּשְׁלִישִׁי לְטֻמְאָה מְטַמֵּא אֶת הַקֹּדֶשׁ וְאֵינוֹ פּוֹסֵל אֶת הַתְּרוּמָה. וְיֵרָאֶה לִי שֶׁלֹּא גָּזְרוּ עָלָיו אֶלָּא כְּדֵי שֶׁלֹּא יְעָרְבוּהוּ עִם בְּשַׂר הַקֹּדֶשׁ וְיָבוֹאוּ לִטְעוֹת וְלִשְׁגֹּג בּוֹ וִידַמּוּ שֶׁהַבָּשָׂר זֶה הוּא חֹל וְהוּא קֹדֶשׁ וְיֹאכְלֶנּוּ בְּטֻמְאָה:
Mishneh Torah (Moznaim)
Featuring a modern English translation and a commentary that presents a digest of the centuries of Torah scholarship which have been devoted to the study of the Mishneh Torah by Maimonides.
When foods are joined together by liquid, they are considered as joined with regard to contracting the impurity associated with foods. There is an unresolved question if they are considered as a single entity from which to count primary, secondary, and tertiary derivatives or the food that was touched by the impurity is a primary derivative and the food that is joined to it is a secondary derivative.
וחִבּוּרֵי אֳכָלִין עַל יְדֵי מַשְׁקִין הֲרֵי הֵן חִבּוּר לְטַמֵּא טֻמְאַת אֳכָלִין וְהַדָּבָר סָפֵק אִם חֲשׁוּבִים כְּגוּף אֶחָד לִמְנוֹת בָּהֶן רִאשׁוֹן וְשֵׁנִי וּשְׁלִישִׁי. אוֹ חוֹשְׁבִים זֶה הָאֹכֶל שֶׁנָּגְעָה בּוֹ הַטֻּמְאָה רִאשׁוֹן וְהָאֹכֶל הַמְחֻבָּר לוֹ שֵׁנִי:
Impure food that is a secondary derivative disqualifies food that is terumah and causes it to be considered as a tertiary derivative. If it touches ordinary liquids, it imparts impurity to them. Needless to say, if it touches liquids that are terumah or consecrated, it imparts impurity to the entire quantity.
זהַשֵּׁנִי שֶׁבְּחֻלִּין פּוֹסֵל אָכֳלֵי תְּרוּמָה וְעוֹשֶׂה אוֹתָן שְׁלִישִׁי. וְאִם נָגַע בְּמַשְׁקֵה חֻלִּין טִמְּאָן וְאֵין צָרִיךְ לוֹמַר אִם נָגַע בְּמַשְׁקֵה תְּרוּמָה אוֹ בְּמַשְׁקֵה קֹדֶשׁ שֶׁהוּא מְטַמֵּא אֶת הַכּל:
Terumah that is a tertiary derivative of impurity that touched consecrated food disqualifies it and causes it to be considered as a fourth degree derivative. If it touches consecrated liquids, it imparts impurity to them and causes them to be considered as primary derivatives. If, however, terumah that is a tertiary derivative touches a liquid that is terumah, it is pure. Similarly, if consecrated food that is a fourth degree derivative touches a consecrated liquid, it is pure.
חהַשְּׁלִישִׁי שֶׁבַּתְּרוּמָה שֶׁנָּגַע בְּאָכֳלֵי קֹדֶשׁ פְּסָלָן וְנַעֲשׂוּ רְבִיעִי. וְאִם נָגַע בְּמַשְׁקֵה הַקֹּדֶשׁ טִמְּאָן וְנַעֲשׂוּ תְּחִלָּה. אֲבָל אִם נָגַע שְׁלִישִׁי שֶׁבִּתְרוּמָה בְּמַשְׁקֵה תְּרוּמָה הֲרֵי הוּא טָהוֹר. וְכֵן רְבִיעִי שֶׁבַּקֹּדֶשׁ אִם נָגַע בְּמַשְׁקֵה קֹדֶשׁ הֲרֵי זֶה טָהוֹר:
When ordinary food is prepared with the stringencies of terumah, if it becomes a tertiary derivative, it is disqualified, as is true with regard to terumah. Nevertheless, if such food touches consecrated food, it does not cause it to be considered as a fourth degree derivative. It does not even disqualify consecrated liquids. When ordinary food is prepared with the stringencies of consecrated food, a tertiary derivative is pure like ordinary food.
טחֻלִּין שֶׁנַּעֲשׂוּ עַל טָהֳרַת תְּרוּמָה הַשְּׁלִישִׁי שֶׁבָּהֶן פָּסוּל כִּתְרוּמָה. וְאִם נָגַע בַּקֹּדֶשׁ אֵינוֹ עוֹשֵׂהוּ רְבִיעִי וַאֲפִלּוּ מַשְׁקֵה קֹדֶשׁ אֵינוֹ פּוֹסֵל. וְחֻלִּין שֶׁנַּעֲשׂוּ עַל טָהֳרַת הַקֹּדֶשׁ הַשְּׁלִישִׁי שֶׁבָּהֶן טָהוֹר כְּחֻלִּין:
A person who partakes of consecrated food that is a fourth degree derivative of impurity is forbidden to partake of other consecrated foods. He is permitted to touch consecrated foods and does not disqualify them. Even when there is cooked food in which consecrated food was mixed, but there is less than an olive-sized portion of consecrated food in a mixture the size of half a loaf of bread, a person who partook of consecrated food that was a fourth degree derivative of impurity should not partake of this mixture. It may be eaten only by one who partook of consecrated food that was removed from impurity by the fifth degree. For he is pure, as we explained.
יהָאוֹכֵל רְבִיעִי שֶׁבַּקֹּדֶשׁ אָסוּר לוֹ לֶאֱכל אֶת הַקֹּדֶשׁ וּמֻתָּר לִגַּע בַּקֹּדֶשׁ וְאֵינוֹ פּוֹסְלוֹ. אֲפִלּוּ תַּבְשִׁיל שֶׁנִּתְעָרֵב בּוֹ הַקֹּדֶשׁ וְאֵין בּוֹ כְּזַיִת בִּכְדֵי אֲכִילַת פְּרָס הֲרֵי זֶה לֹא יֵאָכֵל בִּרְבִיעִי שֶׁל קֹדֶשׁ אֶלָּא בַּחֲמִישִׁי שֶׁהוּא טָהוֹר כְּמוֹ שֶׁבֵּאַרְנוּ:
When a person partakes of terumah or ordinary food prepared with the stringencies of terumah that was a tertiary derivative of impurity, he is forbidden to partake of terumah until he immerses himself in a mikveh. He is permitted to touch terumah, and if he does, it is ritually pure. The Sages imposed a stringency with regard to eating, not with regard to touching.
When does the above apply? To terumah itself. If, however, terumah was mixed into cooked food and there is less than an olive-sized portion of terumah in a mixture the size of half a loaf of bread, such a person is permitted to partake of the mixture, just as he is permitted to touch terumah.
יאהָאוֹכֵל שְׁלִישִׁי שֶׁבַּתְּרוּמָה עַצְמָהּ אוֹ שֶׁל חֻלִּין שֶׁנַּעֲשׂוּ עַל טָהֳרַת תְּרוּמָה הֲרֵי זֶה אָסוּר לֶאֱכל אֶת הַתְּרוּמָה עַד שֶׁיִּטְבּל. וּמֻתָּר לִגַּע בִּתְרוּמָה וַהֲרֵי הִיא טְהוֹרָה. בַּאֲכִילָה עָשׂוּ מַעֲלָה בִּנְגִיעָה לֹא עָשׂוּ מַעֲלָה. בַּמֶּה דְּבָרִים אֲמוּרִים בִּתְרוּמָה עַצְמָהּ. אֲבָל תַּבְשִׁיל שֶׁנִּתְעָרְבָה בּוֹ תְּרוּמָה אִם אֵין שָׁם כְּזַיִת בִּכְדֵי אֲכִילַת פְּרָס הֲרֵי זֶה מֻתָּר לֶאֱכל מֵאוֹתוֹ תַּבְשִׁיל כְּדֶרֶךְ שֶׁמֻּתָּר לִגַּע בִּתְרוּמָה:
Although a person who partakes of terumah or ordinary food prepared with the stringencies of terumah that was a tertiary derivative of impurity is considered as pure with regard to touching terumah, he is considered as a secondary derivative with regard to consecrated foods. For something that is pure with regard to terumah is impure with regard to consecrated food.
When, by contrast, one partakes of ordinary food prepared with the stringencies of consecrated food that was a tertiary derivative of impurity, he is pure. There is nothing that creates a fourth degree derivative of impurity with regard to consecrated foods except consecrated food itself.
יבהָאוֹכֵל שְׁלִישִׁי שֶׁבִּתְרוּמָה אוֹ שֶׁל חֻלִּין שֶׁנַּעֲשׂוּ עַל טָהֳרַת הַתְּרוּמָה אַף עַל פִּי שֶׁהוּא טָהוֹר לִנְגִיעַת תְּרוּמָה הֲרֵי הוּא כְּשֵׁנִי לְעִנְיַן קֹדֶשׁ שֶׁטָּהֳרַת תְּרוּמָה טֻמְאָה הִיא אֵצֶל הַקֹּדֶשׁ. אֲבָל הָאוֹכֵל שְׁלִישִׁי שֶׁבְּחֻלִּין שֶׁנַּעֲשׂוּ עַל טָהֳרַת הַקֹּדֶשׁ הֲרֵי הוּא טָהוֹר שֶׁאֵין לְךָ דָּבָר שֶׁעוֹשֶׂה רְבִיעִי בַּקֹּדֶשׁ אֶלָּא קֹדֶשׁ מִקֹּדֶשׁ בִּלְבַד:
The term "consecrated food" employed with regard to the impurity of foods and liquids refers to sacrificial foods, e.g., meat from sacrifices of the highest order of sanctity, meat from sacrifices of a lesser degree of sanctity, bread from a thanksgiving offering and cakes of a nazirite's offering for which their sacrifice was slaughtered, flour offerings that were sanctified in a consecrated vessel, the two loaves offered on Shavuot and the showbreads when their surface became hardened in the oven. By contrast, the loaves of the thanksgiving offerings and the cakes of nazirite's offering for which their sacrifice was not slaughtered and flour offerings that were not sanctified in a consecrated vessel are not considered as consecrated food, nor as ordinary food. Instead, their status is the same as terumah.
יגכָּל קֹדֶשׁ הָאָמוּר בְּעִנְיַן טֻמְאַת אֳכָלִין וּמַשְׁקִין הוּא קָדְשֵׁי מִקְדָּשׁ הַמְקֻדָּשִׁין כְּגוֹן בְּשַׂר קָדְשֵׁי קָדָשִׁים. וּבְשַׂר קָדָשִׁים קַלִּים. וְחַלּוֹת תּוֹדָה וּרְקִיקֵי נָזִיר שֶׁנִּשְׁחַט עֲלֵיהֶן הַזֶּבַח. וְהַמְּנָחוֹת שֶׁקָּדְשׁוּ בִּכְלִי. וּשְׁתֵּי הַלֶּחֶם וְלֶחֶם הַפָּנִים מִשֶּׁקָּרְמוּ בַּתַּנּוּר. אֲבָל חַלּוֹת תּוֹדָה וּרְקִיקֵי נָזִיר שֶׁלֹּא נִשְׁחַט עֲלֵיהֶן הַזֶּבַח. וְהַמְּנָחוֹת שֶׁלֹּא קָדְשׁוּ בִּכְלִי. אֵינָן לֹא כְּקֹדֶשׁ וְלֹא כְּחֻלִּין אֶלָּא כִּתְרוּמָה:
Challah, the first-fruits, restitution made for terumah and the additional fifth are considered as terumah.
ידהַחַלָּה וְהַבִּכּוּרִים וְתַשְׁלוּמֵי תְּרוּמָה [וְחֻמְשָׁהּ] הֲרֵי הֵן כִּתְרוּמָה:
Tevel, a mixture of ordinary produce and terumah, produce that grew from terumah that was planted, the second and first tithes, and a dough from which challah had not yet been separated are considered like ordinary produce. A primary derivative is impure. A secondary derivative is disqualified and there is no concept of a tertiary derivative.
טוהַטֶּבֶל. וְהַמְדֻמָּע. וְגִדּוּלֵי תְּרוּמָה. וּמַעֲשֵׂר שֵׁנִי וְרִאשׁוֹן. וְעִסָּה הַטְּבוּלָה לְחַלָּה. הֲרֵי הֵן כְּחֻלִּין וְהָרִאשׁוֹן טָמֵא בָּהֶן וְהַשֵּׁנִי פָּסוּל וְאֵין בָּהֶן שְׁלִישִׁי:
Our Sages decreed that whenever an entity would impart impurity to ordinary food according to Scriptural Law if one was certain that they came into contact, when one is in doubt whether it came into contact with dough from which challah was taken, that dough should be prepared in a state of ritual purity. Challah is separated from it, but its status is held in abeyance. It is neither eaten, nor burnt.
טזכָּל דָּבָר שֶׁוַּדָּאוֹ מְטַמֵּא אֶת הַחֻלִּין מִן הַתּוֹרָה גָּזְרוּ עַל סְפֵקוֹ בְּחֻלִּין הַטְּבוּלִין לְחַלָּה שֶׁתֵּעָשֶׂה אוֹתָהּ הָעִסָּה בְּטָהֳרָה. וּמַפְרִישִׁים מִמֶּנָּה חַלָּה וְחַלָּתָהּ תְּלוּיָה לֹא נֶאֱכֶלֶת וְלֹא נִשְׂרֶפֶת: