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A Case Against Omniscience:
Infinite Regress

4. Argument from Infinite Regress of Knowing

The God Argument: The Case against Religion and for Humanism by A. C. Grayling

This second major argument against omniscience, as with the first, trades on the inescapability of the classical theist from an infinite regress. In contrast with the first, it can be stated much more briefly. The argument is as follows.

  1. An omniscient knower knows all truths.
  2. 'An omniscient knower knows all truths' is a truth.
  3. An omniscient knower knows 'An omniscient knower knows all truths' is a truth.
  4. 'An omniscient knower knows "An omniscient knower knows all truths"' is a truth.
  5. An omniscient knower knows 'An omniscient knower knows "An omniscient knower knows all truths"' is a truth.

and so on ad finitum.

Support for Premises

(1) is true by definition. If 'omniscience' means anything, it at least means the omniscient knower knows every truth.[5]

(2) is supported by the fact that any true statement is a truth.

(3) follows from (1) and (2).

(4) is supported by the fact that any true statement is a truth.

(5) follows from (1) and (4).

Analysis and Conclusion

The above argument demonstrates how an omniscient knower's knowing is infinitely recursive. For any proposed set of 'all truths' that an omniscient knower knows, there is always one more truth that is not included in the set. But then that proposed set can't be the set of 'all truths'.

If it be thought that it really is the set of 'all truths', then the fact of an omniscient knower's knowing that it knows this set cannot be in the set. In that case, there is a truth that the omniscient knower does not know. But given the omniscient knower's omniscience, that is not possible. Either way leads to a contradiction. If the omniscient knower knows the set of 'all truths', then it's impossible for it to be the set of 'all truths'. If it is the set of 'all truths', then there is a fact that the omniscient knower does not know—which is also impossible. So, omniscience is impossible. If omniscience is impossible, then the existence of any knower thought to be necessarily omniscient, such as the God of classical theism, is also, ipso facto, impossible.[6]

Footnotes

  1. [5] For alternate definitions of 'omniscience', see Wierenga [2021] and Grim [1983: §1]. These alternate definitions do not, I think, impact the force of my argument here.
  2. [6] This Argument from Infinite Regress may be seen as a cut-down version of Grim's objection that there is no finite set of all truths for God to know [Grim 1984, 2013: §§V–VII]. Grim applies Cantor's theorem to the posited set of all truths, whereas my version of the argument is a less technical formulation that applies to only one kind of truth. My argument has a reduced scope in only applying to the truths about what God can know about his own omniscience. In stating it this way, my aim is to make the argument more accessible.

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