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!
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Sign up to join this communityWhat'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"]).
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.