More math
I can't claim credit for this little redux, it actually owes its existence to one Bertrand Russell, but it does provide a little food for thought:
If 2+2=5, and twice two is four. Subtract 3 from both sides then 1=2. But you and the Pope are two therefore you and the Pope are one. [and therefore you're the Pope!]
Its in that basic form. Two things strike me from this silly little display. First, historically, with the advent of non-Euclidean geometries and various 'logical systems', the whole project of mathematics became one of consistency - not truth as from some outside source. This is why prior to these forays into mathematical extravagance Theology, Mathematics and Philosophy were tied so closely together. Mathematics did not have to appeal to some experience, or observation for its truth, it was in some sense like seeing into the mind of God. Mathematics fell on hard times after that, however. (one is reminded of Gauss' assertion that we should climb three very tall mountains with beams of light to determine what the "actual" measure of the interior angles of a triangle is to determine whether Geometry should be plane (Euclidean), hyperbolic or elliptical) I guess the point is that if you base your mathematics solely on the principle of self-consistent axioms solely, then what was once a rich edifying subject is now just a chess match. Ugh. From a non-mathematical standpoint one finds this very distasteful.
The second thing that strikes me is a caveat pure and simple: Beware taking the solution to an equation for real life. Let God be a mathematician - I find that warming. But if God is a mathematician, I certainly don't think he makes axiomatic consistency His primary rule of thumb. We can certainly create an axiomatic system where 2+2=5, but equating me with another is a much further step. I would caution scientists from doing the same thing.
Its in that basic form. Two things strike me from this silly little display. First, historically, with the advent of non-Euclidean geometries and various 'logical systems', the whole project of mathematics became one of consistency - not truth as from some outside source. This is why prior to these forays into mathematical extravagance Theology, Mathematics and Philosophy were tied so closely together. Mathematics did not have to appeal to some experience, or observation for its truth, it was in some sense like seeing into the mind of God. Mathematics fell on hard times after that, however. (one is reminded of Gauss' assertion that we should climb three very tall mountains with beams of light to determine what the "actual" measure of the interior angles of a triangle is to determine whether Geometry should be plane (Euclidean), hyperbolic or elliptical) I guess the point is that if you base your mathematics solely on the principle of self-consistent axioms solely, then what was once a rich edifying subject is now just a chess match. Ugh. From a non-mathematical standpoint one finds this very distasteful.
The second thing that strikes me is a caveat pure and simple: Beware taking the solution to an equation for real life. Let God be a mathematician - I find that warming. But if God is a mathematician, I certainly don't think he makes axiomatic consistency His primary rule of thumb. We can certainly create an axiomatic system where 2+2=5, but equating me with another is a much further step. I would caution scientists from doing the same thing.
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