fast
Contributor
I'm looking for a quick and concise way to convey a distinction. Ultimately, I need two words, one to describe a particular relationship and one to describe a different relationship.
Before I go into great detail, let's take a journey through categorizational rules of mutual exclusivity and collective exhaustivity, especially the latter, as that's the relevant one for this discussion. There are two numbers in this world: 17 and not 17. Those are the only two options. Don't think so? Give me a number that is not 17 and it'll belong in the not 17 category. Silly, but still, the groups are collectively exhaustive. That's important, and it takes the form of A and Not A. Two possibilities max.
Two groups: natural blonde and natural brunette. That's not collectively exhaustive. Throw in "other" and wallah, collectively exhaustive!
Terms that are opposites, however, are not collectively exhaustive.
Cold and hot isn't, but cold and not cold is.
Practical and impractical isn't, but practical and not practical is
Happy and sad isn't, but happy and not happy is
True and false isn't, but true and not true is
Deductive argument and inductive argument isn't, but deductive argument and non-deductive argument is
Valid and invalid isn't, but valid and not valid is
Punk ass sissy and bad ass dude isn't, but punk ass sissy and not punk ass sissy is
Let's take valid and invalid as an example to explore further. I'm not looking to argue my case. I know I'm right and that's not even the issue. The issue is how do you describe valid vs invalid, and how do you describe valid vs not valid?
In other words, let's say I want to draw attention to an alternate outlook. If an argument is invalid, it's not valid, but the inverse is not necessarily true. Consider an inductive argument that is neither valid nor invalid. It's still the case they are not valid and not invalid. Yes, I'm well aware of the dictionary definitions. The point here isn't to argue my case--just to highlight the distinctions presented.
Category errors can be relevant. If something cannot be one thing or it's opposite, it can still not be one thing and not the other. Let's do another example. It's impractical to cut an acre of grass by hand with scissors. Because there's no category error, there's good reason to consult a dictionary and equate impractical with not practical. If we're dealing with deductive arguments and find that one is invalid, it's reasonable to conclude that it's not valid. However, with category errors, it's a mistake to conclude equivalence. A sentence that is pure garblygook does not express a true proposition, nor does it express a false proposition, yet it's still the case the sentence is not true just as it's the case the sentence is not false. It's neither true nor false.
Is 8 compatible with food? That doesn't make any sense. We shouldn't say it's compatible anymore than we should say they're incompatible. But, you can say they're not compatible without implying they're incompatible. I can say the tree doesn't like me without implying the tree dislikes me. A tree neither likes nor dislikes. My shoe isn't sad, but that doesn't imply my shoe is happy. My shoe isn't happy, but that doesn't imply my shoe is sad.
So, how would you describe the relationship between practical and impractical? Opposites? Okay, how about practical and not practical? Not the same because there is an implication with impractical that isn't present with not practical. Never mind your agreement or disagreement. If you say something is impractical, then practicality has to be a logical possibility. The goal is to describe the relationship. If something can't be happy or sad, then being opposites not one fails to imply the other.
Before I go into great detail, let's take a journey through categorizational rules of mutual exclusivity and collective exhaustivity, especially the latter, as that's the relevant one for this discussion. There are two numbers in this world: 17 and not 17. Those are the only two options. Don't think so? Give me a number that is not 17 and it'll belong in the not 17 category. Silly, but still, the groups are collectively exhaustive. That's important, and it takes the form of A and Not A. Two possibilities max.
Two groups: natural blonde and natural brunette. That's not collectively exhaustive. Throw in "other" and wallah, collectively exhaustive!
Terms that are opposites, however, are not collectively exhaustive.
Cold and hot isn't, but cold and not cold is.
Practical and impractical isn't, but practical and not practical is
Happy and sad isn't, but happy and not happy is
True and false isn't, but true and not true is
Deductive argument and inductive argument isn't, but deductive argument and non-deductive argument is
Valid and invalid isn't, but valid and not valid is
Punk ass sissy and bad ass dude isn't, but punk ass sissy and not punk ass sissy is
Let's take valid and invalid as an example to explore further. I'm not looking to argue my case. I know I'm right and that's not even the issue. The issue is how do you describe valid vs invalid, and how do you describe valid vs not valid?
In other words, let's say I want to draw attention to an alternate outlook. If an argument is invalid, it's not valid, but the inverse is not necessarily true. Consider an inductive argument that is neither valid nor invalid. It's still the case they are not valid and not invalid. Yes, I'm well aware of the dictionary definitions. The point here isn't to argue my case--just to highlight the distinctions presented.
Category errors can be relevant. If something cannot be one thing or it's opposite, it can still not be one thing and not the other. Let's do another example. It's impractical to cut an acre of grass by hand with scissors. Because there's no category error, there's good reason to consult a dictionary and equate impractical with not practical. If we're dealing with deductive arguments and find that one is invalid, it's reasonable to conclude that it's not valid. However, with category errors, it's a mistake to conclude equivalence. A sentence that is pure garblygook does not express a true proposition, nor does it express a false proposition, yet it's still the case the sentence is not true just as it's the case the sentence is not false. It's neither true nor false.
Is 8 compatible with food? That doesn't make any sense. We shouldn't say it's compatible anymore than we should say they're incompatible. But, you can say they're not compatible without implying they're incompatible. I can say the tree doesn't like me without implying the tree dislikes me. A tree neither likes nor dislikes. My shoe isn't sad, but that doesn't imply my shoe is happy. My shoe isn't happy, but that doesn't imply my shoe is sad.
So, how would you describe the relationship between practical and impractical? Opposites? Okay, how about practical and not practical? Not the same because there is an implication with impractical that isn't present with not practical. Never mind your agreement or disagreement. If you say something is impractical, then practicality has to be a logical possibility. The goal is to describe the relationship. If something can't be happy or sad, then being opposites not one fails to imply the other.
