From lojban-out@lojban.org Sat Jul 15 18:32:09 2006 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (qmail 49407 invoked from network); 16 Jul 2006 01:20:21 -0000 Received: from unknown (66.218.66.217) by m23.grp.scd.yahoo.com with QMQP; 16 Jul 2006 01:20:21 -0000 Received: from unknown (HELO chain.digitalkingdom.org) (64.81.49.134) by mta2.grp.scd.yahoo.com with SMTP; 16 Jul 2006 01:20:20 -0000 Received: from lojban-out by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G1vIu-0001ls-7e for lojban@yahoogroups.com; Sat, 15 Jul 2006 18:20:16 -0700 Received: from chain.digitalkingdom.org ([64.81.49.134]) by chain.digitalkingdom.org with esmtp (Exim 4.62) (envelope-from ) id 1G1vHc-0001kj-Me; Sat, 15 Jul 2006 18:18:58 -0700 Received: with ECARTIS (v1.0.0; list lojban-list); Sat, 15 Jul 2006 18:18:48 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G1vH9-0001ka-Ps for lojban-list-real@lojban.org; Sat, 15 Jul 2006 18:18:27 -0700 Received: from web81302.mail.mud.yahoo.com ([68.142.199.118]) by chain.digitalkingdom.org with smtp (Exim 4.62) (envelope-from ) id 1G1vH5-0001kS-Ay for lojban-list@lojban.org; Sat, 15 Jul 2006 18:18:27 -0700 Received: (qmail 13461 invoked by uid 60001); 16 Jul 2006 01:18:21 -0000 Message-ID: <20060716011821.13459.qmail@web81302.mail.mud.yahoo.com> Received: from [70.237.230.20] by web81302.mail.mud.yahoo.com via HTTP; Sat, 15 Jul 2006 18:18:21 PDT Date: Sat, 15 Jul 2006 18:18:21 -0700 (PDT) In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Spam-Score: -0.7 (/) X-archive-position: 12218 X-ecartis-version: Ecartis v1.0.0 Errors-to: lojban-list-bounce@lojban.org X-original-sender: clifford-j@sbcglobal.net X-list: lojban-list X-Spam-Score: -0.7 (/) To: lojban@yahoogroups.com X-Originating-IP: 64.81.49.134 X-eGroups-Msg-Info: 1:0:0:0 X-eGroups-From: John E Clifford From: John E Clifford Reply-To: clifford-j@sbcglobal.net Subject: [lojban] Re: A (rather long) discussion of {all} X-Yahoo-Group-Post: member; u=116389790; y=nmCvkmU9FGxto4y1gdT2J_f1_430yMIrvd9iRQwD4lCwkp6gEw X-Yahoo-Profile: lojban_out X-Yahoo-Message-Num: 26645 --- Maxim Katcharov wrote: > On 7/14/06, John E Clifford wrote: > > > > --- Maxim Katcharov wrote: > > > > > Could you expand the definitions with some examples or brief descriptions? > > > > > > > I send this along for corrections and questions before using it (in its revised form) to > > > answer > > > > Maxim's questions. > > > > > > > > Singular v. Plural Semantics > > > > > > > > Language: > > > > > > > > Variables: > > > > > > What's a variable? > > > > An expression that stands in the place of a name but may have a different referent on each > > occasion (hence the name of it). The useful ones are bound by quantifiers. (Lojban variables > > are, for example, {da, de, di}) > > > > > > Names: > > > > > > What's a name? > > > > > > An expression with a fixed referent. > > An expression is anything that tells us what is being related? An expression is a linguistic object (name, variable, predicate, relation, term, sentence). > > > > > > Predicates: > > > > Relation: Y > > > > > > What's the difference between a predicate and a relation? > > > > Predicates are one-placed *take one argument to make a formula), relations are more (in this > case, > > two). > > Relation: Alice [throws] the ball > Predicate: Alice [throws the ball] > > yes? Or does a predicate ignore the last bit ("Alice [throws]"), and > is therefore just like a relation, but only different in terms of > number? The main difference is in the number of objects involved. However, the example you give is typical of how one gets predicates from relations. > > > > > > Sentential connectives: ~, & (others by usual definitions) > > > > Quantifiers: E > > > > > > Putting quantifiers up here will lead to a limited > > > version/understanding of my position. A quantifier is just a certain > > > type of relation. Given an identity "the students", a quantifier is > > > (roughly) "['the students'] is [students] of number [zo'e]". > > > > We are modeling Lojban, whose quantifiers are first of all over variables, in just this > position. > > I have not incorporated into this simplified version any of the derivative uses of quantifiers > > (including enumeration), because they have no special properties (that I know of yet) > connected > > with the issue of singular versus plural. What do you have in mind? > > > > Language is a representation of thought. Well, I think it is a representation of information, of states of affairs. This need not be totally incompatible with your idea, but it does give a different slant on things. The notion of concepts was introduced partly to give some substance to your way of thinking about this, but now seems not to help. > I think that there is a > distinction between describing the consequences and describing what > actually occurs. The consequences of what? What actually occurs when? I've lost the context here. > Grant that "26 students" is actually a certain > identity, perhaps fitting "X of type 'student' of number 26". I can't grant it until I understand it. What is an identity by you? "26 students" is a noun phrase, presumably referring two a passle of students, numbering 26 in all, some thing(s) satisfying "are individually students and together number 26." What here is an identity? > We can > say that "26 students" is a set of 26, if this fits our purposes. The > fact that it is not anything like a set in the mind is irrelevant. > This describes a consequence - because of X, we can look at it as Y. "26 students" can be taken to name a set (with cardinality 26)for some purposes (e.g., to do semantics in this fashion). Does the rest mean that what is involved, what the phrase really refers to is not actually a set of any sort? What is it then (and don't say "an identity" until you have explained that)? How is being able to look at it as a set, even though it is not one (as the mind thinks of sets? or as it really is in the mind?), a consequence and of what? > I assert that there must be a one-to-one relation between things. I > can't imagine two things being related otherwise (perhaps you can?). "1-to-1" is a precise notion and so I think you may mean something else by it (it's a function whose converse is a function, that is, each thing is mapped in either direction onto only one thing). The normal relation is something that holds between one thing and several others, eachof which might be in that same realtion to other things, like "is a nephew of," say (I was at one time nephew to something like thirty people, who had about twenty other nephews). > At one end, you have something, and at the other end, you have > something else. Would each of these students be simply 'lifted' up > into the consciousness? I assume you mean "at the end of a relation." Well, yes, a relation is a set of ordered pairs (or some such) so in each pair there is just one thing from each end. but there can be other pairs in the relation with the same first member and others with the same second member, even though the remaining member is different. What is this "lifted up into consciousness" about -- I take it it is part of your psychologism, but I am not sure what it cashes out as. Is it something like "the speaker has a clear conception of each student?" Then, no probably not -- even on a psychological approach. > If so, then how would the mind determine what > to 'lift'? If there's nothing there besides the students, then how > does it know to lift those 26? Is it connected to each of them? The > response was no (it's a mass, after all). I've already elaborated on > how this is incorrect regardless (a human cannot conceive of that many > identities [...]). Since I don't know what "lift" means here, I can't answer these questions. I am inclined to think that, insofar as mentation is involved at all here, the process is a symbolic one: setting up a symbol thst takes them all in, without any attention to the details (who they are, say, or what exactly any one of them looks like). But that is from the pluralist point of view. I thought the singularist point (yours, so far as I can tell) was that the 26 constituted a separate object (I'm not sure how -- especially since it now appears not to be a set). > Now, while we /can/ view this in the pluralist sense, but the conflict > regards which of the two ways of treating the language most > approximates thought. I say that my version does - thought treats a > "mass" as in identity, which then allows you to expand {lu'o} using > {gunma}. This isn't just a "way of seeing it" (something based on > consequences), it's what actually happens. The pluralist view is a way > of seeing it. As noted before, the question about thought and language (this question anyhow) does not seem to me to be a significant one, mainly because there does not seem to be any evidence of a relevant relationship. But, inso far as this is meant to be about what "really happens," insofar as I can figure out what you claim that to9 be, it isn't. Of course, you may mean something different by "mass" -- and certainly do by "identity" -- than what I (and the Lojban lore) do, but thought doesn't seem to have anything to do with these. > > So, regarding quantifiers. My point is that I treat them differently - > they're a shortcut for describing a relationship between "the > students" and a number. Your treatment of them seems to be that > they're something quite separate. I don't know the exact explanation > you offer that connects them to how we think. I agree that "the > students" being of number 26 means that we can treat it as 26 > identities being related to something, even though these identities > are yet-undefined, but this is a description of a consequence. Well, I haven't said anything about quantifiers other than the particular applied to variables, to which your comments don't apply. As far as McKay (the sort of standard pluralist) goes, he would seem to be fairly close to you in that he takes them to be (collective) predications (which could at least in some cases be converted to relations between the group and a number). Even stock singularist recognize ordinary quantifiers as second order properties (properties of properties). So, aside from terminologfy and talking about rather different things, I tthink this is not an area of disagreement (I threw it in because it is standard and because ultimately some singular -plural differences appear there, but not unique to quantifiers). I don't suppose this connects in any direct way to how we think -- this is linguistics and logic after all, not psychology. Incidentally, ""the students" being the number 26" literally taken makes no sense; I suppose you mean "the students being 26 in number" or some such. The rest of this section depends upon unexplained notions like "identity" and what (unknown) thigns are the consequences of. If it means what it seems to me to mean then I would say that it is the central act, not the consequence, but that is to hypothetical to enlarge on yet. > > > > Descriptor: t > > > > > > What's a descriptor? > > > > Converts a formula into a name (cf. {le, lo} and the like). > > > > > > > > > > Terms: a variable is a term, a name is a term, if F is a formula containing free variable > > > > x, then txF is a term. > > > > > > What's a free variable? > > > > One not in the scope of a quantitifier on it. > > What does being in the scope of a quantifier mean? The scope of a quantifier is the whole of the shortest complete formula following it, i.e., the F in he definition that makes an expression that begins with a quantifier a formula. > > > > > > Formula: A predicate followed by a term is a formula, A followed by two terms is a > > > > formula, a formula preceded by ~ is a formula, two formulas preceded by & is a > > > > formula, a formula preceded by a variable preceded by E is a formula > > > > > > So a predicate is an abstraction, while a formula is an instance of > > > this? "Runs" would be a predicate, and "Alice runs" (or "runs(alice)") > > > would be a formula? What's a relation? > > > > Well, ""abstraction" isn't quite right, though it is incoplete without its subject. > "runs(alice)" > > is a sentence. A relation is like a predicate but has more arguments. > > > > > > A formula contains a free variable x just in case there is an occurrence of x in that > formula > > > > which is not in any subformula which begins Ex nor in a term which begins tx > > > > > > I don't understand what you mean here. > > > > x is free in Fx but not in ExFx. > > Why is there a free variable x? In what sense of "Why?" It is free because there is no quantifier on x immediately preceding it. It is free as a step in constructing a quantified formula. > So a free variable is just something with {zo'e} in its "of number..." slot. A fee variable is a term, so it doesn't have a slot (only predicates do), nor dores it have anything to do with numbers (another predicate idea). To a certain extent, a free variable could be identified with {zo'e} in its "it doesn't matter what" mode. The real variables in Lojban, {da} etc. are never free. > > > > > > > > > > A sentence is a formula which contains no free variables. > > > > > > > > A singularist model: > > > > > > > > Domain D: a non-empty set > > > > > > What is a set? > > > > Well, I suppose I had Cantorean (usual set theoretical) sets in mind, but nothing hangs on > that. > > L-sets would do as well or we could just have a definite bunch (in the none-technical sense) > of > > things. > > So a domain, D, is just a "meta"-set (i.e. it doesn't matter what kind > of set, we just need a way to talk about several things)? Domain seems > a strange thing to call it. It doesn't even have to be a set (it isn't in the pluralist version); it is just a bunch of things. "Set" provides a bunch of useful tools for talking about things however, and here does no real harm. "Domain" is standard, but yes it is odd, since for most interesting diecussions it is the range. > > > > > > Masses M: Power D - 0. the set of all non-empty subsets of D > > > > > > A mass is a set of all non-empty subsets of D? No. A mass is a certain > > > type of identity. > > > > This is the set of masses, each mass is a non-empty set of things in D. > > I don't understand. An example? A mass is different from any sort of > set. A mass is an identity, especially one that implies that there are > other identities (doesn't matter what they are) as parts of it > (relationship "[the mass] has parts [those identities]"). You got labelled a singularist (because you said that the referent of a plural nounphrase was a single thing) and so, I am afraid, you got the whole standard singularist load foisted on you. You now seem to be trying to differentiate your position from the standard one, but have yet to explain just what the difference is. In words it is that that thing is an identity and not a set, although that identity contains (has as parts) other identities. The "part" talk sounds like L-sets (mereological sums, etc.) and, if that is what you mean then were are back on track, since the set talk can be applied -- even more easily -- to these. > > What does "type of identity" mean? > > What I call a concept, or an abstraction. Human, joy, etc. We see a > one-thing, our referent, we form its identity in our mind, which could > be of type "bear", or "group", or "mass". This is really not yet helpful (although it suggests that your are going off somewhat in the eay pluralists in fact go). But, whatever the the referent of a plural exprression is, it can't be an abstraction of this sort, since that is too encompassing and and cannot bear the local burden. At the least, we need *the* students not just studenthood to do the work (actually, this will work in another areads that is related here, but that is another discussion). > > > > > > Concepts: > > > > > > > > Interpretation: a function, I that assigns to: > > > > Each concept an object from M, with at least one concept for each singleton in M > > > > > > Object from M? What is an object? Singleton? > > > > An object is, in this case, just something in D. A singleton is a set with exactly one > member. > > I don't think I understand what is occurring here. In D, there are > masses? I understand that D is a set of some sort, but which masses > does it have in it? Well, we haven't said what is in D, because it doesn't matter -- things will do. We have set M, the masses, apart so presumably they are not in D. Ahah! Sorry, that should be "an object in M" Thanks for catching that one. > > > > > > Each name a concept > > > > > > Each name is (probably) not a concept. A name refers to an identity. > > > > Note, this sentence is part of what an interpretation does: assigns to each name a concept. > > What is a concept? Is it a predicate? A preicat i9s an expression that takes one term to make a formula. A concept is uindefined, just things other than what is in D or M. (I could fill this out a bit, as the choice of the word "concept" implies, but it adds nothing to the discussion at hand). > > > > > While an identity may be a special case of a concept, I avoid this > > > position because it fails to explain the sharp distinction between > > > instances and abstractions (identities and concepts; Alice and human), > > > and my urge to treat a perfect clone of X as Y (instead of thinking > > > them both X until they differentiate). > > > > I don't see what this is all about. A concept here is just another abstract entity in the > > metalanguage of the given language. I suppose its name may have some useful associations but > none > > that need interfere here. For example it has nothing to do with the differences between things > (in > > D) and properties -- what predicates mean. I don't understand where clones come in. > > > > A concept to me means something along the lines of an abstraction. A > human, time, etc. When you say "Alice is a human", 'human' is a > concept, or something that you mentally "grasp", or can recognize. OK, so you think I should change the name. I'll see what I can come up with. Actually, some parts of what you say (you do know you have said three quite different things, don't you?) is not too bad for what I had in mind. > What I said was probably not relevant, as I think I misread. > > As for clones, just a hypothetical situation, where if a 'named' cup > was cloned, I would not have them named the same, while something like > a concept would still be there - they'd both be cups. Relevance? This seems to come out of nowhere. But, in the present system, they would have different names and they would both be cups. > > > > Each predicate a function from concepts into {0, 1} > > > > > > Relation, predicate, function, formula. How are these different? > > > > Do you know any of the language of set theory or mathematics? These are pretty rudimentry. > But > > if need be I can back up a bit more. A predicate is an expression which needs one term to > make a > > formula, a relation is an expression which needs two terms to make a formula, a function is a > > mapping from one set of things into another set, > > In what sense is it a mapping? That each element in the set fulfills > the relationship that both sets are part of? I think that is about right, so far as I understand it. A mapping is a set of ordered pairs, the first member being drawn from one set, the second from another (though maybe the same), such that every first member is paired with exactly one second member (i.e., no two pairs start the same) > Do you mean a mapping of "Fred" to Fred? Perhaps an example? That is pretty much what an interpretation does, yes -- for all names. > > a formula a predicate or relation filled out with > > appropriate number of terms or some compound of one or more such by connectives and > quantifiers. > > > > > > I(Y) is the function from pairs of concepts such that I(A)(c1,c2) = 1 iff I(c1) is > included > > > in > > > > I(c2) > > > > > > > > A is an assignment iff A is a function from variables to concepts > > > > > > What is an assignment? > > > > A function which gives each variable a meaning for the nonce. > > > > > What is A (regardless of being an assignment or not)? > > > > I don't understand this question. > > if not an assignment, what would A be? If it's not a function from > variables to concepts, what do you call it? and what do you call it > before you decide that it is or isn't a function from variables to > concepts? I don't call it anything because I have no reason even to think of it. But more importantly, if it is this A, then it is an assignment, whether I think of it or not. If it is something else, then it is not this A. > > > > > So variables are identities, and concepts are abstractions? What else, > > > if not a concept, would a certain variable be 'functioned' to? > > > > I don't understand your terminology here. Variables are expression in the language; I gather > that > > identities are not. > > An identity is some one thing. A cat, a group, a mass (by my version), > a single thing in that set of 26 that is wearing a hat. A single student among the 26? So anything that can be attached eventually to a term is an identity. Some identities have parts, other do not(?) That is looking very much like D and M together, with M carryong a convenient mirror of D, so that only M needs to be talked about. > >I am not sure whether concepts are abstraction -- I am probably inclined to > > think of them as thoughts, but nothing hangs on what they are, only on the role they play. > xorxes > > has suggested another approach -- which I found harder to adapt to what I understood to be > your > > position -- in which variables were "functioned" to things (in D). > > > > > > A(c/x) is an assignment just like A except that it assigns the concept c to variable x > instead > > > > of A(x). > > > > > > Example? > > > > A simple assignment Q assigns Charlie to every variable; now for some reason we change and for > the > > particular variable y17, we assign George. This new function is Q(George/y17). > > > > Er, if not a concept (I think that what you call a concept I call an > identity), then what would be assigned to the variable? I don't think that concepts are quite identities (but I am not at all sure), though it may be that some version of all this will eventually get around to that. Well, another approach to this -- which seemed originally more remote from your position, would be to assign things from M (or M and D) directly to variables(and other terms as well). > > > > > > > > If a is a term, R(a) = I(a) if a is a name, R(a) = A(a) if a is a variable, R(a) is a > concept > > > c > > > > such that F is true for I and A(c/x), if a = txF > > > > > > What is R? > > > > It is a function from terms to their referents. > > > > > > > > i is an individual just in case i is in M and is a subset of each of its subsets (is > identical > > > > with each of its subsets, has only one member, i is a singleton). > > > > > > > > > > If I understand you correctly, my clarification is that a mass is an > > > identity. This opposes the pluralist view in that the pluralist mass > > > is not an identity. > > > > Again, I don't underand your use of "identity". The last sentence is just a definition saying > > that we are going to use the word "individual" to refer to sets (Masses) that have only one > > member. > > > > > > > > > > > Where P is a predicate and a a term, Pa is d-true for I and A iff for every individual i > > > > included in I(R(a)) and for every concept c s.t. I(c) = i, I(P)(c) = 1 > > > > > > > > > > I don't understand what "d-true" means. > > > > Distributively > > > > > > Where P is a predicate and a a term, Pa is c-true for I and A iff I(P)(R(a)) = 1 > > > > > > > > > > Nor "c-true" > > > > Collectively (i.e., non-distributively) > > > > > > A Pluralist model > > > > > > > > Domain: Some things > > > > Concepts > > > > > > > > C is a relation between concepts and items in D, such that for every d in D, there is at > least > > > > once c such that c is related by C only to d [We designate a selected such concept C/d, > for > > > each > > > > d] > > > > > > > > > > > > An interpretation I is a function which assigns > > > > To each name a concept > > > > To each predicate a function from concepts into {0,1} > > > > To Y the function from pairs of concepts into {0,1} such that I(A)(c1,c2)) = 1 iff > > > > for every thing d such that c1Cd holds, c2Cd holds > > > > > > > > An assignment A is a function from variable to concepts > > > > A(c/x) is an assignment just like A except for assigning c to x in place of A(x). > > > > > > > > For term a, R(a) = I(a) if a is a name, R(a) = A(a) if a is a variable, is a concept c > such > > > > that F is true for C,I and A(c/x) if a = txF > > > > > > > > Pa is d-true for C,I and A iff for every d such that R(a)Cd, I(P)(C/d) = 1 > > > > Pa is c-true for C,I and A iff I(P)(R(a)) = 1 > > > > > > > > In either case, > > > > > > > > A formula F is true for [C,]I and A > > > > > > > > If it is Pa, for some predicate P and some term a and either Pa is d-true for [C,]I and A > or > > > Pa > > > > > is c-true for [C,]I and A > > > > > > > > If it is Yab and I(Y)(R(a) R(b)) =1 > > > > > > > > If it is ~S for some formula S and S is not true for [C,]I and A > > > > > > > > It is &GH for some formulae G and H and both G and H are true for [C,] I and A > > > > > > > > It is ExG for some variable x and some formula G and for some concept c, G is true for > [C,] I > > > > and > A(c/x) > > > > > > > > Otherwise not. > To unsubscribe from this list, send mail to lojban-list-request@lojban.org with the subject unsubscribe, or go to http://www.lojban.org/lsg2/, or if you're really stuck, send mail to secretary@lojban.org for help.