If the primary responsibility of the atheist is a commitment to reason then supernaturalist claims will always be rejected. Not out of hand, but on the basis of not meeting scientific standards (e.g. providing extraordinary evidence) to meet what is an extraordinary claim. In applying these rigorous scientific standards, the atheist uses his own mind to make decisions as opposed to adopting external beliefs based on dogmas, ancient scriptures or the pontifications of religious pundits..
At the same time we have to admit that as much as we try to impart critical knowledge about basic facts to do with the scientific or empirical process, there are dozens who actively seek to obscure it. Part of this ability to obscure is not due to any inherent substance they bring to the issue, but because the internet is now rife with bunkum and delusionary piffle. Couple that with the ability of the terminally ignorant to search at will (by googling) and there is manifested the illusion of knowing something - when they don't know squat.
Some of these deliberately confuse anecdotal accounts with evidence and also models with theories, and mathematical techniques with empirical methods. All of this is done to browbeat even more ignorant masses into thinking their "guru" knows what he's talking about.But let's look more deeply, beginning with what we mean by "proof".
First, in the strict scientific sense, we don't mean using the same methods as mathematicians- say to prove the Pythagorean theorem! As anyone who does scientific research knows, it is quite impossible to "prove" a particular solution to a scientific problem to be "true" (that is, true for all times and conditions). Solutions of scientific problems are instead assessed for adequacy, that is, in respect to the extent to which the researcher's stated aims have been carried out.
Two categories of criteria are those related to argument and to the evidence presented. To judge adequacy then, we look for the strength and consistency of logical/mathematical arguments, and the goodness of fit of the data in a given context. By "goodness of fit" I mean that two different datasets on comparison are either strongly correlated or anti-correlated. As an example, the rate of growth of tree rings is strongly correlated to the level of activity of a particular sunspot cycle. There is agreement and an excellent "goodness of fit".
All such determinations of adequacy perform the same function for scientific research that quality control does for industry. Most importantly, no determination of adequacy can be rendered until and unless the research is published in a refereed journal. If I am asked to invest mental and emotional energy in some extraordinary (e.g. “supernatural”) claim or other, then what exactly are the rational criteria of adequacy by which I can judge that claim?
Can it be set against original and actual scientific hypotheses? Can it admit the basis of numerous empirical tests- and moreover- can it be susceptible to any form of prediction?
If the answer is ‘No’, then we cannot place it into any scientific context. It will then have to be admitted that “faith” be enjoined to embrace or accept it, since no scientific rationale will permit true scientific inquiry. Since there are no genuine objects of scientific inquiry.
Of course, different theories of science represent different levels of abstraction: quantum theory is at a higher level than general relativity, and general relativity is at a higher level than Newton's theory of gravitation. But-- and here is the key point-- the limits of validity for each theory are ultimately founded in measurements, specifically through careful experiments carried out to test predictions.
It is this testing of reality which provides a coherent basis for scientific claims, and which bestows on science a legitimacy founded in reality rather than wish fulfillment fantasies. This is a basis, moreover, for which theological claims have no counterpart, despite that fact that theologians have often tried to make their claims sound like proven theories.
Let's use an example to illustrate: Which theory, Brans-Dicke or Einstein's General theory - predicts the solar oblation better in order to decide the superior theory of gravity?
Each begins with a hypothesis (call it 'X'), that: "If the solar oblation is less than +/- (x) then Einstein's theory is the default." (Note the oblation is the ratio of the solar polar to equatorial diameter)
You have preliminary information (say from earlier research efforts) that leads to the above hypothesis 'X'. You then continue the process, gathering more data, and accessory information which leads to some predictive result which yields a more refined hypothesis:
X' = x (n+1) = x + P(x)
where x(n +1) denotes an improvement via iteration, with P(x) the predictive confirmation (of x(n +1) from x) that allows it. Later, after more refined data become available:
x(n + 2) = x(n + 1) + P'(x + 1)
And so on, and so on and so forth.
Here, P'(x + 1) denotes the most recent and enhanced measurement, say of the oblateness.
Now, what if at these stage of testing we have:
x(n + 2) = x(n + 1) + P'(x + 1) + E(x + 1)
where E(x + 1) is an ERROR term.
In this process of falsification either one of two things will be true:
E(x+ 1) > > P'(x + 1) (call this E(e'))
I.e. the magnitude of the error term is drastically larger than the prediction value.
Or:
E(x+ 1) < < P'(x + 1) (call this E(e"))
I.e. the magnitude of the error term is drastically smaller than the predicted value.
Brans-Dicke theory then only trumps Einstein's if the relative error magnitudes are such that:
[E(e') + E{e")]/2 < e[P' (x + 1)]
where e[P' (x + 1)] is the error associated with Einstein's prediction.
It is for reasons like this that we need mathematics to show what is going on. We do not require mathematics to "baffle" anyone or to "win arguments" since "all logical efforts etc. have failed" etc.. Hardly! All that's happened is that sundry people with minimal exposure to science (e.g. certain politicos, fundies, QAnon twits et al) attempt to hijack it to their own ends. These morons wouldn't get the arguments if they were signed, sealed and uniformly delivered in single syllables - never mind the math (which they are clearly too innumerate to grasp).
The other role of mathematics is to describe the theory or hypothesis behind a model so it can be quantified in ways that enable measurements. Words alone are inadequate to the task. For example, the hypothesis that certain solar flares are triggered by "double layers" opens itself to test (or falsification) if one realizes that a loss cone is typically associated with a double layer. We define what's called the “loss cone angle” :
sin (q L ) = ± Ö (Bmin / B max )
where Bmin is the minimum magnetic field strength or induction at the apex, say, of a loop magnetic mirror system such as shown below.
where Bmin is the minimum magnetic field strength or induction at the apex, say, of a loop magnetic mirror system such as shown below.
Then B max represents the maximum value, usually at the loop ends or "foot points" as they are called (M1, M2 in the diagram). A special condition obtains which applies to the angle - for which the electrons will be TRAPPED, provided:
Θ (min) > (Θ) L
Thus, Θ (min) = (Θ) L
is said to be the "loss cone" of the system or machine. Now, the criterion for the hydrodynamic loss cone instability requires that the particular condition for the ratio of untrapped to trapped particles:
n/ no > 2 W e / p w e = 0.1
where W e is the electron cyclotron frequency, and w e is the electron plasma frequency. If such a condition were to apply, say to a solar coronal loop, it could elicit an "inverse population" in the transverse velocities (e.g. v⊥ ) for electrons in the loop. If the loss cone instability specified by the preceding condition then occurs in electrostatic waves near the upper hybrid frequency, we can get an anisotropic distribution of the electrons in velocity space. This can give rise to an electron particle beam. More importantly, energy to support the beam - and perhaps trigger a flare. We have then a model in place, quantifiable, and which can be tested to see if a suitable hypothesis is feasible. (Remember, a hypothesis comes before a theory!)
Now, it is important to note that neither Einstein's general theory or Brans-Dicke's are MODELS. A model is not a theory, but (generally) a mathematically described translation of what a hypothesis ought to look like in the real world. For example, Figure 2 below depicts the model for a sunspot in which dynamo action by a Hall electric field generates the rotary motion and outward current density.
Now, in terms of Darwinian evolution, it is not a "model" but a full theory since it has already met a number of its predictions and passed them, as well as other tests for falsification. For example, the theory of evolution as it applies to the elements of common descent, predicts humans and chimpanzees ought to have very nearly the same cytochrome-c protein sequence. This has been found to be the case. It also predicts that the two ape chromosomes designated 2p and 2q ought to be fused in the human to be one: designated '2'.
The theory of evolution has also predicted the full evolutionary development of foraminfera and this is validated. Finally, it predicts that a species - say the German cockroach - subjected to a mutagen like deildrin, will acquire resistance and thereby increase its fitness to the level that it effectively becomes a new, resistant species.
We note here that two quantitative measures for success of natural selection are the fitness (w) and the selective value (s): These can be measured on either absolute or relative scales, but are related algebraically on the latter by:
w = 1 – s, or
s = 1 – w
In natural selection there is a genetic "favoritism", as it were, for certain species' traits or characteristics to be passed on or selected out of a group of competing traits in the gene pool. In more technical terms, preferential alleles[1] appear by virtue of their relative increase in gene frequency. In the case of this cockroach, the favored genotype is DD, the less favored are Dd, and dd.
What natural selection does is to consolidate and direct particular random mutations into a more stable, adaptative adjustment. This is exactly what was illustrated above in the case of the hypothetical cockroach resistance to dieldrin. Without natural selection, very few living organisms could persist over time as recognizable species.
The exceptionally rapid development of the neocortex in Man is also an example of natural selection. By implication, human survival, in competition with large carnivores, was favored by the preferential development of the neocortex. This development permitted abstract conceptualization, enabling weapons to be fashioned as well as sophisticated language for communication and communal organization against larger predators.
As for "proving" or "disproving" God - no scientists in his right mind claims any such thing. The point eluding ardent religionists is that science cannot possibly refute “divine existence” because it cannot hold it as a legitimate hypothesis in the first place. If it is not subject to scientific modeling or test then it is supernatural in its basis and naturalist science rejects it as a suitable object of inquiry.
Unless one can forge or articulate a working hypothesis, one can’t have “refutation”, now or ever. “Divine creation” can’t be a valid hypothesis since it is contingent on a putative non-physical agent - undetectable by any scientific means. Even the Big Bang’s relic radiation can be detected as the isotropic cosmic microwave background – but the same can’t be said for the “divine”.
[1] By which I mean one of the more adaptive forms of a single gene, hence favored to multiply at greater rates in the gene pool.
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