Foundations of Formal Logic
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1 A principle, which is altogether fundamental and which will be taken for granted at each step of our progress, is this : If a propo- sition is true in general, it is because it remains true for all specific meanings of the terms that enter into it, although an untrue propo- sition does not always remain untrue in the same circumstances. Thus y(ab) Z y(ba) is untrue in general, but it becomes true for the case, in which a and b are identical, viz. , y(aa) Z y{aa). Accordingly, when we write {x...(a, b) Z y(a, b)\', we only assert that there is at least one value of a and one value of b which will render x{a, b) Z y{a, b) a false proposition. If it has been estab- lished that x{aa) Z y(aa) is untrue, then we may at once infer that the more general implication, x(a, b) Z y(a, b) is untrue as well. In order to establish the untruth of a given proposition, it will be enough to point to a special instance of its being untrue.
"The Implicative Function is a propositional function with two argu- ments p and q, and is the proposition that either not-p or q is true, that is, it is the proposition p' -f- q.
What to read after Foundations of Formal Logic?
You can find similar books in the "Read Also" column, or choose other free books by Henry Bradford Smith to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
1 A principle, which is altogether fundamental and which will be taken for granted at each step of our progress, is this : If a propo- sition is true in general, it is because it remains true for all specific meanings of the terms that enter into it, although an untrue propo- sition does not always remain untrue in the same circumstances. Thus y(ab) Z y(ba) is untrue in general, but it becomes true for the case, in which a and b are identical, viz. , y(aa) Z y{aa). Accordingly, when we write {x...(a, b) Z y(a, b)\', we only assert that there is at least one value of a and one value of b which will render x{a, b) Z y{a, b) a false proposition. If it has been estab- lished that x{aa) Z y(aa) is untrue, then we may at once infer that the more general implication, x(a, b) Z y(a, b) is untrue as well. In order to establish the untruth of a given proposition, it will be enough to point to a special instance of its being untrue.
"The Implicative Function is a propositional function with two argu- ments p and q, and is the proposition that either not-p or q is true, that is, it is the proposition p' -f- q.
What to read after Foundations of Formal Logic?
You can find similar books in the "Read Also" column, or choose other free books by Henry Bradford Smith to read onlineMoreLess
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