I just read the paper “Omnificence” by John Bigelow[1]. In the preamble he recounts the following argument for an omniscient being

- Any fact (true proposition) is knowable by someone. (Premise)
- Therefore, every fact is known.
- Therefore, someone knows every fact.

Fitch[2] was responsible for showing that (2) follows from (1). One way to see this is a follows: for reductio assume, contrary to (2), that there is some fact *p* that is not known by someone. Then, *p and no-one knows p* is a fact, and by (1) is therefore knowable. Therefore, it is possible that someone knows *p*, and at the same time knows that *no-one knows p*, which is absurd. Thus (2) follows from (1).

The move from (2) to (3) comes from Humberstone[3]. Again, for reductio assume, contrary to (3) that for every person *x*, there is some fact *p(x)*, that *x* doesn’t know. Now let *X* be the conjunction formed by taking all facts of the form *p(x) and x doesn’t know p(x)*. Clearly this conjunction is true. By (2) it follows that there is some *y* who knows *X*. But one of the conjuncts of *X* will be *p(y) and y doesn’t know p(y)*, and since *y* knows *X*, *y* also knows this conjunct, which is absurd. Thus (3) follows from (2).

I’m not going to argue for (1) here, although I must admit I struggle to imagine that there could be a fact that is in principle unknowable. What I found particularly interesting in Bigelow’s paper was the comment that logical positivism entails (1): take the verification principle of that movement, which said that a statement is meaningful if and only if it is verifiable. Now, only meaningful statements can take on a truth value, so it follows that every fact is verifiable, and therefore knowable.

### Notes

- J. Bigelow, “Omnificence,”
*Analysis*65/3 (2005), pp. 187-196. - F. Fitch, “A logical analysis of some value concepts”,
*Journal of Symbolic Logic*28: 135-42. - I. Humberstone, “The formalities of collective omniscience”,
*Philosophical Studies*48: 401-23.