If a=b then a-b=0 thus dividing by a-b gives meaningless results. Neither mathematics nor logic are invalidated by tricks like this.
A lot like a dad watching his 132 lb. freshman son go out for the varsity football team, dreaming of playing offensive tackle. Oh well, you don't stop him, but you do keep the medical insurance current.
But if the dad were an omniscient God he would know perfectly well whether that insurance was going to turn out to be necessary or not. Rather that influencing the outcome, it would constrain it.
proof? The argument from incredulity just isn't good enough.
Free Will vs. Predestination
In fairness, however, I will provide a formal presentation of the argument I am making here. I fear this shall be rather lengthy of necessity, as such formal argumentation normally is.
(The reasons for the numbering and for the repetitions will become clear in the second half of this post.)
1 1.1 It is possible to know infallibly
beforehand that person A will
do X and free will exists.
(Hypothesis)
1.2
1.2.1 It is possible to know infallibly
beforehand that Person A will
do X and free will exists.
(Repetition of hypothesis 1.1)
1.2.2 It is possible to know infallibly
beforehand that person A will
do X.
(Extraction of first half of hypothesis.
If the hypothesis 1.2.1 is true,
then this also must be true.)
1.2.3 That which is known infallibly
is true.
(Hypothesis, already granted as
being true by you.)
1.2.4 It is possible to know infallibly
beforehand that person A will
do X and that which is known
infallibly is true.
(Conjunction of 1.2.2 and 1.2.3)
1.2.5 If it is possible to know
infallible beforehand that person
A will do X and that which
is known infallibly is true, then
person A will do X.
(Logical consequence of 1.2.4.)
1.2.6 Person A will do X.
(1.2.4 is true, therefore 1.2.5 must
be true, therefore this must be true.)
1.3 Therefore, If it is possible to
know infallibly beforehand that person
A will do X and free will exists,
then person A will do X.
(Conclusion starting with hypothesis 1.1
and proceeding with argument 1.2.)
1.4 Person A will do X.
(Given hypothesis 1.1 and conclusion 1.3,
this must follow.)
1.5 Free will exists.
(Extraction of second half of hypothesis.
If the hypothesis 1.2.1 is true, then this
also must be true.)
1.6
1.6.1 Free will exists.
(Repetition of 1.5.)
1.6.2 If free will exists then
person A will do X or it is false
that person A will do X.
(Definition of free will, law of
excluded middle.)
1.6.3 Person A will do X or it is
false that person A will do X.
(1.6.1 specifies the premiss
of 1.6.2, therefore the consequence
of 1.6.2 must be true.)
1.6.4
1.6.4.1 Person A will do X or it is
false that person A will do X.
(Repetition of 1.6.3)
1.6.4.2 It is false that person
A will do X.
(Hypothesis)
1.6.4.3 Person A will do X
(Repetition of 1.4)
1.6.4.4 Person A will do X and it is
false that person A will do X.
(Combination of 1.6.4.3 and 1.6.4.2)
This is a contradiction, and
so cannot be true.
1.6.5 Therefore, it is false that person A
will do X or it is false that person A
will do X.
(Since the statement in 1.6.4.1 leads to
a contradiction at 1.6.4.4, the statement
at 1.6.4.1 must be false.)
1.6.6 Person A will do X or it is false that
person A will do X and it is false that
person A will do X or it is false that
person A will do X.
(This is the logical combination of 1.6.3
and 1.6.5)
This is a contradiction, and
so cannot be true.
1.7 Therefore it is false that free will exists.
(The hypothesis that free will exists stated in
1.6.1 leads to a contradiction at 1.6.6, and so
the hypothesis must be false.)
1.8 Therefore free will exists and it is false
that free will exists.
(Combination of statements at 1.5 and 1.7)
This is a contradiction, and
so cannot be true.)
2. Therefore, it is false that it is possible to
know infallibly beforehand that person A will
do X and free will exists.
Under a de Morgan law, this can be shown to be equivalent to stating that,
It is false that it is possible to know
infallibly beforehand that person A will do
X or it is false that free will exists.
™ Version 4.2