Logical Vulcan take II Rob Zook Wed, 07 Jan 1998 17:34:40 -0600 Hi all, I've been thinking about what Saul said when I talked about having separate logical connectives for sentences. After trying to work it out, I'm going to back off from that idea. I was thinking it might make it easier to express complex logic, but I have come on a better method. In a complex logical argument, one could do as one does in prepositional calculus, and assign a variable to a statement. So I propose using the Vulcan consonants, plus uu, as basic variables: puu, tuu, buu..,etc. So in a complex statement one would assign each statement to a variable and then demonstrate the relationship as a variable. So in Formal Vulcan one probably should demonstrate a proper logical form, or it's not acceptable grammar. To elucidate this with an example, I had to come up with a few more grammar words. So let's back up a second, and see how we could do simple categorical logic with Vulcan: All Vulcans have green blood Spock is a Vulcan Therefore, Spock has Green blood ats whl'q'n,dii krupat'oram plak'at its whl'q'n spok,cee aaz spok krupat'oram plak'at ats, its, and aaz act as "syllogistic operators", if you will. Identifying the major premise, minor premise, and conclusion of a syllogism. In formal Vulcan, one should probably not consider a syllogism grammatically correct, unless it has a valid form. For those of you not familiar with syllogisms, I'll review a bit. A syllogism has three terms each used exactly twice. The minor term is the subject of the conclusion. The major term serves as the predicate of the conclusion. The remaining term is called the middle term. The major premise links the middle and the major term. The minor premise naturally links the middle term and the minor term. The conclusion, of course, links the major and minor terms. So, in the above argument, the major term is "green blood", the minor term is Spock, and the middle term is Vulcan. I created the suffix -dii to indicate "universal affirmation", and the -vu suffix indicates "particular affirmation". They correspond to "all" and "some" respectively. While ni- by itself would act as a "universal negation", and ni- + -vu as "particular negation". Universal affirmation: whl'q'n,dii krupat'oram plak'at "All Vulcans have green blood" Universal negation: niwhl'q'n krupat'oram plak'at "No Vulcan has red blood" Particular affirmation: whl'q'n,vu krupat'oram plak'at "Some Vulcans have green blood" Particular negation: whl'q'n,vu nikrupat'oram plak'at "Some Vulcans do not have green blood" The -cee suffix I created to act as a categorical non-logical connective. It roughly means, "is a member of a catagory/class". The words with the connective, would be members of the catagory or class, and one uses it with a categorical type word, to make an assertion that Y X,cce, or X is in the category Y. For example: whl'q'n spok,cee sarek,cee sybok,cee "Spock, Sarek, and Sybok are all Vulcans". Now we can move to prepositional calculus, or symbolic logic to see those variables I spoke of earlier, in more detail. In formal Vulcan a statement can also be considered grammatically correct if it consist of a valid argument form. One such form, for example, we call Modus Ponens. It consist of the form: p --> q p --------- q Or in English: "If p then q. p therefore q". Where p and q both represent full statements. Now I will propose some more Vulcan grammatical particles, ci, ic and ^. Ci and ic act as starting and ending parenthetical particles. ^ acts as a seperator between the premises of a non-syllogistic argument. For example: "If Spock is a Vulcan then Spock has green blood. Spock is a Vulcan, therefore Spock has green blood." puu ci whl'q'n spok,cee ic tuu ci spok krupat'oram plak'at ic puu'ek tuu'ek ^ puu'a aaz tuu This works equally well with all of the standard argument forms. Let's do another example - a Hypothetical Syllogism: p --> q q --> r -------- p --> r "If Spock is a Vulcan then Spock has green blood. If Spock has green blood then Spock is not a human. Therefore if Spock is a Vulcan then Spock is not a Human." puu ci whl'q'n spok,cee ic tuu ci spok krupat'oram plak'at ic buu ci komi spok,nicee ic puu'ek tuu'ek ^ tuu'ek buu'ek aaz puu'ek buu'ek Now as the arguments get more complicated, one can see how presenting an argument thusly (in 137* characters) seems much clearer and simpler than: ci whl'q'n spok,cee icek ci spok krupat'oram plak'at icek ^ ci spok krupat'oram plak'at icek ci komi spok,nicee icek aaz ci whl'q'n spok,cee icek ci komi spok,nicee icek Which counts up as 171* characters, 20% more than the other example, and no where near as simple in structure. One could also do the same kind of abstracting of the arguments terms with a large syllogism: All Vulcans have green blood Spock is a Vulcan Therefore, Spock has Green blood at krupat'oram plak'at it spok ot whl'q'n ats ot,dii at its ot it,cee aaz it at The terms at, it, and ot refere to the major, minor and third terms, respectively. The abstracted example counts up to 81* characters, the first example of a syllogism had 87* characters. So with larger syllogism that disparity in size would increase. Also one can easily tell the mood and figure of each syllogism. The above would be: AII-1 form of syllogism, which is valid, and therefore grammatically correct. Now the problem with the abstracted form comes in when Vulcans would try to speak like this to humans. In the written form, both races should easily be able to see the structure. But humans have difficulty holding information in short term memory for any period of time. Human short term memory also can only hold a notoriously small amount of information. So if I spoke the above syllogism to another human, they may forget what at, it, or ot represents by the time I get to the aaz. Which may make Vulcan a little harder for humans to learn (not necessarily a bad thing, IMHO). Rob Z. * I used the UNIX command wc to do that counting, so the Vulcan forms would really have less characters than that, since characters like /uu/ or /aa/ would only appear as one character in written Vulcan, and one sound in spoken Vulcan. However, the abstracted form would still come out as having less characters, and in the same proportions. -------------------------------------------------------- Outside of a dog, a book is a man's best friend. Inside of a dog, it's too dark to read. -- Groucho Marx