The most lucid answer with which I'm familiar is Barry Miller's.

God necessarily knows himself. His creating one world rather than another rather than nothing at all is contingent, in the sense that it is contingent that he create this world.

But God is merely Cambridge-related to his creatures (though his creatures are really related to him). The identity condition for God's act of will and God's knowing (which are the same) is its being God's act of willing his own goodness and knowing himself; that these acts and knowings are also (in some possible worlds) willings to create and knowings of contingent facts is not what determines their identity.

One solution that may help is to consider that Aquinas has many different notions of necessity. Absolute necessity and necessity per accidens are distinct. The latter is necessary insofar as something exists, E.G. as I type each key the moment I type the key it is unpreventable that I did so ( Thomas believed that not even God could change the past). Never the less it is not the case that I was necessitated to type each key.

We must also  distinguish necessity on the side of the known and on the side of the knower. The two notions come apart. My knowledge of Modus Tollens may by based on a necessary object of knowledge, my knowing of it is not necessary. With God his knowledge that world x is such a way is necessary, but the object- the world- that he knows is not in itself necessary. 

When God has knowledge of the world he has it through vision in the same sense that I am seeing the screen ( every temporal moment is equally present to God in this way), and just as my knowledge that I am typing right now is necessary per accidens, as the past cannot be changed, what ever happens to be the way the world is grants God necessary knowledge of it per accidens as well. In what ever world God creates those contingent aspects of it are known necessarily per accidens, without being necessary truths themselves. Now there are non-contingent truths that God has necessary knowledge of as well, but that knowledge would be identical across possible worlds. 

When we consider other possible worlds and their contingent aspects it is true that world X with properties ABC and world Y with properties BCD are distinct, and for God to know X as the actual world and then Y as the actual world would change his knowledge and make it non necessary. But God only has one act of creation and knowledge, and thus only knows the other possible worlds that are not actualized as possible worlds, while knowing our contingent world as actual necessarily per accidens. Given that those other worlds are only possible God lacks no knowledge by not knowing them as actual- this would be only for God to believe in a falsity.

Dan K. wrote:

1. What is a real relation?
2. What is a cambridge relation?

If I'm shorter than my sister, and my sister has gained height so that she is taller than me. Does it mean that she is taller than me, and that is a real relation? And that my short-ness is merely cambridge? But in that, what does it mean by such a relation, that it is not real, but only cambridge? I'm having trouble with how exactly it is that real relations and mere cambridge relations are to be distinguished. 

Good question. Geach originally introduced the notion of Cambridge change, and I should note that Miller only extends this notion to Cambridge properties, but I think it's probably natural enough to extend it to relations.

x has Cambridge changed when something has "become true" of x but this has made no "real difference" to x. If your sister grows taller than you, but your height doesn't change, then your becoming taller was a mere Cambridge change. (The notion of whether the change makes a "real difference" is, I think, mostly a linguistic primitive.) A Cambridge property is just one the possession of which does not "make a difference" to x. I imagine a heuristic here might be that a Cambridge property is a property that can be acquired by Cambridge change. One can also consider how the different properties behave in modal contexts.

Notice that this depends what property we are talking about. Say instead you shrink to be shorter than your sister. Your becoming shorter than your sister was a Cambridge change, and the final property you possess, "being shorter than your sister," is a Cambridge property. But you really changed. We can say this because "'P' denotes a Cambridge property" is intensional; that is, we might not be able to substitute extensionally equivalent properties for P.

To put it differently, you underwent a Cambridge change qua becoming shorter than your sister, even though you underwent a real change qua becoming this specific height. So you asked:

Dan K. wrote:

If I'm shorter than my sister, and my sister has gained height so that she is taller than me. Does it mean that she is taller than me, and that is a real relation? And that my short-ness is merely cambridge?

Her being taller than you is a Cambridge property/relation; this is because it is a property that could have been acquired by Cambridge change, that is, by a change that made no real difference to her.

The question of whether your shortness is Cambridge or not is ambiguous. If "being this particular height" is what is meant by "shortness", then it is a real property. Since we're talking about relations, "shortness" probably should be read as "being shorter than your sister" - and that is a Cambridge property/relation.

Last edited by Greg (11/11/2015 12:13 am)

Dan K. wrote:

Anyways, I'm still now understanding how the fact that God's knowledge extends to a multiplicity of objects doesn't violate divine simplicity.

Well, I would suggest trying to formulate an argument to the effect that it does violate divine simplicity and see what's wrong with it. Then see if that defect in the argument could be repaired, etc.

I suppose the claim would have to be that if God knows multiple objects, then he must have multiple mental states, like his knowledge about object x and his knowledge about object y. The reply to this objection is similar to the one made to the objection above; that is, all of God's knowledge is the same act of knowing, but what gives that act of knowing its identity conditions is that it's an act of God's self-knowledge. As it happens, God also creates and knows his creation, but he knows his creation by knowing what he creates.

Dan K. wrote:

Also, if you could I would be pleased if you could guide me to good sources to read on what analogy is. Thanks. 

I haven't read much about analogy in particular, but others here might have more for you.