By J. M. Bocheński (auth.)
The paintings of which this is often an English translation seemed initially in French as summary de logique mathematique. In 1954 Dr. Albert Menne introduced out a revised and a bit enlarged version in German (Grund riss der Logistik, F. Schoningh, Paderborn). In making my translation i've got used either versions. For the main half i've got the unique French version, due to the fact i assumed there has been a few virtue in maintaining the paintings as brief as attainable. despite the fact that, i've got incorporated the extra vast ancient notes of Dr. Menne, his bibliography, and the 2 sections on modal common sense and the syntactical different types (§ 25 and 27), which have been no longer within the unique. i've got endeavored to right the typo graphical blunders that seemed within the unique variations and feature made a number of additions to the bibliography. In making the interpretation i've got profited greater than phrases can inform from the ever-generous support of Fr. Bochenski whereas he used to be instructing on the college of Notre Dame in the course of 1955-56. OTTO chook Notre Dame, 1959 I normal ideas § O. creation zero. 1. concept and heritage. Mathematical good judgment, also known as 'logistic', ·symbolic logic', the 'algebra of logic', and, extra lately, easily 'formal logic', is the set of logical theories elaborated through the final century as a result of a synthetic notation and a carefully deductive method.
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Rule: For a variable 'a', 'b', or 'm' we may substitute 'a', 'b', or'm'. This rule enables us to change the letters. 31 it is often specified that we must not substitute for the variables the names of empty classes (cf. 42). With regard to this, however, it should be remarked: (1) that 37 A PRECIS OF MATHEMATICAL LOGIC this problem has nothing to do with the structure of system 10 and bears exclusively on its interpretation (cf. 002. (2) This problem, known as the 'problem of the empty or null class' raises philosophical questions and is extremely complicated.
26. 'a = fJ' for: '(x) : xea· . xefJ'. Equality of classes. Examples: The class of pipe-smokers is included in the class of smokers; that of French citizens who are 21 or older is equal to the class of men who have the right to vote in France. Note that 'a C fJ' and 'a = fJ' are sentences whereas 'a U fJ' and 'a n fJ' are names of classes. 27. 21-26. 3.
P. 64. 65. 66. 67. ·q=r:=:p=q·_·r EEpEqrEEpqr Associative Law of Equivalence EEpqENpNq p q . _ . '" p q Inversion of Equivalence p - q . _ . '" q - '" p EEpqENqNp 1st Contraposition of Equivalence EENpqENqp '" p q. q p 2nd Contraposition of Equivalence p _ '" q. _ . q _ '" p EEpNqEqNp 3rd Contraposition of Equivalence = = '" = = . 7. Rules of Transformation by which these laws can be developed so as to yield still further laws. 71. 'Chief functor of X' for 'the largest point-group of '=' in X'.
A Precis of Mathematical Logic by J. M. Bocheński (auth.)