Word games #2) Fallacies in Symbol Replacement

[Dissident Dan]

This is the first thread in what may or may not be a series, depending on logical topics that I think need to be addressed.
I want people to understand the fallacies of certain "word games" so they can stop wasting time with fallacioius arguments.

Let's start with what I call symbol replacement. There is probably some official philosophical term, but this is a nice, simple description.

1. 
   A fallacy occurs when you have multiple different things associated with the same symbol, and then equate the two. This is usually done in a syllogism. A syllogism is the following logical construct: A implies B, and B implies C, so A implies B. The notation would be (A->B /\ B->C)->(A->C).
   [/list=1]
   
   Let me use some examples of fallacious arguments to demonstrate. In these examples, do not concern yourself with the truth of the premises, but with whether or not the conclusion logically follows from the premises.
   
   1. 
      Premises
      1) Johnny is not objective in his reporting.
      2) All that exists exists objectively.
      Conclusion
      Therefore, Johnny does not exist.
      [/list=1]
      
      Now what is wrong with this argument? It appears valid. However, there is a problem with the word "objective." "Objective" has a different meaning for Premise 1 from what it means in Premise 2. Therefore, you cannot connect the two statements through this word, "objective." Therefore, you cannot draw the given conclusion from these premises.
      
      • 
        Premises
        1) If you are a female with big breasts and a thin waist, then you are hot.
        2) If you are hot, then you do not need to put on a coat.
        Conclusion
        If you are a female with big breasts and a thin waist, then you do not need to put on a coat.
        [/list=2]
        
        Here, we have a seemingly valid argument by looking at the relationship between the different symbols (words). However, the same symbol is used to refer to two different concepts, so this symbol cannot be used to make the connection between the two premises.
        In the first, "hot" means "sexually attractive."
        In the second, "hot" means "high in average kinetic energy."
        
        So, this is actually not an (A->B /\ B->C) set of premises, but an (A->B /\ C->D) set of premises.
        
        Obviously, woman can be sexy and still require a coat, even if you agree with the premises.

 

[jammieg]

So you are saying the main problem with logical propositions are in the imprecise defenitions of those things, I agree that seems to be the main problem.
Within each try there were two outcomes.
I saw this picket sign that read "diversity is a factor because racism is a factor",
trying to avoid the politics of it,
it is illogical to assume that racism(in the broad sense of believing one's own group to be superior to others in some aspect) and irrational based discrimination are the primary causes that lead to inequality(of income or social postion). It is illogical to assume that adhereing to diversity alone as a factor in admission to something would bring about a long term countering affect to discrimination and so lead to a perfect correction of inequality, and won't there always be inequality among groups? If there wasn't would we still call them groups?
Basically, what are all the factors? How can a sound solution be reached while only considering one unquantified factor? And then only one unquantified factor in the solution? Where's the whole equation?
And, at what point does diversity
based on skin tone or webbed feet or long noses become more discriminating and an ineffective solution? Anyway it's entirely too complex to reduce to a picket sign.

 

[quantumdude]

Dan, FYI the fallacy in your post in the Fallacy of Equivocation. It is one of the most rampant ones at PF's Philosophy forum. For many, many examples, see Lifegazer's thread entitled Relativity.

 

[Mentat]

Originally posted by Dissident Dan
This is the first thread in what may or may not be a series, depending on logical topics that I think need to be addressed.
I want people to understand the fallacies of certain "word games" so they can stop wasting time with fallacioius arguments.

Let's start with what I call symbol replacement. There is probably some official philosophical term, but this is a nice, simple description.

1. 
   A fallacy occurs when you have multiple different things associated with the same symbol, and then equate the two. This is usually done in a syllogism. A syllogism is the following logical construct: A implies B, and B implies C, so A implies B. The notation would be (A->B /\ B->C)->(A->C).
   [/list=1]
   
   Let me use some examples of fallacious arguments to demonstrate. In these examples, do not concern yourself with the truth of the premises, but with whether or not the conclusion logically follows from the premises.
   
   1. 
      Premises
      1) Johnny is not objective in his reporting.
      2) All that exists exists objectively.
      Conclusion
      Therefore, Johnny does not exist.
      [/list=1]
      
      Now what is wrong with this argument? It appears valid. However, there is a problem with the word "objective." "Objective" has a different meaning for Premise 1 from what it means in Premise 2. Therefore, you cannot connect the two statements through this word, "objective." Therefore, you cannot draw the given conclusion from these premises.
      
      • 
        Premises
        1) If you are a female with s and a thin waist, then you are hot.
        2) If you are hot, then you do not need to put on a coat.
        Conclusion
        If you are a female with s and a thin waist, then you do not need to put on a coat.
        [/list=2]
        
        Here, we have a seemingly valid argument by looking at the relationship between the different symbols (words). However, the same symbol is used to refer to two different concepts, so this symbol cannot be used to make the connection between the two premises.
        In the first, "hot" means "sexually attractive."
        In the second, "hot" means "high in average kinetic energy."
        
        So, this is actually not an (A->B /\ B->C) set of premises, but an (A->B /\ C->D) set of premises.
        
        Obviously, woman can be sexy and still require a coat, even if you agree with the premises.

1. 1. • 
        
        Very well posted, Dan. However, isn't this just a product of the misuse of language? language (as many of the posters here know) is logically flawed at it's very heart (definitions) and is thus not the perfect way of conveying logical reasoning. However, it's all we've got. To add to this, it is much further limited by being in written form - with almost no indication of the tone, undertones, nuances, emotions, convictions, etc that the person would have expressed if they had been speaking to you verbally.

 

[quantumdude]

Originally posted by Mentat
However, isn't this just a product of the misuse of language?

Yes; all the informal fallacies are misuses of language.

language (as many of the posters here know) is logically flawed at it's very heart (definitions) and is thus not the perfect way of conveying logical reasoning.

In your quote above, you are touching on some insurmountable difficulties in communicatio. But what Dan is talking about is when the same word is used to denote two completely different concepts, and then he gives examples of when those different concepts are swapped mid-argument.

 

[Mentat]

Originally posted by Tom
In your quote above, you are touching on some insurmountable difficulties in communicatio. But what Dan is talking about is when the same word is used to denote two completely different concepts, and then he gives examples of when those different concepts are swapped mid-argument.

Yes, I know, however this could be a side-affect of our use of language. After all, if we communicated thoughts directly, we would never have such mix-ups, would we?

 

[quantumdude]

Originally posted by Mentat
After all, if we communicated thoughts directly, we would never have such mix-ups, would we?

Sure, and it could also be avoided by not allowing any word to have more than one meaning. But the latter is impossible in pracitce, and the former is impossible even in principle. So, Dan here is trying to admonish everyone to do something that is possible: be more careful.