By Daniel Hill
This publication examines divine nature by way of maximal greatness. It investigates each one characteristic linked to maximal greatness - omnipotence, omniscience, excellent goodness and sweetness, arguing that maximal greatness is critical for divinity.
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In either case we will have a truth: that T1 is a member of that set, or that it is not. There will then be at least as many truths as there are elements of the power set PT . But by Cantor’s power set theorem we know that the power set of any set will be larger than the original. There will then be more truths than there are members of T , and for any set of truths T there will be some truth left out. There can be no set of all truths. (Plantinga and Grim 1993: 267). 32 Omniscience Since there is no property of truth simpliciter, as we have concluded, there is no set of all truths, as, if there were, there would be the property of being a member of that set, which would be equivalent to the property of being true simpliciter.
38 Omniscience I’ll start by analysing the ﬁrst way. Let us examine Kretzmann’s argument against the compossibility of omniscience and individuality in more detail. 28) I am Daniel Hill. 28) expresses a truth, when I utter it, since I am Daniel Hill. Why cannot a divine being know the expressed proposition? 33) Every divine being knows that I am Daniel Hill. This is because, as Hector-Neri Castañeda has argued (Castañeda 1967; repr. Castañeda 1999) usually indexicals in oratio obliqua (reported speech or attributions of propositional attitudes) take their reference from the speaker (or believer, as appropriate).
Every function? Here we ﬁnd the different sorts of necessity. e. 34 A proposition is said to be conceptually necessary if and only if it is mapped to truth by every function that obeys the laws concerning concepts. What are these laws? They are what are discovered by philosophers engaged in conceptual analysis. For example, the sentence ‘If one knows a proposition it is true’ expresses a conceptually necessary truth, since the concept of knowledge includes that of truth. 36 A proposition is said to be nomologically or physically necessary if and only if it is mapped to truth by every function that does not represent a contravention of the laws of nature.