On determinism and the variances of scientific data.

Here's Mark Balaguer (philosopher at California State University) writing in Methode's (methodejournal.org) sublime free will issue (Vol 2, Number 3, 2013) this past year, summarizing the argument against compatibility of free will and determinism:

Let P0 be a complete description of the world at some time in the distant past, before any humans were born;

Let L be a conjunction of the laws of nature; let P be a complete description of the
world at some moment when someone made an ordinary decision that we would
ordinarily think of as free (e.g., for specificity, let’s suppose that at the relevant moment,
Jay decided to order chocolate ice cream rather than vanilla); and let N be
an operator such that ‘N(X)’ means something like ‘X is true and no one has ever
had any choice about it being true’. 

Given all of this, the consequence argument
can be formulated as follows:

(1) N(P0^L).
(2) If N(P0^L), and if determinism is true so that P0^L entails P, then N(P).
Therefore,
(3) If determinism is true, then N(P).
This argument is obviously valid, and the conclusion seems to entail incompatibilism,
so the only real question here is whether (1) and (2) are true.

Of course, in the most accepted version of quantum mechanics, (2) is not an appropriate assertion, because P0^L does NOT in reality entail any exact later description P.  For example, consider the indeterministic decay of the nuclei of radioactive isotopes.  Carbon-14 is a radioactive isotope of carbon which makes up about 1 in a trillion of carbon's atoms on earth. According to scopenvironment.org, there are about 10^20 kg of carbon in the earth's crust, so that there are about 10^11 kg of radioactive carbon in the crust, of which perhaps 10^7, or 10 billion kg, is liable to decay per year. Thus, if at P0 the world contains a certain number of carbon-14 atoms, then it is not determined and cannot by humans ever be predicted exactly how many kg of carbon-14 atoms there will be in the earth a year from now.

The world is thus microscopically indeterminate. And the microscopic thus underdetermines the macroscopic. Whether or not there is provably free will, there is certainly plenty of room for it.

Laws of averages, with the resultant bell curve, often apply here. But true determinism seems false by most interpretations of current physics.

Let's therefore rewrite the above argument:

(1) N( P0^L ).
(2) If N( P0^L ), and if determinism plus a stochastic indeterministic factor,
 then N( P +/- a factor which has a sigma > 0 ).
(3) So we do not have determinism, but continual variation somewhere near a deterministic mean.

The above seems to fit real experience and actual scientific data far better than determinism ever could.