Review of the 36 Arguments for the Existence of God # 30. THE ARGUMENT FROM MATHEMATICAL REALITY
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Pastor Jennifer v2
Feb 23, 2012, 9:02:30 PM2/23/12
to Evidence For God
30. THE ARGUMENT FROM MATHEMATICAL REALITY
( R Goldstein)
1. Mathematical truths are necessarily true (there is no possible
world in which 2 plus 2 does not equal 4).
2. The truths that describe our physical world are empirical,
requiring observational evidence.
3. Truths that require empirical evidence are not necessary truths.
(We require empirical evidence because there are possible worlds in
which these are not truths, and we have to test that ours is not such
a world.)
4. The truths of our physical world are not necessary truths (from 2
and 3).
5. The truths of our physical world cannot explain mathematical
truths (from 1 and 3).
6. Mathematical truths exist on a different plane of existence from
physical truths (from 5).
7. Only something which itself exists on a different plane of
existence from the physical can explain mathematical truths (from 6).
8. Only God can explain the necessary truths of mathematics (from 7).
9. God exists.
Mathematics is derived through pure reason—what the philosophers call
a priori reason—which means that it cannot be refuted by any empirical
observations. The fundamental question in the philosophy of
mathematics is, how can mathematics be true but not empirical? Is it
because mathematics describes some trans-empirical reality—as
mathematical realists believe—or is it because mathematics has no
content at all and is a purely formal game consisting of stipulated
rules and their consequences? The Argument from Mathematical Reality
assumes, in its third premise, the position of mathematical realism,
which isn’t a fallacy in itself; many mathematicians believe it, some
of them arguing that it follows from Gödel’s incompleteness theorems
(see the Comment in The Argument from Human Knowledge of Infinity,
#29, above). This argument, however, goes further and tries to deduce
God’s existence from the trans-empirical existence of mathematical
reality.
FLAW 1:
Premise 5 presumes that something outside of mathematical reality must
explain the existence of mathematical reality but this presumption is
non-obvious. Lurking within Premise 5 is the hidden premise:
mathematics must be explained by reference to non-mathematical truths.
But this hidden premise, when exposed, appears murky. If God can be
self explanatory, why then, can’t mathematical realty be self-
explanatory- especially since the rules of mathematics are, as this
argument asserts, necessarily true?
FLAW 2:
Mathematical reality- if indeed it exists – is, admittedly,
mysterious. Many people have trouble conceiving of where mathematical
truths live, or exactly what they pertain to. But invoking God does
not dispel this puzzlement; it is an instance of the Fallacy of Using
One Mystery to Explain Another.
( R Goldstein)
1. Mathematical truths are necessarily true (there is no possible
world in which 2 plus 2 does not equal 4).
2. The truths that describe our physical world are empirical,
requiring observational evidence.
3. Truths that require empirical evidence are not necessary truths.
(We require empirical evidence because there are possible worlds in
which these are not truths, and we have to test that ours is not such
a world.)
4. The truths of our physical world are not necessary truths (from 2
and 3).
5. The truths of our physical world cannot explain mathematical
truths (from 1 and 3).
6. Mathematical truths exist on a different plane of existence from
physical truths (from 5).
7. Only something which itself exists on a different plane of
existence from the physical can explain mathematical truths (from 6).
8. Only God can explain the necessary truths of mathematics (from 7).
9. God exists.
Mathematics is derived through pure reason—what the philosophers call
a priori reason—which means that it cannot be refuted by any empirical
observations. The fundamental question in the philosophy of
mathematics is, how can mathematics be true but not empirical? Is it
because mathematics describes some trans-empirical reality—as
mathematical realists believe—or is it because mathematics has no
content at all and is a purely formal game consisting of stipulated
rules and their consequences? The Argument from Mathematical Reality
assumes, in its third premise, the position of mathematical realism,
which isn’t a fallacy in itself; many mathematicians believe it, some
of them arguing that it follows from Gödel’s incompleteness theorems
(see the Comment in The Argument from Human Knowledge of Infinity,
#29, above). This argument, however, goes further and tries to deduce
God’s existence from the trans-empirical existence of mathematical
reality.
FLAW 1:
Premise 5 presumes that something outside of mathematical reality must
explain the existence of mathematical reality but this presumption is
non-obvious. Lurking within Premise 5 is the hidden premise:
mathematics must be explained by reference to non-mathematical truths.
But this hidden premise, when exposed, appears murky. If God can be
self explanatory, why then, can’t mathematical realty be self-
explanatory- especially since the rules of mathematics are, as this
argument asserts, necessarily true?
FLAW 2:
Mathematical reality- if indeed it exists – is, admittedly,
mysterious. Many people have trouble conceiving of where mathematical
truths live, or exactly what they pertain to. But invoking God does
not dispel this puzzlement; it is an instance of the Fallacy of Using
One Mystery to Explain Another.
Pastor Jennifer v2
Feb 23, 2012, 9:01:16 PM2/23/12
to Evidence For God
Brock
Feb 25, 2012, 11:12:57 AM2/25/12
to Evidence For God
On Feb 23, 9:02 pm, Pastor Jennifer v2
<jennifer.s.jo...@googlemail.com> wrote:
> 30. THE ARGUMENT FROM MATHEMATICAL REALITY
> ( R Goldstein)
> 1. Mathematical truths are necessarily true (there is no possible
> world in which 2 plus 2 does not equal 4).
> 2. The truths that describe our physical world are empirical,
> requiring observational evidence.
> 3. Truths that require empirical evidence are not necessary truths.
> (We require empirical evidence because there are possible worlds in
> which these are not truths, and we have to test that ours is not such
> a world.)
> 4. The truths of our physical world are not necessary truths (from 2
> and 3).
> 5. The truths of our physical world cannot explain mathematical
> truths (from 1 and 3).
> 6. Mathematical truths exist on a different plane of existence from
> physical truths (from 5).
> 7. Only something which itself exists on a different plane of
> existence from the physical can explain mathematical truths (from 6).
> 8. Only God can explain the necessary truths of mathematics (from 7).
> 9. God exists.
Again, the same limitations apply to this treatment:
> 30. THE ARGUMENT FROM MATHEMATICAL REALITY
> ( R Goldstein)
> 1. Mathematical truths are necessarily true (there is no possible
> world in which 2 plus 2 does not equal 4).
> 2. The truths that describe our physical world are empirical,
> requiring observational evidence.
> 3. Truths that require empirical evidence are not necessary truths.
> (We require empirical evidence because there are possible worlds in
> which these are not truths, and we have to test that ours is not such
> a world.)
> 4. The truths of our physical world are not necessary truths (from 2
> and 3).
> 5. The truths of our physical world cannot explain mathematical
> truths (from 1 and 3).
> 6. Mathematical truths exist on a different plane of existence from
> physical truths (from 5).
> 7. Only something which itself exists on a different plane of
> existence from the physical can explain mathematical truths (from 6).
> 8. Only God can explain the necessary truths of mathematics (from 7).
> 9. God exists.
* 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
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