[lojban] Re: A (rather long) discussion of {all}

[John E Clifford <lojban-out@lojban.org>]

I hope the revised version is clearer.

--- Maxim Katcharov <maxim.katcharov@gmail.com> wrote:

> On 7/15/06, John E Clifford <clifford-j@sbcglobal.net> wrote:
> > --- Maxim Katcharov <maxim.katcharov@gmail.com> wrote:
> >
> > > On 7/14/06, John E Clifford <clifford-j@sbcglobal.net> wrote:
> > > >
> > > > --- Maxim Katcharov <maxim.katcharov@gmail.com> 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.
> 
> Not yet sure what a concept is.


Happily, I don't use them any more.
 
> The best way to describe states of affairs is through how they are
> formulated in thought. I can't think of another way to describe
> information/states of affairs - you'd either do it as thought, or some
> derivative thereof, i.e. language.

I thought states of affairs had to do with things and their relations and actions, i.e., somethng
in the world, not in ones head (except for mental states of affairs).
> >
> > > 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.
> 
> "This is the way that humans process/describe/store
> information/thoughts. As a consequence of this, this alternate way of
> describing it works too."


How exactly, then, does a human process/ describe/ store (these are pretty clearly not the same
thing) information / thoughts (also not the same thing) and how does that lead to the descrition
of what goes on in sentences and the like?  I think I need a full exposition here, since I am not
getting a clear idea of what you have in mind nor how it is relevant to the issue at hand.
 
> >
> > > 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.
> 
> For the sake of the example.

Yes, but an example of what?
 
> > 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?
> >
> 
> An identity in the mind corresponds to a certain thing in physical
> world. 

So an identity is a thought, presumably a thought of a certain thing.

> When I think of a certain pen, I have a certain identity in
> mind. It is something that is related, especially the referent of a
> name. 

"It" being the identity? What is it related to (a thing can't just be related)? Is it related to
the referent of a name or is it just that referent?

> If you look around you, you'll see that you notice whole things.
> A keyboard, a key, a wall, etc. You don't notice a half of a keyboard,
> you don't notice a keyboard and a wall blended together somehow, and
> you don't notice a circular patch of vision at a certain spot with a
> certain radius. You notice things, and these things have corresponding
> mental identities. You can also, of course, think of identities when
> not seeing their corresponding forms, or without there being those
> forms.


Well, that depends on how you are looking.  But, yes, if I am not in a philosophical or
psychological mode, I typically notice ("see" even) what I have otehrwise isolated out as things,
although I can focus or unfocus to the others as well (I admit to having problems with genuine
sensibilia, though).  About the mental identities I am less certain: does this mean that when I
see them I hav an idea of them, a thought about them, an impression of them (three different
things)? I am less sure about that unless it is definitional: seeing just is have such thoughts of
a certain characteristic affect.


> "A student" is an identity. "The mass of 26 students" is an identity
> that implies 26 other identities. "26 students individually" is also
> an identity, but we can just have it refer to the 26 implicit
> identities, since it doesn't matter if we do or do not.

No, "a student" is a singular noun phrase -- or are identities linguistic as well as mental?  The
same is true of "the mass of 26 students." "26 students individually" is a plural noun phrase; it
refers presumably to 26 students individually.  Does "identity" just equal "noun phrase"?  I don't
think that can do the work you want.
 
> > > 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)?
> 
> "26 students" is something like a set or a mass. Set implies much
> mathematical/logical details, this is not how we should treat it. It's
> just an identity (a single thing), with implications of those 26 other
> things. 27 things are implied/explicit in total.

Well, some logical details are going to be needed (whether for L-sets or C-sets or something else)
so that we can make some sense of one thing implying 26 others (i.e., that they exist?). I suppose
the fact that it refers to them implies that they exist (it does in Lojban at least).
 
> > 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).
> 
> Yes, I'm using it in a specific sense. For example, the group itself,
> and its 26 constituent parts are 'mapped' in a 1 to 26 relationship.
> However, each of those parts is one thing mapped to the single 'group'
> identity ("X is part of Y"). It's not like a single line starts
> somewhere, and then somehow splits up into several, or something.

Well, this doesn't look like a function but just a relation between this one thing (whatever it is
-- identity? group? thought?...) and these 26 things.  The converse relation has a single second
relatum, the same for all the first relata (just as the relation has a single first relatum, the
same for all seconds.  So, converse relation is a function, with a uniform value for the each
student as argument. But even that function is not 1-1.  I don't get the analogy you reject but it
does sound a lot like what you just said.
 
 
> > 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.
> 
> I'm just trying to find an illustrative way of describing it. It's not
> so much a term. I'm trying to imagine how thinking of how one thing
> being surrounded by a mass of other things would conjure up each of
> those other things (identities) in the mind. And it wouldn't.


I don't follow this at all.  Is "it" lifting up to consciousness, which is certainly not term in
any sense I can think of? So we imagine one student surrounded by other students and ask whether
thinking about that one student, even about him surrounded by a mass of students, would lead on to
think of the other students (individually>). It certainly wouldn't be necessary, but it might
happens.  But then, just about anything might happen -- there are more or less habitual trains of
thought but they are just habits, not lawlike at all.

> >
> > > 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
> 
> Brought up. Pushed into. Pulled down. (into the consciousness).
> Formulated in the mind? We're talking about a single thing though, a
> corresponding mental representation.

A mental representation of another student coming into one's mind when thinking about (having a
mental repesentation of?)another student.  This happening more or less automatically or not being
possible or at least easy -- and you favor the second position.  Why are we concerned about this?
What fores it have to do with singulars or plurals -- unless you think that a pluralist position
is that thinking about one of the several things involved leads one immediately to think about
another and maybe that thinking about the several things involves thinking about at least one of
them  But it doesn't involve thinking at all in any essential way (althoughat some point there has
been a mental action of symbolization, I suppose). 
 
> > 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).
> 
> A set seems to imply that they are inherently 'part' of it. Like a big
> thing, and it's composed of 26 students or something, and that's what
> I'm thinking of, all together. This is just an identity. You can
> recognize "26 students" as a singular identity, and this singular
> thing implies 26 identities that are related to it in a very certain
> way.

Well, a set implies that it has members, which (for L sets) are also parts.  It sounds like you
want an L-set, a single thing of which all the students are parts.  Is it this set or the thinking
of it that constitutes an identity?  You CAN recognize "26 students" as referring to a single
object which has parts (no one has claimed otherwise, I think).  But the point is that you don't
have to think of it that way.
 
> >
> >
> > > 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.
> 
> You must mean relationships between brain activity and language. Any
> relationship between thought and language would be theoretical at
> best, since I know of no technology that allows us to sense what a
> person is thinking.

We have introspection, for one, and some fairly good bits of observation (not perfect, but
reliable to a fairly high degree).
 
> I find it absurd to suggest that language and thought are not directly
> related. It is our thoughts that we communicate. "We communicate
> information/perceptions of affairs". Yeah, that's exactly it. The form
> of all information stems from the form of our thoughts. Information
> wouldn't be information without a system of thought capable of
> interpreting it. I can't begin to understand how to explain this,
> because I have no idea how it is that it is not obvious that human
> language serves to communicate human thought. Perhaps you can
> enlighten me.

What I have said is that there is no sure correlation between what one says and what one is
thinking while saying it (actors are a sufficient piece of evidence for that but one's own
experience should provide many other cases). The rest of this assumes a fairly strong form of
Sapir-Whorf, which is what we were supposed at one time to be testing.  I suspect however that you
mean something more by "thought" than "what a person is thinking."  I am not sure what more,
however.  As for information, it is information even if no one ever interprets it -- it is just
unused information.  Of course, if it is given in language, there has to be a system for
interpreting it (that's what a language is, in large part).  But where does thought come in in a
systematic and necessary way?



 
> > 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.
> 
> There are several forms of them?

Certainly in Lojban, where every type of sumti can be modified by a quantifier, as can several
other sorts of expressions -- an those are just the external ones.  They are related, of course,
but different enough to have somewhat different treatments.
 
> > 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.
> 
> Linguistics, psychology, and philosophy converge on this subject.
> Psychology in general tends to be about behaviour. What we're talking
> about are the technical or "hard" details of cognitive process.

They don't seem to converge very much; the results are mainly negative, so far as I can see.
 
> > Incidentally, ""the students" being the number 26" literally taken makes no sense; I suppose
> you
> 
> Being /of/ number 26.
> 
> > mean "the students being 26 in number" or some such.  The rest of this section depends upon
> > unexplained notions like "identity" and what (unknown) things 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 too hypothetical to enlarge on yet.
> 
> Yes, you've made me aware that you don't yet know what these things
> mean. It would probably be easier to ignore it until it's explained.
> 
> >
> > > > > > 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 the definition that makes an expression that begins with a quantifier a formula.
> >
> 
> I don't follow. Perhaps an example?


"if F is a formula and x a variable then ExFx is 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 a variable whose quantity hasn't been
> specified? though the wording of your explanations suggest that it is
> more complicated than this.

Actually, it is sorta the other way around:a free variable has (within a given assignemnet) a
fixed value (it is a variable because there are other assignments which give it different values).
 A bound variable is one that does not have an assigned value at all, being under a quatitifer and
thyus able to have any value as the need arises.
 
> >
> > > 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: x1 is a plural of number x2 of type x3
> "the students" A '26' 'student'

What is this?  It is not a translation for the A of the systrm. Nor is it obviously a useful
predicate to have: the various points are more clearly dealt with by separate predicates.  If I
understand its uses.

> Since these variables are part of the A relationship, they all have a
> "of number" slot, x2. When we say "those students", x2 is filled with
> zo'e. When we say "those 26 students, x2 is filled with 26.


What variables?  variables aren't part of any relationship -- they're expressions of the language.
Nor, being terms, do they have slots.  As describing a certain aspect of an interpretation, this
would be about right -- a simple plural does not specify a number.

> > > >
> > > > > >
> > > > > > 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.
> 
> I would say that it is generally unsafe to assume that a person
> believes the entirety of an opposing doctrine based on the observation
> that they support a major point of that opposing doctrine. I'm a
> "singularist" only as far as saying that you can't relate one building
> to 26 students without relating the building to each of those 26
> students, or without relating the building to a group of a certain
> number, to which certain other identities are related as "is a part
> of".


Of course it is unsafe, but given the lack of information it is a good place to start.  The
difference will hopefully emerge in the discussion.  But that is taking a rather long time.  But
that is not singularism, it is just laying out the claim that pluralism and singularism are the
only two ways to go -- which is not in dispute.


> > 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.
> 
> Identities don't contain anything. An identity is just one thing.
> There is one group of students. Incidentally, because there's a 26 in
> a certain slot, we know that there are exactly 26 entities /related/
> to this group.

OK, how are identities related to groups of things?  The identity is not the group since the
identity does not have parts.  Something here seems to have slots (one of which can be filled by
numbers)-- it is not the group for sure, so is it the identity?
 
> > 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).
> >
> 
> "Type of identity" is not "identity". Humans think of singular
> concrete 'things' when they see things, hear things, or even when
> they're just visualizing them in their head. Now, I look at this
> pencil, and it's an identity, of the type "pencil". "Pencil" is a
> concept, an abstraction. I have seen many pencils, and I recognize
> them as being different from other things, and so I form an
> abstraction in my head, the concept of a pencil.

Well, I'll take your word for what you do in your head.  Is it the pencil itself that is the
identity here, as you seem to say? Or do you mean the seeing of the pencil?  Or what?  "pencil" is
a noun; it stands for pencils which are concrete.  There is an abstraction, PENCIL or pencilness
or some such, which may well be in your head (and may well not be, too).  Is this abstraction the
identity? Or is it just that the identity, like the object itself, gets classified as standing in
some special relationship *whatever) to that concept?
 
> > > >
> > > > > > 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 suppose I do, but I was mostly pointing out that my understanding of
> what a concept was apparently different from what you were getting at.
> It would help if you gave the definition of what your 'concept' means.

Well, "concept" as I was using it was just a name for a bunch of objects which played a certain
role in the system  How they were relized is irrelevant (and not ever really considered).  Happily
they are gone now.

> > 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?)
> 
> I don't know what you're referring to.

I think it was abstractions, concepts and things we grasp with the mind, but I recall another
triad that I may have meant -- but can't find at the moment.

> > 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.
> 
> As I said, "What I said was probably not relevant, as I think I misread."
> 
> >
> > > > > > Each predicate a function from concepts into {0, 1}
> > > > >
> > > > > Relation, predic



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