Logic Part 2: Three Types of Logical Reasoning: 

We cannot exist as rational or thinking beings without the practice of using logic in our lives. Logical thinking features in three kinds of reasoning which have been traditionally identified in philosophy.  The three current and commonly recognised argumentative processes are labelled deduction, induction and abduction. It is worth noting, however, that cognitive psychologists do not feel so confined when examining thought more generally. In addition, we should be aware that these divisions could be entirely arbitrary and that the way we reach particular explanations could involve a mixture of these argument types.

Three arbitrarily recognised argumentative processes can be introduced in the following way:

1.  Deduction is a style of argument or reasoning in which conclusions are reached given 2 or more assertions. Deduction is said to be ‘truth-preserving’ when the structure (i.e. use of the connectives) of arguments are ‘valid’. We should take this property of deduction very seriously since valid deduction preserves rather than generates truth.

2. Induction is used to make generalisations from single or repeated observations. The degree of generality of an inductive assertion can vary between being locally valid and some attempt at a more widely applicable explanation. Unlike deduction, which has nothing to say about the input truth value, induction when wisely used can generate probable truths.  The conclusions of induction are often viewed as probabilistic rather than certain. Of course, this begins to sound like deductive arguments in which we have substituted truth for probable truth or possible truth and so have produced an output that is less than certain.

Inductive arguments are, by their definition, not deductively valid. Seeing that as a problem is of course nonsensical.  Despite many arguments to the contrary, there is no ‘problem of induction‘ that somehow places induction in some inferior position to deduction, since both have different types of limitations and are complementary or even inter-related.

3. Abduction is the construction of the best explanation available given certain observations and beliefs.

Psychologists have added the idea of associative memory, thinking or learning. If taken seriously, we can see that associative thinking could form the basis of many human cognitive abilities. Why am I so sure, for example, that hippopotamuses cannot fly? There are lots of characteristics that I ‘associate’ with flying creatures, such as the possession of wings, which are absent from hippopotamus. There are also characteristics of these animals that definitely do not associate with flying such as their heavinesses.

Clearly, there may be domains of explanatory inference where only one type of argumentative process applies.  The formation of new ideas in mathematics and logic, for example,  might be the closest we ever come to a purely deductive process.

We can substitute the idea of truth with some other basis for believing or accepting the premises and still claim to be asserting a form of logical conclusion. If however in the long-term, you find that you have no reason for believing the soundness of an apparently sound deductive argument, you might then wish to question the truth of (or basis for believing) the premises. In certain circumstances, you might even want to abandon the idea of logical truth altogether and pragmatically reason that your belief is merely justified on the basis of certain assumptions and the rules by which certain styles of argument operate.

Steve Campbell
Glasgow, Scotland
2017, 2019

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