Bauhaus-Universität Weimar

Dictionary of philosophy and psychology including many of the principal conceptions of ethics, logics, aesthetics ... and giving a terminology in English, French, German and Italian, vol. 2 [lead-zwing]
Baldwin, James Mark
predicate of a universal proposition : to say 
that ‘ All men are mortal ’ is to say that, taking 
any object X whatsoever, if X is a man, X 
is mortal. This agrees with the definition 
of universal predication given by Aristotle, 
and commonly known as the dictum de omni. 
It will be remarked that this definition does 
not make a universal proposition to assert 
the existence of its subject. 
Now, since in any possible system of logical 
representation illative transformation must be 
performed and be recognized as permissible, 
it follows that any representation of a uni¬ 
versal proposition which treats any other 
relation than that of the conclusion (with the 
premises) to the premises alone as the prin¬ 
cipal relation expressed by the proposition, 
leaves the logical analysis incomplete. 
Three figures (see Figuke, syllogistic) of 
syllogism were recognized by Aristotle, in 
the first of which the middle is subject of one 
premise (the major premise) and predicate of 
the other (the minor premise) ; in the second 
the middle is the predicate of both premises ; 
while in the third the middle is subject of 
both premises. Aristotle recognizes but four 
moods (see Mood, in logic) of syllogism in 
the first figure. Some early Peripatetic, 
Theophrastus it is said, added five indirect 
moods : Baralipton, Gelantes, Dabitis, Fapesmo, 
Frisesomorum. It is rumoured that Galen first 
constituted a fourth figure by transposing the 
premises of these. About the 16th century 
this figure began to be commonly admitted, 
and is now almost universally so. With this, 
the five moods have somewhat unnecessarily 
changed their names. Those now most usual 
are Bramantip, Camenes, Dimaris, Fesapo, 
The logic of Relatives (q. v. ; see also 
Symbolic Logic) throws great light on 
syllogism. It shows that the copulated pre¬ 
mises are, as expressed in Peirce’s algebra of 
dual relatives, in one of the three forms, 
(» + £)(# + »)_ (® + ÿ)ÿ* (xÿ)ÿz 
These give respectively 
x t z xz xT z 
The last is a so-called spurious conclusion, 
but such syllogisms are unscientifically ex¬ 
cluded from consideration in almost all trea¬ 
tises. There remain, therefore, but two kinds 
of syllogism, the universal and the particular. 
Beginning with Barbara, it can be mathemati¬ 
cally proved that every possible necessary 
inference from two premises, both having the 
same form as the conclusion, must depend upon 
a relation of inclusion (see Schröder, Alg. u. 
Log. d. Relative, 337 ff., where the ‘solution’ 
given of transitiveness is the most accurate 
possible definition of inclusion, in that general 
sense in which a thing need not necessarily 
include itself). Thus, 
The S's are included among the M’s ; 
The M's are included among the P’s ; 
The S’s are included among the P’s. 
So, for example, the pseudo-syllogism S 


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