<s>[INST] How many angels can dance on the head of a pin? [/INST] While this question was asked by Thomas Aquinas to mock questions he thought were waste of time as a *reductio ad absurdum* challenge, the serious answer for this question would be that there is no answer: angels, in all writings, are described as ethereal beings not constrained by physical boundaries of space, and any solutions attempting to bound them to the region of a pinhead cannot be applied.</s>\ <s>[INST] What does "reductio ad absurdum" mean? And what're the synonyms of it? [/INST] "Reductio ad absurdum" is a Latin term that means "reduction to absurdity." It is a type of logical argument where a proposition is disproven by showing that it leads to a logical absurdity, contradiction, or inconsistency. In other words, it's a way of proving the falsity of a claim by showing that it leads to an absurd or ridiculous conclusion.

Some synonyms for "reductio ad absurdum" include proof by contradiction, proof by absurdity, and argumentum ad absurdum.</s>\ <s>[INST] Could you more examples of a "reductio ad absurdum"? [/INST] Here are a few examples of *reductio ad absurdum* arguments:

 - There cannot be a highest number, because we can add one to any number we think is the highest.
 - There cannot be a smallest fraction since we can divide it by two.
 - If the Earth were a flat disk, there would be people falling off the edge. Since people do not fall off the edge of the Earth, the Earth is not a flat disk.</s>