Argument Mechanics - The Realm of Reason Part VIII (Generality)

Generality

- some generalisations are causal, some are arrived at by analogy and some arguments which are technically analogical (weather forecasts) methodologically resemble causal and generalising arguments.

- generalisations claim for all something believed known about some.  In each generalisation there is a conclusion and a basis for it.  The conclusions are all general statements, not themselves reasoning, but rather the results of reasoning.

General statements have been characterised by their outward form, by their containing certain terms in certain slots.

Generalisations are about “all”, “no” or the equivalent.  Generalisations can be either true or false.  Generalisations can be factual or definitional.

Hard generalisations are characterised by language such as “each”, “every”, “not one single...” etc. and can be falsified by one or more counter instances.

When a general statement is improperly objected to on the basis of a so-called “exception” which it never was intended to cover, we have the fallacy known as secundum quid or “from a qualified statement to an unqualified one”

Moral behaviour is introduced together with moral language and moral principles.

Moral principles are integral with the whole social fabric.  When moral principles get separated from that fabric, they get reduced to formulas.

Formulas fail as a basis for moral action unless they are accompanied by a deeper understanding.

Scientific laws get evaluated by their range of applicability, by their felicity with other theory, and by the accuracy of the deductions which can be made based on them.

Generalisations distribute - they apply distributively (collective statements)

It is easy to slide into thinking that what holds for the parts of the class must hold for the class as a whole, and vice versa.  To argue from a characteristic  of the parts of a group to a characteristic of the whole is to commit the fallacy of composition.

To argue from a characteristic of a whole to a characteristic of the parts commits the fallacy of division.

In composition the term equivocated upon appears in the premises in a distributive sense and in the conclusion in a collective sense.

In division a term appearing collectively in the premises appears distributively in the conclusion.

Much good reasoning does proceed from parts to whole, and vice versa.

Not many statistical generalisations are distributive.  A statistical generalisation applies a percentage or proportion to a class.

What counts is to generalise intelligently and to be articulate in assessing the generalising of others.

Simple and statistical projections frequently provide exact and powerful tools for getting the job done.

The art of induction, of making intelligent projections, is called sampling.

The goal of sampling is to obtain a representative sample, one which contains proportionally all relevant characteristics of the class projected to.

An unrepresentative sample is said to be biased.

The class projected to and sampled from is called the universe or population.

- sometimes a representative sample can be obtained by making a random or probability sample, one in which each member of the population has an equal chance of being selected.

“Random” is relative.  Random with respect to what population?

Changes can occur in the population between the sampling time and the time of the event projected to.

Sampling can be biased itself as in sampling without replacement.

Failure to distinguish between sampling with and sampling without replacement may account for the psychological trick called the “gamblers” or “Monte Carlo” fallacy, in which the victim imagines that each successive loss increases the chances of a win on the next round.  A vague analogy brought over from the gamblers previous experience in games where non-replacement is practiced.

A stratified random sample can be taken wherever variations in the parent group are familiar and known to effect the result.

Systematic or interval sampling selects every nth item beginning at a randomly selected starting point.

Cluster sampling is taking the sample in clusters as the clusters occur in the parent group.

Quota sampling, an investigator selects so many instances in each stratum of a stratified sample, not at random, but as they are found.

Besides varying the instances, the responsible generaliser should get enough instances.

The topic of proper sample size becomes technical very quickly.

Proper sample size depends on the desired precision of the results, on the number of instances in the sample, on the variation within the sample, and on the size of the population. (perhaps surprising population size is usually the least important factor in the list).

Two important elements in determining what is the appropriate sample size are (1) the margin of error which can be tolerated, and (2) the desired degree of confidence that the result will be within that margin.

The degree of precision in any sample is called its sampling error, an index of the  probability of a sample of that size falling within a certain percentage range (it is theoretical margin of error).

All things being equal, the precision of a sample increases with the square root of the sample size.

Polls and surveys are best seen as morally neutral - tools which can be used for good ends or for bad.

One ought not to take polls at face value.  Any poll worth considering ought to display its methodology.

Opinion survey reports ought to state at least the following (1) the sponsor’s name and surveyor’s name, (2) the sample size (and sampling error), (3) the date of contact, (4) exactly what population is being sampled and the method of contact, (6) the exact questions asked.

Responsible surveys consisting of people’s responses to questions must be designed in order to eliminate the charge that the questions themselves colour the results.  Questions undergo scrutiny by experienced critics in order to uncover poor wording.  Then they are tested on samples of respondents.  The questions are asked, then followed up with questioning designed to bring out respondents comprehension and true feelings.  Alternative formulations may be given to split samples in order to detect differences  between formulations.

Questions must be easy to understand.

Good questions should be short and cover one subject.

Questions should be divided, one question for goal, the other for the means.

Questions should be worded so as to avoid colouring the responses eg. “Are you a racist?”

People are inclined to say what they think the pollster wants to hear, and not what in fact they think.

People also tend to project what they imagine to be a favourable self-image.