Form of Inference, fragment 1
Archival Number: A5b
Author: Lonergan, B.
Page of typescript of "The Form of Inference" used as wrapper for 5A. Treating arguments for the hypothetical form of inference.
Database and descriptions © Copyright 2017 by Robert M. Doran
Fragment, ‘The Form of Inference’ – used as a wrapper for ‘De cognitione et cognito’
This reduction shows why Cesare and Festino may readily be reduced to the first figure; both argue from the presence of one predicate (denoted by the middle term) to the absence of another; this is the same procedure as that of Celarent and Ferio. At the same time it shows why complications arise when a similar reduction of Camestres and Baroco is attempted; for Camestres and Baroco argue from the absence of one predicate to the absence of a second; because the boys are not languid they are not tubercular; such reasoning in the first figure is precluded by the arbitrary laws of the distribution of terms in the first figure. There is further a fourth possibility which syllogism does not recognize, viz., the absence of one predicate implying the presence of a second; e.g., Because this Christian has not sinned, he is in the state of grace. Turning to the third figure, we have:
Darapti, Disamis and Datisi:
If M is P, then S may be P; M is P; therefore, S may be P.
If M is P, then some S is P; M is P; therefore, some S is P.
Because Queen Elizabeth was a statesman, a woman may be a statesman.
If the radio is to be deprecated, some inventions are to be deprecated.
Felapton, Bocardo and Ferison:
If M is not P, then S need not be P; M is not P; so, S need not be P.
If M is not P, then some S is not P; M is not P; so, some S is not P.
Because Peisistratus was not a rascal, a tyrant need not be a rascal.
Because whales are not fish, some aquatic animals are not fish.
No attention has been paid to distribution of terms either in this or the preceding, for distribution of terms has nothing to do with inference; it is but a covert and dignified way of introducing Euler's circles into an analysis of thought; no one thinks of distribution before studying logic and no one normally thinks of it afterwards, except as a general caution for accuracy. It may be noted that as Camestres and Baroco correspond with no first figure argument, still less do the moods of the third figure which is entirely devoted to making instances bear on the point of discussion. Finally, this syllogism in the third figure is restricted to I and O propositions for its conclusion; now, clearly ‘may’ and ‘need not’ are frequently preferable; hypothetical form allows one to use whichever expression best suits the case.
The claim that syllogism should be reduced to hypothetical form is based on two reasons: first, such reduction brings out unmistakably the meaning of any syllogistic argument and in choosing a language pattern of