Jeol, there's one problem with your last syllogism. If would have the be "All Bobs are sponges who live..."

What you've said there is:

A is B
A,
Therefore B.

What you haven't considered in this one is:

Some A's are B's
A,
Therefore, maybe B (possibly something else.)

Very interesting, I'm writing about this topic at school, so this would definitely be helpful :)

Thanks

Bob is a sponge who lives under the sea.
My name is Bob.
Therefore, I live in a pineapple under the sea and am square.

The argument itself is an invalid deductive argument, am I right?

Yep, that's right. Though we would just call it invalid - including the 'deductive' part is a bit confusing.

The reason it is invalid is because it is a weak analogy - While the premises may be true, the conclusion might be false.

Yep, if it's possible for the premises to be true and the conclusion false, then the argument is invalid. Unfortunately, the reason why this argument is invalid can't be shown with propositional logic - the logic that this thread is based upon.
Predicate logic simply cannot represent the proposition: 'Bob is a sponge who lives under the sea'. We have to use predicate logic for sentences like this, which is a bit more complicated (but only slightly).
As it turns out, it's questionable whether this argument is even deductive. The three statements, logically, are unrelated. Consider the following argument:

1) Bob is over there.
2) My name is Bob.
3) Therefore, I am over there.

This is structurally similar to the SpongeBob argument, I've just simplified it so we can see where the flaw is. What this argument lacks is a statement like: 'I am Bob' or 'I am identical to Bob'.
Here, 'Bob' names something, and so does 'I'. But it never says the two are the same thing.

So we have 2 ways to go:

1st stab:

1) Bob is a sponge that lives under the sea.
2) I am Bob.
3) Therefore, I am a sponge that lives under the sea.

Here, the argument is deductively valid but clearly not sound. It commits the fallacy of equivocation.

2nd stab:

1) All Bobs live under the sea.
2) I am a Bob.
3) Therefore, I live under the sea.

This is also deductive valid but not sound. Premise 1 is false.

Hope that helped.

haha

The only reason something is illogical is because of logic itself. Once logic contradicts itself the previous logic is no longer valid, in practical terms. So if it is impossible to gain every bit of knowledge, logic itself is illogical, because there is, and I quote "...an infinite amount of logic". So arguing logic is basically arguing something you don't know if either argument is true, or any common hypothesis.

The only reason something is illogical is because of logic itself. Once logic contradicts itself the previous logic is no longer valid, in practical terms. So if it is impossible to gain every bit of knowledge, logic itself is illogical, because there is, and I quote "...an infinite amount of knowledge". So arguing logic is basically arguing something you don't know if either argument is true, or any common hypothesis.

I feel like I'm in ELA all over again. Santi_ lost me when he said his comment. What did you mean? The sentence made no sense.

idontlikeyou, well, I don't know either.

This is very interesting and has kept me thinking for a long time...

Is this argument valid?

Spongebob lives under the sea
There is only one Spongebob
Therefore, there are no Spongebobs who live above sea level

Is this argument valid?

Spongebob lives under the sea
There is only one Spongebob
Therefore, there are no Spongebobs who live above sea level

You would need the additional premise that nothing that lives under the sea also lives above sea level, but yeah, it's valid. Although you would need to use Predicate Logic to show its validity.