East Grinstead


Logic 1 Introduction

Recommended Books
Academic books are usually expensive and ones on logic are no exception to this. The one I would most recommend is “Introduction to Logic” by Irving M. Copi. However, it is difficult to obtain through libraries and very expensive on Amazon (about £30 in paperback and almost twice that in hardback). There is another logic book that is much cheaper and is available from Amazon. It is quite good and you can preview it on Amazon. The book is “Logic” by Wilfrid Hodges and is on offer at Amazon for £7.69. I will try to remember to bring my copies to our first meeting.

Brief History of Logic
I do not want to spend too much time on this (interesting though it is) but an understanding of how and when logic originated helps to orient us in the subject. There are two main historical strands, one in India and the other in Greece, and both go back between two and three millennia. The Indian strand is the earlier and commences with the “anviksiki” of Medhatithi Gautama (c. 6th century B.C.). It was contributed to fairly continuously up to recent times by several schools and religious movements in India and was, for most of its history, well in advance of anything we had in Europe. The Greek strand starts with Aristotle (384 BC – 322 BC) and his famous syllogism. There was no further development of logic in Europe until a few centuries ago, when logicians began to be influenced by the on-going developments in India. For completeness, I should mention that there was an attempt to originate a form of logic in China in Confucian times; however, it was suppressed and it was not until Buddhism arrived in China in the early centuries A.D. that any form of logic was continued there.
To complete this, essentially very brief, history of logic, I will just sketch the European developments that bring us up to the present. There was very little development of logic in Europe until the middle of the 1800s when, inspired by the success of mathematics, logic became a calculus, the rules of which were determined by the shape rather than the meaning of the symbols used in it. Boole and de Morgan were at the forefront of this movement. Somewhat later, Venn introduced the famous Venn diagrams and later still (but still in the 1800s) Frege introduced quantifiers and the immensely powerful predicate calculus. The early part of the last century saw the development of mathematical logic by Bertrand Russell and others and later the introduction of fuzzy logic.

Types of Logic
Perhaps the most important division between the types of logic that are presently available to us is the one between those systems that are based on definitions and axioms and those based on truth tables. The types that are based on truth tables are called natural logic and it is these that we are mainly concerned with in Europe. When electronic engineers are taught logic, it is natural logic that they are taught.
Another important division is that between systems based on the law of the excluded middle (which is simply a posh way of saying that a statement is either true or it is false – there is no half-way house) and those that are not. Modal logic is an example of this latter type. In modal logic, the type of truth or falsity is specified.

Some Essential Basic Concepts
I want to start with a few concepts that you will need in order to understand what we are talking about when we talk of logic and how logical fallacies arise. Then I think that we can most profitably look at informal fallacies (the ones we commonly fall foul of).
First, the concepts – these are not the only ones but they are some of the more important ones that you need to be aware of:
• What is logic – the study of the methods and principles used to distinguish correct from incorrect reasoning.
• The distinction between the real world and the world of the intellect – a priori/a posteriori, synthetic/analytic, necessary/contingent.
• Propositions – statements that can be asserted or denied.
• Premisses – propositions offered as grounds for accepting the conclusions of arguments.
• Conclusions – the final products of arguments
• Inference – the process by which a proposition or conclusion is reached and affirmed on the basis of one or more other propositions that have been accepted as the starting point of the process.

Real and Intellectual World Distinctions
Briefly, these are:-
A priori knowledge is knowledge that is independent of experience, e.g. all bachelors are unmarried.
A posteriori knowledge is knowledge gained by experience, e.g. some bachelors are very happy.
An analytic proposition is a proposition of which the predicate concept is contained in the subject concept, e.g. all bachelors are unmarried.
A synthetic proposition is one of which the predicate concept is not contained in the subject concept, e.g. some bachelors are very happy.
A necessary truth is one that could not have been otherwise.
A contingent truth is one that happens to be true but could have been otherwise.
These pairs of terms have very much the same meaning and have often been used interchangeably. However they are not quite the same and philosophers have argued over exceptions that they have found. At this stage, though, I think we should not concern ourselves with this but simply notice what they are. Logic operates in the ‘intellectual’ world, not the ‘real’ one.
John Gibbs