Chapter 4

Question 1

Inductive Reasoning

Answer 1

A form of reasoning in which premises strongly support a conclusion, but where we can never be absolutely certain that it is true.

Question 2

4 Tips to Help Focus Thinking

Answer 2

1. Inductive reasoning is at its strongest when we have good reasons to believe that we are seeing a well-established pattern with plenty of evidence in its favour. 2. Inductive reasoning is at its weakest when there is little evidence, no clear pattern or a high degree of unpredictability, complexity or uncertainty. 3. A more general scenario is always more likely than a more specific scenario that’s a subset of the general one. It’s inevitably more likely that ‘a randomly selected passer-by is female’ than that ‘a randomly selected passer-by is female and has long hair’. 4. When assessing inductive reasoning, ask: how far is what you know a good guide to what you don’t know? To what degree is the future, in this situation, likely to resemble your knowledge of the past?

Question 3

Inductive Strength or Inductive Force

Answer 3

A measure of how likely we believe an inductive argument is to be true.

Question 4

Cogent

Answer 4

An inductive argument that has a good structure, but whose conclusion we should not necessarily accept as true (similarly to a valid deductive argument).

Question 5

Inductively Forceful

Answer 5

An inductive argument that has both a good structure and true premises, and whose conclusion we thus have good reason to accept as true (similarly to a sound deductive argument, although without its certainty).

Question 6

Ampliative Reasoning

Answer 6

Another way of describing inductive reasoning – intended to show that such reasoning works by ‘amplifying’ premises into a broader conclusion.

Question 7

Ranking Inductive Arguments

Answer 7

Determining which arguments are more or less convincing relative to one another.

Question 8

Implicit Qualification

Answer 8

When a general statement is not literally intended, some implicit qualification needs to be assumed, indicating the frequency with which it applies.

Question 9

Implicit Qualifying Words

Answer 9

Some, often, might, less likely, almost, many, very few, may, for some time, etc.

Question 10

Choosing & Using Qualifying Words

Answer 10

1. Be careful never to express absolute certainty in the conclusion of an inductive argument. 2. Always keep in mind a range of qualifying words, from least to most confident, to allow you to express inductive conclusions precisely in your writing. 3. For example: Extremely unlikely < unlikely < not that likely < possible < quite likely < probably < almost certainly. 4. Always be ready to make explicit the implicit qualifications you encounter in others’ inductive arguments – don’t make the mistake of taking apparent certainty literally.

Question 11

Probability

Answer 11

The study of how likely something is to happen, or to be true.

Question 12

Rational Expectation

Answer 12

Whatever it would be most reasonable to expect in a particular situation; this can be quite different to what somebody personally expects.

Question 13

Sample

Answer 13

The particular cases you are using to stand for the entire category about which you wish to make an inductive generalization. Representative samples closely resemble the larger group about which claims are being made, while unrepresentative samples fail to do so.

Question 14

n = 1

Answer 14

A sample size of one indicates an anecdote rather than a serious investigation; any inductive argument based on a single instance is likely to be very weak.

Question 15

4 Steps To Picking A Representative Sample

Answer 15

1. Establish as thoroughly and accurately as possible the specifics of the target population: with- out this, there is no way of knowing what variations you need to represent. 2. Determine an appropriate sample size: in general, a larger sample size is better, but the exact size you need depends on how confident you need to be in your result, the level of variability within the population you’re studying, the margin of error in your measurements and the pro- portion of the population displaying whatever attribute you’re interested in (there are plenty of good online tools for calculating sample sizes). 3. Determine an appropriate sampling method: this depends on what you’re studying and on what resources you have at your disposal; all methods have their limitations, and range from relatively simple ‘convenience’ samples based on volunteers or case studies to more complex ‘multi-stage’ samples based on dividing a population into clusters, and then selecting clusters at random for close examination. 4. Consider whether results need weighting: this entails giving more weight to certain results within your sample in order to better reflect the overall situation: for example, giving adults twice the weight of children in a piece of research exploring transit costs, on the basis that adults’ tickets cost twice as much as children’s tickets.

Question 16

Randomized Sample

Answer 16

One selected at random from across a field of study, with no particular element misleadingly over- represented.

Question 17

Sampling Bias

Answer 17

Biases introduced by imperfect methods of selecting a sample.

Question 18

Potential sources of sampling bias to be avoided – or to be aware of in others’ investigations

Answer 18

1. Self-selection: setting up your sample in such a way that a certain type of participant effectively selects themselves. For instance, the kind of person most likely to fill in a detailed survey may differ substantially from the population at large. 2. Specific area selection: selecting your sample so that one particular area is over-represented. For example, conducting research into global urban population trends based only on statistics gathered in London and New York. 3. Exclusion: selecting your sample in a way that disproportionately excludes certain elements. For instance, conducting a wildlife survey only during daylight hours might exclude nocturnal animals. 4. Pre-screening: conducting your sample selection via an initial method that is likely to select only a certain kind of participant – for example, only advertising for volunteers to participate in a health trial in hospital waiting rooms. 5. Survivorship: a sample that considers only successes can be highly biased if failures are also relevant. For instance, an investigation of business debts that looked only at companies with more than ten years of accounts would entirely ignore all companies that had failed within a shorter period.

Question 19

Observational Error

Answer 19

Errors due to the accuracy of your measuring system, usually reported as ±X, where X is the potential difference between measured and actual values.

Question 20

Margin of Error

Answer 20

An expression of the degree to which results based on a sample are likely to differ from those of the overall population.

Question 21

The Problem of Induction

Answer 21

No matter how likely we believe something to be, an inductive argument can never actually prove it to be true.

Question 22

Falsification

Answer 22

The contradiction of something previously accepted as true or obvious.

Question 23

Counter-Example

Answer 23

An example whose discovery makes it necessary to rethink a particular position, because it directly contradicts a generalization previously believed to be true.

Question 24

Black Swan Event

Answer 24

An event that defies both previous experience and expectations based on that experience, making it almost impossible to predict.