Re: The logic of atheism

Paul Holbach wrote:
Paul Holbach wrote:

Plantinga criticizes Grim's Cantorian argument as follows:

"My main puzzle is this: why do you think the notion of omniscience, or
of knowledge having an intrinsic maximum, demands that there be a set
of all truths? "

Plantinga seems to overlook the fact that the impossibility of
omniscience can be shown without any reference to sets or classes:

For any conjunction of truths (true propositions)

Ct = t_1 & t_2 & ... & ... t_n & ...

there is a further truth such as

"It is true that Ct" / "'Ct' is true"

which is not one of Ct's conjuncts.

Therefore, no conjunction of truths is the conjunction of all truths,
the maximal conjunction of truths.

This means that knowledgeability is an imperfectible property.
In other words, nobody can know all, and so nobody can be literally
all-knowing.

Of course, a theist might reply that the theological terminology had
never been intended to convey precise literal meanings that are
rationally fully comprehensible; but that would be an escape into a
woolly and untruthful irrationalism.

But there might be another possible theistic solution, which is more
rational:

"The difference I try to describe amounts, you see, to nothing more
than the difference between what I formerly called the 'each-form' and
the 'all-form' of reality. Pluralism lets things really exist in the
each-form or distributively. Monism thinks that the all-form or
collective-unit form is the only form that is rational."

(William James: "The Pluralistic Universe", 1909:
http://www.gutenberg.org/files/11984/11984-8.txt)

I think the theist may offer the following definition:

"x is each-knowing" (not "all-knowing"! In German: "jedwissend" instead
of "allwissend")
=def
"Each one among the many propositions is such that it is true and
knowably so only if x knows it to be true."

Explication:
There are propositions.
The many propositions there are are /all/ propositions there are. The
many propositions are all present in their entirety. The entirety of
propositions is determinate but neither unified nor unifiable, and,
hence, not a set or class.
That the entirety of propositions is /essentially/ a plurality and not
a unity entails that the many propositions cannot be entirely conjoined
into /one/ overall proposition. For this reason there is no
propositional unit that is the conjunction of all propositions. And, of
course, an each-knowing being is not required to know the truth of
nonexistent propositions, since what doesn't exist has no truth-value.
Futhermore, since the pluralistic entirety of propositions is
(objectively) determinate, so is the meaning of the quantificational
phrase "Each one among the many propositions". That is to say, its
meaning is not vague.

All in all, so the theist may conclude from what's been stated above,
there is a perfectly meaningful and consistent conception of
omniscience, if "to be omniscient" is not interpreted as "to be
all-knowing" but as "to be each-knowing".

#PH

.

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