Encyclopaedia Britannica; or, A dictionary of arts and sciences, compiled upon a new plan … > Volume 2, C-L

LOG
is a disjun&ive pfopofition, the fyllogifm to which it be¬
longs is alfo called disjunftivc, as in the following example :
The world is either feif-exiftent, or the work of fame
finite, or of fame infinite being.
But it is not felfexiftent, nor the work of a finite being.
Therefore it is the work of an infinite being.
Now a disjunctive propofition is that where, of feveral
predicates, we affirm one neceflarily to belong to thefub-
je£t, to the exclufion of all the rdt, but leave that par¬
ticular one undetermined. Hence it follows, that as fooh
as we determine the particular predicate, all the reft are
of courfe to be rejected; or if we rejeCt all the predicates
but one, that one neceflarily takes place. When there¬
fore, in a ditjunttive fyllogifm, the feveral predicates are
enumerated in the major; if the w'/wreftabliffies any one
of thefe predicates, the conclufion ought to remove all
the reft; or if, in the minor, all the predicates but onC
are removed, the conclufion muft neceffarily eftabliffi that
one. Thus, in the disjunfiive fyllogifm given above, the
major affirms one of three predicates to belong to the
earth, viz. felf-exijler.ce, or that it is the work of a
finite or that it is the work of an infinite being. Two
of thefe predicates are removed in the minor, viz.
felfexijlence, and the work of a finite being. Hence
the conclufion neceflarily afcribes to it the third predi¬
cate, and affirms that it is the work of an infinite being.
If now we give the fyllogifm another turn, infomuch that
the minor may eftabliffi one of the predicates, by affirming
the earth to be the produtlion of an infinite being; then
the conclufion muft remove the other two, aflerting it to
be neither felfexifient, not the work of a finite being.
Thefe are the forms of reafoning in this fpecies of fyllo-
gifms, the juftnefs of which appears at firft fight; and that
there can be no other, is evident from the very nature of
a disjunctive propofition.
In the feveral kinds of fyllogifms hitherto mentioned,
the parts are complete, that is, the three propofitions of
which they confift are reprefented in form. But it often
happens, that fome one of the premifles is not only an
evident truth, but alfo familiar and in the minds of all
men ; in which cafe it is ufually omitted, whereby we
have an imperfeCt fyllogifm, that feems to be made up of
only two propofitions. Should we, forinftance, argue in
this manner;
Every man is mortal;
Therefore every king is mortal:
the fyllogifm appears to be imperfeCf, as confifting but
of two propofitions. Yet it is really complete, only
. the minor {Every king is a man\ is omitted, and left to
the reader to fupply, as being a propofition fo familiar
and evident, that it cannot efcape him.
Thefe feemingly imperfeCt fyllogifms are called enthy-
memes, and occur very frequently in reafoning, efpecially
where it makes a part of common converfation. Nay,
there is a particular elegance in them ; becaufe, not dif
playing the argument in all its parts, they leave fomewhat
to the exercife and invention of the mind. By this means
we are put upon exerting ourfelves, and feem to ffiare in
the difcovery of what is propofed to us. Now this is the
great fecret of fine writing, fo to frame and put together
our thoughts, as to give full play to the reader’s imagina-
Vol. II. No. 68. 2
I C. 997
tion, and draw himinfenfiblyintoour very views and courfe
of reafoning. This gives a pleafure not unlike to that
which the author himfelf feels in compofing. It befides
ffiortens dicourfe, and adds a certain force and livelinefs
to odr arguments, when the words in which they are con¬
veyed favour the natural quicknefs of the mind in its
operations, and a fingle expreflion is left to exhibit a
whole train of thoughts.
But there is another fpecies of reafoning with two
propofitions, which feems to be complete,in itfelf, and
where we admit the conclufion without fuppofing ally
tacit or fupprefled judgment in the mind from which it
follows fyllogiftically. This happens between propofi¬
tions where the connection is fuch that the admiflion
of the one neceflarily and at the firft fight implies the
admiffion alfo of the other. For if it fo falls out, that
the propofition on which the other depends is felf-evident,
we content ourfelves with barely affirming it, and infer
that other by a direCt conclufion. Thus, by admitting an
univerfal propofition, we are forced alfo to admit of all
the particular propofitions comprehended under it, this
being the very condition that conftitutes a propofftion
univerfal. If then that univerfal propofition chances to
be felf-evident, the particu’ar ones follow of courfe,
without any farther train of reafoning. Whoever allows,
for inftance, that things equal to one and the fame things
are equal to one another, muft at the fame time allow’,
that two triangles, each equal to a fquare whofe fide is
three inches, are alfo equal between themfelves. This
argument therefore,
Things equal to one and the fame thing are equal to one
another;
Therefore thefe two triangles, each equal to theifquare
of a line of three inches, are equal between them¬
felves,
is complete in its kind, and contains all that is neceflary
towards a juft and legitimate conclufion. For the fim
or univerfal propofition is felf-evident, and therefore
requires no farther proof. And as the truth of the
particular is infeparably connected with that of the uni¬
verfal, it follows from it by an obvious and unavoidable
confequence.
Now in all cafes of this kind, where propofitions are
deduced one from another, on account of a known and
evident connection, we are faid to reafon by immediate
confequence. Such a coherence of propofitions, manifeft
at fit ft fight, and forcing itfelf upon the mind, frequently
occurs in reafohing. Logicians have explained at fome
length the feveral fuppofitiOns upon which it takes place,
and allow of all immediate confequences that follow in
conformity to them. It is however obfervable, that
thefe arguments, though feemingly complete, becaufe
the conclufion follows neceflarily from the fingle propo¬
fition that goes before, may yet be confidered as real
enthymemet, whofe waycr, which is a conditional propofi¬
tion, is wanting. The fyllogifm but juft mentioned, when
reprefented according to this view, will run as follows :
If things equal to one and the fame thing are equal
to one another ; thefe two triangles, each equal to a
fquare whofefide is three inches, are alfo equal between
themfelves.
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