First notions of logic (preparatory to the study of geometry)De Morgan, Augustus
Philosophy
First notions of logic (preparatory to the study of geometry)
De Morgan, Augustus
Logic
In such propositions as ‘Every A is B,’ ‘Some A is not B,’ &c., A is
called the _subject_, and B the _predicate_, while the verb ‘is’ or ‘is
not,’ is called the _copula_. It is obvious that the words of the
proposition point out whether the subject is spoken of universally or
partially, but not so of the predicate, which it is therefore important
to examine. Logical writers generally give the name of _distributed_
subjects or predicates to those which are spoken of universally; but as
this word is rather technical, I shall say that a subject or predicate
enters wholly or partially, according as it is universally or
particularly spoken of.
1. In A, or ‘Every A is B,’ the subject enters wholly, but the predicate
only partially. For it obviously says, ‘Among the Bs are all the As,’
‘Every A is part of the collection of Bs, so that all the As make a part
of the Bs, the whole it _may_ be.’ Thus, ‘Every horse is an animal,’
does not speak of all animals, but states that all the horses make up a
portion of the animals.
2. In E, or ‘No A is B,’ both subject and predicate enter wholly. ‘No A
whatsoever is any one out of all the Bs;’ ‘search the whole collection
of Bs, and _every_ B shall be found to be something which is not A.’
3. In I, or ‘Some A is B,’ both subject and predicate enter partially.
‘Some of the As are found among the Bs, or make up a part (the whole
possibly, but not known from the preceding) of the Bs.’
4. In O, or ‘Some A is not B,’ the subject enters partially, and the
predicate wholly. ‘Some As are none of them any whatsoever of the Bs;
every B will be found to be no one out of a certain portion of the As.’
It appears then that,
In affirmatives, the predicate enters partially.
In negatives, the predicate enters wholly.
In contradictory propositions, both subject and predicate enter
differently in the two.
The _converse_ of a proposition is that which is made by interchanging
the subject and predicate, as follows:
The proposition. Its converse.
A Every A is B Every B is A
E No A is B No B is A
I Some A is B Some B is A
O Some A is not B Some B is not A
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First notions of logic (preparatory to the study of geometry) — John Shaqi
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