Arguments in Action

Inductive arguments

To an extent the definition of inductive is determined by the definition of deductive.

The Higher Course has been using the following definition:

’Inductive reasoning attempts to draw probable conclusions from a given set of premises.’

However, it is important to be aware of some additional complications. It has been traditional to regard all reasoning as either deductive or inductive. When divided this way analogical reasoning and conductive arguments are sub-types of inductive reasoning. There is an increasing tendency, especially in the field of informal logic, to regard this binary division as unsatisfactory. Firstly, in ordinary language deductive arguments turn out to be quite uncommon and, secondly, there are then a very large number of different types of inductive arguments. Some books simply list different types of argument (e.g. deductive, inductive, analogical, conductive, etc.) and say that whatever type of argument being dealt with it is necessary to evaluate it in terms of the adequacy, relevance and sufficiency of its premises. Other books make the binary distinction between deductive and non-deductive arguments, recognising that all non-deductive arguments are attempting to establish a probable conclusion. Both of these strategies means that a different definition of inductive argument has to be given. Govier says, inductive arguments are arguments ‘in which the premises and the conclusion are empirical— having to do with observation and experience—and in which the inference to the conclusion is based on an assumption that observed regularities will persist’ (p283) and that inductive reasoning is reasoning ‘in which we extrapolate from experience to further experience.’ (p284)

Until otherwise informed it is best to use the definition that the SQA has been using to date.

The mandatory documents don't specify which types of inductive arguments should be taught. Pupils are, however, expected to recognise and evaluate arguments and to assist with this it is a beneficial to illustrate the range of inductive arguments. 

Deductive  (for comparison)

I have a bag of blue marbles and have taken one out. I conclude that it will be blue.

 

Simple induction

I have a bag of marbles. I have taken ten out and they are all blue. I conclude that the next one I take out will be blue.

Inductive generalisation 

I have a bag of marbles. I have taken ten out and they are all blue. I conclude that all the marbles in the bag are blue.

Statistical syllogism  

I have a bag of red and blue marbles with equal numbers of each. I conclude that if I take out a handful of marbles about half of them will be blue.

Statcistical generalisation 

I have a bag of marbles. I have taken out a handful of marbles and half of them are blue and the other half red. I conclude that the bag contains an equal number of red and blue marbles.

The common feature of these arguments is that they extrapolate from the known to the unknown, from the observed to the unobserved. They are a special form of analogical argument in that they assume that the known and the unknown are relevantly similar so that what is true of one will be true of the other. Evaluating these arguments involves considering whether there are grounds for questioning this assumption. In particular attention can be given to sample size.

 

Abductive (Sometimes called inference to best explanation. Sometimes considered a form of induction because the conclusion is not certain; sometimes considered a separate type of reasoning.)

There is a bag of blue marbles on the table and one on the floor. I conclude that the one on the floor came from the bag.

 

Conductive  (Sometimes considered a form of induction because the conclusion is not certain; sometimes considered a separate type of reasoning.)

There is a bag of marbles on the table. My older sister said she would bring me some marbles; I know of nobody else who knew I wanted marbles; this type of marble is sold in a shop that is regularly used by my sister; my older sister has a key and could have let herself in. On the other hand my sister said she wouldn't be back home until tomorrow. I conclude that on balance the marbles were put there by my sister.