Reference has already been made to the fact that many arguments are not put in syllogistic form, or are elliptic and omit a stage, or are otherwise so stated that their essential structure is obscured. The first step to be taken towards finding out whether such arguments are valid or not is to restate them in such a way as to make their essential structure clear; and this may involve supplying stages which are missing and altering the wording (but not of course the meaning) of the argument to make it fit the structure of a symbolic scheme. The use of symbolic schemes is an important safeguard against the prejudice that may arise in cases where the argument concerns some subject in which we are closely interested. Illustration by diagram- where this is possible and appropriate-can be used as a further check.
The following examples are intended to show how these restating and checking processes can be carried out. Some of them involve reference to symbolic schemes which have not previously been referred to; but they can be followed and understood without difficulty. In each case the original argument is first stated; then follows the restatement; then the symbolic scheme; and lastly the evaluation-valid or invalid. It is to be noted that only the validity, not the truth, of the conclusion is in question.
(i)
People are flocking to see the new film at the Pantheon because it has a strong romantic flavour and a happy ending.
[All films having a strong romantic flavour and a happy ending are popular:]
the new film at the Pantheon has a strong romantic flavour and a happy ending:
therefore the new film at the Pantheon is popular.
All X's are Y:
S is X:
therefore S is Y.
Valid. (N.B.—Major premiss omitted.)
(ii)
If all people thought rationally, there would be no books on logic and kindred subjects.
If all . . . rationally, there would be no...subjects:
[ but there are books . . . subjects: (denying the consequent)
therefore not all people think rationally.]
If X, then Y:
not Y:
therefore not X.
Valid. (N.B.—Minor premiss and conclusion omitted.)
(iii)
The U.S.A. no doubt contains elements of many different races, but it must be counted among the Anglo-Saxon nations, all of whom are characterised by a strong individualism and a love of freedom. In no other country will you find more devotion to freedom and more opposition to socialism than in the U.S.A.
All Anglo-Saxon nations are individualistic and freedom-loving:
The U.S.A. is individualistic and freedom-loving:
therefore the U.S.A. is an Anglo-Saxon nation.
All X's are Y:
S is Y:
therefore S is X.
Invalid.
(iv)
No one would deny that the Athenians of the fifth century B.C. were highly civilised: their achievements in art, architecture, literature and philosophy have never been surpassed. Such achievements would have been impossible without leisure, and in Athens slave labour made leisure possible. It looks therefore as if civilisation were impossible without some form of slavery.
All civilised states are leisured states:
all slave states are leisured states:
therefore all civilised states are slave states.
All A's are B's
All C's are B's
therefore all A's are C's.
Invalid: A and C are both within the B circle, but they need not coincide. In addition, of course, the argument is based on a generalisation derived from a single instance: therefore any valid deduction made would not be reliable.
(v)
When we are interested in a subject, we are always on the qui vive for matter pertaining to it and so find it more easily than those who are indifferent.
If we are on the qui vive for matter pertaining to a subject, we find it with comparative ease:
if we are interested in a subject, we are on the qui vive for matter pertaining to it:
therefore if we are interested in a subject, we shall find matter pertaining to it with comparative ease.
If B, then C:
If A, then B:
therefore if A, then C.
Valid.
(vi)
The prosperity of a highly industrialised nation like Great Britain depends upon the maintenance of the importation of raw materials. These raw materials must be paid for by the exportation of manufactured goods. If therefore Great Britain fails to maintain a steady flow of such exports, she will cease to be prosperous.
If industries are to be kept going, raw materials must be imported: [if B then C]
If Great Britain is to prosper, her industries must be kept going: [if A then B]
therefore if Great Britain is to prosper, raw materials must be imported. [(therefore) if A then C]
If raw materials are to be imported, manufactured goods must be exported: [if C then D]
therefore if Great Britain is to prosper, manufactured goods must be exported. [therefore if A then D]
therefore if manufactured goods are not exported, Great Britain will not prosper. [ therefore if not D, then not A.]