The Scope of Formal Logic the New Logical Doctrines Expounded With Some Critic
The Scope of Formal Logic the New Logical Doctrines Expounded With Some Critic
Arthur Thomas Shearman
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3*43, to the truth of which appeal is frequently 72 THE SCOPE OF FORMAL LOGIC made, e. G. , in props. 3*47, 3-5 and 4*44. The statement and proof of prop. 3*42 are as follows : |- :. P)q. ):~p)q. ). Q Dem. |- . *3'22 )h :. P)g-):~)~P (1) P, ?, r h :~?)g-). G f :):. ~p)?. )-~?)? : ) : ~P)?-). ? (3) I- . (3). * 3-41. ) I- f. RpH-). -g)gr)'^p)v)'ff ( 4 ) I- . (l). (2). (4). Syll. )h -Prop. The proposition that is here established may be read, " if p implies g, then, if the falsity of p implies the... truth of q, q is true. " In the first line of the proof the significance of prop. 3*22 is set forth, viz. , The principle of Syllogism next referred to, in which ~ (7, ~ p and q are to be substituted for p, q and r respectively, is |- :. P)q. ):q)r. ). P)r. In the third line prop. 3*12, in which also three substitutions are to be made for p, q and r, is Then in line (4) prop. 3*41 is brought to bear upon line (3). The proposition thus adduced is EXAMPLES OF PROOFS IN GENERALIZED LOGIC 73 This proposition being true the proposition that follows the leading implication-sign in line (3) is asserted.
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