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
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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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To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after The Scope of Formal Logic the New Logical Doctrines Expounded With Some Critic?
You can find similar books in the "Read Also" column, or choose other free books by Arthur Thomas Shearman to read onlineMoreLess
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