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I have a disagreement with someone about the logic of an argument. He says the statement "if it doesn't affect you, then you shouldn't care about it" is not an invitation to substitute "it" with "X" because we're arguing about a specific subject. I said that the subject doesn't matter, because the logic has to work out despite the subject. We can form the logical implication "if X doesn't affect you, then you shouldn't care about X." Both he and I agree that there are cases where X doesn't affect you, but you should still care about X, specifically a murder across the country. He says that while that's true, it has nothing to do with the current topic and is irrelevant. I said that maybe the logic works out in one case, but by substituting in that murder across the country for X, we see that the logic of the argument itself is contradictory.

So am I missing something here? To me it seems obvious that the logic has the work regardless of what your subject is, but I can't think of how to explain that, so it has me questioning if it's true that it has to work out no matter what.

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  • You are confusing the validity (a purely formal property that abstracts from all subject-matter) with soundness. To detect whether the argument is valid, you would need to do exactly as you suggest and see whether the argument follows regardless of subject-matter. But your friend is not committed to the claim that "for all x, if x doesn't affect you, then you shouldn't care about x." He's only committing to that for a specific value of x. The question of whether his commitment to that claim is appropriate is a question of whether his premise is true, not whether his argument is valid.
    – transitionsynthesis
    Commented Feb 9, 2021 at 19:34
  • @transitionsynthesis Thanks for the reply, this was helpful. So then what is the utility in saying that an argument is formally invalid? We're actually not arguing ourselves, but arguing about two other people's argument (I'll call them A and B). A said "if it doesn't affect you, you shouldn't care about it." B said "that's a formally invalid argument." Is B not arguing correctly then?
    – Nick Calabrese
    Commented Feb 9, 2021 at 20:01
  • In addition to what transitionsynthesis said, real world arguments are typically informal. This means that they do not need to be formally valid to be valid, because they may rely on some field-specific forms that are not universal, like modus ponens, but hold within that field, see argumentation theory. For example, inductive arguments are common and legitimate in science, even though they are formally invalid. So B's remark is insufficient even if correct, one needs to investigate informal validity.
    – Conifold
    Commented Feb 9, 2021 at 21:05
  • If logic would work in such arguments, all humans would have the same religion, vote for the same political party, but the same products, eat the same food.
    – tkruse
    Commented Feb 14, 2021 at 0:35

2 Answers 2

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A real-world argument doesn't just involve the statements explicitly made, but also the implicit context the participants place those statements in. One obvious point here is the implicit referent of "it," and this is a piece of context you agree on. However, there' is also the issue of the implicit justification for the statements being made along the way. Usually an argument as actually had (as opposed to a rigorous deduction in formal logic) does not state explicitly, at each step, the reason why a given statement follows from the previous ones. Some of this reasoning is swept under the rug.

This becomes an issue if, in a situation where the specific justification is glossed over, the participants have different "default interpretations." That seems to be what's happening here. Specifically, does

"If it doesn't affect you then you shouldn't care about it"

mean

"If topic A specifically doesn't affect you, then you shouldn't care about it because you generally shouldn't care about things which don't affect you,"

or

"If topic A specifically doesn't affect you, then you shouldn't care about it because of [specific feature about topic A],"

or something else?

Your instinct seems to be to assume a general claim as the default - since no particularity of topic A was brought up, you're assuming the justification to be the general principle "If a thing doesn't affect you then you shouldn't care about it." It seems that your friend is not taking the same stance - maybe they have in mind some "obvious" fact about topic A which "obviously" means that you shouldn't care about it if it doesn't affect you.

So it's not really fair to say that the argument is or is not valid, since there is no single argument at issue here; rather, you have a shared "summary" of an argument, but disagree about the actual "complete" argument it is ideally summarizing.

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It's very simple. Of course you guys were using natural languqge in your conversation. A language that can be translated to a formal language (i.e. propositional calculus) in many different ways. A natural language is not precise in a way a formal language is.

So in your informal conversation you were using a sentence: "if it doesn't affect you, then you shouldn't care about it".

You yourself translated it to a proposition with one free variable: "if x doen't affect you, then you shouldn't care about x".

Your friend translated it to a proposition with a variable already substituted: "if A doen't affect you, then you shouldn't care about A".

I'm sorry, I'll paraphrase your question:

Does a word "something" denote the same object as the word "apple"?

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