Introduction
The best way to answer the question, “What is logic?” is with
a definition. But that is easier said than done. Throughout history, many people have
thought and written about the subject of logic and many people have offered definitions.
Some of them are useful and some are not. Josiah Royce, an American philosopher, defined
logic as “the science of order,” but this definition is so general that it
really could include things outside of what we would properly call logic, and so it really
doesn’t tell us much.
Other definitions are a little too simple. The writer Oliver Wendell
Holmes said, “Logic is logic. That’s all I say.” That obviously won’t
help us.
The writers of a book on fallacies defined logic as “the defense
against trickery.” That’s one thing logic is, but certainly not all.
Much better is the definition given by Raymond McCall: “Logic in
general is the science of right thinking.” Jacques Maritain, a very famous
philosopher, had a similar definition: “Logic,” he said, “studies reason as
the tool of knowledge.”
Irving Copi, who wrote a book on logic still used in many colleges and
universities, gets even a little more specific. “The distinction between correct and
incorrect reasoning is the central problem with which logic deals.” As you proceed in
this book, (Traditional
Logic, Book I by Martin Cothran, Memoria Press)
you will see that this is so.
Where
Does Logic Fit In?
The field of philosophy is divided into three recognized divisions. The
first division of philosophy is theoretical philosophy, or philosophy proper. The
sciences in this branch of philosophy are employed solely for the pleasure of knowledge.
These include the philosophy of mathematics, which studies the being of things by virtue
of their quantity (ens quantum); the philosophy of nature, which studies the
being of things by virtue of their sensible properties (ens mobile) and,
finally, metaphysics, which studies the being of things by virtue of their being (ens
in quantum ens). The formal object of theoretical philosophy is the being of things.
The second division of philosophy is practical philosophy. While
the object of theoretical philosophy is a knowledge of the first principles of the theoretical
order, the object of the study of practical philosophy is a knowledge of the first
principles of the practical order. These would include the philosophy of art,
which has to do with man’s ability to make or create, and ethics or moral
philosophy, which has as its object the absolute good of man. The formal object of
practical philosophy is human acts.
Logic is a third branch of philosophy, although it is more properly
considered to be the introduction to the rest of philosophy, since it provides the methods
used in the other two branches. In this sense, logic is less a division of philosophy than
the science or art of which the rest of philosophy makes use. Logic studies the conceptual
being (ens rationis) and directs the mind toward truth.
The
Two Branches of Logic
The two main branches of logic, one called formal or minor
logic, the other material or major logic, are quite distinct and deal with
different problems.
Material logic is concerned with the content of argumentation.
It deals with the truth of the terms and the propositions in an argument.
Formal logic is interested in the form or structure of
reasoning. The truth of an argument is of only secondary consideration in this branch of
logic. Formal logic is concerned with the method of deriving one truth from another.
The distinction between these two branches of logic was nicely
described by G.K. Chesterton:
Logic and truth ... have very little to do with each other. Logic is
concerned merely with the fidelity and accuracy with which a certain process is performed,
a process which can be performed with any materials, with any assumption. You can be as
logical about griffins and basilisks as about sheep and pigs ... Logic, then, is not
necessarily an instrument for finding out truth; on the contrary, truth is a necessary
instrument for using logic--for using it, that is, for the discovery of further truth ...
Briefly, you can only find truth with logic if you have already found truth without it.
This last remark of Chesterton’s is important. It is not the
purpose of formal logic to discover truth. That is the business of everyday observation
and, in certain more formal circumstances, empirical science. Logic serves only to lead us
from one truth to another.
That is why it is best to study formal logic first. In formal logic you
study the form of an argument apart from or irrespective of its content, even though some
content must be used in order to show the form. Maritain put it this way:
To study any complicated machine, a reaper for instance, we must begin
by making it work in the void, while we learn how to use it correctly and without damaging
it. In the same way we must first of all learn how to use reason correctly ... without
damaging it.
Deductive
& Inductive Arguments
An important distinction between arguments according to their form is
that between deductive arguments and inductive arguments. At the most
fundamental level, the difference between the two is that, in a valid deductive argument,
the conclusion asserts no more than what is contained in the premises, while, in an
inductive argument, more is asserted in the conclusion than is contained in the premises.
That is why, in a valid deductive argument, the truth of the premises guarantees
the truth of the conclusion, while, in a valid inductive argument, the truth of the
premises only makes the conclusion probable.
Valid deductive arguments offer sufficient proof for their
conclusions, whereas valid inductive arguments only offer good grounds for
believing in the conclusion. In fact, because induction is a weaker form of proof than
deduction, many people do not even use the term valid for a good inductive
argument, because validity has the sense of necessary proof, which is absent from even a
good inductive argument. They say instead that a good inductive argument is cogent,
a term which has the sense of convincing, rather than demonstrative.
One of the most recognizable characteristics of deductive arguments is
that they argue from the general to the specific, or from the more general to the less
general, by way of a middle term. Inductive arguments, on the other hand, reason from the
specific to the general, or from the less general to the more general and have no middle
term that firmly connects one truth to another. Deduction relies on the acceptance of a
general principle, and reason from that general principle through an iron chain of
reasoning to a conclusion. Induction reasons from repeated particular observations (which
are usually observable) to more general truths through statistical generalizations and
analogies which are sometimes unobserved (and which are considered stronger by virtue of
the number of confirming instances that are appealed to in the premises.
This distinction--between deductive and inductive reasoning—is
often misunderstood in common language. Arthur Conan Doyle, for example, has his character
Sherlock Holmes refer to his own style of reasoning as “deduction,” when, in
fact, Sherlock Holmes is not notable for his deduction, but his induction. Holmes reasons
from particular observations to more general conclusions.
Deductive arguments are more common in theoretical fields, such as
philosophy and mathematics, while inductive arguments are more common in the field of the
natural sciences.
Systems
of Deductive Logic
There are several major systems of formal deductive logic: the first is
traditional or syllogistic logic; the second is modern propositional logic; and the third
is modern predicate logic. Traditional logic concerns itself with the relationships
between terms in an argument, using the “to be” verb (am, is or are) as the
connector. An example would be:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal.
This argument deals with the relationships between and among the terms
are men, mortal, and Socrates.
Modern propositional logic deals with the relationship between
propositions in an argument without taking the interior structure of the statements into
account. It uses logical operators such as if ... then, and, or, only if or if and only if
as the connectors:
If all men are mortal, then Socrates is a mortal
All men are mortal
Therefore, Socrates is a mortal.
This argument deals with the relationships between and among the
statements “All men are mortal” and “Socrates is a mortal.”
Modern predicate logic deals with the relationship between and among both
terms and propositions. It can use many kinds of connectors:
Some angels are evil. Furthermore, some animals are rational.
If there are any angels, then animals are sinful if they are rational.
Therefore, some animals are rational.
In this article, we are concerned primarily with traditional syllogistic logic.
Truth,
Validity, and Soundness
The form of an argument is found in its argumentative structure; the
matter of an argument is found in the statements. Statements of fact, for example, cannot
be called logical or illogical, since these labels refer to form; they can
only be properly called true or false, labels which refer to matter.
Likewise, an argument cannot be called true or false, only valid or invalid.
Only arguments are valid or invalid, and only statements are true or false.
Validity is the term we use when we mean to say that an argument is
logical. The term soundness, however, is a term that refers both to the form and
the content of an argument. It is applied to an argument to say something about both its
truth and its validity.
Truth means the correspondence of a statement to reality. An
argument is valid when its conclusion follows logically from its premises. The term
soundness is used to indicate that all the premises in an argument are true and
that the argument is valid.
An argument can contain true premises and still be invalid. Likewise,
it can be perfectly valid (or logical, if you prefer) and contain false premises.
But if an argument is sound, its premises must be true and it must be valid.
The
Components of an Argument
An argument contains several components. In order to illustrate what
these components are and how they work in the reasoning process, let us begin with a
simple argument:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal.
The first two statements are premises and the last is the conclusion.
All arguments must have at least two premises and one conclusion.
On the face of it, this argument contains a number of words making up
three statements which fit together into what looks and sounds like an argument. But there
is more here than meets the eye.
In formal logic, we recognize three kinds of logical processes. We
recognize that each of these originates in a mental act, but that each also
manifests itself (and is known to us in the form of) as a verbal expression.
The
Term
The mental act involved in the first of these three logical processes
is called simple apprehension. We call the verbal expression of simple apprehension
the term. A simple apprehension occurs when we first form in our mind a concept of
something. When we put this concept into words, we have put this simple apprehension in
the form of a term.
At the point of simple apprehension, we do not affirm or deny anything
about it. We just possess or grasp it. If in your mind, for example, you think of your
computer (the one you’re using right now), you are performing this first logical
process. You are having a simple apprehension. And if you speak or write anything about
it, you will have to use a term, the term computer.
In the argument above (the one about Socrates), there are three terms
representing three simple apprehensions. The first is men; the second is Socrates;
and the third is mortal. Each one of these represents in our mind a concept that we
have transformed into a word. The concept we call the simple apprehension and the
word we call the term.
| Mental Act |
Verbal Expression |
| Simple Apprehension |
Term |
The
Proposition
The mental act involved in the second of these three logical processes
is called judgement. The verbal expression of a judgement is called a proposition.
We perform a judgement any time we think in our mind that something is something
else (which we call affirmation), and also when we think that something is not
something else (which we call denial). To judge is to affirm or deny.
If you think that this computer is complicated, then you are performing
a judgement. If you verbally express this judgement, you will have to do it in the form of
a proposition, the proposition, “This computer is complicated”. The judgement is
the mental act you have when you think that this computer is complicated and the
proposition is the statement you make to express that thought.
In the argument above, there are three propositions expressed. The
first is “All men are mortal”; the second is “Socrates is a man”; and
the third is “Socrates is mortal.” Each one of these represents in our mind a
thought that something is something else: that “all men” are “mortal”;
that “Socrates” is a “man”; and that “Socrates” is
“mortal”.
We should point out that some people use the word statement
instead of proposition. They mean the same thing, but to be consistent, we will use
the word proposition.
| Mental Act |
Verbal Expression |
| Judgement |
Proposition |
The
Syllogism
The mental act involved in the third of these three logical processes
is called deductive inference. We call the verbal expression of deductive inference
the syllogism. A deductive inference occurs when we make the logical connections in
our mind between the terms in the argument in a way that show us that the conclusion
either follows or does not follow from the premises. When we verbally express this in an
argument, we have put this deductive inference in the form of a syllogism.
It is at this point that we are said to make progress in knowledge. It
is through the process of deductive inference, as expressed in a syllogism, that we can
say, as we explained above, that we have gone from one truth or set of truths to another
truth.
Let’s say the reason you think this computer is complicated is
because you think all computers are complicated. If this were true, you would be
performing a deductive inference. You would be thinking to yourself, all computers are
complicated, and this is a computer. Therefore, this computer is complicated. And if you
verbally expressed this deductive inference, you would do it in the form of a syllogism.
The judgement expressed by “All computers are complicated” and “This is a
computer” are different than the judgement “This computer is complicated”.
Through deductive inference, however, you can go from these first two to the last one. In
this way, you have gone from one set of truths to another truth (if indeed they are true).
We would say that the argument above (the one about Socrates), in its
entirety, is a syllogism. It expresses a deductive inference that logically connects
certain simple apprehensions that are parts of three judgements. And this process has been
expressed in the form of a syllogism.
| Mental Act |
Verbal Expression |
| Deductive Inference |
Syllogism |
If we now put this all together, keeping our distinction between mental
acts and verbal expressions, it would look like this:
| Mental Act |
Verbal Expression |
| Simple Apprehension |
Term |
| Judgement |
Proposition |
| Deductive Inference |
Syllogism |
In order to give ourselves a mental picture of these three logical
processes, let us think of a man walking. In order to get from, say, one room to another,
he has to pick up his foot and take several steps in order to get to the room that is his
destination. The initial act—picking up his foot—is like the initial logical act
of simple apprehension. Taking a full step is like making a judgement. And stringing all
the steps together into one movement is like deductive inference—we move from one
place to another.
Conclusion
We started out by defining logic as “the science of right
thinking”. We said logic was one of three divisions of philosophy, the others being theoretical
philosophy and practical philosophy. We said there are two main branches of logic,
one called formal or minor logic, the other material or major
logic. Material logic is concerned with the content of argumentation. Formal logic
is interested in the form or structure of reasoning.
We said that, broadly speaking, there are two kinds of formal logic: deductive
logic and inductive logic. The conclusion of a deductive argument, we said, asserts
no more than is contained (explicitly or implicitly) in its premises, while the conclusion
of an inductive argument asserts more than is contained in its premises. Therefore, we
concluded, while the conclusion of a deductive argument is conclusive, the
conclusion of an inductive argument is only probable.
We defined truth as correspondence with reality. We said an
argument is valid when its conclusion follows logically from its premises. And we
said that soundness indicates that all the premises in an argument are true and
that the argument is valid.
We said also that all arguments must contain two premises and a
conclusion. And we said, finally, that there are three mental acts that make up the
logical process: simple apprehension, judgement and deductive inference.
These three mental acts correspond to three verbal expressions: term, proposition
and syllogism.
Copyright © 1999 by Martin Cothran. All rights
reserved. No part of this article may be reproduced, in any manner whatsoever, without written permission of the author, except as provided by
USA copyright law.
CCH’s
Review of Traditional Logic by Martin Cothran
Traditional Logic by Martin
Cothran
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