The "as it appears" principle: Whatever degree of heat we perceive a body to have when we come in contact with it, that degree of heat it has. (P 165b)

Experiment: "Suppose now one of your hands is hot, and the other cold, and that they are both at once put into the same vessel of water [W], in an intermediate state …" (P 165bf)

Upshot of the experiment:

(1) W feels cold.
(2) W feels warm.
Therefore by the "as it appears" principle, (3) W is both warm and cold.

Claim: it is an absurdity "to think that the same thing should be at the same time both cold and warm" (P 165b)

Hylas's Principle has led to an absurdity.

Reductio: a principle that leads to an absurdity is not true. (P 165b)

"Consequently, the principles themselves are false ..." (P 166a)

Notice that both Philonous and Hylas seem to think that this argument has as its conclusion that heat does not exist in external objects. (P 166a)