What, if anything, is wrong with this argument?
Premise 1: Nothing is better than eternal happiness
Premise 2: Logic is better than nothing
Conclusion: Logic is better than eternal happiness
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Bridges to Autonomy; Paradoxes in Teaching and Learning, by Matt Silliman and David Kenneth Johnson (click on book for more information)
Plato's Dialogues
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Though all posts are open to all visitors, this semester's posts will mostly pertain to my Plato's Dialogues course.
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5 comments:
The problem seems to lie in the ambiguity of the term "nothing." Most people would read Premise 1 as meaning that there could not be anything better than eternal happiness. It does not seem to mean that "nothing" is actually something that is better than eternal happiness. However, in Premise 2 the term is used differently. The implication is not that logic is not better than anything, but that it is better to have logic than nothing at all. The confused usage of "nothing" is what leads the argument to a conclusion that seems to contradict both premises individually.
If you reverse the first premise to "Eternal happiness is better than nothing", you still have the same use of nothing as in Premise 2. And these premises are subjective claims, right? "Nothing is better than eternal sadness" could replace the current phrasing, or "eternal ludicrousness" but neither is a true statement. Unless you add something to the premises like "Nothing is better for your health than eternal happiness", you might get somewhere with the argument. Subjectively, logic is probably better for your health.
The problem originates from the formula that led to this conclusion. Transitive logic - often taught in mathematics, for those that remember - is exemplified by the case: a=b, b=c, therefore a=c. In the two given premises of this post, "b" would subsequently represent the term "nothing"; transitive logic determines "b", or its present equivalent in the premises, is used in the same manner in both premises - that not only the word is the same, but the value is as well. However, as Sean Edwards described, despite the same word appearing in both premises, the value is not across the board, so to speak. In fact, Premise 1 indicates an absolute truth that deflects the conclusion.
From here on in, B1 will be used in reference to the term "nothing" in Premise 1; B2 will be used in reference to the term "nothing" in Premise 2.
In Premise 1, the statement still remains intact when B1 is broken into its elements "no" and "thing"; B1 and is a compound word, and can therefore be broken down so. To say "No thing is better than eternal happiness" is parallel to saying "Nothing is better than eternal happiness". In Premise 2, the statement is incomprehensible when B2 is broken into "no" and "thing" - the statement does not hold its original value. Therefore, ironically yet logically speaking, in the context of the corresponding premises, if the value of B1 = the value of "no thing", and the value of B2 ≠ the value of "no thing", we may conclude that B1 ≠ B2.
Simplistic and straightforward reasoning can lead to overlooking complex values and/with subtle differences. That is what is wrong with this argument.
Sean nailed it. Both instances of "nothing" are colloquial expressions, and they mean completely different things. So the argument is formally valid by (as Colby notes) transitivity, but is unsound (even deliriously goofy) because the middle or linking term, 'nothing,' doesn't mean the same thing in both places. Aristotle would say the middle term isn't distributed.
As Colby points out, if we took the first premise literally, it would indeed contradict the conclusion.
I'm not entirely sure I follow Christopher's point about subjectivity.
As Sean mentioned, the term "nothing" is ambiguous and denotes two separate concepts in each statement. If "nothing" were a word tied with only one concept, the argument might be valid. However, the context of each statement informs us that each "nothing" refers to a separate idea. Were one to rephrase the premises to clarify the difference, it would become much more obvious that the two statements are irrelevant to each other, making the conclusion faulty.
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