All of this is clearly explained but forgot to mention that there are two types of conversion Simple conversion and partial conversion In simple conversion only particular affirmativ (i) and universal negative (E) proposition are valid A and O proposition cannot be converted in simple conversion in PARTIAL CONVERSION this can only be applied to A and E propositions The rules in partial conversion is the quality of the convertend is reduced from universal to particular A is to (i) E is to (O)
If you can please tell why O cannot have a valid conversion would be helpful, since Some P are not S seems logical for some S are not P. e.g. some boys are not poets -> some poets are not boys Is also similar?
That's true, I was shocked when I got a wrong mark when I converted "Asians are filipinos" to "some filipinos are asians". The correct answer is "Asians are filipinos" like how does a subset(filipino) envelop the whole set(asian)? Like, that does not preserve the same meaning as the statement before
Coming from a mathematical standpoint, inversion also works on E-type and I-type statements Inversion works in the following way Take the regular statements/claims and just term-complement both in the statement For example: A-type inversion: All A are B → All non-A are non-B E-type inversion: No A are B → No non-A are non-B I-type inversion: Some A are B → Some non-A are non-B O-type inversion: Some A are not B → Some non-A are not non-B If you replace A and B with some example terms, say A is dogs and B is cats, then it actually makes intuitive sense for E-type and I-type statements No dogs are cats, no non-dogs are non-cats (which by double negating the first term means All dogs are not cats) Some dogs are cats, some non-dogs are non-cats (You can take this to mean Some animals that are not dogs are also not cats) And like Conversion, there's no guarantee that the truth value for the inversion of an A and O statement will be the same.
Thanks for the comment! Unfortunately, this inference would be invalid for E- and I-type statements as well. This can be proven through the use of Venn diagrams (which I hope to make a video about in the future). For now, though, we can stick to coming up with counterexamples. Let's say, for "No A are B," that A stands for "dogs" and B for "cats" such that the statement is "No dogs are cats." The statement "No nondogs are noncats" wouldn't follow. This can be tricky to see because of the complements, but I think it's a bit clearer if we rephrase it as such: "There are no things that are not dogs that are also things that are not cats." But there are plenty of such things. For instance, my washing machine is a nondog that is a noncat. The "no nondogs" bit can't be double negated because the "no" just serves as a universal quantifier indicating the relationship between both categories - it isn't serving to negate the complement. As for I-type statements, this one threw me for a loop! That's because I found it impossible to think of any categories for which "Some non-A are non-B" would be false. There might be an example that I'm just not creative enough to think of. But even here we can prove with the use of Venn diagrams that the inference would be invalid. Even without, if inversion is defined as just swapping each term with its complement, then it should be equally possible to get from "Some non-A are non-B" to "Some A are B," and here we can easily find counterexamples. Consider: "Some nonparrots are nontrees." This is true, some things that aren't parrots are things that aren't trees. If we grab each term's respective complement, we get "Some parrots are trees," which serves as a counterexample.
Did you watch the whole video? He clearly says that Conversion is valid only for E and I, and that Contraposition is only valid for A and O. Check 11:51
O propositions never converts validly and A propositions convert accidentally and not simply like I & E. I came here because I was confused and needed help after bombing my last quiz and the first 30 seconds the video is wrong... thanks I'm now more stressed.
