Demonstrate that each of the following arguments is invalid by means of a counterexample substitution. Formalize each argument using capital letters to stand for the underlined letter in each atomic proposition (e.g. ‘If today is Thursday, then today is a weekday,’ would be formalized ‘If T then W’). Each argument is in fact invalid. You don’t have to write the original argument on your paper, just formalize what’s given and make your substitutions.

PHI 300 – Logic

I. Demonstrate that each of the following arguments is invalid by means of a counterexample substitution. Formalize each argument using capital letters to stand for the underlined letter in each atomic proposition (e.g. ‘If today is Thursday, then today is a weekday,’ would be formalized ‘If T then W’). Each argument is in fact invalid. You don’t have to write the original argument on your paper, just formalize what’s given and make your substitutions.
1. Either Mary loves John or Mary loves David. Mary loves John. Therefore, Mary does not love David.
2. If ideas are important, then philosophy is important. If ideas change lives, then ideas are important. Therefore, if philosophy is important, then ideas change lives[1].
3. All writers are neurotic. No bank presidents are writers. Therefore, no bank presidents are neurotic.
4. No time travelers are social butterflies. Some villains are social butterflies. Therefore, no villains are time travelers.
5. All hipsters are grating. Some PBR drinkers are grating. Therefore, some PBR drinkers are hipsters.
II. Use a Venn Diagram to determine whether each of the following categorical syllogisms is valid or invalid. Use the underlined letters for the abbreviation of each term. In labeling the circles, the minor term is the top left circle, the major term is the top right, while the middle term is the bottom circle. Clearly state whether the argument is valid or invalid.
1. All peaceful afternoons are autumn days. All peaceful afternoons are tranquil. Therefore, all autumn days are tranquil.
2. Some economic views are not worth considering. Every economic view has been held by a blowhard (false, by the way). Therefore, some views held by blowhards are not worth considering.
3. No persons killed in the past may be saved. Some persons killed in the future may be saved (not really, but never mind). Therefore, at least one person killed in the future may not be saved.
4. All Bills fans are into Zubaz. No Steeler fans are Bills fans. Therefore, no Steeler fans are into Zubaz.

[1] To obtain a false conclusion here, try to find a conditional that doesn’t express a good relationship of sufficiency. That is, a conditional where the antecedent doesn’t necessarily lead to the consequent. For example, ‘If today is a weekday, then today is Thursday.’ I would also come up with a false conclusion first, then work backwards to the premises.

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