Lessons in Practical Logic

MS 164: Winter 1869-1870

Lesson 1

The object of this course is to teach something of the art of investigating the truth.

It is really a question of little consequence whether this is a proper definition of logic or not. That is a mere question of words; but men who have not thoroughly studied logic are so apt to confound questions of words and questions of fact--both considering verbal discussions as real discussions and real discussions as merely verbal,--that I shall do well to say a few words in defence of the name that I have given to this course of lessons. And besides, I am perhaps bound to show that the subject to which the instruction is really to relate is the same as that advertized.

Now if you examine Hamilton's logic or any of those logics which are the immediate product of pure Kantianism as his was (--not his peculiar system but his lectures in which his system does not appear as it was worked up later) you will find logic defined as the Science of Thought as Thought--or something of that sort. This is an extremely different conception of the subject from that with which I set out. Take for example Mr. Mansel's admirable <it>Prolegomena Logica<ro> where the Kantian conception of logic is developed in the most consistent and beautiful manner.

 

Consequences

A consequence is the statement that one fact follows from another.
The expression of the former fact is called the antecedent.
The expression of the latter is termed the consequent.

Note. The investigation of consequences constitutes Logic. All questions of psychology are therefore irrelevant to the science of logic generally, though they may, no doubt, be of importance with reference to particular kinds of consequences when a psychological fact is explicitly or implicitly involved in the antecedent.

Consequences may be divided in the first place into material and formal. If the fact expressed in the consequent is the same as that expressed in the antecedent or is a part of it, then the consequence is an empty and meaningless expression unless the forms of expression of the antecedent and consequent differ in which case the consequence is the statement of a fact concerning the relation of these forms of expression. Such a consequence is called formal; but one which expresses a fact concerning the matters in question and not merely concerning the expression of them is termed material.

 

If Socrates is mortal, Socrates is mortal

 

this is empty. It is a particular sort of nonsense. It involves no absurdity, it is not meaningless in its grammatical construction or its terms but it fails to say anything.

Take this

 

Socrates dies; ergo, Socrates is mortal

This is a formal consequence. The meaning of the consequent is involved in the meaning of the antecedent.

 

Socrates dies bravely; ergo Socrates is mortal
Socrates dies before Plato; ergo Socrates is mortal
Socrates dies and Plato lives; ergo Socrates is mortal
Socrates dies and Plato is a man; ergo Socrates is mortal
Some man dies and another lives; ergo, Some man dies
Some man dies and so does every other; ergo, Some man dies
Every man dies; ergo, some man dies.

 

These are all formal consequences.

The following is a material consequence

 

Socrates is a man; therefore, Socrates is mortal

 

for if a man were to discover the Elixir of Life he would not thereby cease to be a man.

This distinction of formal and material consequences is one of the most practically important in the whole range of Logic.