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A Case Against Omniscience:
Infinite Regress

5. Reply to Objections to
Infinite Regress of Knowing

In this final section, I deal with objections to my Argument from Infinite Regress of Knowing. Below is a complete list of objections considered. For other pertinent replies to infinite regress arguments, see my responses to objections to my first argument, the Argument from Infinite Regress of Reasons.

Book cover: Metaphysics: A Very Short Introduction by Stephen Mumford

Objection 1: You have assumed that God is omniscient and then concluded that God is not omniscient. You have contradicted yourself.

Reply: My initial five premises define an omniscient knower as knowing all truths and draw out what logically follows from that definition. These premises nowhere assume that an omniscient knower or God exists. In the Analysis and Conclusion section, I show how assuming that there is a set of 'all truths' leads to a contradiction. If 'God' is defined as a knower who necessarily knows all truths, then it is impossible for God to exist. There is no contradiction between defining 'God' as necessarily omniscient and proving that, in fact, no such knower can exist.

Objection 2: Your argument completely misses the mark because God's perfect knowledge is incomparable to our limited human knowledge.

Reply: My argument makes no comparison between the nature of God's knowledge and human knowledge.

Objection 3: All of your premises assuming God's knowledge is propositional and that his knowledge must be justified using discursive/inferential reasoning are false.

Reply: My argument makes no assumptions and relies on no assumptions about what God knows and how he knows what he knows over and above that he knows 'truths'.

Objection 4: In your analysis, you write that 'the fact of an omniscient knower's knowing that it knows this set [of all truths] cannot be in the set'. Why can't it be? 'An omniscient knower knows all truths' is a truth. As it's not a new truth, that truth is included in the scope of the original claim that an omniscient knower knows all truths. There is no contradiction in supposing so.

Reply: The objector insists that 'An omniscient knower knows all truths' is a truth that is included within the scope of the original claim that an omniscient knower knows all truths. Let's then put this truth in the set of truths the omniscient knower knows in the original claim.

Let constants a, b, c ... z stand for each of the other truths the omniscient knower knows. Then the following is a truth:

  1. (P)
    An omniscient knower knows {a, b, c .... z, 'An omniscient knower knows all truths'}.

That being the case and given that the omniscient knower knows all truths, including (P), there is this truth. Let's call it (Q).

  1. (Q)
    An omniscient knower knows 'An omniscient knower knows {a, b, c .... z, "An omniscient knower knows all truths"}'.

But truth (Q) is not included in the set of truths the omniscient knower knows specified in (P).

If (Q) was included in the set of truths the omniscient knower knows specified in (P), then (P) would have read as such:

  1. (P′)
    An omniscient knower knows {a, b, c .... z, 'An omniscient knower knows all truths', 'An omniscient knower knows "An omniscient knower knows {a, b, c .... z, 'An omniscient knower knows all truths'}"'}.

Note how the set of truths the omniscient knower knows specified in (P′) is expanded compared with the set of truths the omniscient knower knows specified in (P). The truths specified in (P) do not exhaust the truths specified in (P′). There is a truth that the omniscient knower knows in (P′) that it does not know in (P). If that's the case, then the omniscient knower doesn't know all truths—which is a contradiction. Therefore, omniscience is impossible.

Objection 5: Contrary to your argument, God's knowing the truths of arithmetic is not a problem, even though the truths of arithmetic are infinite in number. So why should there be a problem in God knowing the infinite number of truths?

Reply: Even if God can know the infinite number of the truths of arithmetic, his knowledge of what he knows is recursive. That's because, as my argument shows, his knowledge of what he knows is self-referential and therefore cannot be bounded. Attempts in bounding all of God's knowledge of what he knows about his knowledge leads to unavoidable contradictions. So, even if God can know the infinite set of truths of arithmetic, he can never know the complete set of truths. Whenever you try to conceptualize the set of all truths that an omniscient knower knows, there is necessarily at least one truth that is not in the set—which is a contradiction.

Book cover: The Miracle of Theism by J. L. Mackie

Secondly, even for the truths of arithmetic (and for any other set of truths, for that matter), applying Cantor's theorem demonstrates that there is no such knowable object as 'every truth' that is available for God to know. And that is what is required for 'omniscience' to be instantiated; that God know every truth (see f.n. 6).

But let's grant for the sake of argument that there is a set of all truths for God to know. An additional cost for the classical theist is that this concession contradicts other attributes of God; namely his timelessness and immutability. To know that one knows X requires attending to what one knows and evaluating and judging that one knows that one knows X. This reflective activity entails a sequence of events: first the initial knowing and then the reflection on what is known and then the judgment on what is known of the knower. For God to know what he knows requires a temporal sequence in which he changes his state: from knower to knower of his knowing. This necessarily requires God existing in time and the changing of God's state of knowing.

Objection 6: Your argument is not really an argument against the existence of God. At best, it's an argument against God having the attribute of omniscience.

Reply: I agree that my argument is not an argument against the existence of every kind of conceived God. My argument is particularly focused on the classical conception of God as a perfect being. However, perfection in attributes has been seen as a necessary requirement for divinity by key religious thinkers through the ages, from Anselm to Aquinas to Descartes to most modern-day theologians of all stripes. Secondly, if God is not thought of as perfect in all his attributes, then it becomes more difficult to regard such a God as worshipworthy.

Attribution: The spiral diagram shown in Diagram 1 is by Clker-Free-Vector-Images from Pixabay.

Initial draft       Aug 10, 2022
Revised draft  Nov 29, 2022 (Extensive revisions and additions)
Revised draft   Dec 5, 2022 (Added Obj. 7)
Revised draft   Dec 14, 2022 (Expanded Obj. 5 and References)
Revised draft   Jan 4, 2023 (Extensive revisions and additions)

Copyright © 2023

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