Is This What You Call Logic?! - 2

Logic Level 1

What conclusion follows from the statements given below?

$(1)$ Nobody who really appreciates Beethoven fails to keep silent while the Moonlight Sonata is being played.

$(2)$ Guinea-pigs are hopelessly ignorant of music.

$(3)$ No one who is hopelessly ignorant of music ever keeps silent while the Moonlight Sonata is being played.

This problem is from Lewis Carrol (Yes, Alice in Wonderland!), who was an accomplished author as well as a mathematician specialising in logic.

This problem is the part of my set Is This What You Call Logic?!

Guinea-pigs keep silent while the Moonlight Sonata is being played! None of These Guinea-pigs appreciate Moonlight Sonata! Guinea-pigs do not really appreciate Beethoven!

1 solution

Feathery Studio
Apr 30, 2015

To make it easier, I will rewrite statements 1 & 3, and I will add statement 1's logical derivative.

Anyone who really appreciates Beethoven does not make noise while the Moonlight Sonata is being played --> Anyone who doesn't appreciate Beethoven will make noise.
Guinea-pigs are hopelessly ignorant of music.
Anyone who is hopelessly ignorant of music makes noise while the Moonlight Sonata is being played

Now, according to statement 2, guinea pigs are hopelessly ignorant of music, therefore meaning that they make noise. This would fit the logical derivative of statement 1, i.e., guinea pigs do not appreciate Beethoven.

The english phrasing is a bit tricky for me, a non-english speaker.

The logical conclusion is that guinea-pigs won't be quiet during the Moonlight Sonata, which is different from what the given answer is. There is no information to determine if guinea-pigs appreciate Beethoven or not, only that they don't appreciate the Moonlight Sonata.

Carlos Merino - 5 years, 9 months ago

Making noise during the Moonlight Sonata is the indication, from statement 1, that they don't appreciate Beethoven, not that they don't appreciate the Moonlight Sonata. The logical conclusion holds.

Brian Egedy - 5 years, 8 months ago

It seems that the statement that you added following statement 1 is incorrect. It should be "Anyone who really appreciates Beethoven does not make noise while the Moonlight Sonata is being played: --> Anyone who makes noise doesn't appreciate Beethoven."

Let's state it simpler:

A -> not do B

So what follows must be "do B -> not A", not "Not A -> do B"

Because there is no rule about what "not A" can do, there is only a rule about who can not "do B".

In other words, "not A -> do B or not do B", or, Anyone who doesn't appreciate Beethoven can do whatever they wants (make noise or not).

Nhật Hoàng Xuân - 3 years, 9 months ago

Yes, that amendment is correct, and the original post is incorrect.

Adrian Self - 2 years, 5 months ago

I understand the derivation of the answer. I think it would clear it up if you removed the ambiguity between the two terms 'nobody' and 'no one'. Perhaps I am nitpicking, but both these terms are normally interpreted as referring to people, not animals, and so a justified logical translation, say, for sentence one would be 'for all x, if x is a person and x appreciates Beethoven, then x will remain silent while the moonlight sonata is being played.' This therefore means that none of the conclusions follow, as guinea pigs do not fulfill this first part, that is, being a person

Matt Gilchrist - 1 year, 1 month ago

Statement 1 says that nobody who appreciates Beethoven FAILS to keep silent during the Moonlight Sonata, meaning those who appreciate Beethoven will make noise. This is the opposite of your rewrite of statement 1

Niamh Simpson - 4 months, 2 weeks ago

The guinea pigs are just helplesly ignorant, that doesn't mean they don't aprecate the sonata, it means they will not shut up during it. You need to rewrite the answear!

Photo Connoisseur - 3 months ago

Is This What You Call Logic?! - 2

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