This is a series of mashalim attacking Bnai Yisrael and the Torah.
Art Scroll Bechoros Daf 8b(5) note 42 states that the next questions were deliberately absurd in order to test his ability to deal with questions that he could not have considered in advance even of an allegorical level. Maharal says that they must have meant deeper philosophical meanins, though they could be also solved in a superficial sense. The following notes give both interpretations.
The first statement is dealt with in note 45.
The elders asked for an empty statement which would include a false predicate.
Rav Yehoshua did them one better by presenting a tale false in all
its particulars: one with an impossible subject (the foal of a mule)
as well as a preposterous predicate (the foal was born bearing a
By saying the foal of the mare is impossible, they made themselves look ridiculous by implicitly accepting that had he said the foal of a horse, it could have been true.
Gra connects this to the gemara in Avodas Zara 11b that Rome would put an able bodied man (Esav) on the back of a limping man (Yaakov) to show that Rome was in charge.
Rav Yehoshua said that the mule (Zion) would give birth and "collect" all that was owed the Jewish people for the persecution. This is like the declaration of the navi Rani Akarah
When the elders objected and implied that the Jews would never be redeemed (a mule cannot give birth), Rav Yehoshua replied, this is the falsehood. See note 15 on Page 70 of Gra's Commentary on Various Aggados
Kedushas Levi says that the mashal is that the mule represents an evil person.
Rav Yehoshua told of the wicked man who finally performs some mitzvah.
But his act is "born with a demand for a hundred thousand zuz"; the
evildoer immediately feels that he is owed an enormous reward by his
Father in Heaven! Asked the Athenians: Does it ever happen that an
evildoer, submerged as he is in sin, performs a mitzvah? Conceded Rav
Yehoshua: That is part of the fiction! Even the occasional mitzvah
observed by an evildoer is ingenuine, because it is performed not for
its own sake but in expectation of recompense.
Note 46 says about the next set of questions
Because the Athenians were unable to understand Rav Yehoshua's
"absurd" parable, they countered with their own (apparent) absurdities
in the hope that he would not understand their intent. Maharsha
The embryonic sac, which shelters and preserves the developing fetus.
That which preserves what does not exist (the embryo of the mule) is
fit as well to preserve what cannot rot.
In this question, the Torah is called Bris Melach (a covenant of salt) and they attacked saying that the covenant had been broken (the salt was rotted). This is like the "replacement theology" of the gentiles. He responded by saying that the "replacement" does not exist as the gentile avodas zara is false. See Art Scroll Bechoros 8b(6) note 48.
Gra adds that the covenant is upheld by the blameless children who are too young to be obligated by the Torah, but nevertheless study
Torah and perform Mitzvos. Small children are called "afterbirth" in
the phrase, the afterbirth that emerges from between her legs
The elders used the analogy of the mule to claim that once Israel went into exile, Tzion is like a mule that cannot have offspring. Rav Yehoshua responded that the bris with Hashem is like salt that cannot rot and Yisrael will thus be able to "have children" unlike the nations which are indeed like mules.
See also Michtav MeEliyahu II p. 49 who cites a homily by R' Chaim Volozhiner
The next question, the house in the air, shows Rav Yehoshua's connection to the supernatural. Artscroll Bechoros 8b6 note 51 says
One would have expected such a feat to dispel, by itself, any doubts the Athenians may still have harbored regarding R' Yehoshua's capabilities. However, the issue at hand was whether the Jewish Sages were privy to Divine insight, while R' Yehoshua's ascent was a display of supernatural power rather than of supernatural wisdom.
His answer was to show them that they could not "build" such a building without being able to provide the necessary preparations. If the preparations are not possible, the the builder is not at fault for not completing the building (note 52 Maharal)
Maharsha describes this as an attempt by the elders to say that the Jews would never be able to return to a relationship with Hashem (build the temple) because Eretz Yisrael is under the control of the Romans and there is no place on Earth that hte Jews can call their own.
Rav Yehoshua showed that Hashem is accessible to all who cleave to him even "between the sky and the Earth". It is only the worshipers of idols who insist on concrete physical representations that cannot approach Hashem.
Maharal says that the Sages explain that the soul is separate from the body and continues after death. The Athenians held that both body and soul are destroyed by death.They argued that since the sage believe that a person is both a soul and a body then a person should be able to "dwell" in both realms. Since man is restricted to Earth, that proves it is not so.
Rav Yehoshua answered that since man has a bodily component, then that component prevents him from rising to his complete status. Man cannot raise the physical to existance "above the Earth".
According to Nezer Nitzachon, the Athenians denied creation ex nihilo. Rav Yehoshua answered, that Hashem created the universe, it is only man who must build from what already exists.
Rav Yehoshua demonstrated the internal contradiction inherent in the Athenian belief structure.
For although Aristotelian philosophy asserts the eternity of matter,
it also holds that matter draws its existence from an immaterial First
Cause. How, asked R' Yehoshua, if you cannot conceive of a "building
in air", do you intend to elevate bricks to that selfsame air? How can
matter, the fundamental "bricks" of which the world is built, emanate
from a Cause completely immaterial?
The question of the field of knives according to note Artscroll Bechoros 8b8 note 56 is like the salt rotting.
This echoes the earlier question regarding the presevation of salt.
Here too a method is sought to produce an effect on a thing that
usually produces that effect on other things.
This involves providence, Hashem affecting the world and things happening by "chance" (see note 58).
The "field of swords" denotes the troubles of the world. The Athenians say that at most, the concept of Hashem is that of the "watchmaker" who has abandoned the world to run as it happens. Note 58 points out that this is the problem of צדיק ורע לו (A righteous person who suffers).
Have the Jewish Sages, they challenged Rav Yehoshua, any incisive
theoretical "tool" with which to "undercut" our conclusion?
Rav Yehoshua's answer was designed to force their objection.
קרנא דחמרא would use the word חמר not as donkey but as matter. קרן means excellence. They objected that matter is inferior, so how can the "excellence" of matter prevent (or cut off) the ills of the world. Rav yehoshua points out that once you have granted that matter is inferior, you have done away with the problem of evil. As it says in *Shabbos 55a, "there is no suffering without sin". Suffering of perfectly innocent people is not the result of a special Providence, nor of a completely amoral cosmos (nor of "chance") but the inevitable cost of life as corporeal beings.
They result from the innate deficiency of matter: our material bodies,
like all other matter, are inherently unstable ans susceptible to
injury and to dissolution. Man's immortal soul, on the other hand, is
excellent indeed, and offers man his ultimate escapefrom the
vulnerabilities of the flesh. (Maharal; note the conceptual parallel
to his analysis cited in note 52; see also Moreh Nevuchim 3:12, and
Ralbag to Iyov 5:26)
Maharsha and Rambam in Hilchos Teshuva 9:12 speak of the idea that Bnai Yisrael can only perfect themselves in a time of peace and tranquility. The elders pointed out that in the galus, this can never occur. Rav Yehoshua connects the answer to "keren meshicho" as the mashiach is a humble man riding on a donkey (Zecharia 9:9)
*Gr'a connects the "row of swords" to Rome (Esav) who "lives by the sword" (Toldos 27:40.
Who crowed the sages of Athens shall ever vanquish mighty Rome?
Rav Yehoshua answeed that Rome is living off the reward garnered by Eisav for the use of his sword to protect and feed Yitzchak (see Devorim Rabbah 1:15) Once that is used up, Hashem will send the Mashiach to redeem Israel and Rome will fall.