Necessary Being
Saikat Guha
Is there anything that exists necessarily?
(Equivalently: is everything that exists contingent?)
If there is any other newgroup that would be better suited for such a
discussion, please let me know.
The Sophist
> I would like to discuss the following question:
>
> Is there anything that exists necessarily?
If there can be disjunctive objects, and either Armstrong's
combinatorial theory of possibility or Lewis's modal realism or a
similar theory is the correct account of modality, then yes, the object
which is the disjunction of all possible objects is necessary (neither
Armstrong nor Lewis allow worlds where there is nothing at all).
Otherwise probably not.
--
Aaron Boyden
"I may have done this and that for sufferers; but always I seemed to
have done better when I learned to feel better joys."
-Thus spoke Zarathustra
Bob Kolker
Saikat Guha wrote:
>
> I would like to discuss the following question:
>
> Is there anything that exists necessarily?
>
> (Equivalently: is everything that exists contingent?)
Is their any evidence of necessity? The fact that we have one world,
does not in itself prove it is the only possible world.
Bob Kolker
Patrick Crosby
Saikat Guha
> combinatorial theory of possibility or Lewis's modal realism or a
> similar theory is the correct account of modality, then yes, the object
> which is the disjunction of all possible objects is necessary (neither
> Armstrong nor Lewis allow worlds where there is nothing at all).
> Otherwise probably not.
I am guessing that by a "disjunctive object" you mean what Lewis calls
a transworld individual (that is, a mereological sum of worldbound
individuals at different worlds) but I'm not sure. Please explain
what you mean by this term.
Even if there are transworld individuals, it doesn't follow that there
is one that exists at all possible worlds. That would follow only if
you accept standard mereology as well as modal realism.
I don't know much about the details of Armstrong's theory, though I
know what combinatorial approaches in general are like. I take it,
then, that Armstrong is what Lewis called a "linguistic ersatzer" and
that a "disjunctive object" on this theory is an ersatz individual
that represents a transworld individual. Or is that wrong?
On a personal note, Aaron, I regret the quarrel that ended our last
exchange (it was several years ago). I hope no ill feelings remain on
your side. I have since gained much more respect for David Lewis, as
you perhaps know if you've read my review of "On the Plurality of
Worlds".
Saikat Guha
In the context whereof I spoke, I meant "necessarily existing", that
is, "existing at all possible worlds".
>Is this an unambiguous term?
No. The word "necessary" is used in many different ways in different
contexts. As with most ambiguous terms, context resolves ambiguity.
That's why Aaron, for instance, understood what I meant.
Saikat Guha
Yes, I think there is good evidence that something exists necessarily.
> The fact that we have one world,
> does not in itself prove it is the only possible world.
No, it doesn't.
The Sophist
> I am guessing that by a "disjunctive object" you mean what Lewis calls
> a transworld individual (that is, a mereological sum of worldbound
> individuals at different worlds) but I'm not sure. Please explain
> what you mean by this term.
>
> Even if there are transworld individuals, it doesn't follow that there
> is one that exists at all possible worlds. That would follow only if
> you accept standard mereology as well as modal realism.
Actually, I meant something much less plausible than this; I hadn't
thought of transworld individuals. A problem with a transworld
individual as a necessary being is that it doesn't actually exist at any
world (no world has the whole of a transworld individual as a part,
which is what's normally required for something to exist at a world), so
it would be more natural to think of it as an impossible being.
What I was actually thinking of were objects which are essentially
disjunctive, as the object which is either my chair or my sofa. Such an
object is even sillier than the mereological sum of my chair and my
sofa, though some theorists might say that disjunctive states of affairs
are necessary to analyzing quantum theory (I doubt they're right, but my
knowledge of physics is not what it would need to be for me to have a
firm opinion). If there are disjunctive states of affairs, and they are
present wherever their disjuncts are (another assumption which I may be
too hasty in making), and it's possible to have a disjunction of all
possible states of affairs (an assumption even those who like
disjunctive theories are unlikely to make), then that disjunction might
be necessarily existent. I hadn't really thought about it much when I
posted my first message; it now occurs to me that this disjunction may
be impossible in the same way as the ultimate transworld individual you
imagine, though it might be argued that a disjunctive state of affairs
is wholly present in each of its instances. Or something. Disjunctive
states of affairs don't really make sense to me, I was just playing with
the idea. Having played with it a bit more now, I think I don't like
it, and will just say that there is nothing which necessarily exists.
> I don't know much about the details of Armstrong's theory, though I
> know what combinatorial approaches in general are like. I take it,
> then, that Armstrong is what Lewis called a "linguistic ersatzer" and
> that a "disjunctive object" on this theory is an ersatz individual
> that represents a transworld individual. Or is that wrong?
Having been forced to think about it more, it occurs to me that
Armstrong would certainly not allow disjunctive objects. If you want a
bit on his theory, he has a robust metaphysics of properties, and he
determines what is possible in terms of ways in which properties can be
combined. An early form of his theory was explicitly a form of
linguistic ersatzism, though more recent forms of his theory are hard to
pin down. He does seem to have some, perhaps all, of the problems Lewis
raises for the linguistic ersatzist, but considers them tolerable.
Lewis and Armstrong had a lot of influence on one another over the years.
> On a personal note, Aaron, I regret the quarrel that ended our last
> exchange (it was several years ago). I hope no ill feelings remain on
> your side. I have since gained much more respect for David Lewis, as
> you perhaps know if you've read my review of "On the Plurality of
> Worlds".
I must apologize for not remembering the quarrel. I have so many of
them on the net, so don't take this as indicating that you're not
memorable; I hope things go better this time.
Saikat Guha
agree that the notion seems only marginally intelligible. One might
believe in universals, however, that are non-disjunctive
(corresponding to natural kinds, perhaps), and maybe there's a natural
kind that's instantiated at every world. If the universal is wholly
present in its instances, and modal realism is true, then there is a
necessary being. (Note that it makes more sense to say that such a
universal exists at every possible world than to say that it doesn't
exist at any possible world, unlike a transworld individual.)
I firmly believe that modal realism is false. I know you were a
student of David Lewis. Are you a modal realist as well?
I also firmly believe that there is a necessary being and that there
are good arguments for this claim. But whether and to what extent you
would find them convincing depends on your modal metaphysics. Perhaps
you can tell me a bit about your views on modality, then.
The Sophist
> I firmly believe that modal realism is false. I know you were a
> student of David Lewis. Are you a modal realist as well?
I lean toward linguistic ersatzism. Apart from not making the same
level of intuitively implausible claims, I think linguistic ersatzism
has one clear-cut advantage over modal realism. Lewis discusses the
problem that on modal realism there is an argument which seems to show
that there are more worlds than there are. His solution does not strike
me as particularly satisfying, so I think it is a considerable advantage
of linguistic ersatzism that this problem does not arise for it.
On the other hand, I do not think the defects of linguistic ersatzism
are particularly serious; notably the lack of alien properties and the
conflations of possibilities Lewis complains about don't seem like a big
deal to me. Probably this is because of my general pragmatist leanings.
None of the possibilities linguistic ersatzism can't cope with seem to
be of any great theoretical interest, and I am not greatly moved by
arguments that it is intuitively obvious that these things are possible
so our modal theories must incorporate them.
My leanings have been somewhat strengthened by an article in the most
recent _Mind_; I forgot the authors, but they tried to show that modal
realism can't cope with alien properties either. If that's right,
another point for linguistic ersatzism.
mike
@posting.google.com:
i think this is perfect topic. i don't know if there are really
"universals". the form "if, then", is, maybe, not a universal (not because
of the negation, but because of irrelevancy).
"I bought a car, so i must drive." "must drive" would not be a necessary
condition from "car", but there is no other way to drive. a part of the
proposition seems necessary. it could be that we become confused because
the proposition seems to contain more than one element?
Saikat Guha
Do you have an opinion as to what sort of things the ersatz worlds and
individuals are? I mean in terms of ontological category--are they
set-theoretical constructions? If so, out of what? If not, then what
are they, in your view?
Saikat Guha
> of the negation, but because of irrelevancy).
I don't understand this statement. You probably are using "universal"
in some sense different from the one I was using. I have in mind the
sort of thing David Armstrong believes in--repeatable constituents of
concrete things that correspond to their natural properties.
> "I bought a car, so i must drive." "must drive" would not be a necessary
> condition from "car", but there is no other way to drive. a part of the
> proposition seems necessary. it could be that we become confused because
> the proposition seems to contain more than one element?
If this is a correct use of "must", it expresses a modality completely
different from the one I am concerned with, which is that of absolute
necessity(or "intrinsic", or "metaphysical", or "broadly logical"
necessity, whichever label you prefer).
mike
>> the form "if, then", is, maybe, not a universal (not because of the
>> negation, but because of irrelevancy).
>
> I don't understand this statement. You probably are using "universal"
> in some sense different from the one I was using. I have in mind the
> sort of thing David Armstrong believes in--repeatable constituents of
> concrete things that correspond to their natural properties.
that's possible in a specific science discussion, but the "correspond" is a
little vague for a conceptual discussion. if this is the case, then you are
answering your own question in advance.
>
>> "I bought a car, so i must drive." "must drive" would not be a
>> necessary condition from "car", but there is no other way to drive. a
>> part of the proposition seems necessary. it could be that we become
>> confused because the proposition seems to contain more than one
>> element?
>
> If this is a correct use of "must", it expresses a modality completely
> different from the one I am concerned with, which is that of absolute
> necessity(or "intrinsic", or "metaphysical", or "broadly logical"
> necessity, whichever label you prefer).
and yet it is a modality. and if your "necessity" doesn't involve this
modality, then it cannot be a universal. but then, we don't really need
such a universal in science.
>
The Sophist
They are probably set-theoretic constructions. Which is a point for
Lewis, really; in the appendix to his _Parts of Classes_ and in
"Mathematics is Megathology" he argues that sets can be represented by
ordinary objects if you have enough ordinary objects. And there's
little doubt that his modal realism gives him all the ordinary objects
anyone could want, while the actual world may well not contain enough
stuff for the reductionist set theory.
Saikat Guha
*What*'s possible in a specific science discussion? And of what
relevance is that?
> but the "correspond" is a
> little vague for a conceptual discussion.
The notion of one-to-one correspondence is perfectly precise.
>if this is the case, then you are
> answering your own question in advance.
If *what* is the case? And whatever it is, how am I answering my own
question in advance?
> and yet it is a modality. and if your "necessity" doesn't involve this
> modality, then it cannot be a universal.
I don't know what you mean by a "universal".
> but then, we don't really need
> such a universal in science.
I still don't know what you mean by a "universal".
Saikat Guha
Out of what?
> Which is a point for
> Lewis, really; in the appendix to his _Parts of Classes_ and in
> "Mathematics is Megathology" he argues that sets can be represented by
> ordinary objects if you have enough ordinary objects. And there's
> little doubt that his modal realism gives him all the ordinary objects
> anyone could want, while the actual world may well not contain enough
> stuff for the reductionist set theory.
I don't think modal realism provides enough objects for the
set-theoretical universe, unless you have in mind some "nonstandard"
or "deviant" (i.e. unintended) interpretation of set theory, such as
you might get by applying the Lowenheim-Skolem theorems. (In that
case the actual world should be enough for you, assuming you think
there are, say, denumerably many spacetime points; though I think that
sort of thing is mere verbal trickery.) So far as I can tell, Lewis'
possible worlds and individuals give him enough objects for the first
few transfinite cardinals, but no more, certainly not the whole
iterative hierarchy. I would be interested to know why you think
otherwise.
The Sophist
>>They are probably set-theoretic constructions.
>
> Out of what?
Sentences, likely. I did say linguistic ersatzism was the approach I
leaned toward. And sentences are representations of states of affairs;
I'm willing to be pretty liberal about what things can represent what
other things (as Lewis recommends the linguistic ersatzist should be),
despite my lack of any good theory on how things can represent other things.
Not because I've got a proof of it, certainly. You could well be right;
the restriction Lewis imposes to prevent there from being more worlds
than there are may well limit the number of individuals among all the
worlds too much for this point to stand. I haven't looked at the matter
especially closely, I'm afraid.
S
NO.
Glad I could clear that up for you.
mike
@posting.google.com:
>> that's possible in a specific science discussion,
>
> *What*'s possible in a specific science discussion? And of what
> relevance is that?
i start out by assuming that you are much smarter than i am, and that
you've thought about the concept of knowledge enough to recognize that
there are different kinds of knowledge and different approaches to
talking about "knowledge".
>
>> but the "correspond" is a little vague for a conceptual discussion.
>
> The notion of one-to-one correspondence is perfectly precise.
only in a specific kind of conversation. i know what this means for some
activities, but not for others. for instance, "science is the study of
real things" is not a universal correspondence, no? since, here, "real"
is overloaded to mean "the things which science studies".
>
>>if this is the case, then you are answering your own question in
>>advance.
>
> If *what* is the case? And whatever it is, how am I answering my own
> question in advance?
something like, "what is the nature of the True when i do logic"?
>
>> and yet it is a modality. and if your "necessity" doesn't involve this
>> modality, then it cannot be a universal.
>
> I don't know what you mean by a "universal".
"uni". applicable to all situations. we don't know all situations.
>
>> but then, we don't really need such a universal in science.
>
> I still don't know what you mean by a "universal".
you're not giving me any background to form an explanation. this is just,
"wah dat kind???".
aloha
mike
news:82fe4b77.02040...@posting.google.com:
>> Is there anything that exists necessarily?
>
> NO.
except you. and your answer; and your pet gerbal. =)
>
> Glad I could clear that up for you.
i'm glad you're working on this problem. people have always misunderstood
philosophical thinking, thinking it was was about making "wisdom", where
"wisdom" is merlin's magic modality of knowledge. the word "sophos" is the
latin "sapient", the spanish, "sabe", and refers to something you know
about, as does the "wis" in "wisdom". and, if you want, you can say that
the "wis" is cognate to the "vis" in "visable": "seeable" -- probably it
was as dumb as that.
it really isn't to the point to say, as most squeekers do, that a word has
come to mean more than the original meaning, as though we'd finally
discovered the "essence" of the word. "wisdom", as a special knowledge,
can't mean "knowledge acquired through direct obsevation", it just means
objects acquired over time. the proper word for magic acts is "magic", just
as the proper label for scientific study is "habituation".
Saikat Guha
problem has gotten worse than before with this message. Unless you
are able to say something that is intelligible to me, I shall have to
leave your insights, interesting as they may be, unread and
unanswered, since I can't decipher the words and phrases you use to
express them.
Saikat Guha
>
> NO.
>
> Glad I could clear that up for you.
Sadly, your joy was premature, else I would share it. Even if I had
such touching faith in your say-so as to believe whatever you said
without further question, my blind belief wouldn't "clear up" the
matter, for it would still be blind. To clear it up, you will have to
explain *why* there are no necessary beings, in a way that makes it
clear to me that there aren't.
I look forward with bated breath to your explanation.
Saikat Guha
> leaned toward.
What are sentences, in your opinion? Are they, say, sets of concrete
inscriptions? Sets of utterances? Sui generis multiply instantiable
types? Or what?
> Not because I've got a proof of it, certainly. You could well be right;
> the restriction Lewis imposes to prevent there from being more worlds
> than there are may well limit the number of individuals among all the
> worlds too much for this point to stand. I haven't looked at the matter
> especially closely, I'm afraid.
Well, it seems to me that each world will have at most aleph-1 (i.e.
continuum many) spacetime points. Assuming each point to be occupied
by a material object and mereology, there are as many material objects
in the world as there are sets of real numbers, that is, aleph-2.
Then, given the aleph-2 or so possible recombinations on a given
spacetime continuum, we have aleph-2 or so worlds each with perhaps
aleph-2 or so objects. Add transworld mereological sums, and you get
the cardinality of the power set of the union of all of these sets. I
don't know what the cardinality of the union of aleph-2-many sets each
with aleph-2-many members is. I tried posting a message to sci.math
on this, but somehow it didn't appear. (I did get an e-mail
suggesting the matter can't be resolved by the axioms of standard
iterative set theory.) Still, I suppose it must be some transfinite
cardinal, maybe aleph-3 or aleph-4 or something like that. In any
case, since there are infinitely many cardinals bigger than any given
cardinal in the hierarchy, assuming this big set and its power set
*have* cardinalities, even the power set affords only enough objects
to model the part of the set-theoretical universe at or below its
cardinality. The rest can't be modelled, as there aren't enough
objects. Perhaps you will have better luck getting a message through
to a math newsgroup. Or maybe you can tell me what I may have done
wrong in the course of posting the question. Or maybe some
mathematician here can answer it.
mike
@posting.google.com:
i have sympathy for you, but i don't want to talk the way you want to talk.
the comments i made on your post are comments about the concepts behind
your assumptions.
Lisa Gardner
> I would like to discuss the following question:
>
> Is there anything that exists necessarily?
>
Well, I don't know. My first inclination when I read the question
was to ask you, 'in order to do *what*?' i.e., I guess I was
thinking that I would like to see the question rephrased,
'Is there anything that exists necessarily <in order to do thing
A> or <for thing B to happen> or <etc.>.
But I guess that would be me answering, 'No, everything
that exists is contingent, *for all intents and purposes and
insofar as language (and philosphical questioning) is
concerned*.'
But that question is a difficult one. I am not sure what the
answer is... it may be that this type of question is tied in with
some kind of qualification - but then, qualifying the statement
probably means assuming the existence of the thing that is
foundational to the terms used to qualify it, so... I guess I
just really don't know.
Maybe *something* is necessary, but we just cannot get
ahold of it using language and the rational mind.
Lisa
leste...@worldnet.att.net
>skg...@yahoo.com (Saikat Guha) wrote in message news:<14587092.02040...@posting.google.com>...
>> I would like to discuss the following question:
>>
>> Is there anything that exists necessarily?
Actually, yes. Differences. Differences exist, and existence differs.
>>
>> (Equivalently: is everything that exists contingent?)[...]
>
>Well, I don't know. My first inclination when I read the question
>was to ask you, 'in order to do *what*?' i.e., I guess I was
>thinking that I would like to see the question rephrased,
>'Is there anything that exists necessarily <in order to do thing
>A> or <for thing B to happen> or <etc.>.
>
>But I guess that would be me answering, 'No, everything
>that exists is contingent, *for all intents and purposes and
>insofar as language (and philosphical questioning) is
>concerned*.'
>
>But that question is a difficult one. I am not sure what the
>answer is... it may be that this type of question is tied in with
>some kind of qualification - but then, qualifying the statement
>probably means assuming the existence of the thing that is
>foundational to the terms used to qualify it, so... I guess I
>just really don't know.
>
>Maybe *something* is necessary, but we just cannot get
>ahold of it using language and the rational mind.
>
>Lisa
Regards - Lester
Saikat Guha
> was to ask you, 'in order to do *what*?' i.e., I guess I was
> thinking that I would like to see the question rephrased,
> 'Is there anything that exists necessarily <in order to do thing
> A> or <for thing B to happen> or <etc.>.
Such a rephrasing is readily produced, though no more informative than
the original question. To wit:
"Is there anything the existence of which is necessary for the
occurrence of *any possible situation whatsoever*?", or
"Is there anything such that, in order for *any possible situation
whatsoever* to obtain, it must exist?"
> Maybe *something* is necessary, but we just cannot get
> ahold of it using language and the rational mind.
"Something is necessary" is ambiguous; it might mean "It is necessary
that there is something", or it might mean "There is something such
that it is necessary that *it* exists."
Saikat Guha
cardinal lambda, the union of lambda many sets each with lambda many
elements has lambda many elements in it. The power set of the union
would then have 2^lambda many elements. At most, then, it would seem
that the modal realist ontology gives you 2^lambda objects to simulate
sets for some transfinite cardinal lambda.
I also discovered from the same mathematician the following. Given
the generalized continuum hypothesis and ZFC, it follows that the
cardinality of the real numbers is aleph_1, but this doesn't follow
without GCH. Then, using GCH, 2^aleph_1 = aleph_2, and 2^aleph_2 =
aleph_3. So it looks like, given GCH, the modal realist has at most
aleph_3 ordinary objects to play with.
Whether or not GCH is true, the set of all ordinary objects available
to the modal realist has some cardinality 2^lambda, where lambda is
the cardinality of the set of objects in any one world, which is the
cardinality of the power set of the set of real numbers. So his
ontological advantage isn't all that big. He gets one more
cardinality than someone who believes in continuum many spacetime
points and mereology on those points. The same remarks would seem to
apply, mutatis mutandis, to ersatzers who believe in a set of ersatz
possibilia as big as the set of possibilia of the modal realist. It
therefore seems that the space of possibilia is nowhere near big
enough to accommodate the set-theoretical universe.
I do want to return to the discussion of necessary being, but I'm not
sure if you're still interested, seeing as you haven't replied to my
last message. Anyway, I thought I'd let you know what I found out.
The Sophist
> I do want to return to the discussion of necessary being, but I'm not
> sure if you're still interested, seeing as you haven't replied to my
> last message. Anyway, I thought I'd let you know what I found out.
Thanks for the info on the cardinality of the modal realist universe, and I apologize for not replying to your last message. In all likelyhood, I missed it, as usenet is unreliable and I tend to read through these newsgroups fairly quickly; it may either not have reached me or been surrounded by junk so I missed it.
Saikat Guha
Please make sure your lines wrap, as it makes the message hard to read
otherwise. I've been preoccupied for a few days, but am now eager to
return to our discussion.
You say you are a linguistic ersatzist, and that your ersatz worlds
are set-theoretical constructions out of sentences. Let me just
suppose, for simplicity, that they are maximal consistent sets of
sentences in some appropriate worldmaking language. Then to say that
so-and-so is the case at a world is to say that so-and-so is the case
according to (the sentences which make up) that world, and to say that
possibly so-and-so is to say that so-and-so is the case at some
possible world. Again, to say that a world is actualized is to say
that things are as the world in question says they are. (All the
worlds are *actual*, in the sense of being parts of the one and only
world, but only one of the worlds is actualized, in the sense of
representing that one world as it truly is.) Now, given the axioms of
S5, whatever is possible is necessarily possible. So, if P at world
W, then in every possible world it is the case that possibly, P, that
is, that there is a possible world at which P. In particular, if in
place of "P" we put "W is actualized", then at every possible world it
is the case that there is a possible world at which W is actualized.
But, necessarily, the only such world is W itself. So it is the case
at every world that the there is a unique world at which W is
actualized, that is, that the world at which W is actualized exists,
that is, that W exists. So W exists in every possible world, so W
exists necessarily. It follows, then, that each possible world exists
necessarily. Thus it would seem that something does exist necessarily
on your modal metaphysics.
The Sophist
Unless I'm missing something, this argument could have been a lot
shorter. I would grant that it is necessarily true that there exists a
smallest prime number greater than 10. I suppose this could be seen as
committing me to counting 11 as a necessary being, but I somehow feel
that this was not the sort of thing you were looking for in your initial
question. I do not see that I am committed to the existence of the
world W in every world in any more significant sense than I am committed
to the existence of 11 in every world.
If I am missing some difference between 11 and W, please elaborate. If
I am not missing such a difference, then I suppose I must revise my
rejection of necessary being slightly. To the extent that logical,
mathematical, or linguistic entities count as beings (something I find a
little bit sketchy), they are presumably necessary beings. There are,
however, no other necessary beings besides those.
Saikat Guha
> shorter. I would grant that it is necessarily true that there exists a
> smallest prime number greater than 10.
I didn't know that you would grant that, since I didn't know you were
a realist about numbers. When giving an argument, I consider it wise
to begin from premises that I am pretty sure the person I am talking
to accepts. In retrospect I wish I had known this, since then I could
have given a much shorter argument.
> If I am missing some difference between 11 and W, please elaborate.
Well, no, if you are a realist about numbers and you concede the
necessity of arithmetical truths, then there is no difference; for
you, 11 exists just as surely as sets, in particular, just as surely
as the set-theoretical constructions out of sentences that you call
"possible worlds".
>To the extent that logical,
> mathematical, or linguistic entities count as beings (something I find a
> little bit sketchy), they are presumably necessary beings. There are,
> however, no other necessary beings besides those.
Perhaps you can elaborate on the "to the extent". Do you distinguish
between different kinds of being (like Meinong with his "being" and
"existence")? Or is there some other distinction to be made between
the sense in which logical, mathematical, and linguistic entities
exist and the sense in which you and I exist? If so, what is it?
If on the other hand these things exist in the same sense of "exists"
as the sense in which you and I exist, then that suffices for there to
be necessary beings, I would think, since a necessary being is just
something that exists necessarily.
The Sophist
> I didn't know that you would grant that, since I didn't know you were
> a realist about numbers. When giving an argument, I consider it wise
> to begin from premises that I am pretty sure the person I am talking
> to accepts. In retrospect I wish I had known this, since then I could
> have given a much shorter argument.
I am not sure that I am a realist about numbers. Surely there are few
anti-realists about numbers who wouldn't go to great lengths to ensure
that "there exists a least prime greater than 10" can somehow be
interpreted so as to say something true. I am not certain which such
interpretation I favor (or if I really prefer such an interpretation),
but I am pretty certain I would want to give the same account of
possible worlds as of numbers.
>>To the extent that logical,
>>mathematical, or linguistic entities count as beings (something I find a
>>little bit sketchy), they are presumably necessary beings. There are,
>>however, no other necessary beings besides those.
>
> Perhaps you can elaborate on the "to the extent". Do you distinguish
> between different kinds of being (like Meinong with his "being" and
> "existence")? Or is there some other distinction to be made between
> the sense in which logical, mathematical, and linguistic entities
> exist and the sense in which you and I exist? If so, what is it?
Let's see, how can I elaborate on this. Well, as an ersatzist, I am
taking possible worlds with something less than full seriousness; I'm
not saying that anything which exists according to the worlds really
exists. Also, as a linguistic ersatzist, I am using logical rules to
construct the worlds. Thus, if the logic were not held constant, the
project of construction would be hopeless. This does mean that anything
which must exist to make the logic work is necessary, but only because
necessity itself is part of the logic.
I guess another approach I would be fairly willing to take if I had no
alternative is to say that only things in space and time are contingent,
and that is all I want my modal theory to accomodate. I know that
people have tried to suggest that there are things other than numbers
and sets which are outside space and time (God, for example), but to the
extent that I can make sense of spirits, or any of the other non-logical
sometimes thought to be outside space and time, I find that I can only
make sense of them as being temporally or spatially located. So I'm
reasonably comfortable saying that people who locate God outside space
and time are either talking nonsense or worshipping numbers. However, I
guess I do have a mild preference for some alternative to making it
necessary that every contingent thing exist in space and time.
I don't want to try to make Meinongian distinctions, so if I have to say
that 11 exists, then it just exists. The differences between that and
saying that the earth exists are just the usual; the earth is in space
and time and has causal influences and so forth, and 11 doesn't.
Saikat Guha
> anti-realists about numbers who wouldn't go to great lengths to ensure
> that "there exists a least prime greater than 10" can somehow be
> interpreted so as to say something true.
Well, we are considering a realism which counts that statement as
something necessarily true, not just true (else I couldn't prove a
necessarily existing number like this). The only kinds of
anti-realism about numbers that I know of that have *that* feature
make numerical existential statements depend on some other necessarily
existing things (sets or linguistic entities, perhaps). And it's
plausible to suppose that they would have to do that, since whatever
these existential claims depend on, they must depend on the existence
of some objects, be they numbers or something else. If the statements
are necessary truths, it seems the objects they supervene on must be
necessary beings (else they're not guaranteed to all be around). But
if you have a version of numerical anti-realism that avoids the need
to assume any necessary entities to "do duty for" numbers, I would be
interested to see how that goes.
> Let's see, how can I elaborate on this. Well, as an ersatzist, I am
> taking possible worlds with something less than full seriousness; I'm
> not saying that anything which exists according to the worlds really
> exists.
No, but I initially supposed you do think the worlds really exist.
After all, you provide truth-conditions for possibility claims that
quantify existentially over certain set-theoretical constructions that
you call "possible worlds". Unless you have some sort of anti-realist
account of the metalanguage of modal logic, it seems you are committed
to the real existence of the worlds, though not of their merely
possible "denizens". Or do you have some unusual, non-Quinean account
of ontological commitment? If so, what?
> Also, as a linguistic ersatzist, I am using logical rules to
> construct the worlds. Thus, if the logic were not held constant, the
> project of construction would be hopeless. This does mean that anything
> which must exist to make the logic work is necessary, but only because
> necessity itself is part of the logic.
This part I don't understand; it's a bit too cryptic, or maybe just
too compressed.
> I don't want to try to make Meinongian distinctions, so if I have to say
> that 11 exists, then it just exists. The differences between that and
> saying that the earth exists are just the usual; the earth is in space
> and time and has causal influences and so forth, and 11 doesn't.
Here I'm on Quine's side; it seems to me that those are differences in
the way 11 is as opposed to the way the earth is, not that there are
two different senses of "exists" at work here. (Which is what you
seem to be saying, though it isn't absolutely clear.) I am
sympathetic to the idea that talk of different kinds of existence is
just talk in slightly different language about major differences in
what features things have, such as those distinguishing different
ontological categories. But that doesn't in my view correspond to
different senses of "exists", but to different predicates constructed
with adverbial modifiers from "exists", such as "exists physically"
(meaning "is identical to a physical thing"), "exists abstractly"
(meaning "is identical to an abstract thing"), and so forth. These
are analogous to the standard definition of existence by way of
identity, on which "exists" means "is identical to something".
The Sophist
> Well, we are considering a realism which counts that statement as
> something necessarily true, not just true (else I couldn't prove a
> necessarily existing number like this). The only kinds of
> anti-realism about numbers that I know of that have *that* feature
> make numerical existential statements depend on some other necessarily
> existing things (sets or linguistic entities, perhaps). And it's
> plausible to suppose that they would have to do that, since whatever
> these existential claims depend on, they must depend on the existence
> of some objects, be they numbers or something else. If the statements
> are necessary truths, it seems the objects they supervene on must be
> necessary beings (else they're not guaranteed to all be around). But
> if you have a version of numerical anti-realism that avoids the need
> to assume any necessary entities to "do duty for" numbers, I would be
> interested to see how that goes.
OK, I'm confused now. There are forms of anti-realism about numbers
which don't count "there is a least prime greater than 11" as
necessarily true? They think it's contingent? Which theories would
those be?
>> Also, as a linguistic ersatzist, I am using logical rules to
>>construct the worlds. Thus, if the logic were not held constant, the
>>project of construction would be hopeless. This does mean that anything
>>which must exist to make the logic work is necessary, but only because
>>necessity itself is part of the logic.
>
> This part I don't understand; it's a bit too cryptic, or maybe just
> too compressed.
OK, let's take a specific example of linguistic ersatzism. Carnap
proposes that "necessary" should be understood as meaning "true
according to every state description." Carnap also proposes rules for
constructing state descriptions, and they are, of course, our ordinary
logical principles. It is therefore inevitable that nothing which
violates our ordinary logical principles will end up being true in any
state description, as the rules of state-description construction rule
out the construction of a state description which makes any such claim
true. Though I was recently re-reading Meaning and Necessity, I don't
recall whether Carnap explicitly discussed mathematical notions, but
certainly I would want the best non-modal logic I know of for
constructing my state descriptions, and I expect he would have
concurred. So the logic had better include enough to get us mathematics
as well. And that would be why "there is a least prime greater than 11"
comes out necessarily true, because in order to falsify it a state
description would have to be constructed in a way which violates the
rules, which is ruled out by the definition of state descriptions.
Now, the way we might get necessary being out of this is that if we need
sets or numbers or any other entities to make our logic work, and all of
our state descriptions are by their nature descriptions of possible
worlds where our logic works, then it would seem that all of our state
descriptions are of worlds with our sets or numbers or whatever, and so
these logical or mathematical entities are necessary beings. I hope
this explains why I think any form of mathematical anti-realism is
likely to solve the problem; if our mathematics doesn't require numbers
or sets or anything like them, then the state descriptions won't depend
on the existence of such entities and so won't automatically entail them.
Saikat Guha
> which don't count "there is a least prime greater than 11" as
> necessarily true? They think it's contingent? Which theories would
> those be?
The most straightforward examples are theories which model arithmetic
by way of contingent objects. If you have denumerably many things
that are ordered as a progression by some relation, you can use those
things to model the natural numbers. (The ordering relation itself is
free of charge; surely if the things exist, there are infinitely many
such relations among them.) The things could be events, spacetime
points, or even material objects if there are enough of them. Then
take Peano's axioms (written, for simplicity, with "successor" as the
only primitive) and Ramsify it as Lewis does with set theory. (The
critical point here is that you need only mereology plus plural
quantification to do all this--no abstract objects at all. You can
use the technique Lewis' co-authors outline in "Parts of Classes",
though much simpler techniques will suffice for a system as elementary
as Peano arithmetic.) What you get is a Ramsey sentence that
(somewhat informally speaking) starts out "There is a relation, call
it successorship, and a collection of things, call them numbers, such
that . . ." Other arithmetical claims are to be interpreted as saying
this plus "Any relation and collection of things such that . . . is
also such that . . . ". The sentences of the Ramsified theory are
guaranteed to be true as long as there are denumerably many things.
(Because the ordering relation is free.) But *only* so long as there
are denumerably many things. In a world with finitely many contingent
objects (and no necessary objects), the theory is false. Since the
theory doesn't assume any necessary abstract objects--just ordinary
contingent ones--it doesn't assume that what it says is necessarily
true.
Again, if you have continuum many ordinary objects (spacetime points,
say, or events) to model the real number system, then, given mereology
and plural quantification, you can model a pretty large chunk of
classical mathematics, I would guess everything in the theory of real
and complex numbers, ordered n-tuples thereof, and maybe functions on
these. Spacetime points seem especially nice for the purpose, as they
don't overlap; if they are used to simulate real and complex numbers
and ordered n-tuples thereof, mereology can be used to simulate talk
of sets of such numbers and n-tuples, and plural quantification can be
used in some measure to simulate talk of mappings among them. I
haven't developed such a theory, of course, and it may be beyond my
mathematical competence to do it in detail, but Lewis' work on
"megethology" makes me pretty confident that the project can be
completed. Note that doing this is a long way from modelling set
theory (with its intended meaning, not a Skolemized interpretation),
or the entirety of mathematics, but it does count as anti-realism
about *numbers*. Anti-realism about numbers isn't the same thing,
obviously, as anti-realism about all mathematical objects.
> >> Also, as a linguistic ersatzist, I am using logical rules to
> >>construct the worlds. Thus, if the logic were not held constant, the
> >>project of construction would be hopeless. This does mean that anything
> >>which must exist to make the logic work is necessary, but only because
> >>necessity itself is part of the logic.
> >
> > This part I don't understand; it's a bit too cryptic, or maybe just
> > too compressed.
For some reason I thought there was a "not" following "does" in "This
does mean that . . ." That's what confused me.
> I hope
> this explains why I think any form of mathematical anti-realism is
> likely to solve the problem; if our mathematics doesn't require numbers
> or sets or anything like them, then the state descriptions won't depend
> on the existence of such entities and so won't automatically entail them.
I agree that a form of general anti-realism about mathematical objects
(one that didn't invoke any other necessary abstracta to simulate the
objects) that somehow still countenanced the necessary truth of
mathematics might have the resources to do away with necessary beings,
though I have no idea what a viable form for such an anti-realism
would be. I cannot imagine any way of showing that set theory, say,
is necessarily true even though there are neither any sets nor any
other necessarily existing abstracta or any other necessarily existing
things. Do you know how such an anti-realism would work? If so,
please tell me. This would be something quite new for me.
By the way, do you accept Quine's views on ontological commitment?
Also, what did you think of what I said about different kinds of
existence?
The Sophist
> I agree that a form of general anti-realism about mathematical objects
> (one that didn't invoke any other necessary abstracta to simulate the
> objects) that somehow still countenanced the necessary truth of
> mathematics might have the resources to do away with necessary beings,
> though I have no idea what a viable form for such an anti-realism
> would be. I cannot imagine any way of showing that set theory, say,
> is necessarily true even though there are neither any sets nor any
> other necessarily existing abstracta or any other necessarily existing
> things. Do you know how such an anti-realism would work? If so,
> please tell me. This would be something quite new for me.
I wonder if this is the problem. Linguistic ersatzism says that to be
possible is to be true according to some appropriately constructed
linguistic entity like one of Carnap's state descriptions. Of course it
would be possible for there to be no languages, but this doesn't mean
that it's possible for nothing to be possible; what's possible is what's
true according to the state descriptions we construct, not what's true
according to whatever other possible beings might or might not call
state descriptions in alien languages. I am not completely certain
whether a state description could describe a world of such impoverished
resources that that world would have nothing which could play the role
of the language of our state descriptions, but even that wouldn't mean
that nothing would be possible according to that world. What's possible
according to any world is just what's true according to some state
description which can be constructed using our logic. Sometimes I get
the sense that the problem is that you don't feel like this would be an
adequate account of necessity, so you're assuming I must mean something
other than this.
> By the way, do you accept Quine's views on ontological commitment?
> Also, what did you think of what I said about different kinds of
> existence?
As I said, I'm not a believer in Meinongian distinctions. I guess I'm
more inclined to go with Carnap (again) and say that existing according
to a theory is, as Quine would have said, to be one of the entities the
theory quantifies over, and to say that there doesn't seem to be much of
a way to make sense of existing other than according to a theory.
Saikat Guha
> possible is to be true according to some appropriately constructed
> linguistic entity like one of Carnap's state descriptions. Of course it
> would be possible for there to be no languages, but this doesn't mean
> that it's possible for nothing to be possible; what's possible is what's
> true according to the state descriptions we construct, not what's true
> according to whatever other possible beings might or might not call
> state descriptions in alien languages. I am not completely certain
> whether a state description could describe a world of such impoverished
> resources that that world would have nothing which could play the role
> of the language of our state descriptions, but even that wouldn't mean
> that nothing would be possible according to that world. What's possible
> according to any world is just what's true according to some state
> description which can be constructed using our logic. Sometimes I get
> the sense that the problem is that you don't feel like this would be an
> adequate account of necessity, so you're assuming I must mean something
> other than this.
One constraint that I think applies to any adequate account of
modality is that it should respect logical truths, in particular modal
logical truths, and even more particularly the S5 principle that
whatever is possible is necessarily possible. According to your
linguistic ersatzism, this is equivalent to the following claim:
(S5) Anything that is true in some linguistic ersatz possible world
is, in every linguistic ersatz possible world, true in some linguistic
ersatz possible world.
(Where "in" means "according to".)
Let me abbreviate "linguistic ersatz possible world" by its initials:
"lepw". According to you, there is a (unique) lepw, the actual one,
such that whatever is true in it is true (period) and whatever is true
(period) is true in it. One thing that is true in this lepw is that
Aaron Boyden studied under David Lewis. Let us call this truth "A".
Then, since A is true in the actual lepw, A is true in some lepw. By
(S5) above, in every lepw A is true in some lepw. "A is true in some
lepw" means "there is an lepw in which A is true", and an elementary
logical consequence of this is that there is at least one lepw. Since
truth-in-a-possible world is closed under elementary logical
consequences, in every lepw there is at least one lepw. Now it is
impossible that there is at least one lepw and there are no lepws.
Therefore in no lepw is it the case that there is at least one lepw
and there are no lepws. But "There is at least one lepw and there are
no lepws" is an elementary logical consequence of "There is at least
one lepw" and "There are no lepws". Since truth-in-a-possible world
is closed under elementary logical consequences, there is no lepw in
which there is at least one lepw and in which there are no lepws. But
since there is at least one lepw in every lepw, there is no lepw in
which there are no lepws.
Now this argument is perfectly rigorous, and an equally rigorous
argument can be made out that each lepw exists in every lepw, and this
according to you is equivalent to the claim that each lepw exists
necessarily, which (together with the fact that there are quite a lot
of lepws in your view) entails that quite a lot of things exist
necessarily. (I've probably already bored you with the argument of
the previous paragraph, so I won't give the argument for the claim
that each lepw exists in every lepw.) You say you are not a
Meinongian and you don't distinguish different senses of "exist", yet
somehow you *seem* to be saying that your view isn't committed to the
necessary existence of anything, at least in the sense that you and I
exist. The only sense I can make of this is that you reject the S5
principle which makes these arguments tick. If that is what you mean,
I do indeed think you've got an inadequate account of necessity. If
that isn't what you mean, then I don't understand you, and I ask you
to explain in more detail just what you do mean. In particular, will
you please explain just where, in your view, these arguments go wrong.
(They must go wrong somewhere if your view isn't committed to
necessary beings.)
> As I said, I'm not a believer in Meinongian distinctions. I guess I'm
> more inclined to go with Carnap (again) and say that existing according
> to a theory is, as Quine would have said, to be one of the entities the
> theory quantifies over, and to say that there doesn't seem to be much of
> a way to make sense of existing other than according to a theory.
Presumably you can make sense of truth--you'd better, else you
couldn't distinguish the actual lepw from the others! Given the
notion of truth it seems to me quite easy to make sense of existing
simpliciter, that is, existence as something other than just existing
according to a theory. To wit: existing is existing according to a
*true* theory. Or, if you like, existing is existing in the actual
world. (Where "the actual world" must be taken nonrigidly.) Yet
another way to define "exists" is available to you if you understand
the notion of identity and elementary logical notions such as
quantification. Then, existing is being identical to something. I
can't therefore see any difficulty in understanding existing as
something other than just existing according to a theory.
The Sophist
>>As I said, I'm not a believer in Meinongian distinctions. I guess I'm
>>more inclined to go with Carnap (again) and say that existing according
>>to a theory is, as Quine would have said, to be one of the entities the
>>theory quantifies over, and to say that there doesn't seem to be much of
>>a way to make sense of existing other than according to a theory.
>
> Presumably you can make sense of truth--you'd better, else you
> couldn't distinguish the actual lepw from the others!
Truth according to a theory, sure. Truth independent of a theory, I
have the same problems. Hence, what follows doesn't for me. And I
distinguish the actual lepw from the others using some theory or other,
whichever happens to be convenient at the moment.
In any event, I have tried so far to be agnostic about whether 11
necessarily exists. You've presented various arguments that this
agnosticism is untenable; it seems to me that all of these arguments
presuppose the realism about logical/mathematical entities that they
were intended to establish, but I am beginning to think I'd have to pick
a specific variety of anti-realism to explain how. I could go off and
do that, but since as I said I'm agnostic rather than being a committed
anti-realist, I'm interested in the other side of the question. Suppose
11 necessarily exists. So there are necessary beings. So what? Does
anything else important follow from that?
Saikat Guha
> have the same problems.
What problems? (Just curious.)
> In any event, I have tried so far to be agnostic about whether 11
> necessarily exists. You've presented various arguments that this
> agnosticism is untenable; it seems to me that all of these arguments
> presuppose the realism about logical/mathematical entities that they
> were intended to establish, but I am beginning to think I'd have to pick
> a specific variety of anti-realism to explain how.
Realism about mathematical theorems (as opposed to realism about
mathematical objects) is nothing more than taking them at face value
(or naively, if you like) and believing that they are necessary
truths. Do that, and together with Quine's criterion of ontological
commitment it follows straightaway that certain necessary mathematical
entities exist. Sometimes it is wrong to take a class of statements
at face value, because the statements should be taken in some other
way. Or it may be that such statements should not be supposed to be
true (either necessarily or contingently, whichever one would naively
suppose). He who says that this is so with mathematical statements is
an anti-realist on that subject. Or one might say that Quine's
criterion is wrong. Those are two ways to avoid realism about
mathematical objects.
As near as I can tell, you have taken both ways. On the one hand you
side with Carnap against Quine about the intelligibility of "external"
versus "internal" ontological questions. On the other hand you seem
to be saying that there is some way to reconstrue mathematical (and
metalogical, and linguistic) claims so as to avoid commitment to
abstract things, though you remain agnostic about which of the various
proposed ways is correct. If this is not a fair statement of your
view, please tell me wherein I have erred.
If this is a fair statement of your views, I find it curious that you
should take both of these routes to anti-realism about mathematical
objects. Either by itself seems sufficient, if it is workable. (The
hard part is to make it work.) Both together seem excessive, and to
give you more work than you need.
> I could go off and
> do that, but since as I said I'm agnostic rather than being a committed
> anti-realist, I'm interested in the other side of the question. Suppose
> 11 necessarily exists. So there are necessary beings. So what? Does
> anything else important follow from that?
Well, one thing that I think follows is that naturalism is false, for
I think it is pretty clear that no material things, or any other
things that the natural sciences study, could be necessary beings, if
only because the Big Bang need not have taken place. (And if it
hadn't, I don't suppose any of the natural objects that do exist would
have existed--or anyway they might not have existed.) For the same
reason necessary beings couldn't very well depend on anything natural.
And this leads to interesting philosophical problems. For instance,
what is the relation between these necessary beings and the natural
world? Are they outside the natural world altogether? Does that mean
they are outside space and time? (Presumably the answer is "Yes".) If
so, can they interact causally with us or anything we can interact
with? If so, how? If not, what explains the fact that we know so
much about them? And so on.
By the way, while I believe there is a necessary being, I don't think
I qualify as a believer in abstract objects. The only necessary
beings I believe in are God and God's mental states, and I don't
suppose these qualify as abstract objects. I am willing to identify
numbers, sets, properties, propositions and the like with certain of
God's mental states, but I think if you do identify them thus, you can
no longer call them abstract objects. (I am not certain that thus
identifying them is the right way to go, but I am friendly to the
idea.) Thus, while I am certain that necessary beings exist, I don't
think there are any necessary abstract objects, and I don't know if 11
necessarily exists or not. But if it does necessarily exist, then it
is one of God's mental states. I am only telling you this because it
would be misleading not to. I think, though, that the evidence for
necessary beings is of much broader appeal than the evidence for my
particular beliefs about what necessary beings there are, and thus the
case for necessary beings can be more profitably argued without
arguing for a particular view (mine or any other) of what necessary
beings there are. The reason is that there are philosophical problems
which I think cannot be adequately solved without invoking necessary
beings, and these problems are problems for all philosophers. An
indication of this is that many atheistic philosophers nonetheless
believe in necessary (abstract) beings, because they feel bound to
posit such things to avoid the problems to which anti-realism is heir.
To argue the case for necessary beings without arguing for a
particular view of which ones there are merely requires showing to be
inadequate all the solutions to these problems that don't posit any
necessary beings. That is what I am trying to do.
The Sophist
> As near as I can tell, you have taken both ways. On the one hand you
> side with Carnap against Quine about the intelligibility of "external"
> versus "internal" ontological questions. On the other hand you seem
> to be saying that there is some way to reconstrue mathematical (and
> metalogical, and linguistic) claims so as to avoid commitment to
> abstract things, though you remain agnostic about which of the various
> proposed ways is correct. If this is not a fair statement of your
> view, please tell me wherein I have erred.
>
> If this is a fair statement of your views, I find it curious that you
> should take both of these routes to anti-realism about mathematical
> objects. Either by itself seems sufficient, if it is workable. (The
> hard part is to make it work.) Both together seem excessive, and to
> give you more work than you need.
Well, here are two obvious reasons to take an interest in both routes.
First, as I said, I don't really know what the answer is, and a
disjunction is of course always more likely to be true than either
disjunct. More productively, and a reason to take both routes at once,
accepting Carnap's separation between internal and external questions
doesn't mean abandoning the goal of theoretical unification; even if
mathematical discourse can perfectly well be accepted entirely on its
own merits, an account which reconstrues mathematical discourse might be
part of a larger integrated theory with pragmatic advantages.
On naturalism, I think it comes in two varieties; one form of naturalism
makes claims such as Armstrong's claim that the spacetime system is all
that exists. I think it is clear that Armstrong intends this as an
external claim, and so I feel about it as you would expect (that is, I
don't so much reject it as find it silly). The other form of naturalism
is quite different and not to be confused with the first; I think for
many people naturalism should be taken as no more than a committed
rejection of spooky stuff (the usual suspects, God, souls, intrinsically
motivating moral properties external to those making moral judgments,
and so forth). Spooky stuff is surely not a natural kind, and so the
rejection of spooky stuff can't be a result of grand metaphysical
theorizing; rather, it is a modest empirical doctrine. It is just a
common sense result based on various case by case evidence concerning
individual bits of spooky stuff and a general feeling that all this
spooky stuff is related.
Saikat Guha
> First, as I said, I don't really know what the answer is, and a
> disjunction is of course always more likely to be true than either
> disjunct.
I thought you accepted the conjunction, not the disjunction--and the
former is less likely to be true than its conjuncts.
As to naturalism, why isn't rejection of "spooky stuff" an external
claim just as much as Armstrong's? A *different* external claim, to
be sure; but aren't these naturalists of yours saying that there is no
God, period, not that there is no God only according to a certain
theory? (Which theory?!)
Also, I remain curious as to what arguments, if any, you have for
rejecting the intelligibility of external ontological questions.
The Sophist
> As to naturalism, why isn't rejection of "spooky stuff" an external
> claim just as much as Armstrong's? A *different* external claim, to
> be sure; but aren't these naturalists of yours saying that there is no
> God, period, not that there is no God only according to a certain
> theory? (Which theory?!)
The answer to "which theory?" is common sense, as I believe I suggested
in my previous post. There are other candidates for theories according
to which spooky stuff is to be rejected (various scientific views, for
example). There are also theories according to which spooky stuff
exists, of course, but I am not aware of any which seem to be useful
replacements for common sense or science, so while they may have a
supplemental role (possibly in the artistic realm or something) they
would not affect the common sense claim that there is no God.
> Also, I remain curious as to what arguments, if any, you have for
> rejecting the intelligibility of external ontological questions.
Unfortunately, this is a point where I part company with Carnap. I
don't like his criterion of intelligibility, and I don't have a good
proposal for a substitute. So let's just say I've never met a putative
external ontological question which I could make sense of without
transforming it into an internal question of some theory or other.
Saikat Guha
> in my previous post.
I'm not sure there is a theory going by the name "common sense", but
let us put that aside. This seems to me a gross mischaracterization
of the views of the naturalists you spoke of. For according to this,
these naturalists do not disagree with all theists. If a theist
concedes that God does not exist according to common sense, but says
that God does exist nonetheless, these naturalists, on your
characterization, wouldn't disagree with him. But virtually all
naturalists of the spooky-stuff-is-bunk variety that I know of say
(some of them quite vehemently) that there is just no God at all, that
*all* theists are wrong in their theistic beliefs. You may well be
the only naturalist whose views are correctly described by what you
have said (well, you and Carnap). And I didn't ask you to
characterize your particular brand of naturalism. I asked you to
explain why the ontological claims made by all the other naturalists
shouldn't be taken at face value--as external ontological claims.
> So let's just say I've never met a putative
> external ontological question which I could make sense of without
> transforming it into an internal question of some theory or other.
Well, let us consider the question, "Does God exist?". This would
seem to be a paradigm case of an external ontological question. Now
what's your difficulty with making sense of it as such?
Saikat Guha
messages on this thread. I wanted to find out which if any of the
"spooky stuff" atheists there would accept your characterization of
their views. The thread is entitled "Two Forms of Atheism". I hope I
have been fair to your views. If not, let me know.
The Sophist
> Well, let us consider the question, "Does God exist?". This would
> seem to be a paradigm case of an external ontological question. Now
> what's your difficulty with making sense of it as such?
Well, as usual, the difficulty with making sense of it as such is that I
have no idea what it would mean in that case. I know of a bunch of ways
people have tried to fit God into various theories, and can comment on
any of those if there's one you'd like to discuss, but absent any
theory, I can't figure out what is being claimed.
The Sophist
Unfortunately, I don't read alt.atheism; too much pointless traffic. I stick to alt.atheism.moderated and alt.atheism.holysmoke for my atheist reading needs.
Saikat Guha
> have no idea what it would mean in that case. I know of a bunch of ways
> people have tried to fit God into various theories, and can comment on
> any of those if there's one you'd like to discuss, but absent any
> theory, I can't figure out what is being claimed.
Well, let's try this. Someone tells you the following story.
"There is someone who made the world. He knows everything there is to
know about the world. In fact, he is as knowledgeable as anyone could
be. Also, he is as powerful as anyone can be. He doesn't have a body,
as you and I have, but he has a mind. He has thoughts and beliefs and
feelings and wants, just as you and I do. He is a good person. In
fact, he is a perfectly good person. You and I may slip up from time
to time; surely each of us would agree that we could be better people
than we are. But this person could not have been better than he is,
and not only that, no-one could possibly be better than he is. This
person created you and I and everything else that there is besides
him."
Do you understand what's being claimed here? If you don't, I will
have to chalk this up to a case of incurable philosophical
incomprehension. I'll bet you would have understood this story as a
child, whether or not you do now. In fact, I'll bet you were told
this story, or something like it, as a child, and have held various
propositional attitudes towards it. And please note that those who
tell this story do not claim to be saying how things are according to
any theory; they claim to be saying how things are, period.
The Sophist
> Well, let's try this. Someone tells you the following story.
>
> "There is someone who made the world. He knows everything there is to
> know about the world. In fact, he is as knowledgeable as anyone could
> be. Also, he is as powerful as anyone can be. He doesn't have a body,
> as you and I have, but he has a mind. He has thoughts and beliefs and
> feelings and wants, just as you and I do. He is a good person. In
> fact, he is a perfectly good person. You and I may slip up from time
> to time; surely each of us would agree that we could be better people
> than we are. But this person could not have been better than he is,
> and not only that, no-one could possibly be better than he is. This
> person created you and I and everything else that there is besides
> him."
Well, I've already said I think common sense is a theory. I don't think
there are always sharp lines between theories and parts of theories.
This story seems to make claims which are false given the theories I use
to talk about persons, minds, bodies, and the world as a whole; as best
I can tell, people always have bodies, for example. Indeed, some of
them not only aren't but can't be true on the best theories I can
construct; no plausible moral theories I'm familiar with can quite make
sense of perfect goodness. These sorts of things are the reason I said
the non-existence of God is a matter of common sense.
I remain open to the possibility that these claims could be interpreted
in some other way than according to my best efforts at common sense
theorizing, of course. I don't know of such a way, but I generally have
doubts about a priori claims restricting the range of possible
theorizing, so I try not to make such claims myself.
> And please note that those who
> tell this story do not claim to be saying how things are according to
> any theory; they claim to be saying how things are, period.
Perhaps they mean something else by theory than I do. Probably they
haven't thought about the matter. My best theory of theories would
maintain that they are saying how things are according to a theory,
regardless of whether they're happy with the words I use to describe
their activity.
Saikat Guha
> in some other way than according to my best efforts at common sense
> theorizing, of course. I don't know of such a way, but I generally have
> doubts about a priori claims restricting the range of possible
> theorizing, so I try not to make such claims myself.
Look, the point is quite simple. You said you were unable to make
sense of the claim that God exists, only claims of the form "God
exists according to theory T". Now, how have you interpreted the
story I produced? Apparently as making claims about how things are,
claims which are false according to common sense. Presumably the
story does not in your view say that those claims are true according
to a certain theory. If that is so, then the theory in question is
some theistic religious theory. How could it be false according to
common sense that that story is false according to some theistic
religious theory?
> Perhaps they mean something else by theory than I do. Probably they
> haven't thought about the matter. My best theory of theories would
> maintain that they are saying how things are according to a theory,
> regardless of whether they're happy with the words I use to describe
> their activity.
If that's so, how can what they say be false according to common
sense?
The Sophist
> Look, the point is quite simple. You said you were unable to make
> sense of the claim that God exists, only claims of the form "God
> exists according to theory T". Now, how have you interpreted the
> story I produced? Apparently as making claims about how things are,
> claims which are false according to common sense. Presumably the
> story does not in your view say that those claims are true according
> to a certain theory. If that is so, then the theory in question is
> some theistic religious theory. How could it be false according to
> common sense that that story is false according to some theistic
> religious theory?
Lots of terms from common-sense theory showed up in that story; I
mentioned some of them in my previous reply. Terms like "body," "mind,"
"person," "good," and so forth. I think I know what they mean, but only
according to common sense theory. Thus, I interpreted the story as
being an extension of common sense theory, and interpreted as such it
seemed to be false. Of course, as I said, I am open to the possibility
that it might have been some other theory (a theistic religious theory
as you suggest, perhaps). In that case, "body" and the rest presumably
did not mean what they mean according to common sense, so I would no
longer be able to claim to understand any part of the story.
Saikat Guha
> mentioned some of them in my previous reply. Terms like "body," "mind,"
> "person," "good," and so forth. I think I know what they mean, but only
> according to common sense theory. Thus, I interpreted the story as
> being an extension of common sense theory, and interpreted as such it
> seemed to be false.
False according to common sense, you mean? So let me see. You
interpreted the story as saying, "So-and-so is true according to
common sense". And you argue that it is false according to common
sense that so-and-so is true according to common sense. So your
"common sense" is an inconsistent theory?
The Sophist
I've been trying to figure out where you think the inconsistency is, and
it really didn't leap out at me. However, I do now think that I should
probably have inserted an "intended as" between "being" and "an
extension" above. Would that resolve the inconsistency you think you
see? That's the only thing which looks questionable to me above.
Saikat Guha
> it really didn't leap out at me. However, I do now think that I should
> probably have inserted an "intended as" between "being" and "an
> extension" above. Would that resolve the inconsistency you think you
> see? That's the only thing which looks questionable to me above.
Having thought the matter over, I've concluded that I don't really
understand even how the notion of inconsistency would be defined in
your view, and I don't really understand the view. The main
difficulty for me is that, as near as I can tell, all statements in
your view are semantically incomplete. To wit:
"There are chairs" means "There are chairs according to theory T"
"There are chairs according to theory T" means "There are chairs
according to theory T according to theory T'"
"There are chairs according to theory T according to theory T'" means
"There are chairs according to theory T according to theory T'
according to theory T''"
And so on. The reason is that you say you cannot make sense of any
statement's being true, period, so every statement would have to be
relativized to a theory, and that in turn to another theory, and so
on. The only way I see out of this is to deny that "It is true that
P" is equivalent to P, which again would make your view unintelligible
to me.
Anyway, I am going to do other things for a while, and won't be
posting to the Usenet in the near future, so I am afraid this
discussion will have to end here. I think I have learned some things,
and I hope you gained something from it as well.