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QUANTIFICATION SYMBOLS FOR PROPOSITIONS Contemporary logicians have a way of analyzing A, E, I, and 0 statements, as well as other types of propositions, A Handbook of Logic 24 by using a symbolic notation for quantifiers. use greatly assIsts the analysis of propOsitionS. - - - -- -. " Such propositions may be put in very simple notation by letting the caeitalletters, such as F, G, H, ~tand for predicates, while small letters a through w stand for the name of the indiyidu~J. d ap()ut. ) So the proposition: Davy Crockett is a pioneer.

But if, for example, "Some mice have tails" is assumed to be false, its superaltern, "All mice have tails," will also be false; but its subcontrary, "Some mice do not have tails," will be true. We should see why the truth of an I proposition does not in and of itself imply the truth of its subcontrary. If "Some S is P" is true, it does not follow that "Some S is not P" is also true. If I know that some cases of arthritis are curable, and nothing beyond this, then it mayor may not be the case that some cases of arthritis are incurable.

We note that this syllogism also violates an earlier rule, since the middle term is twice undistributed. Thus, it commits the fallacy of the undistributed middle as well as that of the two particular premises. 7. If one premise is negative, the conclusion must be negative. An example of a violation of this rule would be: No hats are viola players. All bats bite toes . ' . Some that bite toes are viola players. 8. If one premise is particular, the conclusion must be particular. Here is an example of a violation of this rule: Bedlington terriers look like lambs.

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A handbook of logic by Joseph Gerard Brennan

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