“It must be a given in the system. One cannot adopt the position of a user of the rules of chess whilst playing the game and simultaneously question the rules by moving in ways that break the rules. My moving my knight to checkmate the king is being guided by the rules of chess. Of course I might wonder why the game has to end so arbitrarily and imagine another game in which there were no rules governing “checkmate” but this would be a different game to chess, if indeed one thought that a game without an end was a game at all. If my opponent makes a mistake and carries on playing after I have checkmated his king, I do not celebrate his invention of a different game and join him in playing this game without an end. I correct his mistake by appealing to the rules concerning checkmate. Similarly, in mathematics we count in accordance with the rule n plus 1 and if we happen to skip a number we don’t let the mistake alter the formulation of the rule to n plus 2. We correct the mistaken behavior by appealing to the rule”. A Mathematics major known to Sophia asked her: “But then how do we submit the rule to philosophical reflection?” Surely critical reasoning goes all the way up in the system and does not stop at a particular level.” Sophia looked around for assistance in answering the difficult challenge but Robert came tentatively to her rescue whilst looking to Jude for support “We have had a similar discussion earlier but perhaps a more nuanced answer is possible now. I don’t know enough about mathematics to be certain of this but on what we have heard so far, Mathematics is a form of life with its own rules which allow game-like moves which are its calculations, to be made by the agents engaged in the form of life. These rules have been formed by the calculations and the point of the game, over a long period of time….” Jude acknowledged that Robert was in difficulties, nodded in acknowledgment of Robert’s point, and continued. “….by the dialectical process exploring extreme alternatives which have detracted from the point of the game. If the point of counting is more to do with the measurement of time than the quantification of a number of objects in our environment then n+1 rather than n+1/2 or n+2 would seem to have many advantages when using a clock for example to measure time. The Greek idea of 12 hours being one day then serves as a system or framework for the counting of units of time rather than the decimal based- system that of course allows calculations to be done more easily. With the introduction of the decimal-based system the point of mathematics becomes more complex and more capable of measuring a continuum by the division of numbers into decimals and those decimals into decimals. So if time is an actual continuum it becomes theoretically possible to chart continuous changes. In the old dozen - based system, the second was the resting point. Theoretically one could have divided it into 12 parts but this would not have been a manageable system. The reason that 12 was selected as an important unit had to do with the fact that light and day at the equator appeared to be equally distributed in 12 hour periods.” An Economics major, threw up their hands in desperation: