Religion

Could God have made pi a simpler number?

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For an answer to a similar question, go here.

There are a few distinctions we need to make before we can addressthis question. The work we need to do to make these distinctions is anice example of how philosophy can help us be clearer about whatquestion we're asking.

Ask first: Could π have beena different number? Most philosophers today would answer that it could nothave been, just as Richard Nixon could not have been someone other thanRichard Nixon. The expression "π" is a name of a certain number, andthat number is whatever number it is; itcould not have beena different number. That this is the right thing to say is somethingthat has been widely appreciated only for about the last thirty yearsor so, as a result of groundbreaking work by Saul Kripke.

If that is right, then God could not have madeπ anything other than π, for then π would have been something otherthan π, which it could not have been.

That'sprobably not the intended question, though. Rather, the intendedquestion was probably: Could God have made it the case that the ratioof a circle's circumference to its diameter were something other thanπ, say, 3? Do not say that, in that case, π would have been3. Perhaps we would then have used the expression "π" to refer to 3,but that's different. π is the number that is actually theratio of a circle's circumference to its diameter, and in the imaginedcircumstances the ratio of a circle's circumference to its diamaterwould not have been what it actually is, that is, would not have been πbut would have been some other number, 3. (That's all Kripke, again.)

Ifthat's thequestion, then we need to ask: Could the ratio of a circle'scircumference to its diamater have been other than what it actually is?One other clarification: The ratio of a circle's circumference to itsdiameter will always be π only if we are assuming that the underlyinggeometry is Euclidean. There are plenty of non-Euclidean geometries,and modern physics tells us that the geometry of space is, in fact, notEuclidean. It follows that the ratio of the circumference of an actual circle in actualspace to its diameter is not usually π, though it is usually close,because space is generally quite close to being Euclidean. (What is theratio? It varies: There need be no fixed ratio in non-Euclideangeometries.) So, in a sense, if God created the world, then God didmake a world in which the ratio of a circle'scircumference to its diamater isn't π, and perhaps God could have madea world whose geometry was Euclidean, in which case God could have madea world in which the ratio of a circle's circumference to its diamaterwas always π. But again, I take that not to be the question beingasked, though it's a question worth asking.

The question I take to be at issue is: Could the ratio of a circle'scircumference to its diamater, in a Euclidean space, have been other than what it actually is? Hereagain, most philosophers would answer "no", on the ground thatmathematical facts are necessary, and the fact that the ratio of acircle's circumference to its diamater is π is a mathematical fact ifany is. If so, then God once again could not have made the ratio of acircle's circumference to its diamater, in Euclidean space, something other than π, since it could not have been other than π.

So, with that all said, see question 26,as Jyl suggested, for some discussion of the question how God'somnipotence is supposed to be related to questions of necessity.

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