# A Case Against Omniscience: Infinite Regress

## 2. Argument from Infinite Regress of Reasons

Before I present my argument based on an infinite regress of reasons in numbered premise form, let me summarize the core of it in a more informal way. My argument basically hinges on the question: How would an omniscient knower guarantee that it really is omniscient? For an omniscient knower to know that it is omniscient, it must have a good reason for believing itself omniscient. That good reason is then an item of knowledge it knows. But to know that item of knowledge, it must have good reason for believing it true. Knowing that good reason then constitutes another item of knowledge, and so on ad infinitum. Without ever being able to complete the chain of reasons for knowing that it is truly omniscient, it is impossible for any knower to be omniscient. The diagram below illustrates the unending spiral an omniscient knower is caught in, oscillating between knowing (on the right side of the diagram) and justifying (on the left side of the diagram) and back to knowing.

Diagram 1 – Spiral of infinite regress of reasons

I will now state my argument somewhat more formally in a way that will disclose some underlying assumptions and make clear the direction of entailments from one set of premises to another.

### Informal Natural Language Argument

1. If X is omniscient, then X knows every truth .
2. If X is omniscient, then 'X is omniscient' is a truth.
3. If X knows Y is a truth, then X has a justificatory reason for believing Y is a truth.
4. If X has a justificatory reason for believing Y, then 'X has a justificatory reason for believing Y' is a truth.
5. If X is omniscient, then X knows
'X is omniscient'
is a truth.
6. If X is omniscient, then X has a justificatory reason for believing
'X is omniscient'
is a truth.
7. If X is omniscient, then X knows
'X has a justificatory reason for believing "X is omniscient"'
is a truth.
8. If X is omniscient, then X has a justificatory reason for believing
'X has a justificatory reason for believing "X is omniscient"'
is a truth.
9. If X is omniscient, then X knows
'X has a justificatory reason for believing "X has a justificatory reason for believing 'X is omniscient'"'
is a truth.

Now let the term 'X' stand in for any knower. And let the term 'Y' stand in for any truth.

What is evident from premises (1) to (9) is that any knower that is purportedly omniscient is caught in an endless spiral of epistemic justifications for believing that it is omniscient. The sequence of justifications from premises (7) to (8) repeat without end as each item of knowledge that a particular belief is justified adds a new belief that requires justification if it is to count as genuine knowledge.

### Support for Premises

Before analysing and drawing a conclusion from the above Argument from Infinite Regress of Reasons, I provide the following support for each of the premises in the argument.

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

(2) is supported by the fact that if a knower is omniscient, then a well-formed sentence ascribing omniscience to that knower expresses a truth.

(3) is supported by the principle that 'X knows Y to be true' if and only if 'X has an epistemically relevant reason for believing Y and no epistemically relevant reason for denying Y'. Absent such a justificatory reason, X's cognitive state is no more than mere belief, whim or opinion that Y is true.

(4) is supported by the fact that if a knower has a justificatory reason for believing a truth, then a well-formed sentence ascribing a justificatory reason for believing to that knower expresses a truth.

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

(6) follows from (3) and (5).

(7) follows from (1), (4) and (6).

(8) follows from (3) and (7).

(9) follows from (1), (4) and (8).

### Analysis and Conclusion

Now that I've tried to show how each of the premises is reasonable, what ought we conclude from the Argument from Infinite Regress of Reasons? Firstly, notice how the argument shows how an omniscient knower's knowledge of its own omniscience is infinitely recursive. The argument traverses two loops of the recursion through X knowing a truth and X knowing that it has a good reason for knowing that truth. The argument ends at premise (9) with what X knows as an omniscient being. Beyond premise (9), the recursive loop then continues with X having a justificatory reason for that item of knowledge, and so on ad infinitum.

There appear to be two ways for X to escape this infinitely recursive loop. Consider the truth that X knows in premise (5) as an omniscient knower:

1. (P)
X is omniscient.

Either X is justified in believing (P) or it is not. If it is not justified in believing (P), then it has a mere belief, whim or opinion and not knowledge. In that case, X is not omniscient.

On the other hand, if X is justified in believing (P) and is omniscient, then it must have a justificatory reason for believing (P). If that justification is that its knowledge of (P) is self-justifying, then that knowledge presumes the epistemological principle that at least one truth is self-justifying. If X is omniscient, then X must know the truth of that principle. However, to know that principle is true, X must have a justificatory reason for believing it. Otherwise, X is entertaining a mere belief, whim or opinion. X's knowledge of that principle, then, spawns a new infinitely recursive loop of justifications. Or it terminates in another foundational epistemological principle that itself requires justification if it is to be more than mere belief, whim or opinion.

So, the first way out of the infinitely recursive loop is to admit that X is not omniscient. The second way out of the infinitely recursive loop only starts a new infinitely recursive loop. In that case, X's belief in its own omniscience is never justified, robbing X of omniscience. In either case, assuming X is omniscient leads to the self-contradiction that X is not omniscient. It's impossible, then, for any knower to be omniscient. 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.

### Footnotes

1. [1] 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.