Review of the 36 Arguments for the Existence of God # 29. THE ARGUMENT FROM HUMAN KNOWLEDGE OF INFINITY

[Pastor Jennifer v2]

29. THE ARGUMENT FROM HUMAN KNOWLEDGE OF INFINITY
(by R Goldstein)
1. We are finite, and everything with which we come into physical
contact is finite.
2. We have a knowledge of the infinite, demonstrably so in
mathematics.
3. We could not have derived this knowledge of the infinite from the
finite, from anything that we are and come in contact with (from 1).
4. Only something itself infinite could have implanted knowledge of
the infinite in us (from 2 and 3).
5. God would want us to have a knowledge of the infinite, both for the
cognitive pleasure it affords us and because it allows us to come to
know him, who is himself infinite.
6. God is the only entity that both is infinite and could have an
intention of implanting the knowledge of the infinite within us (from
4 and 5).
7. God exists.
FLAW:
There are certain computational procedures governed by what logicians
call recursive rules. A recursive rule is one that refers to itself,
and hence it can be applied to its own output ad infinitum. For
example, we can define a natural number recursively: 1 is a natural
number, and if you add 1 to a natural number, the result is a natural
number. We can apply this rule an indefinite number of times and
thereby generate an infinite series of natural numbers. Recursive
rules allow a finite system (a set of rules, a computer, a brain) to
reason about an infinity of objects, refuting Premise 3. COMMENT: In
1931 the young logician Kurt Gödel published a paper proving The
Incompleteness Theorem (actually there are two). Basically, what Gödel
demonstrated is that recursive rules cannot capture all of
mathematics. For any mathematical system rich enough to express
arithmetic, we can produce a true proposition that is expressible in
that system but not provable within it. So even though the flaw
discussed above is sufficient to invalidate Premise 3, it should not
be understood as suggesting that all of our mathematical knowledge is
reducible to recursive rules.

[Brock]

On Feb 23, 9:00 pm, Pastor Jennifer v2

<jennifer.s.jo...@googlemail.com> wrote:
> 29. THE ARGUMENT FROM HUMAN KNOWLEDGE OF INFINITY
> (by R Goldstein)
> 1. We are finite, and everything with which we come into physical
> contact is finite.
> 2. We have a knowledge of the infinite, demonstrably so in
> mathematics.
> 3. We could not have derived this knowledge of the infinite from the
> finite, from anything that we are and come in contact with (from 1).
> 4. Only something itself infinite could have implanted knowledge of
> the infinite in us (from 2 and 3).
> 5. God would want us to have a knowledge of the infinite, both for the
> cognitive pleasure it affords us and because it allows us to come to
> know him, who is himself infinite.
> 6. God is the only entity that both is infinite and could have an
> intention of implanting the knowledge of the infinite within us (from
> 4 and 5).
> 7. God exists.

Again, the same limitations apply to this treatment:

* there is no one "THE ARGUMENT ...", rather it refers to a general
category of arguments, thus to defeat one specific example is not
adequate to dismiss the category
* the argument, to the degree it is a paraphrase, doesn't adequately
represent (either intentionally or accidentally) the argument as put
forward by a proponent, and faces the danger of being simply a straw-
man

Regards,

Brock