# How can I explain the distribution of an O proposition's predicate?

A student raised a tough question while I was teaching formal fallacies: couldn't the statement that "some cats are not tabbies" be made with confidence upon seeing a single cat that is not a tabby? Why would anything need to be known about the entire class of tabbies?

My first instinct was to say that his line of thought obverts the original proposition, making it essentially "some cats are non-tabby cats," which doesn't have a distributed predicate. How should he think of it instead, then? I've always had problems understanding or explaining O propositions at an intuitive level. Does it come down to existential import? Is it accurate to say, e.g., that you couldn't claim that the Holy Grail is not on my bookshelf unless you thoroughly searched it because it is unknown whether one or zero Holy Grails exist?

Does anyone have a better explanation for this?

• See Categorical proposition for the "cryptic" ref to "O propositions". – Mauro ALLEGRANZA Dec 12 '17 at 13:05
• And yes: a single example of a cat that is not tabby is enough to corerctly infer that "there are cats that are not tabbies". The issue of existential import is related to the inference from ∀x Ax to ∃x Ax. See also the post does-this-syllogism-by-russell-show-that-aristotelian-logic-doesnt-work. – Mauro ALLEGRANZA Dec 12 '17 at 13:13
• The "intuition" is: ¬∀x Tx is equivalent to ∃x ¬Tx. Thus, checking that in the room there is a Siamese cat, we can assert that "not every cat is a Tabby" that is equivalent to: "there is some cat that is not a Tabby". – Mauro ALLEGRANZA Dec 12 '17 at 13:19
• Regarding Holy Grail, it is a definite description that acts like a proper name. We know that HG does not exists; how to "manage" its "name" ? According to Russell's analysis: ∃x ((HGx and ∀y(HGy → y=x)) and MyBSx). The statement is false* because there are no Holy Grails (i.e. ¬∃x HGx). – Mauro ALLEGRANZA Dec 12 '17 at 13:55