I'm not aware of these phrases being the same. I took mathematical logic in graduate school many years ago and I've used logically sound to be something different than sound argument.
I'm not disagreeing that valid would have been a better word choice. I did clarify my meaning in a subsequent post. I rewrote my point without using either sound or valid in an effort to be more precise.
Sound and valid are terms of art in deductive logic. They have clearly defined meanings.
Validity means the form of an argument is such that it's impossible for its premises to be true while the conclusion is false i.e. if the premises are true then the conclulsion must be true. Validity is a formal property of arguments and the relationships between premises. An argument can be valid even if its premises are false.
Soundness means that an argument is valid and that the premises are true (and therefore the conclusion must be true).
These are standard terms that have been used for over a century. You're going to generate a lot of confusion if you choose to use them differently to everyone who has ever studied elementary logic.
Obviously I'm speaking in the vernacular and as I stated I used the terms as they meant to me.
Besides logically sound and sound argument aren't the same thing in my mind. One refers to soundness of logic and the other to soundness of the argument. And that was the essence of my point. There's a difference in talking about an argument and talking about the logic used. Logical fallacies are only useful in determining if the reasoning was flawed.
I didn't disagree with anything you wrote and even clarified my meaning so as to be clear. There is also the fact that, linguistically speaking, every person has a unique language. The meaning of words can vary slightly between people who nominally speak the same language. That's why I mentioned to me in my previous post.
Clearly I was not writing in a mathematically precise way. I took mathematical logic in graduate school many years ago but am not qualified to use all of the terminology in a mathematically precise way. But this is an internet forum and not a course in mathematical logic. The standards of rigor are not so strict. Hence my phrase to me ought to have sufficed as far as clarification.
> An argument can be logically sound but with a false conclusion.
That doesn't sound right. An argument is sound iff it is logically valid and its premises are true, right? From Wikipedia:
> In deductive reasoning, a sound argument is an argument that is both valid, and all of whose premises are true (and as a consequence its conclusion is true as well)
IIRC, in logic, an argument is essentially a function that takes premises and produces a conclusion. It's valid as long as the conclusion follows from the premises. The catch is that an argument being valid is not the same as the conclusion being true.
From my logic studies ten years ago I recall that an argument is considered 'Valid' if true premises must lead to a true conclusion (ie, no gaps in the logic); to be 'Sound', however, it must be Valid and have true premises.
This seems Valid to me so far. I guess the peer review (formal and crowd-sourced) will test for Soundness.
In logic, the soundness of a proof in fact has to do with its interpretation in some universe of discourse. To be sound, the argument has to be deductively valid, and its premises have to have true interpretations in the chosen world where it is applied.
Here we have a valid mathematical argument which is unsound in this world, where its assumptions do not hold up.
It's "logically sound" in the sense that it's sound by disjunctive introduction. For most people, that's not an interesting sense of "soundness" (you haven't told me anything interesting by saying "it's either cloudy or not cloudy" when I've asked you for the weather.)
A proper deductive argument that contains no errors will be valid, but it won't necessarily be sound if the premises are incorrect. In that sense deduction can most certainly be "wrong".
"Logically correct" and correct argument are oftentimes not the same thing. "Logically correct" but unpersuasive arguments oftentimes starts with wrong model of the world to which they then apply logical rules - e.g. ignores reality, rephrases 60% as "majority" and then proceeds to talk about them as "almost everyone", simplifies long complex theory into something misleadingly simple etc.
Kind of like when they logically explain you that x should be better then y, but you tried both and still remember x being a hell. May sound logical, but you know something is wrong.
sound argument
logically sound
I'm not aware of these phrases being the same. I took mathematical logic in graduate school many years ago and I've used logically sound to be something different than sound argument.
I'm not disagreeing that valid would have been a better word choice. I did clarify my meaning in a subsequent post. I rewrote my point without using either sound or valid in an effort to be more precise.
reply