ENSAYOS DE LABORATORIO PARA EL MATERIAL PÉTREO

In Judaic Logic⁴¹, I expressed some misgiving concerning the consistency of the concept of omniscience. The following is an attempt to analyze the issue further.

The form (a) “I know that (I know nothing)” is inconsistent, since it implies “I know something” and “I know nothing”

(i.e. “I do not know anything”).

The following forms are, however, consistent: (b) I do not know that (I know nothing); (c) I know that (I know something); (d) I do not know that (I know something).

Strictly speaking, the paradox in (a) yields the conclusion (b), rather than (c), i.e. it does not exclude (d) at the outset.

Unless we regard “I know nothing” as inherently paradoxical too, in which case “I know something” is implied: I think this is justified by reflection, i.e. once “I know nothing” is affirmed, we can classify it as a claim to knowledge, and thus reject it as implicitly inconsistent. Another way to the same result is to say that the “I do not know...” forms, (b) and (d), are implicitly claims to knowledge, about the state of one’s knowledge or ignorance, so that they imply (c).

41 Chapter 14.

Self-consciousness, even of one’s ignorance, implies consciousness, and therefore knowledge. Or simply put, (c) is logically true of all self-conscious beings (i.e. humans and God, at least - perhaps some higher animals too). However, we cannot claim (c) true for seemingly merely conscious beings, we can only say for them “they know something”.

The form of omniscience is (e) “I know that (I know everything)”. The simpler form “I know everything” implies the reflexive, because if you know everything, then you must also know that fact. This is self-consistent, and therefore claimable for God. The form (f) “I do not know that (I know everything)” is not self-consistent, since it both implies “I do not know something” and allows for “I know everything”.

Similarly, (g) “I know that (I do not know everything)” is self-consistent, as is the prior form “I do not know everything”, and this is the situation for humans and perhaps some higher animals (in both cases) and merely conscious animals (in the non-reflexive case). The form (h) “ I do not know that (I do not know everything)” implies both “I do not know something” and “I do not know everything”, the former of which implies the latter of which: there is no inconsistency.

The difficulty in the concept of omniscience is not deductive, but inductive. Granting you know everything, then of course you know that you know everything. But it is also conceivable that you have arrived at total knowledge gradually, by inductive processes, in which case, how would

you know for sure that you know everything? And if the latter possibility exists, then whoever is apparently in a state of total knowledge (even by non-inductive means) is also a bit in doubt about it. That is, in practice, “I know everything”

does not imply “I know that (I know everything)”, or more precisely, even granting the fact that so and so knows everything, it does not follow that so and so knows it for a fact. That is, omniscience does not necessarily include the reflexive knowledge of one’s omniscience. In a sense, this result looks paradoxical, but in a way it confirms my general suspicion towards self-inclusive classes.

There is also to consider the conceptual compatibility between the Divine attributes of omniscience and freewill.

Theologians have considered the compatibility of God’s omniscience and Man’s freewill, though in my view not satisfactorily; that is, those who have sought reconciliation have not so far as I know really succeeded - it was rationalization rather than true resolution (I attempt a more convincing argument above). But have they at all asked how God could have both freewill and omniscience? If God knows everything, including in advance what He will do, how can He be said to freely choose what He does? I think my attempted answer to the first question (in the preceding section) can also be applied to the second. For God, all of time is one moment, so there is no before or after, and all knowing and doing are effectively simultaneous.

With regard to logical issues in the concept of Omnipotence, the following should be added. Omnipotence cannot be consistently defined in an unlimited manner, as literally the power to do anything whatsoever. We must rather say: God can do anything do-able in principle.

What distinguishes Him from all other entities is that whereas we finite beings can only do some (indeed, very few) of the things that are in the realm of the possible, God can do all that can conceivably be done. What He cannot conceivably do is illogical things like “creating Himself”, or “creating things that are both A and non-A, or neither A nor non-A”, or

“annulling His own omnipotence”, or “annulling the factuality of past facts”. We might presumably add to this list the impossibility of His self-destructing (which would contradict His eternity), or of destroying His other defining characteristics. Moreover, I would personally — perhaps because I am a Jew (I say this so as not to offend the sensibilities of Christians, Hindus and others) — consider God incapable of incarnating, i.e. concentrating His being in a finite body, while remaining infinite.

It is not however inconceivable that God would eventually annul, circumscribe or reverse natural laws that are logically (as far as we can tell) replaceable. Here a distinction has to be drawn between natural modality and logical modality (see my work Future Logic, in this regard). In this context, local and temporary “miracles”, as are described in the Bible (e.g. the parting of the Red Sea) or other religious books, are quite

conceivable – as punctual exceptions to natural law. Natural laws that are not logical laws may well be conditional upon the non-interference of God – this concept would in no way diminish their effective status as laws. Notwithstanding, it must be remembered that many such laws are logically interrelated to others, so that they might not be by-passed in isolation, but God would have to make multiple or systemic changes to produce a desired effect.

But we do not need to consider God’s every interference in the world as an abrogation of natural law. God might well have reserved for Himself a role as a powerful player within Nature.

This remark can be understood, if we consider the analogy of human will (or, more generally, animal will). The latter is conceived by us as able to overpower the natural (i.e.

deterministic) course of event; furthermore, one human’s will may be more powerful than another’s. Humans (and other animals) are nevertheless considered as part of Nature, in a broader sense. We can similarly, by extension, on a larger scale and at deeper levels, regard God’s providence. To refer again to Biblical examples: He may have split the waters of the sea as we would make waves in our bathtub; He may have influenced Pharaoh’s decisions as we would suggest things to weaker minds.

If we limit our concept of Nature to deterministic events, then even human and animal will, let alone God’s will, must be classified as unnatural. But if we understand the concept of

Nature as covering whatever happens to occur, then not even God’s eventual ad hoc interference in the ordinary course of events (deterministic or of lesser volitions) is unnatural.

Thus, to conclude, God’s omnipotence cannot be conceived anarchically. God’s will, in contrast to ours, is undetermined by “external” or “internal” forces and influences. But the concept remains, as for the other defining attributes, subject to consistency and other rational and empirical checks, i.e. to the laws of logic.