38. Knowledge in mathematics: Here one has to keep on reminding oneself of the unimportance of the 'inner process' or 'state' and ask "Why should it be important? What does it matter to me?" What is interesting is how we use mathematical propositions.
39. This is how calculation is done, in such circumstances a calculation is treated as absolutely reliable, as certainly correct.
This section offers the difference between multiple choice and short answer questions on math tests. A student pencils in on his ScanTron the letter 'b'; a student finds the integral of an equation thereby solving a related rates question. (He shows all his work.) The two answers are given to the same question; there are two different sets of instructions. If both students came about to the same, correct answer then would you say that the former was somehow less correct than the latter? No.
Are inner states being denied? No. The child prodigy that learns the calculus at age four and the college sophmore 15 years his senior who lumbers through the subject offer the same results within the language game of calculus. If I guess correctly the answer to a math question and my partner claims to know the answer and answers correctly--what is the difference?