LOGIC. 
lift of Categorical proportions, as a feries of predicates-, 
the latter of Hypothetical, as a feries of consequences. 
Falla clous Conclufions — Paralogifns—Sophifr-ns. 
90. A Rational Conclufion, which according to form 
is falfe, though it has the appearance of acorreii conclu¬ 
fion, is termed a Paralogifm , when we deceive ourfelves by 
it; a Saphtfm, when we endeavour to deceive others by it. 
Remark. The ancients applied thernfelves greatly to 
the conltruftion of fuch fophifms. Hence arofe the va¬ 
rious kinds of them ; for inftance, the Sophifma figure die - 
tionis ; where the middle term is taken in various Signifi¬ 
cations, fallacla a dido fecundum quid ad diBum fimpliciter ; 
fophifma heteroxetifeos, elenebi, ignorationis 5 and the like. 
Leap in Concluding. 
91. A Leap (faltus) in concluding or proving, is con¬ 
necting one of the premifes with the conclufion, while 
the other is omitted. Such a leap is legitimate when the 
premife is eafily fupplied ; but illegitimate when the fub- 
lumption is not clear; for here we conned: a remote 
mark with a thing, without an intermediate mark. 
Begging the Quejlion, and Pro-ving in a Circle. 
92. By begging the Queftion is to be underftood the 
ufinga polition, by way of proof, as an immediately-certain 
one, though it is itfelf unproved. Proving in a Circle is, 
laying the propofition we intend to prove as the ground 
oi its own proof. 
Remark. It is often difficult to difeover when we have 
proved in a circle ; and this fault occurs molt frequently 
in difficult demonftrations. 
Proving too much and too little. 
93. A proof may prove too much, and alfo too lit¬ 
tle. In the latter cafe, it only proves a part of what was 
to be proved } in the former, it applies to that which is 
falfe. 
Remark. A proof that proves too little may be true 5 
it is therefore not rejectable ; but, if it proves too much, 
it proves more than is true, and mull confequently be falfe. 
PART II. 
METHOD OF PURE UNIVERSAL LOGIC. 
Manner and Method. 
94.. All Knowledge mult be conformable to a rule, if it 
is to produce a whole ; for irregularities are at the fame 
time irrationalities. But this rule is either that of mon¬ 
ster (free), or that of method (cor.ltrained).. 
Form of Science. — Method. 
95. Knowledge, when confidered as a fcience, mud be 
planned according to a Method. For Science is a Whole 
of Knowledge, as a Syftem 3 not merely as an Aggregate. 
It implies therefore Syftematical Knowledge, which has 
been compiled agreeably to predetermined Rules. 
‘The ObjcSl and End of Method. 
96. As the Elementary Doctrine of Logic has for its ob¬ 
ject the Elements and Conditions of the Perfections of 
Knowledge ; fo the Method of Logic, as its fecond part, 
has to treat of the form of a Science in general, or of the 
manner and mode of connecting various Knowledge into 
a Science. 
Means of advancing the Logical PerfeFlions of Knowledge. 
97. Method mud inform us how we are to arrive at the 
Perfections of Knowledge. Now the molt elfential logi¬ 
cal perfections of Knowledge confilt in its Clearnefs, and 
in its fyftematic arrangement as a Science. Method will 
accordingly have to point out the means by which thefe 
perfections of Knowledge are advanced. 
Conditions of the Clearnefs of Knowledge, 
98. The Clearnefs of Knowledge, and its connection 
Von. XIII. No. 885. 
2.9 
into a Syftematic whole, depends upon the clearnefs of 
conceptions, both with refpeCt: to what is contained in 
them and what is clafTed under them. The clear con- 
feioufnefs of the Contents of a Conception is advanced by 
Expofition and Definition. . The clear confcioufnefs of the 
Sphere of a Conception is advanced by Logical Divifion. 
We fhall therefore firft treat of the means to advance the- 
Clearnefs of Conceptions with regard to'their Contents. 
I. Advancement of the Logical Perfection of Knowledge by 
Definition, Exposition, and Description of Con¬ 
ceptions. 
Definition. 
99. A Definition is a lufficiently clear and adequate 
conception 3 (conceptus rei adequatus in minimus terminis 3 
complete determinatus.) 
Remark. Definition, alone, is to be confidered as a lo«i- 
cally-perfeCt conception, for it unites in itfelf the two ef- 
fential perfections of Clearnefs and Perfpicuity ; (that is, 
completenefs and preciiion in clearneis, or quantity of 
clearnefs.). 
Analytical and Synthetical Definition. 
100. All Definitions are either Analytical or Synthetical. 
The former are definitions of a given Conception, the 
latter of a. produced one. 
Given and produced Conceptions , a priori and a pofieriori. 
toi. The given Conceptions of an analytic definition, 
are given either a priori or a. pofieriori 5 as the produced 
conceptions of a Synthetical definition are produced either 
a priori or a pofieriori. 
Synthetical Definitions by Expofition or Conflruclion. 
J02. The fynthefis of produced conceptions, from- 
whence arife Synthetical definitions, is either that of Expofi¬ 
tion (of the phenomena), or that of ConflruCion (of the 
mathematical). The latter is the fynthelis of arhitrarily- 
produced Conceptions 3 the former of empirically-pro¬ 
duced Conceptions 3 that is, from given phenomena; 
(Concept usfaChtii vel d priori vel per Jynthefin empiric am.) 
Thearbitrarily-produced conceptions are the Mathematical. 
Remark. All definitions of mathematical, as well as of 
empirical, conceptions, fo far as the latter can take place, are 
produced Synthetically. For in the empirical conceptions of 
Earth, Air, Fire, Water, &c. we have not to diffeCl what 
lies in thefe conceptions ; but to learn by experience what 
belongs to them 3 confequently, all empirical conceptions 
mult be confidered as produced conceptions, whole fyn- 
thefis is however not arbitrary, but empirical. 
Impojfibility of Empirical Synthetical Definitions. 
103. As the fynthefis of empirical conceptions is not 
voluntary, but empirical, (becaufe in experience we may 
always difeover more and more marks of a conception,) 
it follows that empirical conceptions never can be defined. 
Remark. Arbitrary conceptions alone, therefore, can be 
fyntheticaily defined. Such definitions of arbitrary con¬ 
ceptions as are both poffible and mcejfary, and which mult 
precede that which is exprefted by an arbitrary concep¬ 
tion, may be called Declarations 3 for we hereby declare 
our thoughts, or explain what is to be underitood by cer-. 
tain wards . This is the cafe in the Mathematics. 
Analytical Definitions of given Conceptions by DiffeBion, both 
a priori and u pofieriori. 
104. All given conceptions, whether given d priori or 
d pofieriori, can only be defined by Analyfis 5 .for we can. 
only render them evident by making their marks fuc- 
ceffively clear. If all the marks of a given conception 
are made clear, the conception is perfedlly-evident. If it 
does not contain too many marks, it is precife. Thus 
arifes a definition of a Conception. 
Remark. As we never can be certain that we have ob¬ 
tained all trie marks of a given conception by analyfis s 
ail analytical definitions mu ft be confidered as uncertain. 
£ Eififiitim 
