-Reasoning is based upon internal and external observations, and any "reasons" would be those that humans think up based upon their perceptions
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7. By 2, God is omniscient and therefore his mind is infinite.
What if there are only finitely many knowable propositions? Why would a mind have to be infinite in order to know only finitely many knowable proposions? If you think that there are infinitely many knowable propositions, why do you think so? However, even if it is provably the case that there are infinitely many knowable propositions, if the Christian god can act outside of human reason, why couldn't there still be only finitely many knowable things, thus making the Christian god's omniscient mind finite?
I see no prima facie reason to accept that there is any fact that is is unknowable-in-principle. It appears to be nothing more than an appeal to invicible ignorance and places an arbitrary limit on human endeavor. I wonder why anybody would care about trying to learn something new when they feel justified in simply declaring that it's "the unknowable will of god". I also wonder why you're apparently attempting to reason about something when you explicitly claim that reasoning is not relevant to it?
No, it is not. It is merely pointing out that unless you can show that the set of all knowable propositions is non-finite, it isn't valid to conclude that omniscience implies having an infinite mind.
Also, I'm not discussing "knowable by us", but "knowable in principle", that is: a proposition, p, is knowable-in-principle if and only if it is possible that there exists a being, b, such that there is a possible situation, s, in which b can exist, such that b can know p is situation s; knowability-in-principle (of p) is logically independent of the contingent features of any actually existing minded beings, as all it requires that there is a possible being that could know p if said being was situated properly.
If god is omniscient, god actually knows all truths; therefore, if god is omniscient, all truths are knowable-in-principle.
Not to nitpick from the wrong side of the fence, but there are infinite knowable propositions. The representations in arabic numerals of all real counting numbers is but one set. Simply knowing the law of addition and proof-by-induction is not enough to be considered complete knowledge of the set. Each representation must be known separately, IOW, grokked in the fullness.
Don't feel bad about it. I wanted somebody to say something like that or at least to bring up the provable non-finiteness of formally undecidable propositions in a second- or higher-order logic with identity; I just didn't want to give it to them.
However, strict constructionalists would say that the numbers don't exist until the representations have been constructed, as numbers and numerals aren't distinct. I'm not convinced of that, for pragmatic reasons, but it's still an argued position in the philosophy of mathematics.
However, the last bit still holds: if god is omniscient, then all truths are knowable-in-principle.
Sometimes, my fingers type too much, apparently. Not having an edit function for comments on LJ is disconcerting; it would be useful if it was restricted to 5 minutes after posting the comment, for instance. I will have to investigate how to bring up this idea to the maintainers of this site.
Knowable by something in some situation; your question doesn't apply because I'm not talking about contingent knowability relative to the limits of some type of being, but about knowability-in-principle.
What reason do you have to believe that there is anything that is knowable-in-principle that isn't knowable by humans through either direct observation or reasoning from observations?
Re: Again, please see the big picture.empirical_logicFebruary 5 2006, 03:12:46 UTC
If god knows it, it is still the case that it is knowable-in-principle. Anyway, if god knows it, he could just divinely inspire somebody with true beliefs and, granting that divine inspiration that results from a truly omniscient, omnipotent being justifies those beliefs, the person thus inspired would know it too. So, if god knows it, it's knowable by humans.
What if there are only finitely many knowable propositions? Why would a mind have to be infinite in order to know only finitely many knowable proposions? If you think that there are infinitely many knowable propositions, why do you think so? However, even if it is provably the case that there are infinitely many knowable propositions, if the Christian god can act outside of human reason, why couldn't there still be only finitely many knowable things, thus making the Christian god's omniscient mind finite?
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Also, I'm not discussing "knowable by us", but "knowable in principle", that is: a proposition, p, is knowable-in-principle if and only if it is possible that there exists a being, b, such that there is a possible situation, s, in which b can exist, such that b can know p is situation s; knowability-in-principle (of p) is logically independent of the contingent features of any actually existing minded beings, as all it requires that there is a possible being that could know p if said being was situated properly.
If god is omniscient, god actually knows all truths; therefore, if god is omniscient, all truths are knowable-in-principle.
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However, strict constructionalists would say that the numbers don't exist until the representations have been constructed, as numbers and numerals aren't distinct. I'm not convinced of that, for pragmatic reasons, but it's still an argued position in the philosophy of mathematics.
However, the last bit still holds: if god is omniscient, then all truths are knowable-in-principle.
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Sometimes, my fingers type too much, apparently. Not having an edit function for comments on LJ is disconcerting; it would be useful if it was restricted to 5 minutes after posting the comment, for instance. I will have to investigate how to bring up this idea to the maintainers of this site.
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Knowable by whom and what?
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When I say "we can't know," I expect people to know what I'm talking about- namely people.
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After that, you could take a crack at my oldie-but-goodie "Mountain Allegory":
http://www.geocities.com/nanikore.rm/mountain.html
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I want to see scientists try the same thing by rewinding past the "big bang" event.
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