Friday, August 20, 2004

Welcome!

Welcome to the CAS 105: Paradoxes class blog.

14 Comments:

Blogger Howeman said...

1. If you tell a student the blog is part of his grade, he will come
2. Brendan is a student
3. Brendan has been told the blog is part of his grade
4. Therefore, Brendan has come.

Actually, this could be fun if we get some good debate going on in here.

September 3, 2004 at 4:36 PM  
Blogger dscheffe said...

I guess we are assuming that Brendon cares about his grade, because if he did not care, then he wouldn't necessarily come to the blog.

September 4, 2004 at 7:42 AM  
Blogger Steve said...

1. If X is a student taking a class Y and X cares about his grade in Y, then X will perform all the required tasks for Y.
2. The blog is a required task for CAS105: Paradoxes.
3. Brendan is a student taking CAS105: Paradoxes.
4. Brendan cares about his grade in CAS105: Paradoxes.
5. So, Brendan will "perform" the blog.

That seems like a nice compromise between the above two comments.

September 5, 2004 at 4:19 PM  
Blogger Howeman said...

But, the next problem becomes getting there.

For Brendan to get there, he has to go halfway first. But to get there, he has to go half the half, but before go half that and half that and half that.

But, I suppose we aren't dealing with that till week 13 or something

September 6, 2004 at 7:07 PM  
Blogger Higgins said...

I'm not sure it matters if Brendan cares about his grade. That more argues the truth of one premise than it clarifies validity. The original argument is Deductivley Valid so it isn't nessaccary to add another premise only to argue the truth of the stated pemises.

September 8, 2004 at 4:44 PM  
Blogger April said...

This comment has been removed by a blog administrator.

September 9, 2004 at 4:21 PM  
Blogger April said...

Never assume that everyone who reads the argument will assume the same things. dscheffe and Steve are simply safeguarding against someone making the assumption that, if they do not care, they may not put forth the effort to write in the blog. So, by adding the premises “if x cares about his grade, then he will write on the blog” and “x cares about his grade,” the argument, while it was deductively valid previously, and still is, is now stronger because it allows less room for personal bias of a reader.

September 9, 2004 at 4:23 PM  
Blogger Alissa said...

It is not a question of if the student does or doesn't care about their grade. If the argument is deductively valid then the premises support the conclusion, therefore the student would have to care about his or her grade to make the conclusion true. If one were to assume that the student did not care about their grade, then the conclusion would not follow from the premises and the argument would no longer be deductively valid.

September 12, 2004 at 5:59 PM  
Blogger Steve said...

Is anyone writing about the Body-minus paradox? What do you think is the weakest premise and why? I separated the paradox into 4 premises and a conclusion. I found the premise "Both Body-minus and Tibbles exist after the accident" to be the weakest premise. I gave the following reasoning:
Tibbles, in the sense used in premise (1) [the premise that states that both Tibbles and Body-minus exist before the accident], no longer exists. In premise (1), the word “Tibbles” means “The set of molecules composing the cat named ‘Tibbles.’” In premise (3) it is clear that “Tibbles” no longer refers to this same set of molecules. Instead, the sense of premise (3) is that “Tibbles” means “The set of all molecules composing Tibbles, except for the molecules composing the tail,” which is exactly how Body-minus would have to be defined in premise (1). Hence, the argument uses the word “Tibbles” to refer to two distinct objects, while assuming that the meaning of the word does not change.

September 12, 2004 at 6:15 PM  
Blogger Steve said...

Just a follow up....
Strictly speaking, by my reasoning, that premise is OK. The one that fails is "Body-minus and Tibbles are identical after the accident." This may be true, but the author must explicity make clear what is meant by "Tibbles." By my interpretation, this premise is false.

September 12, 2004 at 6:21 PM  
Blogger Howeman said...

(First of all, I assume that our conclusion is that a paradox exists?)

The point about Tibbles (from my understanding), is that the cat continues to exist as a cat, even without his tail. Thus, Tibbles and body-minus are identical.

Personally, I dont' think body-minus is a paradox at all. 1. If you can't have 2 objects occupy the same space at teh same time, then the initial set up of the problem is the flaw, becuase body-minus is in teh same space as tibbles. 2. What this really is is an exercise in names, just like the statue. If I call an object Bob, and someone else calls it Sally, then I guess we must have a paradox because two identicle objects in the same space. The statue is a little more entertaining, but it's still really all semantics.

I suppose the Theseus is also the same in the end, but I enjoy it more and I think it poses a more interesting problem.

September 12, 2004 at 7:17 PM  
Blogger Steve said...

Howeman,
1. If you can't have 2 objects occupy the same space at teh same time, then the initial set up of the problem is the flaw, becuase body-minus is in teh same space as tibbles.
That's really a brilliant observation... I agree that there's no paradox. However, I wasn't able to put the reason why into such clear terms. It appears to be merely a matter of semantics. Actually, I had at first wanted to attack the first premise, that Body-minus exists before the accident, because just giving a name to something doesn't necessarily make it exist.
In fact, you are correct: Body-minus isn't so much distinct from Tibbles, as it is a part of Tibbles.

September 12, 2004 at 8:44 PM  
Blogger Chris Tillman said...

This is a nice discussion of the Tib-Tibbles case. Hopefully we can address some of these issues in class. Steve: could you post your original comment on Body-minus as a separate post, rather than as a comment on the 'Welcome' post?

September 13, 2004 at 7:39 AM  
Blogger Steve said...

I would have given it a new section... if I knew how. I'll try to figure out how, and next time I'll do that.

September 13, 2004 at 12:57 PM  

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