Interesting topic. Immediate inference by converse relation seems to work with some relations but not others. An example where it doesn't seem to make sense is this: "Every boy loves some girl", and the converse relation is "Some girl is loved by every boy". But this doesn't have the same meaning as the first statement.

Hi Mike - I would express the relation "X is bigger than Y" as "X is bigger than Y"! There is no question of changing this into an Aristotelian proposition "X is [bigger than Y]" - this is not the point. This proposition "X is bigger than Y" is treated by ordinary language logic exactly as it stands, or even as "X > Y". The only difference is that we should not engage in pretentious claims that symbolizing it in accord with the conventions of modern logic somehow magically makes it something special, more profound, like some sort of incantation. Behind symbols are always ordinary language. Thus, the claim that modern logic brings something new to logic that classical logic cannot handle is just so much hype.

Hi Student,
sorry I took so long replying to your question (two years)! I must have missed it.

I just want to inform you that in my new book, A Fortiori Logic, published in late 2013, in Appendix 7, you will find further critiques of Modern Logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox.

Thinking about this and after doing a little searching online, it seems there is a name for this fallacy -- it's called quantifier shift.

https://en.wikipedia.org/wiki/Quantifier_shift

The problem is in the ambiguity of "some". In the statement "Every boy loves some girl" does it mean some particular girl or "some girl or other"? If the latter, then every boy could be loving a different girl.

Actually, it seems to me that IF the statement is true (however you interpret "some"), then it does follow that "Some girl is loved by every boy".

ie,

first case:

Every boy loves some (particular) girl
Therefore, Some (particular) girl is loved by every boy

second case:

Every boy loves some girl or other
Therefore, Some girl or other is loved by every boy

The fallacy only arises when the meaning of "some" in the conclusion is different from its meaning in the premise.

Change of meaning of a term is obviously fallacious, and rather common.

Regarding your specific example and comment, '"Every boy loves some girl", and the converse relation is "Some girl is loved by every boy". But this doesn't have the same meaning as the first statement.' - my feeling is that the two are identical, really, because you could reverse the order of 'conversion' (as you call it). This sort of 'conversion' is, to my mind, just a change in the order of wording, but not really logical conversion.

Like saying, "her, I love" instead of "I love her" - just a small change of emphasis perhaps.

Something about you (optional) logician-philosopher