Monday, August 11, 2008

Gripping Brainteaser to Kick Start 2008-9

The rule that no statement can be both true and false is sometimes called the Law of Noncontradiction. The separate, but related, rule that every statement is either true or false – one or else the other - is sometimes called the Law of the Excluded Middle.

These two Laws are thought by many people not only to be true, but to be the most fundamental principles of rational thought. But consider whether you think the following tirade from my old roommate Charlie Schmidlapp calls any of this into question.

Charlie says:

Consider the following statement:

H: It's hot outside now in Farmville.

This seems directly to contradict this statement:

C: It's not hot outside now in Farmville.

But can either (H) or (C) be said to be true? According to the above "Laws", at most one of them can be true, and exactly one of them is true. But isn't that nuts? Allow me to fill in some details if you don't see what I mean.

Imagine that two people are at the same location in Farmville, and one of them (call him "Harry") sincerely utters sentence (H) and the other (call him "Keanu") sincerely utters sentence (C). This isn't hard to imagine. In this case, Harry and Keanu seem to be disagreeing about the weather in Farmville; sentence (H) certainly appears to contradict sentence (C); if one of them is true, then the other is false. But some of us may perhaps be convinced that they both may be true. Others of us may perhaps want to say that sentence (H) is in some way true but also in some way false, and that the same goes for sentence (C).

Shouldn't these considerations make us reject any "Law" which says that every statement is either true or false but not both?


How shall we respond to Charlie?

8 comments:

Mike Webb said...

Charlie, perhaps you should remove your hat, gloves, and coat. It's August for crying out loud!

or

Charlie, you know you could transfer to Curry or Fraser, but then you'd have to deal with thin walls and a low ceiling.

Anonymous said...

This riddle seems to just point out how imprecise language can be, and how a single term can have different meanings to different people in different circumstances. I mean, suppose that Harry has just stepped out of a walk-in freezer, and Keanu has just come back from a nice steaming at the local spa. I think "hot" here is more of a comparative term that is based on individual experiences rather than a description of absolute fact. It's probably safe to assume that neither Keanu nor Harry seems to be comparing the current weather conditions to the platonic form of "hotness" or anything like that, so I don't think it really has any implications for the two laws mentioned.

Anonymous said...

I think i agree with ben. Either statement made by harry or keanu is really a statement of opinion. when harry says, it is hot outside in farmville right now, what he is really saying is that it feels hot to him in his opinion in farmville right now. So really he is stating an opinion not a fact, so it really has no relavence to the law of true and false statments. becuz to harry it may indeed feel hot which would be true and not false and keanu might actually feel cold which would also be true and not false even though they are both percieving the same weather conditions.

Ps. as creator of the club and a bad spellor, i reserve the right to use lame internet abrieviations, its in the constitution . . .

pss. ill get back to u about schedualing a date for that proof.

Anonymous said...

I find ur retort vexing. There is a distinction between factual statements and statements of opinion. Should charlie say, the earth is round like a beach ball. he could be told that he is wrong. becuz the earth is stretched at the equator, making it less spherical than the beach ball would proportionally be. but should he say that in his opinion the earth is round like a beach ball there is more room for error becuz we realize that he is just trying to say to someone that the earth has a general spherical shape, not unlike a beach ball. and we would not bother to correct him on this minor factual infraction. Further more even if he was completely wrong when he stated that say, the earth is triangular like a triangle. we could not say his statement is false becuz unless he is lying then his opinion is his opinion. While the earth is not in fact triangular it can still be his opinion that it is. though he is wrong about his facts.

but even if im wrong about all of that . . .

A statement concerning a fact must either be true or false. it could be a fact that harry feels hot, and it could also be a fact that keanu feels cold. Just becuz they are both recieving input from the same source at the same time and place really does not pose any paradox for both of these statements to simultaneously be true.

whats charlie got to say about that?

rjw498 said...

sorry left out the sum up thought for the first paragraph there. So while charlie would be false in saying, the earth is round like a beach ball. he would not be false in stating that, in his opinion, the earth is shaped like a beach ball. so they are not equivalent statements.

Anonymous said...

just read something in that last post that u might pick on so im gonna fix that real quick.

sorry left out the sum up thought for the first paragraph there. So while charlie would be false in saying, the earth is round like a beach ball. he would not be false in stating that, in his opinion, the earth is round like a beach ball. so they are not equivalent statements.

Mike Webb said...

I had to think about this for a couple days. This is what I was able to come up with, which includes some reflection of comments made about the original post.

All opinions are relative. Opinions may vary from person to person. Two people may share conflicting opinions where it is not possible for two people to share conflicting facts. One fact must be true while the other is false. However, *any* statement, according to the laws in question, is subject and not just statements of fact.

Suppose there comes a time when Harry and Keanu agree. There might be a change of seasons and the temperature becomes colder. They might say something like sentence (C) in sincerity. But their friend from Alaska may be visiting at that time and sincerely utter sentence (H). For whatever reason, maybe environment acclimation, the friend from Alaska has a different opinion which now conflicts with both Harry and Keanu. This doesn't make any of them wrong about the temperature.

I think that the infinite possibilities that create any individual's experience form opinions, among other things, that may coincide or conflict with opinions held by others. I don't think that cushioning a statement with "in my opinion.." alters what is being said in the statement; which might be what Senn was trying to say.

I may have to add to this later. Having to work on a hot saturday is making me incapable of coherent thought...

P.S. It will be hot in Yorktown. Or maybe that's just my opinion?!

Anonymous said...

we should kick charlie in the balls