Philosopher Antony Flew died on April 8, 2010. He was 87. During the last decade of his life, he had moved from a long-held religious agnosticism, which he called “negative atheism,” to deism. Flew believed in a creator god, but not the God of any revelation, not an object of ritual worship, nor the host of an afterlife. Flew’s relatively tiny shift of irreligious identifcation generated enormous and heated discussion, much of it about the elderly Flew’s mental acuity.
These essays assess the rationality of Flew’s belief changes, from a broadly and approximate Bayesian perspective. First up, we’ll consider whether empirical observations might possibly increase rational believers’ confidence in their religious beliefs, despite the general incompatibility of natural and supernatural reasoning. Flew changed his mind about that issue first, before he later changed his mind about the question of God.
In the beginning, there was a garden
Flew launched his academic career in the middle of the last century with a widely reprinted short article, “Theology and Falsification.”
The paper focused on John Wisdom’s Gardener Parable. Two people, let’s call them Believer and Sceptic, discover a garden in a remote wild jungle. Both are impressed by the orderliness of the place, but they disagree about whether or not it is actively tended by a gardener.
Let us suppose that Believer and Sceptic do not much differ in their a priori opinions about whether or not the hypothetical gardener exists. Without any nearby human habitation or jungle paths, both would disbelieve in regular human visits, except for the garden. Neither professes certainty about the question one way or the other. Let’s discuss their disagreement about the bearing of the evidence.
Both agree that an attentive gardener would be a sufficient explanation of what they see,
P( garden | gardener ) = 1
They disagree about the prospects for such order without a gardener. For simplicity, we’ll say Sceptic thinks the orderliness is almost as likely to occur with or without the gradener,
P( garden | ~ gardener ) = 1 or slightly less than 1
while Believer can scarcely imagine the order happening in any other way,
P( garden | ~ gardener ) << 1, very much less than 1
An ordinary Bayesian measure of the force of evidence is the likelihood ratio, in this case:
P( garden | gardener ) / P( garden | ~ gardener )
For Sceptic, the ratio is one, or only slightly greater than one. That is, the evidence makes little or no change in Sceptic’s initial opinion. Sceptic can easily maintain that it is less probable than not that the gardener exists.
For Believer, the ratio is very much bigger than one. Any value bigger than 1 is evidence in favor of the gardener, and the more the ratio is greater than 1, the stronger the evidence. Believer can easily maintain that it is more probable than not that the gardener exists.
Bayesian analysis has nothing to say about whose appraisal of the evidence is correct. Estimates of likelihood in cases like this are subjective, matters of judgment. Both people are rational in the sense that all of each person’s beliefs are consonant. Only one of them is factually correct.
Can there be useful active investigation in the garden?
Our heroes perform a series of experiments, perhaps to find signs of the gardener’s comings and goings. They patrol the grounds with bloodhounds, erect an electrified fience around the perimeter, search carefully for footprints, and so forth. All the experiments turn out the same way, they find no traces of the gardener.
Both parties agree that a sufficient explantion of their failure to find any traces of the gardener would be that there is no gardener,
P( tracelessness | ~ garderner ) = 1
The parties also agree that each new experiment’s outcome is conditionally independent given every other experiment and of the orderliness of the garden. That is, the state of the garden and the performance of the bloodhounds (say) have nothing to do with each other, except that both might be affected by the recent whereabouts of the gardener.
That’s convenient, because the likelihood ratio of all the evidence is then found simply by multiplying the likelihood ratios for each piece of evidence. Simple is good.
The Sceptic also thinks that
P( tracelessness | gardener ) << 1
and expects Believer to agree. They might still disagree about the total bearing of all the evidence, but at least it won’t be as favorable to the gardener hypothesis as it was before.
But the Believer has a surprise. Having read Duhem, Believer knows that all experiments incorporate assumptions about how well the experiment tests the hypothesis of interest. For example, the bloodhound experiment doesn’t rule out that a gardener was there. Maybe it only means that no smelly gardener was there. The failure of the electrified fence might mean the gardner wears rubber outerwear, and so on. The assumptions that determined the experimental protocols, the Believer thinks, may not have been “good assumptions;” they may not have been fair tests of the hypothesis in dispute.
This maneuver isn’t part of Bayesian analysis, but its effect can still be captured with Bayesian concepts. The Believer asserts
P( tracelessness | ~ ( gardener AND good assumptions) ) = 1
P( tracelessness | gardener AND good assumptions ) << 1
and concludes that the observations of tracelessness strongly support
~ ( gardener AND good assumptions)
or, as De Morgan’s Law rewrites it,
~ gardener OR ~ good assumptions
Believer cooly announces that he thinks that the experimental assumptions weren’t so good, and that the gardener hypothesis is still fine. The hypothesis stands untested, in his view, except for the orderliness of the garden.
Sceptic objects. Not that Sceptic disputes Duhem, but these “assumptions” concern attributes of the gardener. If he doesn’t smell, doesn’t leave footprints, isn’t stopped by an electrified fence, … then what is he? If you perform enough of these experiments, then the repeated appeal to poor assumptions leaves you with a “gardener” that can scarcely be distinguished from a figment of the imagination or someone who simply doesn’t exist at all.
Young Flew clearly sided with the Sceptic. He provided philosophical arguments that supported the Sceptic’s outright rejecton of the gardener as a misbegotten concept.
“Sorry to disappoint, …” in 2001
One kind of evidence that the duo might agree is Duhem-proof is orderliness itself. They both think that being an agent of orderliness is essential to the very idea of the gardener.
In August, 2001 Flew wrote a short article entitled “Sorry to disappoint, I’m still an atheist.”
In that paper Flew concludes,
“I recognize that developments in physics coming on the last twenty or thirty years can reasonably be seen as in some degree confirmatory of a previously faith-based belief in god, even though they still provide no sufficient reason for unbelievers to change their minds. They certainly have not persuaded me.”
Back in the garden, an analogous argument could be offered if new kinds of order were discovered there. For example, maybe the soil has been disturbed differently for neighboring plants of different species.
Once again, the parties might agree about the sufficiency of the gardener hypothesis to account for order.
P( new-order | gardener ) = 1
They might also agree that the new orderliness is conditionally independent of the oriignal kind of orderliness. That is, we can simply multiply likelihood ratios for each piece of evidence to get the bearing of all the evidence taken together. But some degree of conditional independence is also crucial, since we seek new evidence, not just an extended restatement of what we already know.
Sceptic might see the new kinds of order to be just as equivocal as the old kinds, despite their genuine novelty,
P( new-order | ~ gardener ) = 1 or slightlly less than 1
Believer, meanwhile, may once again assess that the new kind of order is very unusual without a gardener,
P( new-order | ~ gardener ) << 1
And thus, Believer might, in principle, develop naturalistic evidence that rationally enhances Believer’s own confidence. That the same observation does nothing to change Sceptic’s beliefs is irrelevant to Believer’s rationality.
Something more interesting might happen if Sceptic sees some of the new kinds of orderliness as at least slightly hard to explain without invoking a gardener.
P( new-order | ~ gardener ) < 1, strictly less than 1, even if just a little
What if even more orderliness evidence came to be be developed, horticultural counterparts of Flews’ recent “developments in physics?” If each new piece made a tiny, but conditionally independent, contribution to Sceptic’s appraisal of the evidence for the gardener, then the cumulative effect of evidence in favor of the gardner might eventually overtake any uncertain prior disadvantage of the hypothesis. Eventually, this accumulation might produce any posterior strength of confidence short of absolute certainty.
Empirical evidence might, in other words, come as close as you like to verifying the existence of the gardener to a Bayesian Sceptic’s satisfaction, without actually needing to produce the gardener. Natural evidence, then, might come as close you like to verifying the existence of a supernatural being, as close as passes without remark for some contingent features of the natural world.
“Natural theology” isn’t impersonally valid, but it isn’t an oxymoron, either.
Flew’s 2001 note is more than a technical cavil about the paper which launched his career. The note devastates the force of his earlier argument. As his 2001 title suggests, though, that wasn’t enough for Flew to abandon his agnostic “negative atheism.” But the door was open, for the first time in decades.
Next time: Flew surveys the line between science and philosophy.