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  566. Ary Bu  Suppletion might not work in the man/men example for historical reasons. I think of the past tense form of GO as suppletive ("goes", "going", "gone"... but... "went" !?!). GO and WENT have separate etymologies - English took forms from one word ("wenden") and shoved them into another word's ("gon") grammatical paradigm. However, man/men did not take its forms from another lexical item. Consider the history of English and Germanic. Initially, Germanic mann- took a regular plural ending -iz: *mann-iz. That little "i" influenced the pronunciation of the root "a" (assimilation, more specifically, Germanic "Umlaut"). For comparison, these are the German words for man/men: Mann, Männer (roughly pronounced Menner). Unlike German, English lost the plural noun ending on "men". That loss obscured the etymology of "men", giving the impression that the only factor is a vowel switch. English now has internal inflection where Germanic once had a suffix morpheme + assimilation in the root morpheme. Now we have three analyses: 1 morpheme analysis: "men" (unbreakable, and means something different than "man") "mice" (unbreakable, and means something different than "mouse") 2 morpheme analysis, using Germanic ROOT + UMLAUT: "man" + UMLAUT = "men" "mouse" + UMLAUT = "mice" Historical analysis, using suffix > assimilation > apocope: mann + iz > menn + iz > men When it comes to stem homosemy, "man" and "men" may belong to the same lexeme. But basic definitions of allomorph do not allow for changes in meaning, so "man" and "men" don't work like allomorphs of the same morpheme would. I hope this makes things a bit clearer (well, as clear as Umlaut can be... sheesh!).
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  628. I get you. You're taking a logic or math class, right? I'll assume so for this answer. Distributing universal quantifiers over a conjunction (P ∧ Q) works as you'd expect: (∀x)(Fx ∧ Gx) = (∀x)(Fx) ∧ (∀x)(Gx) If F and G are true of every element in domain, then F is true of every element in the domain and G is true of every element in the domain. "All cats and dogs" doesn't differ logically from "all cats and all dogs", if you don't mind the rough example. Distributing universal quantifiers over a disjunction (P ∨ Q) doesn't work: DANGER! : (∀x)(Fx ∨ Gx) =/= (∀x)(Fx) ∨ (∀x)(Gx) If F or G is true of every element in the domain, then F isn't necessarily true of every element in the domain and G isn't necessarily true of every element in the domain. The first means that for each individual x, F is true of x or G is true of x. The second one means that F is true of every x, or G is true of every x. "All the ones that are cats or dogs" does differ logically from "all the ones that are cats or all the ones that are dogs", to extend my rough example. Agreed? Imagine going through members of a set one by one. Conjunction expects you to take this one AND that one AND the next one... You end up with all of them. This is like the universal quantifier, which distributes nicely over conjunctions: (∀x)(Fx ∧ Gx) = (∀x)(Fx) ∧ (∀x)(Gx) Disjunction lets you go through the members and take this one OR that one OR the next one... You end up with one (or maybe more) of them. This is like an existential quantifier, which distributes nicely over disjunctions: (∃x)(Fx ∨ Gx) = (∃x)(Fx) ∨ (∃x)(Gx) Now the fun part. P → Q is equivalent to ~P ∨ Q. It's worth deriving this yourself if you don't see it right away, with truth tables or Venn diagrams for visual help. So your examples (∀x)(Fx → Gx) and (∀x)(Fx) → (∀x)(Gx) are equivalent to (∀x)(~Fx ∨ Gx) and (∀x)(~Fx) ∨ (∀x)(Gx). Now what was that we agreed to earlier about universal quantifiers and their distribution over a disjunction? ;) Let me know if this helps!
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