What the Tortoise Said to Achilles

IN 1895 Lewis Carroll published in Mind1 a brief dialogue, `What the Tortoise said to Achilles’. The Tortoise says that there might be someone who accepted the two propositions:

(A) Things that are equal to the same are equal to each other, and

(B) The two sides of this triangle are things that are equal to the same,

but did not accept

(C) If things that are equal to the same are equal to each other, and if the two sides of this triangle are equal to the same, then the two sides of this triangle are equal to each other. For arguments which are said to have suppressed premises are said to be valid in virtue of having them, and valid arguments do not need to be strengthened.

Source: www.math.dartmouth.edu