Third possibility

[Speakpigeon]

Well yes, they are perfectly synonymous but only when applied to things that are applicable. When the applicability is lost, the distinction becomes relevant. Invalid implies not valid, but not valid does not imply invalid. It may as well imply it but only if applicable. For instance, a tree is not valid. Heck, what would it even mean to say that? From that, however, we oughtnt say that a tree is invalid unless a tree could be the kind of thing that could be either.

Deductive arguments are valid or invalid. Deductive arguments therefore are valid or not valid.

Inductive arguments are neither valid nor invalid, yet it's true they are not valid, and it's true they are not invalid.

You make a good point. True and not true are exhaustive, but true and false aren't, because some things aren't truth apt.

Exactly.

The only room for exception is when ambiguity rears its ugly head and a term is used in accordance with other meanings. For instance, X is not criminal, yet people disagree by invoking a clearly different meaning of the word, "criminal."

This is seriously confusing for me. I can't seem to be able to shake the impression that the way you're suggesting we should deal with this issue makes logical deductions that are not valid somewhat similar to trees.

As I see it, saying a tree is not valid isn't the same kind of statement as saying a deduction is not valid, whereby we could substitute anything to X in the proposition "X is not valid", regardless of what we mean by that. Saying a tree is not valid is really saying the qualifier "valid" doesn't apply to things like trees. Nothing like saying a deduction is not valid.

If you want exhaustive formulas, you need to reason within specific coherent contexts. Nothing like this mixed bag of deductions and trees.
EB

 

[Wiploc]

The only room for exception is when ambiguity rears its ugly head and a term is used in accordance with other meanings. For instance, X is not criminal, yet people disagree by invoking a clearly different meaning of the word, "criminal."

In that case, "invalid" and "not valid" both apply. The moral argument is based on that sort of equivocation, and the cosmological argument frequently uses it.

 

[fast]

The only room for exception is when ambiguity rears its ugly head and a term is used in accordance with other meanings. For instance, X is not criminal, yet people disagree by invoking a clearly different meaning of the word, "criminal."

In that case, "invalid" and "not valid" both apply. The moral argument is based on that sort of equivocation, and the cosmological argument frequently uses it.

What I mean is if and only if the technical usage of "valid" is used (and as such no inductive argument is valid), then although inductive arguments are not valid, they are not therefore invalid; however, a counter argument that utilizes "valid" with a common usage might yield a true statement regarding inductive arguments as invalid, but such a counter argument would be based on a foundation of ambiguity resulting in talking past one another.

 

[Wiploc]

Okay, that works.

 

[fast]

Okay, that works.

Thank you.

So, if there is a law that permits violence against women on courthouse grounds and I say that such an act is not criminal (as it's permitted by law), I am not therefore incorrect even if violence against women regardless of location is criminal (per some moral law).

The denial that I am correct is improper because that word merely has an alternate meaning where I would be incorrect had I used it the alternative way. It's tricky. I can assert something, but we oughn't allow multiple meanings factor into the assessment of the truth value of my assertion. The ambiguity is highly misleading even when recognized, as it gives people the impression that the statement is equivalent with the sentence.

For instance, "the bank is by the river." Is that true? Even though it's true that "the bank2 is by the river," that is wholly irrelevant since the proposition originally expressed was "the bank1 is by the river."

Bank1--financial institution
Bank2--raised land near water

Context disambiguates such that in context, had I provided some, you might have gleaned I meant bank1. Now that you know I mean financial institution, you and I may be on the same page, but other people (many people) still feel the need to disagee simply because a word CAN and DOES have other meanings, as if the ambiguity of the word allows for disagreement EVEN WHEN they know what I mean by what I say.

We see this all the time. I can be explicit and express clearly that by "possibility" I mean physical possibility, yet because others recognize that "possibility" can refer to logical possibilities, others will deny I am correct when claiming that something is impossible.

 

[humbleman]

All of this still is confused to me... I can't discern if what you claim really has inpoint or has no point.

 

[fast]

All of this still is confused to me... I can't discern if what you claim really has inpoint or has no point.

Don't think the tree dislikes you merely because it doesn't like you.

 

[Speakpigeon]

Well, careful here, this doesn't disprove the fact that even trees dislike him.
EB

 

[humbleman]

Well, careful here, this doesn't disprove the fact that even trees dislike him.
EB

Who loves ya, baby?

 

[Don2 (Don1 Revised)]

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.

I'd call one pair "extremes." The excluded middle is in between. The other pair disjoint, [mutually] exclusive, orthogonal or some such other term to convey sets that do not overlap, my preference being mutually exclusive as it has a certain connotation.

 

[steve_bank]

As definition practical and impracticle are mutually exclusive if based on probabilities and technical analysis.

In the greater real world based on experience impractical may a view based on limited experience and practical to someone may be overly optimistic. The subjective is always contextual and relative.