Numbers Games

Used correctly, statistics are an invaluable aid to correct reasoning.

The discipline called 'statistics' is a mathematical science that establishes criteria and techniques for meaningful, mathematical evaluation of numerical data (descriptive statistics, inferential statistics). This discipline is not to be confused with the vernacular meaning of statistics, which merely refers to any collection of numbers connected to a topic.

"Statistics can be made to prove anything - even the truth." ~Author Unknown

"Statistics may be defined as "a body of methods for making wise decisions in the face of uncertainty."" ~W.A. Wallis

As applied within the softer sciences, statistical methods provide the means by which to ascertain whether or not data have arisen purely by chance or whether they accurately reflect that which they are intended to measure. That is, inferential statistics provides confidence limits that indicate the probability that the data have not arisen purely by chance.

"The theory of probabilities is at bottom nothing but common sense reduced to calculus." ~Laplace, Théorie analytique des probabilités, 1820

However, as for so many other areas that are abused by what passes as human reasoning, statistics can be manipulated and misinterpreted to serve the special prejudices of hate-tankers and junk-tankers. The fact that numbers can be manipulated and misinterpreted does not mean that statistics always lie or even that statistics often lie. It is people who lie, and people who are mistaken either through simple ignorance or deliberate self-delusion.

"He uses statistics as a drunken man uses lampposts - for support rather than for illumination." ~Andrew Lang

"Statistics are like women; mirrors of purest virtue and truth, or like whores to use as one pleases." ~Theodor Billroth

"Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: "There are three kinds of lies: lies, damned lies, and statistics." ~Mark Twain, autobiography, 1904 (there is no actual record of this under Disraeli's authorship)

The oft-cited "Borel's Law" is prime example of the sort of manipulative numbers games to which creationists resort in an attempt to discredit the enormously likely probability of biopoiesis. Here's an example of creationist nonsense:

"...Mathematicians generally agree that, statistically, any odds beyond 1 in 10⁵⁰ have a zero probability of ever happening.... This is Borel's law in action which was derived by mathematician Emil Borel...."

Rot and twaddle – only a zero probability is a zero probability.

Whenever there are close to or more than 10⁵⁰ possibilities that the particular event will occur, then the event cannot have zero probability. Even if there was a single chance for that event to occur, the event could occur, so its probability is not zero.

Of course, since for whatever deluded reasons creationists choose to take Genesis literally, those who are already convinced that they are the product of special creation will be enamoured of such a ridiculous argument. No matter how stupid or unlikely an idea, those who dogmatically cling to that idea for emotional reasons will be unmoved by reason, logic, facts, or legitimate statistics.

The other form of illogic that attaches itself to numbers lies in two related but separate fallacies of logic – argumentum ad numerum and argumentum ad populum.

The reverse of these recognized fallacies is a form of fallacio fallacy, namely that just because a large number of credible authorities state something, this does not make the assertions of experts well-founded. Such an assertion is a fallacious argument against authority. The faulty reasoning runs, "I don't like this idea, therefore no matter how many genuine authorities say that such-and-such is true, because I don't want to believe it, all the authorities are incorrect."

Quo Vadis?
...section index...

Epistemology

Epistemology is a branch of philosophy that deals with the nature, origin and scope of knowledge.

The term 'epistemology' derives from the Greek words episteme (knowledge) and logos (word/speech). Epistemic is an adjective that signifies being of or relating to epistemology.

Epistemologists are primarily interested in propositional or theoretical knowledge rather than in skill sets.

A belief is some proposition that the individual holds to be true. For a belief to count as knowledge, no matter how strongly the individual feels the belief to be true, the belief must actually be true. That is, to count as knowledge, a belief must be justified, and, according to Gettier, must be justified for the correct reasons (justified true belief that depends on no false premises, also termed 'no false lemmas'). The term 'justification' signifies that the person who believes something has an epistemic reason to thinking that the belief is true. A belief that consists of accidentally stumbling upon the truth does not constitute knowledge.

Relevant, empiric evidence can never provide inductive proof for a principle, because inductive proof is logically impossible. This means that failure to provide inductive proof is not necessarily failure of a theory given the facts upon which the induction is based. This also does not mean that there is not an underlying principle (mechanism) that is in reality responsible for the observed phenomena. Thus, some inferred principles are much more likely to reflect the actual underlying mechanism than are others, though a principle can never be proved by induction from the observations.

Scientific method can lead only to disproof (falsification) or to experimental corroboration that a scientific hypothesis or theory is the most probable explanation for observed phenomena. Similarly, correlation may result from causation, but it may also reflect some other relationship other than cause and effect, so correlation alone cannot be taken to indicate causation.

Epistemic probability refers to degree of belief in judgement-requiring propositions, uncertain events, or problems. Bayes' theorem (rule, law) derives from probability theory, a branch of mathematics that deals with the analysis of random phenomena. Bayes' theorem relates the conditional and marginal probability distributions of random variables.

Bayesianism is the philosophical tenet that the mathematical theory of probability can be taken to apply to the degree of plausibility of a statement, or to the degree of believability contained within the rational agents of a truth statement. When a statement is employed within the Bayes' theorem, the statement becomes a Bayesian inference.

Conditional probability is the probability of some event A, given the occurrence of some other event B – P(A│B) – the conditional probability of A, given B. P(A│B) is also called the posterior probability because it depends upon the specified value of B. P(B│A) is the conditional probability of B given A.

Marginal probability is the probability of one event, P(A), regardless of the other event, P(B). P(A) is termed the prior probability or marginal probability of A. P(B) is the prior or marginal probability of B, and acts as a normalizing constant. The marginal probability is derived by integrating the joint probability over the unrequired event (marginalization).

The joint probability is the probability of the two events in conjunction (both events together), where the joint probability of A and B is written P(A∩B) or P(A,B).

Bayes' Theorem: the conditional probability of event A given event B = the likelihood of event B given event A x the prior likelihood of event A, divided by a normalizing constant (the prior probability of event B) .


................................... likelihood x prior
......... posterior =... _______________

................................. normalizing constant

......... posterior = standardized likelihood x prior


In some interpretations of probability, Bayes' theorem is taken as a guide of how to update or revise beliefs in light of new a posteriori evidence. Here, Bayesian probability is an interpretation of Bayesian theory, which holds that the concept of probability can be defined as the degree to which a person believes a proposition.

Quo Vadis?
...section index...