https://www.reddit.com/r/askphilosophy/comments/1iblhc2/what_makes_an_argument_valid/
created by JackOnTheBox_ on 27/01/2025 at 22:02 UTC
22 upvotes, 4 top-level comments (showing 4)
I'm currently a month into an Intro to Logic course, and I still can't seem to wrap my head around some cases of valid arguments. I was doing an assignment for the course surrounding validity and soundness of arguments and two questions stood out to me that I didn't quite understand even after answering them correctly Could anyone explain to me the reasons that make these two arguments valid? The first is "2+2=5. Therefore, the moon is made of cheese." and the second is, "The moon is made of cheese. Therefore, 2+2=4." I was reading an earlier post on this subreddit about a similar case and I feel like I almost understood the reasoning, but I am not sure.
The best I could do to explain it to myself is that since 2+2 does not actually =5 then the premise could never be true, meaning that the premise being true and the conclusion being false would never occur. For the second one, I understood it as; since 2+2 always =4 no matter what the premise is, the conclusion will always be true, making it valid.
Am I going about this the right way?
Comment by AutoModerator at 27/01/2025 at 22:02 UTC
1 upvotes, 0 direct replies
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Comment by drinka40tonight at 27/01/2025 at 22:16 UTC
27 upvotes, 4 direct replies
You pretty much got it. An argument is valid if and only if it's not possible for the premises to be true and the conclusion false. Read that several times and really try to understand it.
Take this example:
1. 2+2=5
2. Therefore the moon is made of cheese.
Now, consult the above definition. Is it possible for the premises to be true and the conclusion to be false? No, because it's not possible for the premise to be true. 2+2=5 is necessarily false, it cannot be true, it's not possible for it to be true.
1. The moon is made of cheese.
2. Therefore 2+2=4.
It's not possible for the conclusion to be false. So, "it's not possible for the premise to be true and the conclusion to be false." And so it's valid.
Comment by Angry_Grammarian at 28/01/2025 at 06:55 UTC
2 upvotes, 0 direct replies
You got it.
Just remember that the system is designed so that one thing can't happen: we can't have true premises lead to a false conclusion.
That would be really bad, right? We input truth and our system outputs falsity. A system like that would be worthless. So, in our system, that's the one thing that can't happen. Everything else is fine, as far as structure is concerned.
Comment by ConceptOfHangxiety at 27/01/2025 at 22:14 UTC*
2 upvotes, 1 direct replies
The two examples you provide are odd to me, since they are both one premise and a conclusion. Ordinarily, we would have two premises and a conclusion. This is not to say that we can't have one premise arguments--but I don't see how your two examples work here (although this might be a failing on my part).
But to answer your question, there are two ways to think about logical validity.
1. An argument is logically valid *if* accepting the truth of the premises means that the conclusion *must* be true.
2. An argument is logically invalid *if* accepting the truth of the premises *and* rejecting the truth of the conclusion would lead to a logical contradiction.
Logical validity has precisely nothing to do with the actual truth or falsity or the premises or conclusions being examined.
I guess that these will not be satisfactory clarifications, so please ask follow up questions.
EDIT: I am not a logician, so defer to other answers.