s of proposition recognised
by Formal Logic constitute a very meagre selection from the list of
propositions actually used in judgment and reasoning.

Those Logicians who explicitly quantify the predicate obtain, in all,
eight forms of proposition according to Quantity and Quality:

[Transcriber's Note: The Greek characters used in the original are
represented below by the name of the character in square brackets.]

U. Toto-total Affirmative -- All X is all Y.
A. Toto-partial Affirmative -- All X is some Y.
Y. Parti-total Affirmative -- Some X is all Y.
I. Parti-partial Affirmative -- Some X is some Y.
E. Toto-total Negative -- No X is any Y.
[eta]. Toto-partial Negative -- No X is some Y.
O. Parti-total Negative -- Some X is not any Y.
[omega]. Parti-partial Negative -- Some X is not some Y.

Here A. I. E. O. correspond with those similarly symbolised in the usual
list, merely designating in the predicates the quantity which was
formerly treated as implicit.

Sec. 4. As to Relation, propositions are either Categorical or Conditional.
A Categorical Proposition is one in which the predicate is directly
affirmed or denied of the subject without any limitation of time, place,
or circumstance, extraneous to the subject, as _All men in England are
secure of justice_; in which proposition, though there is a limitation
of place ('in England'), it is included in the subject. Of this kind are
nearly all the examples that have yet been given, according to the form
_S is P_.

A Conditional Proposition is so called because the predication is made
under some limitation or condition not included in the subject, as _If a
man live in England, he is secure of justice_. Here the limitation
'living in England' is put into a conditional sentence extraneous to the
subject, 'he,' representing any man.

Conditional propositions, again, are of two kinds--Hypothetical and
Disjunctive. Hypothetical propositions are those that are limited by an
explicit conditional sentence, as above, or thus: _If Joe Smith was a
prophet, his followers have been unjustly persecuted_. Or in symbols
thus:

If A is, B is;
If A is B, A is C;
If A is B, C is D.

Disjunctive propositions are those in which the condition under which
predication is made is not explicit but only implied under the disguise
of an alternative proposition, as _Joe Smith was either a prophet or an
impostor_. Here