Petitio Principii, ”Assuming the Initial Point”, (or ”Begging the Question”)

Last time, two weeks ago, I examined what may be termed ”the cross-paradigm fallacy” when attempting to look into the future. The fallacy may be said to derive from assuming – falsely – that contemporary statistical relations remain valid in radically different circumstances. But those different circumstances need not be in the future. They can equally well have occurred in the past, and I will explore this possibility in the following.
This different, but related fallacy, is the well-known petitio principii, ”assuming the initial point”, or ”begging the question”. Let’s critically consider a well-known argument, viz. –
”Human ingenuity is without bounds; the divide that humanity in general and western civilization in particular is now facing and must soon cross with respect to energy supply is inconsequential. We have successfully spanned similar divides several times earlier on (human to animal power, on to wood/charcoal, on to coal, to oil/gas, with some hydro and nuclear power...). - We will do it again; there is positively no need for concern!”
Yes, we have succeeded several times before, but is that important? Not at all! It is irrelevant and misleading. The problem is, that if civilization had not succeeded some earlier challenge then we would not be around to consider the question. Our society would instead be found on history’s ”junkyard” of past civilizations together with those of Sumerians, Mayans, Easter Islanders, and countless others. The so-called Bayes’ theorem states it very succinctly:
P(AlB) = P(BlA)*P(A)/P(B)
- where
· P is Probability, typically expressed as a percentage, 0-100%
· ‘A’ denotes current [or future, soon-to-be] successful transformation of energy supply,
· ‘B’ denotes past successful transformation(s) of energy supply.
(Cf. Wikipedia):
· P(A) is the prior probability, or marginal probability, of A. It is "prior" in the sense that it does not take into account any information about B,
· P(AlB) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from, or depends upon, the specified value of B,
· P(BlA) is the conditional probability of B given A,
· P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Now, obviously P(B) is 100% (since ”we know, we’ve made it so far”), and P(BlA) is also 100% (since ”if we make it again, then we can still be certain we made it before”). Therefore:
P(AlB) = P(A)
In so many words, the probability ”we can make it again, since we did it before” is equal to the probability that ”we can make it again” – in this case past successes are simply irrelevant to future possibility of success!

A similar line of false reasoning applies when one all too frequently hears a statement like; -
“It doesn’t matter people in third world countries have many children today. It was just like that here in the developed countries a 100 years ago. My great grandmother was out of a family of SOOooo many siblings... And we all have such ancestors – don’t we? – so it was really the same thing, - right?”
Dead wrong! But why is this anecdotal reasoning plain nonsense? Well, make some simplifying assumptions, notably that there are equally many boys and girls, and enter some simple combinatorial statistics...
1. Where a family in a third world country today averages 6 children, that means that each woman on average gives birth to 3 girls/women in the next generation,
2. Assume that in the developed world 100 years ago the pattern was [not too far off]
200 of a 1000 women had no children (0; of which 0 girls)
150 of a 1000 women had 1 child (150; of which 75 girls)
150 of a 1000 women had 2 children (300; of which 150 girls)
150 of a 1000 women had 3 children (450; of which 225 girls)
150 of a 1000 women had 4 children (600; of which 300 girls)
100 of a 1000 women had 6 children (600; of which 300 girls)
100 of a 1000 women had 9 children (900; of which 450 girls)
Now, with this distribution 1000 of each generation of women gave birth to 1500 girls/women in the next generation – just half of what has been and in many places still is prevalent in the third world today.
Also, it is easy to see why today we almost all have ancestors with many siblings: There is NO possibility that our great grandmother had ZERO children – or we wouldn’t be around to ponder the probability! - Conversely, there is (300+450)/1500*100% = 50% probability that our great grandmother was out of a family of 6, or more, children. The remainder 50% is the probability our great grandmother was out of a family of 1 to 5 children. Given the fact that we all have four great grandmothers, it is further possible to make a simple estimate that NONE of them was out of a family of at least six children:
½ * ½ * ½ * ½ * 100% = 6%
Conversely, there is (100-6)% = fully 94% probability each of us can point to a great grandmother out of a family of 6, or more, children, even though the total number of children in the developed countries at that time only amounted to half of what is still the case in many developing countries today.
Now, THAT is a real fact presented to you by simple application of basic statistics, and any denial of it is a damned lie. – Stay tuned here at morlin’s BI blog to see what follows next!