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or (2) All men are mortal,
Therefore Socrates is mortal; or (3) All men are mortal,
And Socrates is a man. Reasoning often takes the form of a chain in which the conclusion of one syllogism is used as one of the premises of another, e.g.:
All A's are B's;
All A's are C's;
The syllogism which supplies such a premise is called a Prosyllogism; that which uses it, an Episyllogism.
When an Episyllogism depends upon a Prosyllogism which is only partly expressed the argument is called an Epicheirema, e.g.:
All A's are C's, for they are B's;
Therefore all A's are D's. This is “a double Epicheirema, containing reasons for both premises”.
A Sorites is a chain of prosyllogisms and episyllogisms in which all the conclusions but the last are unexpressed, e.g.: All A's are B's;
All Athenians are Greeks; All B’s are C's;
All Greeks are men; All C's are D's;
All men are mortal; All D's are E's;
All mortals fear; Therefore all A's are E's
... All Athenians fear.
* Where the major premise is omitted the enthymeme is said to be of the first order ; where the minor, of the second ; where the conclusion, of the third,
If we put in the suppressed conclusions, the Sorites is resolved into these syllogisms:
All A's are B's; All B’s are C's; .:. All A's are C's. All A's are C's; All C's are D's; .:. All A's are D's. All A's are D's; All D’s are E's; .:. All A's are E's. With reference to a Sorites it should be observed :
1) That almost invariably the minor premise of each syllogism involved is written first. A Sorites which begins at the other end seems jagged.
2) That in any valid Sorites every premise but the first (i.e., the minor premise of the first prosyllogism) must be universal and every premise but the last (i.e., the major premise of the last episyllogism) affirmative.
3) That while the last syllogism involved (the episyllogism) may be in any figure, each prosyllogism must be in the first; and that in the case of each prosyllogism it is the minor premise which the previous prosyllogism supports.
BLUNDERS IN WORD AND BLUNDERS IN THOUGHT.
FALLACIES or blunders in reasoning are usually divided into two great classes: ‘Logical” or “ Formal’ (Fallaciæ in dictione) and Non-logical' or 'Material’ (Fallaciæ extra dictionem or in re). When logic is regarded as a science of the ‘forms of thought' or the science which treats of the proper arrangement of words in correct thinking (on the assumption that the forms of thought and the forms or arrangements of words correspond) this distinction presents no difficulties: logical or formal fallacies are those which result from a violation of the rules which logic lays down for correct thinking and the corresponding arrangement of words; and material or non-logical fallacies are those which occur in spite of the observance of these rules—they do not depend upon the general laws of thought or arrangement of words at all, and can only be avoided by a knowledge of the matter thought about.
In the foregoing pages I hope it has been made plain that the same arrangement or form of words cannot be counted upon to always express the same thought. I hope it has been made plain too that the so-called “laws' and 'forms' of thought with which it is often said that logic deals have no meaning whatever apart from the things thought about and the way in which the relations of these things involve each other. If these views are correct it is quite impossible to make any fundamental distinction between fallacies which
are due to some perversion of the forms of thought and those which are due to some mistake about the relations of things. But we might still distinguish between fallacies which are due to some misconception about the 'matter' under discussion and those which depend in some way upon the ' form of words used in discussing it.
So with the terms ‘logical' and 'extra-logical'. They may be taken to mean that some fallacies result from a violation of logic while others do not, or they may be taken to mean that some are, and others are not, concerned with logoi or words.
Now it is true that logic has not made such elaborate provision against every fallacy possible as it makes against those already discussed, and yet fallacious thinking is always illogical and there is no reason but one of convenience why books on logic should discuss some and not others. It is not appropriate therefore to divide fallacies into those that violate the rules of logic and those that do not. But there is a reason why we should divide fallacies into those that result in some way from the improper use of words and those that do not. We may therefore accept this division into logical' and 'extra-logical' or 'material on the understanding that it is equivalent to a division into blunders that result mainly from the careless use of words and those that do not.
The ‘logical' fallacies are usually subdivided into two classes called 'Purely logical', " where the fallaciousness is apparent from the mere form of expression ”', and 'Semilogical ’, where the fallaciousness is not apparent from the mere form of expression but is due to some ambiguity in the language used or some misunderstanding as to its meaning. Of the ' semi-logical ’ fallacies we shall have nothing more
We have seen already how insidious they are, why they arise, and how best to guard against them.
With the 'purely logical’ fallacies we are also familiar. They are such blunders as we make when we ignore the cautions of the syllogism, or convert A simply or O at all, or
reason that because all S is P all non-S is non-P, or infer the falsity of a consequent from the falsity of its antecedent, or the truth of the antecedent Purely,
logical.' from the truth of the consequent, or the falsity of a conclusion from the falsity of the premises, or the truth of the premises from the truth of the conclusion. In all such cases it is ' apparent from the mere form of expression' that the reasoning is inconclusive; the blunder can be detected without inquiring into the truth of the premises or even into the meaning of the terms; so that a purely logical fallacy, unlike any of the others, can be detected when the terms are mere unmeaning words or symbols such as S, M and P, or X, Y and Z.
The strange thing about these so-called purely logical fallacies is that they are committed so often. How is it possible, we may ask, to think so badly? If the reader will ask the following questions to some unsuspecting person and does not allow very much time to elapse between the answering of one and the asking of the next, the result of the experiment may help to make the matter clear:
Who was the first man ?
Abel did not kill Cain, but his name will usually be mentioned, or at least come to mind, merely because it comes naturally at the end of the series * Adam, Eve, Cain' and fits into the atmosphere of murder. It is largely a mere matter of the verbal jingle, the answer resulting from the same law of habit in the nervous system that accounts for putting one's pen in the paste-pot after using the brush. Most of these so-called purely logical fallacies come in precisely the same way. Inference is in the air and the jingle seems to fit, so we spurt out something when the premises will not justify any inference whatever, or an ‘All’or a No' that fits the jingle when the premises justify only a Some',
If we say: