A Logical Problem

[Eleatic Stranger]

BWSF = Better to Win with Small Force

If W then BWSF. If -W then -BWSF. Therefore, W or -W, BSF.

I thought leaving L in it's unsubstituted form was clearer to explain, but I agree that with you that because of statement #1, "L" is equivalent to "Not W (-W)"

Somehow there is a form fallacy being presented. I was promoting the idea that formal syllogisms relate to 3 variables...

If A then B. If B then C. Therefore, If A then C. But ES has presented one with 4: W, L, BWSF, BLSF, and perhaps a 5th one in the conclusion BSF.

Perhaps it is still 4 with W, -W, BWSF, and -BWSF but when I originally analyzed it this way it made me think like many others that it was a violation of the law of indirect reasoning: If valid reasoning from a statement S leads to a false conclusion, then S is false. And most of us feel Statement #2 is false. Still, for the king such a subjective statement might be true - so I decided my best argument was to call it ill-formed. And leaving the equivalence (L= -W) unsubstituted seemed the most clear.

Actually the form of the argument as presented is a fairly straightforward (and valid) one.... (Though it's hard to render in syllogistic form as it takes, obviously, four lines.)

It goes like this:

1. A Or B
2. If A Then C
3. IF B Then C
4. Therefore: C

Where, of course, A:"I win the battle"; B "I lose the battle"; and C "It is better to use a small force".

(The fact that A and B in this case seem like polar opposites defineable as the negations of the other term is nice, but really not relevant to the form -- all that is needed is that the premise is true, and in the fact that they are polar opposites just means that it's trivially the case that A or B has to be true.)

This means of course that if it isn't a good argument then the fallacy involved can't be a formal one.

 

[Atlas]

Oh poop.

Wait. What about my argument about the election?

If Republicans want to win then they should not vote for Kerry.
If Democrats want to lose then they should not vote for Kerry.
Therefore, win or lose, Republicans and Democrats should not vote for Kerry.

I noticed you didn't mention any flaws there.

Don't I get half credit or something?

 

[csense]

Given: All battles which are not won are battles which are lost.

If I am to win this battle, then it would be better to have won with only a small force.
It would be better to have won with only a small force because it is the strategy that will bring me the most prestige.
Therefore, to acquire the most possible prestige, I must battle with only a small force.

If I am to lose this battle, then it would be better to have lost with only a small force.
It would be better to have lost with only a small force because it is the only strategy that would still leave me with adequate protection.
Therefore, to insure I retain adequate protection, I must battle with only a small force.

You have to define win and lose...and you must define them quantitatively, as is everything else in the argument. This means that you can only define both negatively:

To lose [implies, infers, assumes] there are no units left to fight for the king...the soldiers are dead.

To win [implies, infers, assumes] there are no units left to fight for the other king...the other soldiers are dead.

Now plug it into the form that ES posted:

1. A Or B
2. If A Then C
3. IF B Then C
4. Therefore: C



Thus, and keeping in mind that the order of 2 and 3 is irrelevent:

3. If all the [kings] soldiers [in battle] are dead, then it is better to have lost with a small force. With better loosely defined as the least amount of casualties.

The statement makes sense.


2. If all the other [kings] soldiers [in battle] are dead, then it is better to have won with a small force.

The statement does not make sense.

Statement 3 is proposing in the negative and can be known.
Statement 2 is proposing in the positive and can not be known.

 

[Atlas]

You have to define win and lose...and you must define them quantitatively, as is everything else in the argument. This means that you can only define both negatively...

I'm still not entirely with you.

I think it's not about quantification but subjectivity. What if it weren't a king but a rotten old skinflint.

1.) My kids will grow up to be rich or poor.

2.) If they end up to be rich, then it would be better for them to have grown up deprived.

3.) If they end up to be poor, then it would be better for them to have grown up deprived.

4.) Therefore, rich or poor, It's best for them to grow up deprived.

(edit: Both the king and the skinflint make an error of completeness. For whatever reason, they manufacture a very tiny world of possibility and stop at the answer they structured into the design in the first place. That is, their conclusion is logical, for the same reason a blind man doesn't turn on the light. They're unable to see any more anyway.)

(edit2: I'm slipping back toward what I alluded to earlier. It's a violation of the law of indirect reasoning: If valid reasoning from a statement S leads to a false conclusion, then S is false. Where you and I agree Csense, is that Statement #2 is false. )

 

[Eleatic Stranger]

2. If all the other [kings] soldiers [in battle] are dead, then it is better to have won with a small force.

The statement does not make sense.

Statement 3 is proposing in the negative and can be known.
Statement 2 is proposing in the positive and can not be known.

And yet we can very easily propose states or introduce considerations in which it is clearly true that it is better to win with a small force.*

Also, defining victory as the death of all the other soldiers strikes me as significantly mistaken - victory is when the other army surrenders. By your definition of victory the Allies didn't win WWII.

There's no reason behind defining terms quantitatively -- and especially not defining them quantitatively in bizarre ways like that.

(*For instance, having to pay soldiers; or not wanting to tire out soldiers for potential future battles; or, yes, the impressive propaganda tool involved; and so on.

Note that all the second premise says is that it would be better -- ie, would be more beneficial -- to win with a smaller force than to win with a larger one. Unless similar considerations can be adduced in favor of winning with a large force I don't see that it's plausible to cast doubt on the second premise.)
-----------------------------------

Wait. What about my argument about the election?

If Republicans want to win then they should not vote for Kerry.
If Democrats want to lose then they should not vote for Kerry.
Therefore, win or lose, Republicans and Democrats should not vote for Kerry.

I noticed you didn't mention any flaws there.

Well, it's a structurally valid one, at least if taken sententially.
(It comes out looking something like:

1. If P then Q
2. If R then Q
3. Therefore: If (P And R) then Q.

Of course then it's obvious that the argument is just concluding that If (Republicans want to win and Democrats want to lose) then they should not vote for Kerry. Which is perfectly true, though entirely unlikely. It's not much of a paralell to the other argument though.)

 

[Atlas]

I'm not making any progress to the solution ES is has in mind. So I thought I'd confuse the issue once more with a parallel.

It's also a little like Pascal's unremembered, crumpled, and discarded first formulation...

1) There is either a heaven or not

2) If heaven exists, then the best life lived is a one of joyful hope as a Christian.

3) If heaven doesn't exist, then the best life lived is still one of joyful hope as a Christian.

4) Therefore, heaven or no, the best life lived is a one of joyful hope as a Christian.

Has this reasoning ever been debunked? Anyone?

The big difference I see in this and the king's battle is here statement 3 dismisses out all remaining possibility whereas with the king's battle it was statement #2. Is it nothing more than argument by assertion that we are entertaining?

 

[Skep]

It's also a little like Pascal's unremembered, crumpled, and discarded first formulation...

1) There is either a heaven or not

2) If heaven exists, then the best life lived is a one of joyful hope as a Christian.

3) If heaven doesn't exist, then the best life lived is still one of joyful hope as a Christian.

4) Therefore, heaven or no, the best life lived is a one of joyful hope as a Christian.

Has this reasoning ever been debunked? Anyone?

The big difference I see in this and the king's battle is here statement 3 dismisses out all remaining possibility whereas with the king's battle it was statement #2. Is it nothing more than argument by assertion that we are entertaining?

Well, in the case of Pascal's unknown syllogism, I'd have to say that both 2 and 3 are assertions. It does not follow that if there is a heaven that the best life lived "joyful hope as a Christian." (I don't mean that in the judgmental sort of way, I mean it in the formal sort of way. 2 and 3 are conclusions, not factual statements, so they don't belong unless they are proven with additional statements.)

Now, as for "Has this reasoning ever been debunked?" One has to ask, what reasoning? Pascal's Wager (which you loosely refer to) or your syllogism, which you have already pointed out is argument by assertion? Or, are you asking if there is a logical proof that living a life in hope of being rewarded by vengeful supreme being is pointless? (Say, the antithesis of Pascal's Wager...)

 

[csense]

I'm still not entirely with you.

I think it's not about quantification but subjectivity.

And you're not alone in this from what I've read of the responses. If you think it is about subjectivity though, or quality rather than quantity, then you'll likely find yourself in specious arguments without ever solving anything, and this is true because you can't compare the quantitative with the qualitative. They are both fundamental principles.

Witness:
I will either win or lose this battle.
2. If I win this battle, then it is better to have won with a small force.
3. If I lose this battle, then it is better to have lost with a small force.
4. Therefore, whether or not I win or lose, it is better to send a small force into battle

In the above argument, as it literaly stands, the phrase small force is identified as a quantity, not quality. If you now plug in qualitative definitions for the other terms, then......

 

[csense]

And yet we can very easily propose states or introduce considerations in which it is clearly true that it is better to win with a small force

Not according to the terms of the argument

Also, defining victory as the death of all the other soldiers strikes me as significantly mistaken - victory is when the other army surrenders. By your definition of victory the Allies didn't win WWII.

Ever see the movie Aliens?

The only way to be sure is to nuke the site from orbit

This is a true statement.
Now ask yourself why this is a true statement.

 

[csense]

There's no reason behind defining terms quantitatively -- and especially not defining them quantitatively in bizarre ways like that.

In addition to the other reasons concerning the inherent problems with comparative analysis of qualitative/ quantitative....

...it is the only way to be sure logically speaking.

 

[csense]

....But, don't let me spoil everybody's fun with simplicity, so, carry on.

 

[csense]

2 and 3 are conclusions, not factual statements, so they don't belong unless they are proven with additional statements....

Statements 2 and 3 are not conclusions...they are propositions.

edited to add: oops, sorry, I thought you were talking about the topic argument

 

[Atlas]

Well, in the case of Pascal's unknown syllogism, I'd have to say that both 2 and 3 are assertions. It does not follow that if there is a heaven that the best life lived "joyful hope as a Christian." (I don't mean that in the judgmental sort of way, I mean it in the formal sort of way. 2 and 3 are conclusions, not factual statements, so they don't belong unless they are proven with additional statements.)

Now, as for "Has this reasoning ever been debunked?" One has to ask, what reasoning? Pascal's Wager (which you loosely refer to) or your syllogism, which you have already pointed out is argument by assertion? Or, are you asking if there is a logical proof that living a life in hope of being rewarded by vengeful supreme being is pointless? (Say, the antithesis of Pascal's Wager...)

Welcome to the forum Skep. Good Post. I pretty much agree. I wonder if you'd compare the second statement of Pascal's unknown syllogism (I like that) with the Eleatic Stranger King's second statement.

Both to me are the same kind of short sighted assertion looking at a subjective best case scenario whose underlying reasoning is not presented.

My Pascal #3 statement is decidedly weaker. And the king's #3 statement sounds fairly prudent but we are forced to infer much that may not be implied.

[derail] Since you asked, I'm of the opinion that a life well lived is it's own reward and pretty much the only reward that one should expect.(Edit: As I reread you post, perhaps you didn't ask - Sorry.) [/derail]

 

[Atlas]

There's no reason behind defining terms quantitatively -- and especially not defining them quantitatively in bizarre ways like that.

In addition to the other reasons concerning the inherent problems with comparative analysis of qualitative/ quantitative....

...it is the only way to be sure logically speaking.

Csense, I started my considerations noting the inference I was making that you have made explicit. That is, it seemed clear from the first reading that the advantage of the small force in losing was in limiting the lives lost. Likewise on the plus side, winning with a small force may have you capture the other king and spirit him away in the night with no lives lost.

But we have no way of knowing if that was the king's calculus. I built two fairly clear syllogisms above from statements 2 and 3 assuming the king was interested in other thing besides his subject's lives.

Furthermore I presented a skinflint's syllogism that seemed in parallel with the king. There was perhaps a greediness implied by the skinflint that you may quantize but it may not have been in his calculation. He may honestly feel that depriving children makes them grow up mean and hard and ready for whatever the world throws at them.

Finally, ES has weighed in against assuming that your inferred underlying maning is necessary or correct.

I'll be interested in the answer. ES seemed to suggest there was a fallacy to be recognized and named here if the logic is flawed, and most of us agree it is.

This means of course that if it isn't a good argument then the fallacy involved can't be a formal one.

I think that was a hint. But not a big enough one for me.

 

[Skep]

Welcome to the forum Skep. Good Post. I pretty much agree. I wonder if you'd compare the second statement of Pascal's unknown syllogism (I like that) with the Eleatic Stranger King's second statement.

Both to me are the same kind of short sighted assertion looking at a subjective best case scenario whose underlying reasoning is not presented.

My Pascal #3 statement is decidedly weaker. And the king's #3 statement sounds fairly prudent but we are forced to infer much that may not be implied.

[derail] Since you asked, I'm of the opinion that a life well lived is it's own reward and pretty much the only reward that one should expect.[/derail]

Yes, I would compare the two propositions, but I think it is better to compare the original #2 with your Pascal's unknown syllogism #3 because both are the weak points. In the original, no reason is given why it should be better to win with a small force. (Many posters have given possible reasons, but the syllogism needs to stand on its own to be valid. (Oh, and no, I don't want to get into a deep argument about what "stand on its own" means in this post—maybe later.)) Likewise, in your Pascal's unknown syllogism #3 no reason is given why it should be better to live a hopeful Christian life when there is no afterlife.

As for Pascal's original wager, I'd have to say Pascal was hopelessly credulous. (In Pascal's wager, Pascal opined that the reward of heaven was so great and the cost of belief so small that the cost benefit ratio demanded belief, kind of like accepting a free winning Lottery ticket. Unfortunately for Pascal, his proposition is indiscriminate and requires that one believe any and all things that could be considered a large reward if the cost is small. And, given Pascal's definition of a small cost--a lifetime of giving one's mind, body, soul and hard cash over to the church--I'd say that were he around today he'd have to sign on to every religious and paranormal belief system there is. Or he’d have to settle for the most outrageous payout (Scient0logy?)

 

[csense]

Csense, I started my considerations noting the inference I was making that you have made explicit. That is, it seemed clear from the first reading that the advantage of the small force in losing was in limiting the lives lost.

And this limiting is expressed in the larger force [or difference of] that is inferred, which does not engage in battle, yes?

Now, the only way to be sure that the battle is over, is when there is no one left to do battle with...which is contingent to those doing battle only.

There is no other way to know that the battle is over other than quantitatively, and if you can't infer an end to battle, then the argument is unanswerable. Period.





Likewise on the plus side, winning with a small force may have you capture the other king and spirit him away in the night with no lives lost.

But we have no way of knowing if that was the king's calculus. I built two fairly clear syllogisms above from statements 2 and 3 assuming the king was interested in other thing besides his subject's lives.

Furthermore I presented a skinflint's syllogism that seemed in parallel with the king. There was perhaps a greediness implied by the skinflint that you may quantize but it may not have been in his calculation. He may honestly feel that depriving children makes them grow up mean and hard and ready for whatever the world throws at them.

I'll be interested in the answer.

Unless one is has complete understanding of the argument, then analogies only serve to confuse things.

I have little, if any, affinity for argument by analogy, and please don't take that as a personal insult.

 

[Skep]

A False Tautology

Actually the form of the argument as presented is a fairly straightforward (and valid) one.... (Though it's hard to render in syllogistic form as it takes, obviously, four lines.)

It goes like this:

1. A Or B
2. If A Then C
3. IF B Then C
4. Therefore: C

Where, of course, A:"I win the battle"; B "I lose the battle"; and C "It is better to use a small force".

I'd say you could simplify this even more. There are actually only two variables:

1) A or Not A
2) If A Then B
3) If Not A Then B
4) Therefore: B

In this case, because #2 in the full argument is flawed (B is not entailed by A (many posters have tried to justify why B should be true in #2, but this is the job of the argument and it fails to do so)) and the result is a false tautology.

Edit:

It seems like you could simplify this even more:

1) B

--with about as much justification...

 

[csense]

Finally, ES has weighed in against assuming that your inferred underlying meaning is necessary or correct.

ES is entitled to his/her opinion....I of course disagree.

It seems simple enough to me.....

 

[Atlas]

Re: A False Tautology

I'd say you could simplify this even more. There are actually only two variables:

1) A or Not A
2) If A Then B
3) If Not A Then B
4) Therefore: B

Did you mean..

1) A or Not A
2) If A Then C
3) If Not A Then C
4) Therefore: C

I think that's what you were getting at.

 

[Atlas]

And this limiting is expressed in the larger force [or difference of] that is inferred, which does not engage in battle, yes?

Yup.

I have little, if any, affinity for argument by analogy, and please don't take that as a personal insult.

Nope

I'm trying to find other attacks. This might be one

Argumentum ad ignorantiam (argument to ignorance). This is the fallacy of assuming something is true simply because it hasn't been proven false.

Might the king be guilty of this in his propositions?

I don't know... not particulary convincing. I'll keep looking.