Tag Archives: mathematics

“Other ways of knowing” – some sense at last

There’s been a lot of rubbish written about “other ways of knowing”. So it’s quite refreshing to read Richard Carrier’s classification of methods of knowing. This is from his book Sense and Goodness Without God: A Defense of Metaphysical Naturalism. Well worthy reading by the way.

He starts by pointing out that no method of obtaining knowledge can produce absolute certainty. We can always be wrong, make mistakes. But we can list possible methods in order of reliability:

What is rational is to assign degrees of conviction to degrees of certainty established by a tried-and-tested method. What is rational is reasonable certainty, not absolute certainty.”

The methods of logic and mathematics are well-developed and provide the greatest certainty we have yet been able to find regarding anything, other than a present, uninterpreted experience. The next greatest certainty has been found in the application of scientific methods to empirical problems. In third place is our own daily experience, when interpreted with a logical or scientific mindset. Fourth is the application of critical-historical methods to claims about past events. Fifth is the application of the criteria of trust to the claims of experts. Sixth is the untested but logical application of inferential generalizations from incomplete facts—that is, plausible deductions. Such is the scale of methods that we have historically been able to discover and confirm as effective.”

“Experience shows that our degree of certainty will generally be weaker with regard to facts at each stage down this six-rung ladder, though within each category lies its own continuum of certainty and uncertainty, and the ladder itself is a continuum of precision and access to information: the more data we have to ground our conclusions, the farther up the ladder we find ourselves. Thus, mathematics is just perfected science; science, perfected experience; experience, perfected history; and history, perfected attention to experts; while plausible inference is what we are left with when we have none of those things.”

“Lacking any of the above approaches to the truth, we are faced with untrustworthy hearsay and pure speculation, where only the feeblest of certainty can ever be justified, if at all.”

Carrier writes that accurate methods of knowing have the properties of predictive success and convergent accumulation of consistent results.  However, these should be evaluated intelligently. Even the best method may produce faulty knowledge if used incorrectly.

So how do the different methods rate?:

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Human Morality II: Objective morality

This is the second in a series of four posts on morality. They are aimed at countering the usual religious claims for a god-given morality with current scientific understanding of how the morality of our species arose. Also, they attempt to justify a non-theist objective basis for much of the moral decisions we make. The first post (I: Religious confusion) discussed some of the problems religion has in its understanding of morality. This second post argues that there is an objective basis for human morality and no god is required for this.

Recently I was dipping into Roger Penrose’s book The Road to Reality: A Complete Guide to the Laws of the Universe. In the first chapter he argues for an objective basis for mathematics and mathematical logic. I think that the objective basis of morality can be seen in the same way (see Where did our morals come from?). So, I was pleased to read that Penrose also believes that objective “‘existence’ could also refer to things other than mathematics, such as morality or aesthetics.”

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The Lotto “miracle”

lotto-2-ballsApparently some local Christian apologists believe that the New Zealand Lottery Commission performs a miracle each week with its Lotto draw. They claim that:

“Given the complete randomisation of 40 balls, falling into any sequence of six is 1:2,763,633,600.”

If they are correct, and given New Zealand’s population, we would  expect a winner only every 15 years or so. Despite this there is a winner most weeks. In September 1993  38 people won First Division! With these odds they might be justified in calling most of the winning miracles.

However, these poor souls got their maths wrong. They forgot to divide by 720. The real odds are 1:3, 838, 380. That sounds more like it, doesn’t it?

So, no miracles. But the mathematical error was really caused by their desire to describe the regular Lotto result as “extraordinary”:

“Consider the lottery reported last night on television as one such event. The chances of winning, or indeed any random sequence of numbers, is extraordinarily improbable, yet if it is true that extraordinary claims require extraordinary evidence, you should never believe it happened. Weighing the probability of the extraordinary event will swamp the reliability of the witnesses every time so that you should never believe it. Even if the programs reporting is 99.9% accurate.”

So, they claim, if we can accept the Lotto “miracle” on the hearsay evidence of a news report we don’t need extraordinary evidence to accept “God raised Jesus of Nazareth from the dead.”

Can’t see what Lotto has to do with it. The event itself is not extraordinary (nor is the selection of “any random sequence of numbers” which actually has a probability of 1) and while the actual numbers drawn are pleasantly extraordinary to the winner – they aren’t to the rest of us.

But what about the evidence? We know that there is a legal requirement for police observation of the draw as well as other checking of the equipment and procedure. The winners ticket is also thoroughly checked. We just wouldn’t be investing our hard-earned cash in Lotto if this checking didn’t occur. Seems like pretty extraordinary evidence to me.

These Christian apologists claim that because we accept the Lotto result we should accept the hearsay claims of biblical miracle with no real evidence.

Now, if they could just produce evidence of their miracles with similar thoroughness and robustness to that used in the Lotto draw we would have something to look into – wouldn’t we?

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