Way back in primary school they teach you basic geometry, and you learn that the corner angles of a triangle always add up to 180°. In high school you learn more rules, and in first year uni maths you learn how to abstract the concepts of geometry to numbers with vectors and complex numbers. However it would probably take many further years of study before you come across the concepts of
Non-Euclidean geometry (I'm certainly not there yet). However entirely consistent and all-encompassing our 'normal' geometry seems, there is another whole realm where everything we learnt is wrong. Geometries where the angles of a triangle add up to more, or less, than 180°, where truly parallel lines diverge, and where the even weirder happens. These geometries are entirely mathematically sound, and indeed they've probably helped us understand our 'standard' Euclidean geometry further.
In another part of the universe, philosophers (and maybe a few mathematicians too) have come up with many logical arguments against God. Some of these I would say have logical fallacies (like the
omnipotence paradoxes), but others like the question of
predestination vs
free will, really do seem to be logically sound. I've seen no convincing argument that allows God to have complete sovereignty in the universe, while giving humans complete free will. Both are important parts of Christian theology, so must one therefore be wrong?
I had an idea, which along the lines of non-Euclidean geometry, asks whether there could be such a thing as 'non-Euclidean logic'. This would in no way deny any of our current understanding of logic (such as
paraconsistent logic) but instead holds our current mathematical logic in highest regard. What it does do, is asks whether there could be
another logic incompatible with our current one, but still just as mathematically valid. If despite all our experience in Euclidean geometry, other geometries are still valid, could other logical systems be valid too? As logic is part of the universe, it was created by God, so surely he could create others as well.
So finally, in the diagram above, the concepts of God's sovereignty and our free will are represented by parallel lines. In Euclidean geometry they would never meet, and so in traditional logic they are incompatible. But in a elliptic geometry they can meet. Is there a logical system where they can meet too? Is that really how our universe works?
« Last Edit: May 24, 2007, 04:16:01 PM by Dannii »
April 25, 2007, 07:41:01 PM
April 26, 2007, 04:24:00 PMP. Burke
I don't think the relationship between paraconsistent logic and classical logic is much different from the relationship between Lobachevskian and Euclidean geometry. You can't use both at the same time, but there's no reason why they shouldn't both be good for different applications. For some reason, people get the strange idea in their heads that there is One True Logic, but I don't see why you'd have to use the same logic for every application.
Graham Priest has a nice intro book on non-standard logics (not just paraconsistent logics), which I would recommend. I will warn you that it uses proof trees, which is a little annoying.
With respect, I do think the religious stuff is a bunch of hooey. But if you find a way of making it make sense, please let me know and I'll have learned something new.
May 12, 2007, 12:49:18 PMjchfleetguy
Hi,
You contributed to the Christian Carnival during the last 10 or so Carnivals.
As you may or may not know, the Carnival hit a bit of a speed bump when Dory, its administrator, sort of fell off the radar.
It is back.
- The
current Carnival (171) is up- The deadline for the next carnival is Tuesday, May 15th at 9:00pm Eastern time
- Submissions can be sent through
Blog Carnival to emailed to the
submission only gmail account or to mailto:
- A new notification group has been formed at
Google Groups. Go join at if you wish to be notified of upcoming Carnivals - and when Carnivals are posted and ready to read.
The Carnival administrators would appreciate you passing this information on to your readers so we can rebuild the Carnival contributors, and mailing list.
Take care,
John
Brain Cramps for God.