A Primer of Logic

Cover A Primer of Logic
A Primer of Logic
Henry Bradford Smith
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In the propositions, x / y, x//y, and x///y, x is called the inferior, y the superior form.
Since x and y may take on any of the four forms a, /3, 7, e, there will be sixteen possible propositions of each type, x / y, x //y and x///y, obtained by permuting the letters two at a time and by taking each letter once with itself. The following postulates and principles will yield all the valid moods of each type. We have assumed four principles here because the principles for the deduction of the in
...valid moods may be derived from these four as theorems.
Principles: i. (x / y) (y //z) Z (x///z) iii. (x / z) (y///z) Z (y //x) ii. (x / y) (z //x) Z (z///y) iv. (x / z) (y // z) Z (y / x) Postulates: /3/a; 6/7; 7//a.
Theorems: 7/0; e//0; e///a.
APRIMER OF LOGIC w We may also formulate rules for the derivation of the moods. It will then be necessary to assume one pos- tulate only.
Definition: In the propositions, x / y, x //y and x///y, the relation connecting x and y is known as the worse-relation.


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