# A Case Against Omniscience: Fallibility

## 3. Formal Natural Language Argument

I have included below a more formally rigorous version of my argument against omniscience compared with the colloquial version presented in the previous section. The key advantage of this version is that it remains readable by non-logicians while preserving logical precision. In the next section, this same argument is presented in symbolic form.

In the following statement of the argument, the variable 'x' ranges over all thinkers that think itself God and the variable 'y' ranges over all sentences in natural languages.

- For all x, if x is omniscient, then for all y, if y is a true proposition, then x knows the truth of y.
- For all x, if x is omniscient, then 'x is omniscient' is a true proposition.
- For all x, if x is omniscient, then x knows the truth of 'x is omniscient'.
- For all x, if x knows the truth of 'x is omniscient', then x has no epistemically relevant reasons for doubting the truth of 'x is omniscient'.
- For all x, it's not the case that x has no epistemically relevant reasons for doubting the truth of 'x is omniscient'.
- For all x, it is false that x knows the truth of 'x is omniscient'.
- For all x, it is false that x is omniscient.
- For all x, if x has attributes posited by classical theism, then x is omniscient.
- For all x, it is false that x has attributes posited by classical theism.
- It is false that for some x, x has attributes posited by classical theism.

### Support for Premises

(1) is true by definition.[4]

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

(3) is derived from application to (1) and (2) of the following rules of inference: universal specification, theorem and universal generalization.

(4) is supported by the principle that '*X* knows *Y* to be true' if and only if '*X* has epistemically relevant reasons for believing *Y* and no epistemically relevant reasons for doubting *Y*'.

(5) is supported by the fact that it is logically possible that at least one proposition believed by Thinker *X* is false. Two scenarios in which Thinker *X* believes a false proposition are that Thinker *X* is a brain in a vat (see Putnam [1999]) being manipulated by other more powerful beings or is being deceived by Descartes' demon [Descartes 1641]. A third scenario is that Thinker *X* is experiencing delusions or some other serious mental dysfunction. This third scenario in fact plays out with persons suffering from psychosis. Some psychotic patients actually believe that they are God (see, for example, Moralis [2008: 260] and Rudalevičienė *et al* [2008])[5]. Note that the truth of (5) does not need to meet the stronger requirement that it is possible that an omniscient thinker is mistaken. It only needs to meet the weaker requirement that Thinker *X* cannot epistemically justify the proposition that it is impossible that it is a brain in a vat or is suffering delusions or some similar epistemic distortion.[6]

(6) is derived from application to (4) and (5) of modus tollens (denying the consequent: if *P* entails *Q*, and *Q* is false, then *P* is false).

(7) is derived from application to (3) and (6) of modus tollens (denying the consequent: if *P* entails *Q*, and *Q* is false, then *P* is false).

(8) is true by definition of 'God' under classical theism.

(9) is derived from application to (7) and (8) of modus tollens (denying the consequent: if *P* entails *Q*, and *Q* is false, then *P* is false).

(10) is derived from application to (9) of De Morgan's law (all x is not F entails it is not the case that some x is F).

### Footnotes

- [4] 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.
- [5] Pearce [2013] has further suggestions for how a thinker can be mistaken, such as that he may not be aware of another inaccessible dimension run by another God, that he is plugged into the Matrix and that he is part of an experiment programming him to think that he is omniscient.
- [6] For a discussion of the conditions under which agents know that they know and under which they don't know that they know, see Feldman [1981].