What's the correct interpretation of "seemingly universal" statements that do not use quantifiers?
For example, p:"Roses are red". Is this equivalent to q:"All roses are red."? What's the correct way of representing p in an Euler diagram?
Thanks!
"Correct" is a bit of a loaded term here.
Arguably, the correct way is to say that the English is ill-formed for use in quantified logic or at best unclear as to whether it is making a universal claim.
Probably, the simplest rendering will be seeing it as equivalent to "all roses are red." See "girls are humans."
But it might be "many roses are red" or the even weaker "at least one rose is red."
if it's homework and the person insists its well-formed, then I'd go with all roses are red but I'd also want to raise the problem of translation on this example. (sentences are not the same as logical claims or statements [depending on how you use "claim" or "statement"]).
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I see. I usually encounter such statements being used as premises on problems related to valid arguments form. Obviously, the unclarity arises once you try to express the statement as an Euler diagram because you only have Euler D representations for statements with All, Some, No/None, at least in texts that I read. In practice, I just interpret them (i.e., assumed) as universal statements. I asked this question now to check if what I'm doing is ok. Thanks! – ultrajohn Sep 19 '19 at 1:51
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1My take: it's generally okay. But sometimes people pedantically either insist that is correct or that it is completely wrong because it's ambiguous in the meaning of the words. It's one of the many places where the lesson is that natural language and its logical translation are not perfectly identical. – virmaior Sep 19 '19 at 2:16
It's ambiguous between "Some" and "all" in English. We use natural language weirdly, we use universal claims as metaphors for "a lot of roses" or "most roses", and the context decides things.
You could give both the existential quantifier and universal quantifier interpretations and say they're both possible readings of the sentence.
