Wednesday, September 21, 2005

The logic challenge

If you’re still having your doubts about logic, then I have a couple of challenges for you. The first challenge is this: Take a piece of paper and draw a four-sided triangle. The second challenge is this: Take a piece of paper and draw three straight lines, labeled A, B, and C, such that A is longer than B, B is longer than C, and C is longer than A. When you fail, ask yourself why. (Hint: Both challenges entail logical contradictions.) You will notice that logic is not a mere matter of language. It actually applies to the external world. You need not search the universe to see if there are any four-sided triangles. You can already see that there aren’t just by noticing that a four-sided triangle is a contradiction.

[A few years ago, I started two threads on beliefnet where I made these two challenged to anybody who denied logic. I was going to post a link to those threads here, but I can't find them. If I find them, I'll post a link in the comments section.]

15 Comments:

At 9/21/2005 1:18 PM , Blogger daleliop said...

lol

the logic challenge

another logic challenge

 
At 9/21/2005 1:37 PM , Blogger ephphatha said...

That's it! Thanks, Dale!

 
At 9/21/2005 3:28 PM , Blogger daleliop said...

I have a comment about the first post you made about logic.

You said that knowledge is justified true belief.

Suppose Peter walks into a party and sees Alice sitting on the couch. So, Peter justifiably concludes that Alice is in the room. The fact is, though, that what Peter sees is actually a papier-mâché version of Alice that is not really her. The real Alice is actually hiding underneath the coffee table, out of sight. But since Alice is indeed in the room, Peter's belief is apparently true. Therefore, Peter has justifiable true belief that Alice is in the room. But is this knowledge?

I think they call this the Gettier Problem.

 
At 9/21/2005 5:32 PM , Blogger ephphatha said...

Dale, that is a good question. I think the Gettier Problem shows that the definition of knowledge as "justified true belief" needs to be tweeked a little to be more precise, but as a general definition, I think it captures fairly well what we all mean when we say we know something. To tweek it, I would probably add something about the connection between the justification and the truth. Knowledge is justified true belief when there is a necessary connection between the truth and what justifies the belief in that truth. How about that?

Sam

 
At 9/21/2005 5:32 PM , Blogger Paul said...

It may also be meaningful to note the implicit qualifiers on the belief that "Alice is in the room," i.e., she is in the room and sitting on the couch right there, the very object that I am looking at and taking to be Alice.

 
At 9/22/2005 2:35 AM , Blogger daleliop said...

Sam,

What kind of necessary connection are you talking about?

 
At 9/22/2005 4:06 AM , Blogger ephphatha said...

Dale, in your analogy, there was a necessary connection between the paper mache version of Alice, and Peter's belief that Alice was in the room. His "justification" for thinking Alice was in the room was the paper mache version of her.

In my revised version of knowledge as justified true belief, I'm stipulating that there's a necessary connection between the truth and what justifies the belief in the truth. The truth in your scenario was the real Alice, and there was no connection between the real Alice and the reason Peter believed Alice was in the room. His belief in Alice being in the room had nothing to do with the real Alice; rather, it had everything to do with the artificial Alice. Do you see what I mean?

Sam

 
At 9/22/2005 9:58 PM , Blogger daleliop said...

I think I understand the idea, but that wasn't exactly what I was getting at; I want to know precisely what this necessary connection is (i.e. what are the conditions for there to be a 'necessary connection'). As it stands, the term seems pretty vague.

I asked the question because when I first read the new modification, it seemed like there was something odd about it.

I've been trying to put my finger on why I think it's odd, but am still putting my case together. But here's what I have so far:

What you are saying is that the Gettier counterexamples do not apply according to this new defintion because you have added the condition that there must be a necessary connection between the truth and the justification. In other words, the justification has to actually apply to the truth, meaning the justification must not have false premises nor be invalid, i.e. the reasoning of the justification must be "sound" (necessary). You critisize the Peter/Alice scenario because Peter didn't really see Alice, he was seeing a fake version of her, so his reasoning that "The real Alice is in the room because I see what looks like to be Alice sitting on the couch" is bad, since the hidden premise "If I recognize someone, then it is really them" is false in this case. Since the reasoning is bad, then this example is excluded from the definition of knowledge by your new condition, that the reasoning of the justification must be completely sound.

Now, if I have just interpreted your modification correctly, let me tell you why I don't think it works. First, here is what I think is the basic reasoning behind Peter's justification of Alice:

1. I see what looks like Alice.
2. I'm usually right about what I see.
3. Therefore, I see Alice.

{Premise 2 is not the absolute "If I recognize someone, then it is really them" (stated earlier), but a probable premise, that is, "I'm usually right about what I see."}

As you can see, the premises are true, and the conclusion follows from the premises. It's just that the argument is inductive, so the conclusion can't necessarily follow from the premises. Therefore, it can not be sound. However, it is still a pretty cogent argument, and therefore remains "good evidence" or "justification" for believing the conclusion.

But with your new modification, any case which applies inductive reasoning will be ruled out as knowledge, like inferring rain from storm clouds, because the conclusion will not necessarily follow from the premises. It is impossible to have that kind of certainty with an inductive argument. But we use inductive reasoning all the time, and it seems to us that inductive reasoning counts as good evidence to believe something is true.

 
At 9/23/2005 3:46 AM , Blogger ephphatha said...

Dale, sorry for not being clear. I guess I need to flesh out what I mean by "necessary connection." I don't mean the premises of the justification or false or that the justification isn't good. If that were the case, then I would just say Peter doesn't have knowledge because his belief isn't justified. If all you have is a bad argument, then you really have no justification at all. In Peter's case, assuming the paper mache was an incredibly good likeness, I think Peter was well-justified in believing Alice was in the room.

What I mean is that the true Alice being in the room had nothing to do with why Peter believed Alice was in the room. In fact, there is nothing about Alice being in the room that caused Peter to believe Alice was in the room. Peter had a justified true belief, but the justification was not connected in any way to the real Alice. So there was no connection between the "true" and the "justified."

By saying necessary connection, I mean that without the truth, the proper justification (not the misleading one) wouldn't exist. In other words, before Peter can really know that Alice is in the room, then it has to be such that whatever justification caused Peter to believe Alice is in the room wouldn't have been there had Alice not been in the room.

Suppose that in your scenario, the real Alice wasn't actually in the room, but the paper mache doll was. Peter would still have had justification for believing Alice was in the room. So Alice being in the room is irrelevent to the justification Peter had. What I am saying is that Peter can only have knowledge if Alice being in the room does matter. If it does matter, then Peter would not have knowledge-creating justification if Alice were not in the room. The reason is that without Alice being in the room, no knowledge-creating justification could exist that Alice is in the room. Alice being in the room must somehow be the cause of Peter believing she's in the room. Alice being in the room must somehow create the justification necessary for Peter to have knowledge.

Sam

 
At 9/23/2005 4:06 AM , Blogger ephphatha said...

This whole thing reminds me of something that happened when I was in middle school. I had this friend (can't remember his name) who had a girlfriend. One day, as a joke, I told him that his girlfriend was going to break up with him. He got all worried about it, and then I told him I was just kidding. The next day, he came up to me really mad, because his girlfriend did break up with him. He was mad at me for telling him it had been a joke. He thought I really knew she was going to break up with him.

When I first told him that his girlfriend was going to break up with him, he had a justified true belief that she was going to break up with him. But he didn't have knowledge, because there was no connection between the actual fact that she was going to break up with him (the truth), and the reason he had for thinking she was going to break up with him (the justification). The justification he had was not the proper justification, so it was not knowledge-creating justification.

I couldn't pass up the opportunity to bring up a real life example. :-)

 
At 9/23/2005 4:53 AM , Blogger daleliop said...

Sam,

lol that was a funny story (not for him, though).

For what necessary connection means, I think you clarified the issue for me fine. Perhaps you can call it a necessary causal connection.

 
At 9/23/2005 5:42 AM , Blogger ephphatha said...

How about if we just say knowledge is properly justified true belief? Then, if somebody wants to know, we can explain what kind of justification would be proper.

 
At 9/23/2005 1:41 PM , Blogger daleliop said...

That would work too. This is reliabilism, no?

A proposition P is knowledge if and only if P is true and P was arrived at by some reliable process.

Did you come up with the definition just now or did you have some idea about this before?

 
At 9/23/2005 3:02 PM , Blogger ephphatha said...

Well, I had heard of the Gettier Problem before, so I had thought about how to respond to it, but this is the first time I've ever written anything about it. This is the first I've heard of reliablism. It's nice to know somebody else thought of the same thing.

 
At 9/23/2005 4:15 PM , Blogger daleliop said...

lol you'll make a fine Professor

 

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