# Thread: Probability Relations and Induction

1. Originally Posted by reason
SW,

You really need to go and learn something about logic.
You've got it backwards buddy, you're the ones propounding conclusions without stating arguments to support them. On the few occassions you do have arguments, they are subtly fallacious. And of course, the way you responded to this charge shows that you're not knowledgeable or skilled enough to see the obvious howlers. (E.G equivocation fallacy where you define provoker as a hamster and at the same time maintain that provoker as a person who posts on this message board.)

I bet you haven't done a single SL proof in your entire life.

2. Originally Posted by Evan
Ah. Sure. But then you could rewrite the premises to be general too. I guess that means my previous statement is kinda useless. I probably should have specified non-tautologies.

Huh?

You seem to think his conclusion is "provoker is a hamster and a member of typecentral" instead of just what it says.
The premise of that argument defines provoker as a hamster. If I say Evan is a hamster, I define Evan as a hamster. (In this context it is not implied that Evan is a human being, as nothing of the like is stated specifically. You are the one assuming that Provoker/Evan (substitute it with any name), is a person instead of what it says. All it says is that Provoker/Evan/any name is a hamster. Nothing else.)

In other words, what is meant by my proposition is not 'provoker=person who posts at this forum AND provoker=hamster who is a member of this forum' but simply this: provoker=hamster is a member of the board, and only this.

The expression provoker=human being who posts on this board is outside of the context of this argument because the premises defined provoker as a hamster only.

3. Originally Posted by SolitaryWalker
You've got it backwards buddy, you're the ones propounding conclusions without stating arguments and on the few occassions you do have arguments, they are subtly fallacious. And of course, the way you carry your discussions shows that you're not knowledgeable and not skilled enough to see the obvious howlers.
Backwards? I didn't write anything about me.

So if I have it backwards, then you still need to go and learn some logic, since I need to go and learn more logic, too.

4. Originally Posted by SolitaryWalker
The premise of that argument defines provoker as a hamster. If I say Evan is a hamster, I define Evan as a hamster. (In this context it is not implied that Evan is a human being, as nothing of the like is stated specifically. You are the one assuming that Provoker/Evan (substitute it with any name), is a person instead of what it says. All it says is that Provoker/Evan/any name is a hamster. Nothing else.)
Uh....

I don't really know how to respond here.

The point was that if the premises are false (so assume that provoker is not a hamster), the conclusion can still be true.

5. Originally Posted by Evan
This is meant to illustrate the point that there are an infinite number of hypotheses that are consistent with a set of data. So not only do we need a way to modify the strength of our beliefs based on data we see, we also need to be able to explain why we prefer certain kinds of hypotheses when an infinite number are all consistent with the data we've gotten.
Become a constructive empiricist a la Bas von Fraassen.

6. Originally Posted by Evan
Uh....

I don't really know how to respond here.

The point was that if the premises are false (so assume that provoker is not a hamster), the conclusion can still be true.
Let me try and walk you through this reasoning process more carefully and thoroughly.

Premise 1: Provoker is a hamster. (What I mean here is that the identity of a provoker is a hamster. )
Premise 2: All hamsters are members of the message board.

Conclusion: Provoker (a person who is the author of this thread) is a member of the message board.

This argument is deductively invalid. The premise that there is a hamster named provoker and the premise that all hamsters are members of the message boards do not guarantee the conclusion that the person who authored this thread is a member of this message board.

Plug it into the truth table. Have statement H represent provoker is a hamster. Statement M represent that all hamsters are members of the message board. Statement P represent that provoker is a member of this message board. You will find one instance where both of the premises are true and the conclusion is false.

-----------------------------------------------------

I shall expound upon the rationale behind the views expressed above once more.

The conclusion that we are trying to prove is this: A person named Colin who uses the account of Provoker, the author of this thread is a member of the message board.

This is one of our starting points: Provoker is a hamster. Another way of saying this is that there is a hamster who is called provoker.

This is another one of our starting points: All hamsters are members of the message board.

The above starting points (premises) do not prove the conclusion. They have nothing to do with the person named Colin who is the author of the thread. They only prove the conclusion that there is a hamster who is called provoker and is a member of the message board. This, however, is not the conclusion we intended to reach. The conclusion we intended to reach was that there is a person named Colin who uses the account of Provoker and is the author of this thread. Proving this is a radically different result from proving that there is a hamster who is called provoker.

----------------------------------------------

What you seem to be confused by is the following phenomenon, the definition of provoker as the person who interacts with us on the message board and the definition of provoker as a hamster (as stated in premise one). This is merely a play on words, as two different creatures seem to have the same name.

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Finally, what is my point?

Originally Posted by Evan
The point was that if the premises are false (so assume that provoker is not a hamster), the conclusion can still be true.
This is true, but the argument selected by reason does not provide an adequate example to support this point. The adequate example to support this point is the argument with contradictory premises that I have cited.

7. Originally Posted by reason
Backwards? I didn't write anything about me.

So if I have it backwards, then you still need to go and learn some logic, since I need to go and learn more logic, too.
That is true. The conversation can be summarized as the following: X said that Y needs to learn logic. The reversal of this would be this: Y said that X needs to learn logic.

Indeed, you did not say that you knew logic and for this reason, the reversal of my proposition does not entail the conclusion that I do not need to learn logic and you do. However, the fact that you are utterly unresponsive to carefully constructed arguments and frequently neglect to support your views lead me to guess that your experience with formal logic is limited. Either that is the case or you are inordinately intellectually lazy or terribly obstinate.

In any case, I stand by my claim that you've committed the equivocation fallacy as you have failed to construct an argument to refute this view.

8. Originally Posted by SolitaryWalker
Let me walk through the rationale behind the argument again.

The conclusion that we are trying to prove is this: A person named Colin who uses the screenname of Provoker, the author of this thread is a member of the message board.

This is one of our starting points: Provoker is a hamster. Another way of saying this is that there is a hamster who is called provoker.

This is another one of our starting points: All hamsters are members of the message board.

The above starting points (premises) do not prove the conclusion. They have nothing to do with the person named Colin who is the author of the thread.
When you use one term twice in an argument, it seems like a good assumption that you're referring to the same thing.

The argument can be rewritten as this:
All As are Bs
x is an A
therefore
x is a B

Another way of thinking about this is that IF the premises are true, the conclusion is true. It says nothing about IF the premises are false. If the premises are false, we know nothing about the conclusion. Therefore the conclusion could be true or false. In this case, the conclusion is true.

It's like this. If you know A->B, and ~A, you know nothing about B.

9. Originally Posted by Evan
When you use one term twice in an argument, it seems like a good assumption that you're referring to the same thing.

The argument can be rewritten as this:
All As are Bs
x is an A
therefore
x is a B

Another way of thinking about this is that IF the premises are true, the conclusion is true. It says nothing about IF the premises are false. If the premises are false, we know nothing about the conclusion. Therefore the conclusion could be true or false. In this case, the conclusion is true.

It's like this. If you know A->B, and ~A, you know nothing about B.
Lets see if we are on the same page.

If the argument is deductively valid, then IF the premises are true, the conclusion is necessarily true. A deductively valid argument is false if and only if the premises are false, as by definition, all truth-preserving premises in a deductively valid argument entail a truthful conclusion.

In this regard, I agree with your statement that in a deductively valid argument, the conclusion could be either true or false.

However, there appears to be a communication gap that has not yet been bridged.

Lets consider the following argument.

Premise 1: Provoker is a hamster. (There is a hamster who is called provoker)
Premise 2: All hamsters are members of the message board.
Conclusion:Provoker is a member of the message. (A hamster who is called provoker is a member of the message board.)

This argument is deductively valid, however the conclusion is false because the premises are false. If I was to make a logical fallacy and at the conclusion define provoker as a human being, my argument would be invalid. (As I said in my previous post, the fact that there is a hamster who is called provoker and the fact that all hamsters are members of the message board has nothing at all to do with a human being named provoker possessing membership at a message board. In other words, this argument is deductively invalid because EVEN IF the premises are true, there is no guarantee that the conclusion will be true. Remember, the definition of the deductively valid argument is that the truthfulness of the premises guarantees the truthfulness of the conclusion. If there is no such guarantee, then the argument in question is necessarily invalid. In this case, as I have explained, even if both premises are true (that there is a hamster called provoker and all hamsters are message board members) there is no guarantee that the conclusion( that a human being named provoker) is true. Therefore this argument is invalid.

Here, I have demonstrated why equivocation is a fallacy: in this instance it directly leads to a deductively invalid chain of reasoning.

----------------------------------------------------------------

Again, what is my point.

Originally Posted by Evan
When you use one term twice in an argument, it seems like a good assumption that you're referring to the same thing.

The argument can be rewritten as this:
All As are Bs
x is an A
therefore
x is a B.
In the context of formal logic, what you have said here is false. The assumption precludes the possibility of people making the equivocation fallacy. At times (as it has occured in this case) people mean different things when they use the same word twice. This is known as a play on words. It has value in poetry and literature, but does not carry any weight in formal logic. It is known as the equivocation fallacy.

As aforementioned, if there is no equivocation fallacy in the argument above(the word means the exact same thing both times it is used), the result is the following: the conclusion is false, but the argument is deductively valid. Reason claimed that this example proves that an argument can have false premise(s) and a true conclusion. I have shown that this argument has false premises and a false conclusion.

See the figure below.

Premise 1: Provoker is a hamster. (There is a hamster called provoker)--Lets say that this is true. There may be a hamster somewhere in the world who is called provoker.

Premise 2: All hamsters are members of the message board. (This is our false premise, no hamsters are members of the message board.)

Conclusion: Provoker is a member of the message board. (False, there is no member of the message board who is a hamster and is called provoker.) This statement, however, would be true if premise 2 was true.

10. Evan,

All SolitaryWalker is saying that the concept of "Provoker" includes the property "non-hamster," so my premise "Provoker is a hamster" is like saying "A non-hamster is a hamster" i.e. a contradiction. (It's still not an equivocation, though).

However, this reminds me of people who say they have solved the problem of induction, because swans are by definition white, and if we ever found a "black swan," it wouldn't really be a swan at all.

To say that such an objection is besides the point is an understatement, and I would advise anyone who said such a thing to go and learn some logic.

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