Another Controversial Problem

Logic Level 3

True or False:

Every animal in an empty cage is a pig.

Bonus: If true then prove, otherwise explain why this is false.

No answer True no answer False

1 solution

Paul Ryan Longhas
May 19, 2016

Proof of the argument:

Assume that there is an animal not a pig in an empty cage. So, it must be a contradiction since a cage is empty. Therefore, the argument is true.

Nice. You repeated a possible answer...

This statement has a particular name in Logic, but I don't remember it at this moment. A similar well-known statement is: the France's king is hairless. Logicians do not agree about the truthfulness of the statement because we cannot say (and even less assure) anything about something that does not exist.

Mateo Matijasevick - 5 years ago

In logic, a statement like this is known as a vacuous truth : it asserts that all elements of the empty set have a certain property. As such, this is not a controversial statement: Logicians agree that a vacuous truth is, well, true ;)

@Mateo Matijasevick 's "French king" example is of a very different nature, since it involves a "definite description:" The current king of France. That one is indeed controversial. Philosophers like Russell and Frege have come to different conclusions: "False" vs "no truth value. " For Russell, the existence and uniqueness of a current king of France is part of the statement (and it is false), while for Frege this existence and uniqueness is a "presupposition."

Otto Bretscher - 5 years ago

This is a pretty good clarification , especially for setting the problem in it's theoretical context yet can you explain also why what logicians agree that is true is true ? I suppose it is right in the form of reasoning but under the interpretation of "elements of an empty set" it requires clarification because , it can be said , it is not completely clear and articulate what can be affirmed and predicated about an empty set and therefore if it is right to say there is any truth value for it.

And you made me curious about Mateo's example too so might you happen to know if there is some other pretty influential opinion on this subject ? I mean if there is some other philosopher form the analytical tradition who elaborated a different view from the ones of Frege and Russell even if to me it pretty much seems that you can interpret that statement in both ways equally likely therefore not being any complete and reasoning by principle to suppose it must be in just one way.

A A - 5 years ago

I'm no expert on this, and I'm afraid that what I wrote in my post is just about all I know on this issue. I studied a little logic at my Alma Mater, the University of Zürich, some 40 years ago, taking a particular interest in the logic of Gottlob Frege. Frege wrote a very interesting book, "Sinn und Bedeutung"; people can't even agree how to translate these terms into English. Bedeutung is roughly the "truth value", while Sinn (or "sense") is the "thought the statement expresses". Fictional writing will (hopefully) have Sinn, but no Bedeutung. The statement "the current king of France is bald" makes sense (Sinn), but it does not have a truth value. The way I understand it, Russell claimed that the sentence "the current king of France is bald" (this is his exact example) really is three statements conflated into one: existence, uniqueness and baldness. Since the first is false, the whole thing is false. I have no sense as to how these two positions fit in with contemporary views in Logic.

Otto Bretscher - 5 years ago

@Otto Bretscher – This fits more into the topic of analytic philosophy than just logic. Russel's claim would mean that you can't say a proposition which has no truth value since for something , say A to be stated must be a unique existent stuff which has some propriety (baldness) while Frege does make a distinction of this by speaking of Sin ("sense") and Bedeutung("truth value"). As such it would pretty much be easy to understand that Russel presupposes that any statement speaks of existence which is pretty clear is not true while Frege exactly for observing this made in my opinion a better characterization. I suppose things should be more complicated than this because if they are just like that it should be no problem and controversy as not all that is said or in other words predicated speaks of and maintains the necessary existence of something (as Russel says by this) thing to which everyone can agree and follow Frege's distinction anyways. Anyways thanks for sharing the things you know. If you liked Frege's book you might also like the views of Husserl but his works require a lot of time and be followed rather systematically anyways.

A A - 5 years ago

@A A – I look forward to reading philosophy again (Husserl and many more) when I'm retired, which will happen pretty soon ;) Thanks for the dialogue!

Otto Bretscher - 5 years ago

@Otto Bretscher – Well , that's great then. Hope you'll have a great and as fulfilled as it can retirement.

A A - 5 years ago

@Otto Bretscher – And thanks for the dialogue too. And for the fact that you remind me that are people like you that have this type of more evocative and cultural concerns also anyways.

A A - 5 years ago

Assume that there is a dino and not a pig inside the cage. But the cage is empty (contradiction) Thus there is a dinosaur inside every empty cage. So why is the false answer wrong?

Prithwish Roy - 3 years, 7 months ago

Another Controversial Problem

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