Question

Hello,
I listen to the Rabbi’s online lessons on Talmudic logic, and I wanted to ask the Rabbi a few questions about the third lesson, on a fortiori reasoning.
1. The Rabbi argued in the lesson that a Talmudic a fortiori argument is induction and not deduction, since the logic of the argument can be refuted by adding data, whereas deduction, by contrast, cannot be refuted. And in the previous lessons the Rabbi argued that this follows from the fact that deduction works from rules to particulars (and therefore cannot be refuted, because the information is contained in the premises), whereas induction goes from particulars to rules, and therefore there is room for error. Can the Rabbi explain this principle in the case of a fortiori reasoning? In other words, what are the particulars of the a fortiori argument from which we derive a general inference?
2. The Rabbi explained that the relation between horn and tooth/foot is the same relation as between the public domain and private domain, so why does the a fortiori argument from the injured party’s courtyard to the public domain yield the result that horn pays half-damages in the injured party’s courtyard, whereas the a fortiori argument from horn to tooth and foot yields the result that horn pays full damages in the injured party’s courtyard?
3. Even if we assume that the law derived from the a fortiori argument really does change when you reverse it, why did the Sages argue against Rabbi Tarfon on this a fortiori argument with the principle of “it is enough,” if the law of full damages can be learned without adding to the original case?
Thank you.