Now, the question is as follows. Do you know that you know these things to be true? Or do you just believe that you know these things to be true?
An honest answer is that we can never know that we know things to be true. We can only believe that we know things to be true. There is always the possibility that there are mistaken assumptions or other things that are leading us to incorrect conclusions. No doubt, there are certain "facts" that we "know" today which will one day turn out to be quite different.
This seemingly arcane question has become very relevant to the recently-revived crusade to delegitimize the rationalist approach to Chazal and science.
Rabbi Moshe Meiselman, in Torah, Chazal and Science, claims that Chazal would not make a definitive statement unless they knew with absolutely certainty that it is true. "A major thesis of this book is that if Chazal make a definitive statement, whether regarding halachah or realia, it means that they know it to be unassailable" (p. 107; see too p. 33). In other words, when they say something about the natural world, it is not the case that they merely believe that they know it to be true. Rather, they know that they know it to be true. Accordingly, to say that they are mistaken is an attack on their integrity, and is therefore utterly wrong and heretical.
And thus, according to Rabbi Meiselman, when Chazal say definitively that any species in which the male has internal genitalia, lays eggs, this must be true, and accordingly, either elephants used to lay eggs or they used to possess external genitalia. When Chazal say definitively that the gestation of animals such as wolves is three years, it must be that this used to be the case. Similarly, when Chazal said that the atalef (bat) lays eggs, they must have been referring to creatures such as the duck-billed platypus, rather than mistakenly referring to the animal that every Torah scholar always understood the word atalef to refer to - the bat. Likewise, when Chazal say definitively that there is a salamander that is generated from fire, this must be true.
There are innumerable other such cases. In all these instances, according to Rabbi Meiselman, if you say that Chazal merely sincerely believed such things to be true (as did countless others in antiquity, and as we do about everything we think we know) and could thus be mistaken, you are a heretic. Instead, you are obligated to believe that Chazal knew these things to be true, and thus that these things are indeed true. (It remains unclear to me why Rabbi Meiselman considers the spontaneous generation of insects to be impossible, and thus insists that Chazal never believed in any such thing, but accepts the spontaneous generation of salamanders.)
Rabbi Yaakov Menken applies this to Rambam as well, at least in one case. Rambam says firmly that pi is irrational, and adds that only fools think otherwise. It happens to indeed be correct that pi is irrational, but did Rambam actually know this, or just believe it? According to Rabbi Menken, this cannot be simply a matter of Rambam's belief, similar to the way in which many other people in the medieval and possibly even the classical era believed pi to be irrational, since Rambam says it so definitively. Rabbi Menken argues that even though the irrationality of pi was only formally proved in the 18th century by Lambert, Rambam was uniquely privy to another, even more conclusive source - namely, some mysterious source in Chazal that he refuses to mention (!). Just as Rabbi Meiselman argues regarding Chazal, Rabbi Menken argues regarding Rambam, that if he states it definitively, he must have had conclusive knowledge of the fact. He didn't just believe it to be true - he knew it to be true.
But is that itself actually true? Let's take a look at some other definitive statements of Rambam:
"It is not impossible… that vermin be created from rot inside food, except as far as the fools who have no knowledge of the natural world are concerned, as they believe that all creatures cannot be generated except via a male-female relationship since this is what they see transpires in most cases." (Rambam, Sefer HaMitzvos, Lo Sa’ase 179)Here we see Rambam likewise stating definitively that spontaneous generation takes place, and dismissing those who think otherwise as being fools. Yet did Rambam know this to be true? Of course not - because it is actually false! The "fools" are correct, and there actually is no such thing as spontaneous generation! Rather, Rambam believed it to be true. And it is not mocking Rambam's integrity or intelligence to point out that it is false. Belief in spontaneous generation was perfectly normative until quite recently, and it is only to be expected that even an extraordinary genius such as Rambam would subscribe to such a belief.
In exactly the same way, when Rambam said with certainty that pi is irrational, it does not mean that he had any more reason for his certainty than when he said that spontaneous generation is a fact. He sincerely believed pi to be irrational, and he may well have had very good reason to do so - after all, the existence of irrational numbers had been demonstrated a thousand years earlier, and mathematicians had spent centuries failing to calculate an exact value for pi. As we have seen, there were several mathematicians in the medieval period who asserted that pi was irrational, and this was a common belief that turned out to be correct. But Rambam did not have the basis to know that pi is irrational. (And nor, let us again point out, has Rabbi Menken proposed what this alleged basis actually was.)
And in exactly the same way, when Chazal said various statements about the natural world, it does not mean that they knew these to be true. Rather, they believed them to be true. Accordingly, it is not remotely impugning Chazal's integrity, or the authority of the Gemara, to note that these statements are not necessarily true.
(Hat tip to R. David Ohsie for inspiring this post)