Can Existence Be Quantified Away?

I’ve been following some interesting stuff by Bill Vallicella about the “thickness” or otherwise of existence. I think the general debate is this: if you can use logical quantifiers to define “Socrates exists” in a sort of Quinean way then you remove at a stroke Heideggerean concerns about the import of “exists”. Thick theorists such as Mr Vallicella believe such reductionism to be misconceived. I think the idea is that the quantifiers import what they aim to omit and if they don’t they leave out other issues that are at leat as important etc….

Anyway there is no point in getting on board with this stuff without going back to primary texts so I opened Graham Priest’s texbook on non-classical logic to find that “A set X, is a collection of objects….”

OK: so how does the reductionism get off the floor then if set theory at its most anodyne uses a concept such as “object” which is, shall we say, metaphysically neutral?

(I realise that there’s an apples and oranges issue there but the point obtains doesn’t it? If you’re attemtpting to avoid ontological promiscuity via logical austerity had’t you be careful what you’re notation commits you to?)

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68 Comments.

  1. Are you referring to this blog entry by Vallicella?

    “Nausea at Existence: A Continental Thick Theory”

    http://maverickphilosopher.typepad.com/maverick_philosopher/2012/07/nausea-at-existence-the-thick-theory-illustrated-in-sartres-nausea.html

  2. You might be interested in the chapter “Existence” of the following book, in which Colin McGinn argues against quantificational reductionism that “‘exists’ is a predicate and that it expresses a property just as other predicates do (whatever properties are and whatever it is for predicates to express them).” (p. 50)

    * McGinn, Colin. Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Oxford University Press, 2000.

  3. Both Priest and McGinn argue for the disentanglement of quantification and ontological commitment. The so-called existential quantifier had better be called “particular” (Priest) or “intentional” (McGinn) quantifier and be existentially neutral. Priest uses “S” for the particular quantifier, and if we also introduce a primitive predicate “E!” (as used in free logic), the classical, ontologically committing existential quantifier can be defined as follows:

    ExFx : Sx(Fx & E!x)

    There is/exists something such that x is F
    iff
    Something is such that it is F and exists.

    I think this is a very good and useful idea.
    With the existentially neutral particular quantifier at hand, we can have true statements of the form “Sx~E!x”/”Some things don’t exist”, whereas statements of the form “Ex~E!x”/”There is/exists something that doesn’t exist” are necessarily false.
    For more, see:

    * Priest, Graham. “Not to be.” In The Routledge Companion to Metaphysics, edited by Robin Le Poidevin, Peter Simons, Andrew McGonigal, and Ross P. Cameron, 234-245. Abingdon: Routledge, 2009.

  4. @Myron: yes that’s one of the blog entries. I don’t know if Inwagen has Vallicella on his radar or not but would be interested if you have an input. Thanks for the McGinn “heads up”.

  5. I wrote:
    “…we can have true statements of the form ‘Sx~E!x’/…, whereas statements of the form ‘Ex~E!x’/…”.

    Correctly speaking, “Sx~E!x” and “Ex~E!x” are statements rather than forms of statements.

  6. @myron

    Thanks for the Priest pointer. The contrarian in me aadmires a guy who argues for true contradictions so will take a min to think that through….

  7. If we read an existential statement such as “Dogs exist” as “Some objects fall under the concept ‘dog'”, as “The number of objects falling under the concept ‘dog’ is greater than zero”, or as “The property of being a dog has some instances”, then, as Vallicella and McGinn argue, there are still tacit existential presuppositions:

    – “Some existent objects fall under the existent concept ‘dog’.”
    – “The existent number of existent objects falling under the existent concept ‘dog’ is greater than zero.”
    – “The existent property of being a dog has some existent instances.”

    Arguably, it is not possible to reductively quantify these away. In my view, the property account of existence is not completely reducible to the quantifier (or second-order Kant-Frege-Russell-Quine) account of existence.

    “[T]he standard prima facie objections to treating ‘existence’ as a predicate have been effectively disposed of. Whether deeper interpretational objections are forthcoming or not, none have been put forward so far. …Thus there can be no objection to an attempt to find a formal counterpart to the phrase ‘a exists’.”

    (Hintikka, Jaakko. “Existential Presuppositions and their Elimination.” In Models for Modalities: Selected Essays, 23-44. Dordrecht: Reidel, 1969. p. 29)

    That’s what free logic has successfully done by introducing the logical predicate “E!”, which expresses a property of individuals: http://plato.stanford.edu/entries/logic-free/

  8. @andy walsh:
    There’s nothing self-contradictory about “Some things do not exist” as long as you don’t start reading it as “There are/exist some things which do not exist” (*. So you can—as I do—reject dialetheism and at the same time accept the logical separation of ontological commitment from quantification.

    (* Some, e.g. Jody Azzouni [Deflating Existential Consequence, OUP 2004] argue that even “there is/are” can be used in an ontologically noncommitting way, e.g. in “There are fictional detectives”, where the ontological commitment is pragmatically annulled. But, on the other hand, there are philosophers who do believe in the existence of fictional objects and correspondingly don’t regard that statement as existentially neutral. Another problematic point is the question what “there is/are” means if it is used neutrally, and what the difference between it and “there exist(s)” is. Well, is there an intelligible difference between being and existing? Van Inwagen doesn’t think so, and neither do I.)

  9. Dudley M. Jones

    “Can Existence Be Quantified Away?” – does this mean all that stuff I learned in physics classes is not true? Every once in a while going through life I bump into a physics example (the way your body feels when a bus goes around a corner, the way a candle reflects through a glass of water) and without fail the physics is consistent with my experience. Every one of these examples can be numerically quantified. Is this an illusion that is fostered by my ignorance of theory of mind stuff?
    Best wishes from New Jersey

  10. Interesting post, albeit an elliptical one! Nice to see you back, Andy.

    @Myron:
    Thanks for your comments.

    There’s nothing self-contradictory about “Some things do not exist” as long as you don’t start reading it as “There are/exist some things which do not exist” (*. So you can—as I do—reject dialetheism and at the same time accept the logical separation of ontological commitment from quantification.

    Under Priest’s influence, I must confess that I’ve been converted over to the dark side.

    On the one hand, I would like to agree with you that contradictions are not assertable, since contradictions indicate confusion about the use of descriptions with respect to things in the world, and it’s best as a policy not to tolerate them. When someone asserts a contradiction, the burden is on the speaker to show that it is benign.

    But putting assertability aside, I do think there are cases where there is just no further point in denying that contradictions are true. These cases involve broadly indexical contents, perhaps like that from Sartre’s Nausea, cited in Vallicella above.

    Take the banal case of “the man on the threshold”. If all parties in conversation are in agreement about the general point of using the general terms, and all parties have access to the same perceptual information about the man’s relation to his surroundings, then there’s just nothing apart from a love of the law of non-contradiction which is preventing us from saying that the man both is and is not on the threshold. And if the only thing which prevents us from making that claim is that we don’t want contradictions, then really it’s question begging against the dialetheist.

    (Full disclosure: I’ve had dinner with Graham Priest and think he is a wee bit awesome. But I was sympathetic to his proposals for these reasons before I met him.)

  11. @BLS Nelson:
    I’ve enjoyed reading Priest’s thought-provoking books, but as for begging the question against dialetheism, I’d like to quote David Lewis, who is a “wee bit awesome” as well:

    “No truth does have, and no truth could have, a true negation. Nothing is, and nothing could be, literally both true and false. This we know for certain, and a priori, and without any exception for especially perplexing subject matters. …That may seem dogmatic. And it is: I am affirming the very thesis that Routley and Priest have called into question and—contrary to the rules of debate—I decline to defend it. Furthermore, I concede that it is indefensible against their challenge. They have called so much into question that I have no foothold on undisputed ground. So much the worse for the demand that philosophers always must be ready to defend their theses under the rules of debate.”

    (Lewis, David. “Logic for Equivocators.” 1982. In Papers in Philosophical Logic, 97-110. Cambridge: Cambridge University Press, 1998. p. 101)

    “I’m sorry; I decline to contribute to your proposed book about the ‘debate’ over the law of non-contradiction. My feeling is that since this debate instantly reaches deadlock, there’s really nothing much to say about it. To conduct a debate, one needs common ground; principles in dispute cannot of course fairly be used as common ground; and in this case, the principles not in dispute are so very much less certain than non-contradiction itself that it matters little whether or not a successful defence of non-contradiction could be based on them.”

    (Lewis, David. “Letters to Beall and Priest.” In The Law of Non-Contradiction: New Philosophical Essays, edited by Graham Priest, JC Beall, and Bradley Armour-Garb, 176-177. Oxford: Oxford University Press, 2004. p. 176)

    Peace! :-)

  12. I’m not sure whether or not my own views would be ones that Priest would affirm or deny, but I do think we can do better than Lewis. The key is to hone in on a very central claim in the passages you quoted: “Nothing is, and nothing could be, literally both true and false.” Emphasis there on the word, “literally”. Priest ought to say, “oh, right on; still, dialetheism is correct all the same”.

    As a rule, we should resist the practice of asserting contradictions. But the question is: why do we do this? Here is what I think the answer is: to protect the literal.

    Consider my reasons. I think that most (or all) of the time we engage in assertions, we use descriptions. (“It was rainy today”, for instance, is both a description and assertion.) It seems to me that the whole point of using descriptions, the whole reason descriptions were invented in the first place, is to get us all to talk about the same things — to coordinate together in order to refer to the same stuff in the world. You can think of descriptions as a kind of ‘solution’ to a ‘problem’, which is the problem of referring.

    Now, suppose there were a class of cases which there was simply no problem of reference. Suppose, by magic or whatever, that everybody just was on the same page — everybody has broadly the same idea of what the point of the use of words may be, and everybody has access to the same information in the context. It may be the case that the utterance of the sentence, “The man is and is not on the threshold”, will turn out to be not literally assertable. And to be sure, in most cases, if something is not rationally assertable, it isn’t even intelligible, because the main point of asserting something is to introduce new beliefs or thoughts to the listener, and you can’t introduce new thoughts or beliefs by using a defective medium.

    But suppose that in this case, there is no problem to solve. Suppose, that is, that the proposition was intelligible and known to all parties from the start. Suppose everybody just happened to be on the same page — they all, by magic, telepathy, or common ground all knew the contents of the proposition being conveyed, and were all attuned to what was being referred to and why. If that is so, then the proposition which is represented by the utterance of the sentence “The man is and is not on the threshold” will turn out to be true, even though the utterance itself is literally nonsense. The contradictory proposition represented by that sentence is true, while the sentence/utterance do not meet the minimum requirements for conversation.

    You can think of the rule of non-contradiction as being kind of like M-O from Wall-E. It only has a purpose when it has some language to clean up. Without that purpose, it’s just sort of optional. It has no deep metaphysical significance; it’s just (to abuse a phrase from Dave DeVidi) a “municipal byway of thought”.

  13. Andy Walsh seems to be saying is that the following statement has no content: I think, therefore, I am. It does have content even though the concept of existence can’t be defined or explicated. The reason is that we know other human beings exist. You exist and I exist, but I am not you and you are not me. In other words, humans are finite beings. This means an infinite being exists, which western religions call God.

  14. I am always amused by people trying to tackle metaphysics without considering the metaphysical assumptions that underlie their analysis.

    The moment you say “there exists a ……” you have already made several fundamental choices about the nature of the world you are talking about.

    1/. That existence is a concept that has meaning
    2/. That the world actually comprises objects that can be distinguished one from another (by some agency of intellect?) and
    3/ . Because of the above, set theory itself has validity.

    None of these are demonstrably true. Ergo we are when manipulating these concepts not talking about a real world, but about a world of ideas.

    It does seem to me that the ‘thicker’ philosophers whilst as demented as the thin ones in this matter, have at least appreciated that beyond the pointless clutter in their brains and the endless sophistry with which they match their erudition with their fellows, something else is at some level far removed, going on. Sadly it seems to take a mystical revelation before they do.

    When we say ‘Dragons don’t exist’ that has a perfectly clear meaning: We understand it to mean that whereas we can create a model of a dragon in our heads it has no observable mapping in ‘physical space time’. Ordinary people it seems are far less confused about this than philosophers.

    And “dragons exist and don’t exist” also has meaning. Dragons exist in mind-space, not on material reality-space.

    The confusion arises because philosophers can no longer understand the difference.

    All of the confusion drops away if a different metaphysic is adopted. Kant/Schopenhauer would say firstly that existence itself is merely an assumption we have to make to explain our experience, and that the reification of the world into a phenomenal universe in space time is merely a way of representing it to our intelligence.

    The ‘thicker’ philsophers merely dimly realise that something like that has taken place, whereas the analysts no longer even notice the real world at all: they are concerned only with the fine detail of their internal maps.

    And that is why they cant really understand ‘dragons don’t exist’ They have confused their internal world of objects and theories with actual existence, but they have never actually experienced existence at all.

    Given that we have mindware that can create concepts used to map aspects of what is there, into ‘creatures’ it is not impossible to (ab)use such concepts into forming new concepts of things that have no referent in the so called ‘real world’. Whether or not dragons exist is a question of whether or not you consider a concept itself to have ‘existence’. Of course the final irony is that such statements lead in the end to the paradox of every realist. By naming dragons as a concept, they take on an existence in the world, even as imaginary concepts: But realists will not allow of any reality above or beyond the physical, so they are stuffed basically. Stuck in endless arguments about the real nature of things, whereas the simpler approach is that things have no real nature. Only The Thing in Itself has nature, but its so far removed from how we experience it the question is meaningless. Everything else is a conceptual pattern that we recognise more or less in the world we create from our experience, and thereby make an approximate statement like ‘there is a cat’

    This doesn’t mean that cats exist per se, or that they are real, or, indeed any more than ‘here is a common part of our experience, common enough for us to have named it ‘

    To try an reduce that to the sets of ‘cats’ and ‘not cats’ is of course absurd because the logic and the pattern is fuzzy..there are ‘sort of cats’ ‘a bit like cats’ ‘not very like cats’ ‘pictures of cats’ ‘dead cats’ ‘parts of cats that have fallen off’ and so on.

    It doesn’t stop endless argument about it though, does it?

    Logic is a fine thing, and slicing and dicing experience down to the last detail and categorising everything into little boxes is after all merely a more socially useful form of obsessive compulsive disorder.

    The problem is that even at the physical level, the universes it seems is not information compressible: That is, experience cannot be categorised into shorthand concepts without losing something. The smell of the cat, the exact shade of every hair, the exact number of and DNA sequences of the fleas that live on it..and so on

    In reality ‘cat’ merely means ‘small enough to beat, not big enough to eat, handy for catching mice, purrs a lot when stroked, smells pretty bad’ Its irrelevance to us is in terms of its use to us. Those aspects of it that are not interesting don’t really form part of the ‘cat concept’ at all.

    So we cant ever even define any given object in its totality without defining the whole universe, and we need a whole universe to do that…. which ought to alert people to the fact that Realism can never be more than a useful approximation.

    So arguing over whether something exists in Reality is as pointless an exercise as its possible to get. Because Reality itself is only an approximation created by the human mind.

  15. Talking Philosophy « New Evangelist, David Roemer - pingback on August 1, 2012 at 6:04 am
  16. @David Roemer

    I’m not saying that at all. I might even be saying the opposite. It is straightforward to me that the analysis of existential claims into ontologically thrifty terms leaves out the good bits. I don’t see why it isn’t obviouss also to Mr Van Inwagen (et al).

  17. Leo:

    And “dragons exist and don’t exist” also has meaning. Dragons exist in mind-space, not on material reality-space… The confusion arises because philosophers can no longer understand the difference.

    Whether or not “Dragons exist in mind-space” is a meaningful statement is really the whole issue, my man. The realists claim that this is a bogus and uninformative contrivance. That’s not a deep, trenchant, esoteric piece of philosobabble — it’s something you can and do find echoed in everyday talk. If you say “Dragons exist in mind-space”, you can expect somebody to pipe up and correct you to say, “Er, in other words dragons don’t exist”.

    Of course, it’s perfectly intelligible to make further distinctions here. Say, between existence and subsistence. One could say, “Dragons exist in mind-space, but they do not subsist.” That’s what Meinong did, and went down in history as Russell’s foil, though I suspect he deserved a bit better. But you don’t hear people quoting Meinong in the coffee shop.

  18. What does the phrase “mind-space” mean? I know what is meant by the word “mind,” and I think that the human mind is a mystery. My guess is the phrase “mind-space” is an attempt to state that there is nothing mysterious about the mind, just as there is nothing mysterious about the human brain. Just as the brain takes up space, so too does the mind take up space.

  19. Leo Smith: “The moment you say “there exists a ……” you have already made several fundamental choices about the nature of the world you are talking about.
    1. That existence is a concept that has meaning
    
2. That the world actually comprises objects that can be distinguished one from another (by some agency of intellect?) and
    3. Because of the above, set theory itself has validity.
    None of these are demonstrably true. Ergo we are when manipulating these concepts not talking about a real world, but about a world of ideas.”

    1. The verb “to exist” (and the corresponding verbs in other languages, e.g. “existieren” in German) is meaningful because we use it meaningfully. It is a semantically primitive word, but indefinability is not the same as meaninglessness.

    “I suspect that it is impossible to provide any analysis of ‘exist.’ Some concepts are so fundamental that it appears impossible to say anything much about their meaning, except give simple paraphrases. (The notion ‘set’ is like this – collection, bunch, group.) And concepts don’t come much more fundamental than existence.”

    (Priest, Graham. “Not to be.” In The Routledge Companion to Metaphysics, edited by Robin Le Poidevin, Peter Simons, Andrew McGonigal, and Ross P. Cameron, 234-245. Abingdon: Routledge, 2009. p. 234)

    “The concept of existence is probably basic and primitive in the sense that it is not possible to produce an informative definition of it in terms that are more clearly understood and that would tell us something important and revealing about what it is for something to exist.”

    (Kim, Jaegwon, and Ernest Sosa, eds. Metaphysics: An Anthology. Oxford: Blackwell, 1999. p. 3)

    2. The concept of existence is applicable to a one- or zero-object world as well; and it is applicable to any ontological category: object, substance, event, process, state, property, relation, state of affairs, fact, institution…

    3. One needn’t interpret “There are/exist Fs”/”Fs exist” as “The set of Fs is nonempty”. Being a nominalist about abstract objects, I regard the sentence “The set of dogs is nonempty/has at least one member” as false not because dogs don’t exist but because sets don’t exist.
    The (first-order) property account of existence is independent of set theory.

    Leo Smith: “And “dragons exist and don’t exist” also has meaning. Dragons exist in mind-space, not on material reality-space.
    The confusion arises because philosophers can no longer understand the difference.”

    I’m certain that nobody ever had a dragon in his mind or head. What there are in our minds/heads are verbal or pictorial representations of dragons, and no representation of a dragon is a dragon. Dragon representations exist somewhere (inside and outside our minds/heads) but dragons exist nowhere.

    Leo Smith: “Whether or not dragons exist is a question of whether or not you consider a concept itself to have ‘existence’. Of course the final irony is that such statements lead in the end to the paradox of every realist. By naming dragons as a concept, they take on an existence in the world, even as imaginary concepts:…”

    Whether dragons exist is one question, and whether the concept /dragon/ exists another. Dragons aren’t concepts but objects, and the concept /dragon/ isn’t an object (in the narrow ontological sense) but a concept.
    For example, when someone says “God is only an idea in our minds”, then I read this as “God doesn’t exist, but our idea of God does”. But the idea of God certainly isn’t called God, since the name of the idea of God isn’t “God” but “the idea of God”/”the God-idea”.

  20. BLS Nelson: “You can think of the rule of non-contradiction as being kind of like M-O from Wall-E. It only has a purpose when it has some language to clean up. Without that purpose, it’s just sort of optional. It has no deep metaphysical significance; it’s just (to abuse a phrase from Dave DeVidi) a “municipal byway of thought”.”

    As this is beginning to be off-topic, here’s only a short reply:
    I do think that the language- and thought-independent fact that no state of affairs can be both actual and nonactual, both obtain and not obtain (at the same time) is metaphysically significant. No fact can be both absent and present.

  21. @Myron

    To insist that this proposition is true: “Bradley Wiggins won the Olympic gold medal in the time trial AND Bradley Wiggins did not win the Olympic gold medal in the time trial”…..is sort of odd. Do dialethists also think that their true contradictions are also false?

  22. First of all, it needs to be mentioned that Priest uses a nonclassical semantics of negation (in his dialetheia-friendly logical system LP:

    Classical:

    1. T~p ‹–› ~Tp
    2. ~Tp ‹–› Fp
    3. ~T~p ‹–› F~p

    Nonclassical (Priest):

    T~p ‹–› Fp
    F~p ‹–› Tp

    As you can see, Priest has logically disconnected falsity and untruth. Classically, a proposition is false iff it is untrue, but according to Priest’s logic propositions can be both false and true; and a proposition which is both false and true is false but not untrue.
    Nevertheless, even when using his peculiar semantics of negation, he cannot evade the logical fact that true contradictions aren’t non-contradictorily assertible, because they are both true and false themselves. Here’s a simple proof:

    1. p & ~p [assumption]
    2. T(p & ~p) [from 1]
    3. Tp & T~p [from 2, semantics of conjunction]
    4. F~p & Fp [from 3, substitution by virtue of LP’s semantics of negation]
    5. Fp & F~p [from 4, commutativity of conjunction]
    6. F(p & ~p) [from 5, semantics of conjunction]
    7. T(p &~p) & F(p & ~p) [from 2+6, &-introduction]
    8. T(p & ~p) –> (T(p &~p) & F(p & ~p)) [from 2+7, –>-introduction]
    9. (T(p &~p) & F(p & ~p)) –> T(p & ~p) [assumption, follows from: (p & q) –> p]
    10. T(p & ~p) ‹–› (T(p &~p) & F(p & ~p)) [from 8+9: ((p –> q) & (q –> p)) ‹–› (p ‹–› q)]
    q.e.d.

    That is, a true contradiction is never only true but always also false, which means that it isn’t consistently assertible. But Priest is prepared to bite the bullet: He accepts the logical fact that all true contradictions are both true and false themselves—a consequence which strikes me as absurd.

  23. @Myron

    If you’re going to start with a contradiction why be so punctilious about the formal compositions between the premises?

  24. @David,
    I think he meant something like the ‘space of reasons’. “Space” is being used as a kind of metaphor.

    @Myron,

    As this is beginning to be off-topic, here’s only a short reply:
    I do think that the language- and thought-independent fact that no state of affairs can be both actual and nonactual, both obtain and not obtain (at the same time) is metaphysically significant. No fact can be both absent and present.

    Ah, to be clear, my proposal is about assumed common ground — shared thoughts and signals which succeed in referring independently of the use of language. So if you want to talk about thought-independent states of affairs, we’ll be talking past each other.

    But you’re right, this seems to be a digression.

  25. Vincent Francone

    Seems to me that existence must be whatever shows up—-what else have we got? I mean if it does not exist–in some way—-how could it be attended to? It would be entirely absent.
    Whatever you want to say shows up—it must first show up; whether you say what shows up is thought or sense or whatever ontological category, it must show up or in effect it does not exist.
    I may say that the line of reasoning or point of view or fact or possibility or some such, just presented here, exists. And you may deny this assertion. But if the assertion and the denial do not first show up—what is there? Whether existence may or may not be eliminated by the presumptions of formal logic, the showing up, it seems to me, is patently the fundament. I mean really, what else have we got?

  26. @Vincent Francone:
    Psychologically speaking, for babies the difference between “exists” and “doesn’t exist” is the difference between “is present in my perceptual, especially visual field” and “is absent from my perceptual, especially visual field”. It takes some time until children have learned that things can leave their perceptual field and continue to exist, and that one and the same thing can leave it, continue to exist, and reenter it. Funnily, adult idealists still deny that existence is independent of perception. Just consider the question of nonspatiotemporal abstract objects: if such objects exist, they will never show up in your perceptual field in principle.

    As for objects of thought or imagination, there is a distinction between merely intentional pseudopresence in thought or imagination and transintentional presence in reality.

  27. By the way, if to exist were to be perceived/perceivable, then perceivings (perceptual processes) wouldn’t exist, since I don’t and can’t see my seeings, hear my hearings, etc. I’m aware of them but I don’t perceive them.

  28. A friend of sense-data would say that through sensation I perceive a sense-datum but I don’t perceive my sensation of it. That is, for example, when I see a colour, I see the colour rather than my seeing (of) the colour.

  29. @Myron
    Well said! The way Bernard Longergan puts it is this:
    Seeing that something is blue means more than that light is entering the eye and a signal is going to the brain. I means an “awareness” of this. What is this “awareness”?

  30. @BLS Nelson

    (I don’t really mean to pick on you particularly, but this comment of yours gives me a convenient way into making a broader point.)

    Whether or not “Dragons exist in mind-space” is a meaningful statement is really the whole issue, my man.

    Well, I think Leo made his meaning clear enough. So a more pertinent objection might be that Leo is using “exist” in a non-standard sense. But I say that “exist” has a range of meanings, and Leo’s usage is reasonable given the pre-existing range. We often talk about having things (ideas etc) in our minds, and it’s a reasonable extension to say that those things exist in our minds or in “mind-space”.

    It seems to me that philosophers often fail to fully appreciate the fuzziness and diversity of meaning that a word can have. For example, I find discussions of whether numbers exist to be misguided. Mathematicans usefully make statements like “there exist X prime numbers between Y and Z”, so it seems pointless to deny that there is some meaningful sense in which numbers exist. The interesting question is in what sense do they exist. It’s clear to me that they exist in a rather different sense from physical objects.

    For people to use words in a variety of different senses is not necessarily a problem, as long as speakers and listeners understand what’s meant and don’t conflate different senses. The latter is a big problem, though. In my view many philosophical errors arise from conflating multiple senses of words. But this is less likely to occur if we fully appreciate just how fuzzy and context-dependent language is.

    That said, it’s arguable that Leo did end up conflating meanings, when he wrote:

    By naming dragons as a concept, they take on an existence in the world, even as imaginary concepts: But realists will not allow of any reality above or beyond the physical, so they are stuffed basically.

    The first part seems either to be conflating existence as a concept in people’s minds with some more significant sort of existence, or else stating an insignificant near-tautology which does nothing to justify the second part.

  31. Richard Wein wrote:
    “Well, I think Leo made his meaning clear enough. So a more pertinent objection might be that Leo is using “exist” in a non-standard sense. But I say that “exist” has a range of meanings, and Leo’s usage is reasonable given the pre-existing range. We often talk about having things (ideas etc) in our minds, and it’s a reasonable extension to say that those things exist in our minds or in ‘mind-space’.”

    There is an essential difference between having a thing and having an “idea”, i.e. a mental representation, of a thing in one’s mind. For example, when I imagine a unicorn, there exists no unicorn in my mind but only a mental image of a unicorn. The mental image exists but what it represents doesn’t, since unicorns don’t exist. Of course, no unicorn-image is a unicorn, and so it is confusing and misleading to say that unicorns exist (only) in our minds.

    Richard Wein wrote:
    “It seems to me that philosophers often fail to fully appreciate the fuzziness and diversity of meaning that a word can have. For example, I find discussions of whether numbers exist to be misguided. Mathematicans usefully make statements like “there exist X prime numbers between Y and Z”, so it seems pointless to deny that there is some meaningful sense in which numbers exist. The interesting question is in what sense do they exist. It’s clear to me that they exist in a rather different sense from physical objects.”

    There are different kinds of existents but there aren’t different senses of “existence”.
    In sentences such as “Numbers exist” and “Dogs exist” “exist” has the same sense. The ontological difference between numbers and dogs is not due to their existing in different senses of the term but to their belonging to different ontological categories: abstract objects vs. concrete objects.
    Consider the following argument, which seems perfectly valid:

    1. Numbers exist.
    2. Dogs exist.
    3. Numbers and dogs are different kinds of things.
    4. Therefore, at least two kinds of things exist.

    If the meaning of “exist” in 1 is different from its meaning in 2, then what about its meaning in 4. Is there a third meaning of “exist”? If yes, what is it?
    If “exist” hasn’t the same meaning in 1, 2, and 4, the argument becomes (informally) invalid and unintelligible. But it clearly seems neither invalid nor unintelligible, which fact can only be explained in terms of “exist” having one and the same meaning in 1, 2, and 4.
    The view that there are different senses of “exist(ence)” is untenable.

  32. @Richard

    Feel free to pick on me if you think something productive comes of it! :D

    Well, I think Leo made his meaning clear enough.

    Suppose he has, in a sense. But if dragons can only be tokened in “mind-space”, I still don’t know:
    a) whether or not dragons exist simpliciter;
    b) if “existing-in-mindspace” is even the same kind of thing which is like existing simpliciter;
    c) if “existing-in-mindspace” has any semantic relationship at all with existing simpliciter.

    The first approach you might take is this: the entire point of making claims about how something “exists” simpliciter is that a thing is or is not tokened in a state of affairs. The idea is that “exists” just means it is real, that it is “more than appearances” — more than mind-space. On this view, we cannot say that “Dragons exist” can be understood as an elliptical form of “Dragons exist in mind-space”. To say that “Dragons exist in mind-space” is to say something like, “Dragons are part of the state of affairs independent of how I see them — and yet only exist in my mind”. That’s very confused, not to say confusing. Perhaps the sentence might have non-logical connotations, but (barring dialetheia) it has no logical meaning.

    The second approach is to say that “existing-in-mindspace” is just a totally different meaning from “existing simpliciter”, and that philosophers equivocate between the two terms. That’s the move you and Leo are both making. You’d have to deny that there is any ontological priority in expressions like “existence” — that it is primarily a logical or conceptual notion, not a metaphysical one.

    But just because somebody wishes for the words to be understood in a certain way, does not necessarily entail that those words ought to satisfy the speaker’s expectations. If a man says, “I have arthritis in my thigh”, and the doctor points out how silly this assertion is, the man might then go on to redefine “arthritis” in such a way that it designates a condition that can be found outside the joints. And that’s fine. But the literal meaning of the word probably isn’t going to catch up with his attempt at redefinition. Why? Because: a) his use is unconventional, and literal meanings are conventions; b) nobody else sees any relative advantage in amending their own vocabulary in this way; c) the new definition threatens to obscure a legitimate common use of the word.

    And it’s not clear to me that laymen would, in fact, infer “Dragons exist in mind-space” from “Dragons exist”. It’s not clear to me that, even if they did, this would be relatively advantageous. And it’s not clear to me that, even if they did, it wouldn’t come at great cost.

    Given these unclarities, we might take a third approach: we might just say that we have no good answers to the (a-c) questions yet. And without answers to these questions, then arguably our first instinct ought to be to revolt against the more obscure vocabulary (of ‘existing-in-mindspace’) and opt for the clearer vocabulary (of ‘existing’ simpliciter). In which case, it’s not at all obvious how “existing in mind-space” is meaningful. It may be that it can be explicated in some way, but I am not confident that either you or Leo have done that yet.

    (Of course, that argument can be put on its head: you might assert that the existing-in-mindspace vocabulary is the clearer one. But philosophers have tried to go down that road before, and it has resulted in some very obscure and unnatural ways of speaking.)

  33. The distinction between “to exist simpliciter” and “to exist in the domain (of quantification) D” corresponds to Carnap’s distinction between external and internal questions of existence. For instance, “Is there a greatest natural number?” is an internal question and “Do numbers exist?” an external one, because it is a question about the domain of numbers as a whole. From the internal mathematical perspective, there are infinitely many numbers, but from the external ontological perspective of mathematical antirealism, there isn’t even one number. Of course, “There are infinitely many numbers” implies “There is at least one number”, which statement contradicts the statement “There are no numbers”. So these two statements cannot both be true. So which one is false? Being a mathematical fictionalist, I claim that “There is at least one number” and “There are infinitely many numbers” are both false. From the internal perspective of the working mathematician, they are “correct” in the sense that they are validly deducible from the axioms of arithmetic; but mathematical correctness thus defined is not the same as truth. Alternatively, following Mark Balaguer, one could define “p is mathematically correct” as “If mathematical platonism were true, p would be true”.
    “Thus, on this view, a mathematical sentence is fictionalistically correct if and only if it would have been true if there had actually existed abstract mathematical objects of the kinds that platonists have in mind. Balaguer argues that if fictionalists adopt this view, they can avoid the above problem with Field’s view and, more generally, they can completely solve the problem of objectivity because they can mimic everything platonists say about objectivity.” – Mark Balaguer

    See: http://plato.stanford.edu/entries/fictionalism-mathematics/

  34. Myron — that’s true, about Carnap.

    I avoided saying anything about Richard’s example of mathematics because that’s a whole thing unto itself, and is after all just meant as an example. It’ll probably just lead to a digression, but I’ll bite anyway.

    For the sake of argument, let’s suppose that neither math nor morals needs to correspond to ontologically objective reality, existing independent of any mind — that some variety of mathematical anti-realism is correct. Even were that so, I’m still very much disinclined to be a fictionalist about mathematics, just as I’m not inclined to be a fictionalist about institutions. That is because mathematics simply is an institution and a technology. And institutions are epistemically objective objects of inquiry, which we can make claims about, and which can be publicly justified as correct or incorrect. If you accept minimalism about truth, the fact that our math-sentences can be open to public rational evaluation indicates that there are standards by which we can say that these sentences are true or false.

    If that is right, then you can say “It is true that ‘The smallest positive natural number is one'”. You can also say, “That one cup on the table exists (simpliciter)”. But you cannot say that “The smallest positive natural number exists (simpliciter)”. And, all things considered, those results sound intuitively on target.

    In sum: you can be an anti-realist about numbers, and also a cognitivist and an objectivist about number-sentences.

    (Of course, if you think the whole division between internal and external questions is silly (as Quine did) then all of this comes out sounding pretty pretentious. And I admit that Quine’s critique is pretty forceful. But then, he thinks mathematical entities exist simpliciter.)

  35. Mathematical fictionalists certainly aren’t fictionalists about mathematics as a social institution but about (nonlinguistic) abstract mathematical objects. And they certainly don’t deny that there are (literally) true numeral-containing sentences such as “There is one capital of France”. That is, they don’t deny the existence of numerical signs but of numbers as nonlinguistic abstract objects. A mathematical fictionalist may also be an antirealist about linguistic types such as types of numerals, which are abstract objects as well, but mathematical fictionalism doesn’t per se include the denial of the existence of abstract numerical sign-types. It is the claim that the world of mathematical platonism is fictional:
    “Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices.”
    http://plato.stanford.edu/entries/platonism-mathematics/

  36. Fair. It may be a quibble. To some extent, the label — ‘fictionalism’ — is very misleading, and I’d prefer the label “constructivism” to describe the sort of configuration of views that seem most plausible. Perhaps that might just mean that I endorse a kind of fictionalism with lots of caveats.

    However, going back to your link to fictionalism: I absolutely reject thesis (c), that “our mathematical theories are not true”. That proposal strikes me as entirely off base, so if fictionalists are committed to this view, then I am not one!

  37. Myron, thanks for replying.

    There is an essential difference between having a thing and having an “idea”, i.e. a mental representation, of a thing in one’s mind.

    I agree. You’ve misunderstood me. I’m not conflating the two. Similarly, I’m not conflating the claim that unicorns exist as physical objects with the claim that people have a mental representation of dragons. I’m just saying that “unicorns exist in our minds” is a reasonable way of expressing the latter claim. People do sometimes speak in roughly this sort of way, and other people seem to understand them. Such people do not mean (or take it to mean) that we have little physical unicorns inside our heads.

    To me this is just a question of whether such a usage is sufficently in keeping with the way people speak to be considered a reasonable way of speaking. That’s a fuzzy question and a matter of judgement. How many people have to speak some way before it becomes an acceptable way of speaking? This is similar to the question faced by grammarians and dictionary-compilers. It takes time for new usages to become accepted. Personally, in the past I’ve treated the expression “between you and I” as not being correct English. But as that usage becomes (seemingly) more and more common, I’m starting to adapt to it and see it as more acceptable. As languages change there’s no precise time at which a usage goes from being wrong to right. It’s a matter of interpretation and judgement. Linguistic correctness is a fuzzy concept.

    If your judgement is that “unicorns exist (only) in our minds” is not a reasonable way of speaking, then so be it. It’s not an important point in itself. The important point is that philosophers need (it seems to me) a fuller appreciation of the ambiguity and fuzziness of language. The illusion of linguistic precision (and the reification of concepts) is the cause of much philosophical error. I believe this is the realisation that led Wittgenstein to abandon the formalism of his early work.

    With regard to the existence of numbers, I’m afraid your argument about numbers and dogs doesn’t get us anywhere. I would merely respond that, yes, at least two kinds of things exist, but they don’t all exist in the same sense. I think your 4 is ambiguous. If we’re prepared to interpret it as…
    4a. Therefore, at least two kinds of things exist (but possibly in different senses)
    …then I would say the argument is valid. If we interpret it as…
    4b. Therefore, at least two kinds of things exist (in the same sense of exist)
    …then I would say it commits a fallacy of equivocation (conflating the two senses of exist).

    By analogy:
    1. Rivers have banks.
    2. Financial systems have banks.
    3. Rivers and financial systems are two different kinds of things.
    4. Therefore, at least two different kinds of things have banks.

    Rivers and financial systems both have “banks”, but in two different senses of “bank”. I assume you would agree with that. This argument faces just the same challenge as yours does (on the hypothesis that “exist” has two different senses).

    This isn’t the sort of thing that’s going to be settled by any simple argument. It’s quite a deep question about the nature of language and meaning. And it’s also a rather fuzzy question, which is open to interpretation. So I’m not going to offer an argument in support of my view. But let me ask whether it would be any more acceptable to you if I said that numbers and dogs exist in different ways, rather than in different senses of “exist”?

  38. P.S. Oops. A dragon sneaked in among my unicorns. Please read all my “unicorns” as “dragons”, or vice versa.

  39. @BLS (or should I say Bill?)

    I think you and Myron have both misunderstood me, so I guess I didn’t write clearly. I hope the first part of my response to Myron will make my position clearer. It might still be useful for me to address your questions. But I’ll ignore the hypothetical ‘if dragons can only be tokened in “mind-space”’. As far as I understand what that means, it doesn’t describe my position.

    a) whether or not dragons exist simpliciter;

    I think we must always interpret words according to the context. Even if someone asks me “Do dragons exist?” out of the blue, I have the context of whatever I know about the speaker. Normally, in the absence of any contrary indications I would assume that the questioner means me to address the subject of the physical existence of dragons. I would take it that way and answer no, they don’t exist.

    In the present case I don’t know what you’re asking. Perhaps you are asking about the physical existence of dragons, but given the context (where we’re considering multiple senses of “exist”) I don’t think that’s a safe assumption to make. I suspect you have in mind that “exist simpliciter” is a distinct sense of “exist” which can be picked out regardless of the context. I don’t think there is any such sense.

    b) if “existing-in-mindspace” is even the same kind of thing which is like existing simpliciter;
    c) if “existing-in-mindspace” has any semantic relationship at all with existing simpliciter.

    Let me clarify that I’m taking “dragons exist in mindspace” to be another way of saying something like “people have a concept of dragons”. I’m not making some surprising factual claim. It’s just another way of speaking.

    With that clarified, “dragons exist in mindspace” and “dragons exist as physical objects” obviously mean very different things. But I wouldn’t necessarily say that they’re altogether different. Arguably there is some common element in both sorts of existence. But I see that as a rather fuzzy and unimportant question.

    I’ll take the liberty of skipping the rest of your comment, as I think it’s based on a misunderstanding of what I was saying. Feel free to repeat any parts you think are still relevant.

  40. @Myron

    Being a mathematical fictionalist, I claim that “There is at least one number” and “There are infinitely many numbers” are both false. From the internal perspective of the working mathematician, they are “correct” in the sense that they are validly deducible from the axioms of arithmetic; but mathematical correctness thus defined is not the same as truth.

    Interesting. It seems you’re prepared to accept that “correct” has a different sense in mathematics (than the more usual sense). But you’re not prepared to accept that “exist” and “truth” have different senses in mathematics. Why not grant to the word “true” the same sort of variation in meaning that you grant to the word “correct”? After all, both mathematicians and others often use those words interchangeably.

  41. BLS Nelson wrote:
    “I absolutely reject thesis (c), that ‘our mathematical theories are not true’. That proposal strikes me as entirely off base, so if fictionalists are committed to this view, then I am not one!”

    If there are no abstract mathematical objects and facts, then there is nothing in reality which could make (purely) mathematical propositions and theories true.
    Here’s the main argument for fictionalism: http://plato.stanford.edu/entries/fictionalism-mathematics/#MaiArg

  42. @Myron, okay, but nothing apart from fallacy commits us to the idea that the truth of a theory depends upon what is independent of the mind.

    @Richard, my name’s Ben. :) I think you were pretty clear — I was the one who was unclear. You’re arguing for the contextual relativity of meaning. That’s the view I attributed to you and to Leo. In my reply, though, I focused on the context-invariant or literal meaning, since that was what I was claiming Leo hadn’t established in the first place.

    In my reply above, I mentioned the arthritis case, which I’ll keep using. When the patient thinks that he has arthritis in his thigh, the doctor might be able to figure out what the patient means. We might put that concession in a few different ways: we might say that the doctor has figured out the speaker’s meaning of the utterance, or that the utterance has contextually qualified meaning.

    But even so, I need to know how far do you really want to take this contextualism business. What’s the difference between a context and mere whimsy? If the patient is just saying “I have arthritis in my thigh” on a whim, then in what sense do we say we’ve understood the sentence, “The man has arthritis in his thigh” to be true? It seems as though it is not true at all. It wasn’t uttered with a focused intent. The realist would argue that Leo’s sentence is one of that kind (though I would not be so uncharitable).

  43. Richard Wein wrote:
    “I’m just saying that ‘unicorns exist in our minds’ is a reasonable way of expressing the latter claim. People do sometimes speak in roughly this sort of way, and other people seem to understand them.”

    Yes, but a colloquial, colloquially accepted way of speaking is not always a philosophically reasonable way of speaking and sometimes actually a false way of speaking, strictly speaking.

    Richard Wein wrote:
    “If your judgement is that “unicorns exist (only) in our minds” is not a reasonable way of speaking, then so be it. It’s not an important point in itself.”

    Yes, it is, because that statement is false, strictly and literally speaking. It also blurs the important distinction between the (representational) content and the object of imagination or thought, of which many or even most people are unaware.

    Richard Wein wrote:
    “The important point is that philosophers need (it seems to me) a fuller appreciation of the ambiguity and fuzziness of language. The illusion of linguistic precision (and the reification of concepts) is the cause of much philosophical error.”

    I beg to differ. The cause of a great deal of philosophical error, confusion, and misunderstanding is linguistic, conceptual imprecision. A perfect precisification of the philosophical vocabulary may be unfeasible, but a philosopher (in the analytic tradition) should nonetheless seek to minimize the vagueness or ambiguity of his concepts and statements.

    Richard Wein wrote:
    “This isn’t the sort of thing that’s going to be settled by any simple argument. It’s quite a deep question about the nature of language and meaning. And it’s also a rather fuzzy question, which is open to interpretation. So I’m not going to offer an argument in support of my view. But let me ask whether it would be any more acceptable to you if I said that numbers and dogs exist in different ways, rather than in different senses of ‘exist’?”

    It is acceptable for me to say that there are two ways or modes of existing: accidental and necessary existence. (But I deny that there can be things which exist logically necessarily.)

    “[T]here are various informally valid forms of argument such as argument (A)
    below:

    (A) (1) The number seven exists,
    (2) The University of Leeds exists.
    (3) The number seven and the University of Leeds are non-identical.
    (4) Therefore: at least two things exist.

    [Gilbert] Ryle is committed to denying that ‘exists’ in (1 ) has the same sense as ‘exists’ in (2). Either he has to deny that (A) is informally valid, although such a denial would be implausible. Or he has to explain the argument’s validity by saying that (4) involves a yet further sense of ‘exists’. Perhaps this sense could be defined disjunctively as: exist in the sense in which bodies exist or exist in the sense in which minds exist. But since such a sense of ‘exists’ is available to us, it is not clear on what grounds Ryle thinks that (1) and (2) use different senses of ‘exists’. It is open for us to say that they use the same sense of ‘exists’, since we have seen how at least one shared sense can be defined. And how is it that a claim such as (4) can be true, without its specifying which of the (allegedly) many senses of ‘exists’ it is using?
    [W]e should draw distinctions only if there is some useful theoretical purpose in doing so. What is the purpose of introducing additional senses of ‘exists’? It seems ad hoc to introduce new senses of ‘exists’ just to guarantee the informal validity of certain arguments. There is a variant of Ockham’s razor, Grice’s razor, which says that we should not multiply the senses of words unnecessarily. So if we can account for the informal validity of arguments such as (A) by taking ‘exists’ to have a univocal sense, that is the view that we should take (unless there is prevailing reason otherwise).”

    (Daly, Chris. “To be.” In The Routledge Companion to Metaphysics, edited by Robin Le Poidevin, Peter Simons, Andrew McGonigal, and Ross P. Cameron, 225-233. Abingdon: Routledge, 2009. pp. 229-30)

  44. Richard Wein wrote:
    “It seems you’re prepared to accept that “correct” has a different sense in mathematics (than the more usual sense). But you’re not prepared to accept that “exist” and “truth” have different senses in mathematics. Why not grant to the word “true” the same sort of variation in meaning that you grant to the word “correct”? After all, both mathematicians and others often use those words interchangeably.”

    From the nonplatonistic point of view, we need a predicate other than “true” that enables us to distinguish between two classes of mathematical propositions: those which follow from the mathematical axioms and those which don’t.
    “Valid” might be more suitable than “correct”. (I know that in logic validity is normally ascribed to arguments rather than to single propositions.)

    Generally, I prefer to have and use two unequivocal words/phrases rather than one equivocal word/phrase.

    For example, the fictional statements “Sherlock Holmes lives in Baker Street” and “Sherlock Holmes lives in Sloane Street” are both false, yet there is a relevant difference, the expression of which requires a predicate other than “true”/”false”: The former statement is faithful (to the Sherlock Holmes story) and the latter is unfaithful (to the Sherlock Holmes story). To utter a faithful fictional statement is to be right about what the corresponding story says, about what is the case according to the story in question.

    Grice’s Razor: Senses are not to be multiplied beyond necessity!

  45. BLS Nelson wrote:
    “@Myron, okay, but nothing apart from fallacy commits us to the idea that the truth of a theory depends upon what is independent of the mind.

    Truth is correspondence with reality, so how could there be mathematical truths when there is no corresponding mathematical reality?

  46. Myron, but that’s just begging the question, because I reject the most popular forms of the correspondence theory of truth. As I put it above, “If you accept minimalism about truth, the fact that our math-sentences can be open to public rational evaluation indicates that there are standards by which we can say that these sentences are true or false.”

    I’m not sure how useful my further comments are going to be. In what follows, I’ll assume you have a background in the philosophy of language. If not, then I’m about to blather a lot of what sounds like gobbledygook.

    Some sentences have truth-conditions without any fixing conditions. e.g., to borrow a nice example from someone at B&W, “The rock next to the German border in the year 1,200,000AD is black” is a quantifiable sentence even if we suppose that humanity has gone extinct and the land masses of Europe have shifted unrecognizably. In that case, the truth-conditions of the sentence are certainly intelligible. After all, the sentence can be translated into a meta-language using the T-schema, etc. It appears to be meaningful. But we have no idea whether or not there are any conditions under which that sentence corresponds to some state of affairs in reality. If it refers at all, we don’t know how it could — not even an account that is based on causal chains is going to do any work, since we don’t know which causal chains we can pick out. And we aren’t really all that sure if we can even have the right kinds of intentions that are required to refer to it. It is a fundamentally indeterminate expression.

    So, at best, the use of this sentence is just another happy move in a language game which we get away with because we assume that it refers to something. And that’s all you need for truth: the assumption of reference (and the assumption that it makes sense according to some community of practice). But you need to do more than that when you’re making a claim about whether or not a thing exists. A claim about existence is a stronger gambit, and you don’t get to get away with mere assumptions when you make it.

  47. Myron,

    A perfect precisification of the philosophical vocabulary may be unfeasible, but a philosopher (in the analytic tradition) should nonetheless seek to minimize the vagueness or ambiguity of his concepts and statements.

    Certainly. But it seems we disagree as to how much precision is possible. I think we have very different theories of language, probably too much so to settle our differences here.

    It is acceptable for me to say that there are two ways or modes of existing: accidental and necessary existence. (But I deny that there can be things which exist logically necessarily.)

    So I take it you accept that dogs and numbers exist in different ways/modes. For me there’s not such a big difference between saying they exist in different ways/modes and saying they exist in different senses. I’m not going to try to persuade you of that. But I would say (with regard to Daly’s argument) that it’s no more unparsimonious to invoke multiple senses than to invoke multiple ways/modes.

    From the nonplatonistic point of view, we need a predicate other than “true” that enables us to distinguish between two classes of mathematical propositions: those which follow from the mathematical axioms and those which don’t.
    “Valid” might be more suitable than “correct”.

    I think that what we “need” is irrelevant here. We must distinguish between stipulating useful new senses of words and reporting existing senses. And we already have a word for distinguishing between those classes of mathematical proposition, namely “true”.

    From my point of view, again, this is more of a linguistic question than a substantive one. I think we roughly agree on what it is that makes mathematical propositions correct/valid/true. We just disagree on which of those words can appropriately be used to express this status.

    I’m not taking a platonistic position here, far from it. I’m taking a naturalized view of language: our interpretation of language must be guided by how people actually speak, not by what would make their speech clearer.

    Generally, I prefer to have and use two unequivocal words/phrases rather than one equivocal word/phrase.

    Certainly, when a word is ambiguous it’s often a very good idea to stipulate that you will only use it in one of its senses (at least within a certain technical sphere). But that doesn’t mean that other people are mistaken when they use it in the other sense. Your stipulation does not fix the meaning of the word for everyone.

  48. Ben,

    If the patient is just saying “I have arthritis in my thigh” on a whim, then in what sense do we say we’ve understood the sentence, “The man has arthritis in his thigh” to be true?

    You’ve actually given two different sentences here. The latter sentence is not the patient’s, so there seems no good reason to take it in the sense meant by the patient (or worry about the absence of such a sense). If you ask me about the original sentence, I would say we have a choice of taking it the way the patient meant it (if any) or taking it the way it would usually be understood. It might be true given one interpretation and untrue (or lacking a truth state) given another interpretation.

    That’s not to say that all usages are equally reasonable. Usage can be more in keeping with standard usage or less so. If someone uses “I have arthritis in my thigh” to tell me that the stock market is up, that’s an extremely peculiar use of language. But, if I’m familiar with his idiosyncracies and understand him, he can still be communicating true information to me.

  49. P.S. Myron, since you are prepared to say that there are different modes of existence, perhaps you would also be prepared to say that there are different modes of truth. You might be prepared to say that “Sherlock Holmes lives in Baker Street” is true within a certain fictional world, or that it’s true in a fictional mode. Since you’re a mathematical fictionalist, perhaps you could go on to say that mathematical statements are also true in a fictional mode. If so, we can say that you think real-world and mathematical statements are true in different modes, while I say they’re true in different senses. This would then parallel our difference over modes/senses of existence.

    Since I see relatively little difference between senses and modes, I think we are not so far apart.

  50. Richard, but when you say “But, if I’m familiar with his idiosyncracies and understand him, he can still be communicating true information to me”, you’re arguably abandoning the literal meaning of the sentence in order to talk about speaker’s meaning. I’m interested in talking about the literal meaning of the sentence, since that is what my initial complaint to Leo was about (though I was not clear on this).

  51. @BLS Nelson:
    Do you think that reference entails existence?
    Should we say “‘Pegasus’ refers to nothing” or “‘Pegasus’ refers to something nonexistent”?
    I would say that reference to nonexistents is but intentional pseudoreference. So real reference is existence-entailing.

  52. Richard Wein wrote:
    “So I take it you accept that dogs and numbers exist in different ways/modes.”

    I think that abstract objects such as numbers do not exist at all, and what doesn’t exist at all doesn’t exist in any way. Depending on what exactly is meant by “necessary existence”, I might accept the counterfactual statement that if numbers existed, they would exist necessarily (rather than accidentally such as dogs).

    Richard Wein wrote:
    “For me there’s not such a big difference between saying they exist in different ways/modes and saying they exist in different senses.”

    There is a difference because “exists” is used unequivocally in “exists accidentally” and “exists necessarily”. That is, different ways of existence aren’t different meanings of “existence”. For instance, the difference between driving quickly and driving slowly is not a difference between meanings of “to drive”.

    Richard Wein wrote:
    “We must distinguish between stipulating useful new senses of words and reporting existing senses. And we already have a word for distinguishing between those classes of mathematical proposition, namely ‘true’. From my point of view, again, this is more of a linguistic question than a substantive one. I think we roughly agree on what it is that makes mathematical propositions correct/valid/true. We just disagree on which of those words can appropriately be used to express this status.”

    The nontrivial problem is that we end up with confusingly different concepts of truth if we use “true” in senses other than “corresponds to/represents reality”: “truth1″ & “truth2″ & …
    I really don’t want to read or write sentences such as “‘1+1=2′ is untrue1 but true2″.
    When I write instead (from the fictionalist point of view) “‘1+1=2′ is false but valid (= validly deduced/deducible from the axioms of arithmetic)”, then I don’t use two different concepts of truth/falsity.

    A basic principle is: If (it is true that) x is Y, then x exists.

    If someone claims that there are cases where (it is true that) x is Y but x doesn’t exist, then, if he says that his concept of truth is the correspondence-theoretical concept of truth, I’ll tell him that his claim is unintelligible to me; and if he says that his concept of truth is different from the correspondence-theoretical concept of truth, I’ll tell him that his claim equivocates on the concept of truth:
    – I claim that if it is true1 that x is Y, then x exists.
    – He claims that there are cases where it is true2 that x is Y but x doesn’t exist.
    So his alleged cases aren’t counterexamples to my principle.

  53. Richard Wein wrote:
    “P.S. Myron, since you are prepared to say that there are different modes of existence, perhaps you would also be prepared to say that there are different modes of truth. You might be prepared to say that “Sherlock Holmes lives in Baker Street” is true within a certain fictional world, or that it’s true in a fictional mode. Since you’re a mathematical fictionalist, perhaps you could go on to say that mathematical statements are also true in a fictional mode. If so, we can say that you think real-world and mathematical statements are true in different modes, while I say they’re true in different senses. This would then parallel our difference over modes/senses of existence.”

    The alleged modal analogy between “exists accidentally/necessarily” and “is really/fictionally true” is a false one, because to exist accidentally/necessarily is to exist, whereas to be fictionally true is not to be true. Of course, you could stipulatively define a concept of fictional truth which is identical with the concept of fidelity (to a story):

    “p is fictionally true” =def “According to fiction F, (it is true that) p”

    But what is true only according to some fictional and thus false story, isn’t true at all. Fictional truth (different from fidelity) is pseudotruth rather than a “mode of truth”.

    “What we call truth in a fictional world is not a kind of truth. The phrase ‘In the world of the Unicorn Tapestries,’ preceding ‘a unicorn was captured,’ does not indicate in what manner or where or in what realm it is true that a unicorn was captured, or anything of the sort. This is not true, period. ‘It is believed (desired, claimed, denied) that p’ is used not to assert that p is true but to attribute a different property to it, to assert that this proposition is believed, or that someone desires or claims or denies it to be true. Likewise, ‘It is fictional that p’ and its colloquial variants attribute not truth but fictionality to p.”

    (Walton, Kendall L. Mimesis as Make-Believe: On the Foundations of the Representational Arts. Cambridge, MA: Harvard University Press, 1990. pp. 41-2)

  54. @Myron, I share your inclination to say that reference entails existence. However, meaning does not guarantee reference. “The kind of France is bald” is a significant sentence, but it does not refer to anything. The fact that we know the truth-conditions of a sentence, does not entail that they are equivalent to the referring-conditions of the sentence. And my other example demonstrates that we know the sentence has truth-conditions even if we don’t even know if it has correspondence-conditions (or referring-conditions).

    The fact that we cannot trivially infer correspondence conditions from truth-conditions indicates that they are distinct concepts. So if we expect a theory of truth to just explicate a trivial set of conditions involved in talking about truth, then one might naturally say, ‘nuts to that kind of correspondence theory of truth’.

    And if we expect a theory of truth to explain how we talk about truth, and not just explicate our talk, then it has to explain all the ways we talk about truth that don’t even bother trying to refer to real things: statements about the good, the right, and so on. According to a minimalist theory, we should just stop trying to explain it.

  55. BLS Nelson wrote:
    “I share your inclination to say that reference entails existence. However, meaning does not guarantee reference.”

    At least not “existentially satisfied” reference.

    BLS Nelson wrote:
    “‘The kind of France is bald’ is a significant sentence, but it does not refer to anything.”

    Is reference a relation that obtains independently of all acts of referring?
    Does “‘a’ refers to a” mean the same as “‘a’ is used (by me/you/us) to refer to a”?
    Well, we do use names and definite descriptions to refer to nonexistent intentional objects, don’t we? And there is clearly a difference between talking or thinking about nothing (i.e. not talking or thinking about anything) and talking or thinking about something nonexistent (fictional/imaginary), isn’t there? So, in a minimal pragmatic sense, reference might require no more than intentional reference: “‘a’ refers to a (by being used to refer to it), with a being an (existent or nonexistent) object of thought/subject of discourse.”

    BLS Nelson wrote:
    “The fact that we know the truth-conditions of a sentence, does not entail that we know the correspondence-conditions (or referring-conditions) of the sentence.
    The fact that we cannot trivially infer correspondence conditions from truth-conditions indicates that they are distinct concepts. So if we expect a theory of truth to just explicate a trivial set of conditions involved in talking about truth, then one might naturally say, ‘nuts to that kind of correspondence theory of truth’. And if we expect a theory of truth to explain how we talk about truth, and not just explicate our talk, then it has to explain all the ways we talk about truth that don’t even bother trying to refer to real things: statements about the good, the right, and so on. According to a minimalist theory, we should just stop trying to explain it.”

    I expect a metaphysical theory of truth to explain (nonpluralistically) what truth is.
    Does “‹p› is true iff p” alone tell me satisfyingly what truth is? I don’t think so.

    (By the way, I think this principle is false because it presupposes that facts as actual states of affairs and propositions/statements necessarily coexist. But I think that worlds devoid of statements/propositions or generally of representations needn’t be and aren’t factless worlds. So the principle needs to be qualified: ‹p› is true iff p exists and p.)

    “We will work, then, with the following theory of the nature of truth:
    p (a proposition) is true if and only if there exists a T (some entity in the world) such that T necessitates that p and p is true in virtue of T.”

    (Armstrong, D. M. Truth and Truthmakers. Cambridge: Cambridge University Press, 2004. p. 17)

    “Not all the ways the world can be represented are ways the world is, so a particular species of creature found it necessary to employ the following convention to distinguish representations from misrepresentations. Representations that indicate the way the world actually is they called ‘true’, and representations that failed to do so they called ‘false’.
    Truth is a relation between two things—a representation (the truth bearer) and the world or some part of it (the truthmaker).”

    (Martin, C. B. The Mind in Nature. Oxford: Oxford University Press, 2007. p. 24)

    This theory of truth may be regarded as a sort of correspondence theory, even though it doesn’t need to mention the word “correspondence”. For it suffices to say that representations are true iff they represent reality or realities (existence or existences) and false iff they don’t.
    And, in my view, this theory of truth isn’t trivial.

    Of course, there is the problem of the identification of truthmaker(s), i.e. of those entities or realities which make the true propositions true. And here the problem of the referential relations between the (linguistic) representations of reality and the represented reality/realities comes into play. Arguably, there is no 1:1 isomorphism, and so things can get rather (but not hopelessly) complicated.

  56. BLS Nelson wrote:
    “And if we expect a theory of truth to explain how we talk about truth, and not just explicate our talk, then it has to explain all the ways we talk about truth that don’t even bother trying to refer to real things: statements about the good, the right, and so on.”

    As an antipluralist about truth I can counter with error theories about moral, aesthetic, and fictional truth talk. People may behave as if there were moral/aesthetic/fictional truths, but they may be (unknowingly) wrong.

  57. @Myron,

    “Is reference a relation that obtains independently of all acts of referring?
    Does “‘a’ refers to a” mean the same as “‘a’ is used (by me/you/us) to refer to a”?”

    No, it is doubtful that the reference involved in literal expressions obtains independently of any usage of that expression in order to refer. The meanings of sentences are intentionality-dependent, which (arguably) presupposes the existence of at least one mind. And the information profile carried along with some sign must stick to the sign in relatively context-invariant way, or else it ends up being assimilated into speaker’s meaning. This is cashed out to mean that “”A” refers to (a)” means that at least somebody somewhere intended to refer to (a) by way of ‘A’. (So long as we don’t over-intellectualize our account of ‘intentions’, that sounds more or less right to me.)

    Even so, that doesn’t mean that every utterance of ‘A’ involves a Gricean intention to refer to (a). Hence, we have fictional discourse, sarcasm, etc. (This doesn’t mean that everybody more or less knows what they’re talking about; rather, it just means that you can’t have a community of language speakers who have all and always been liars and bullshitters.) When we say that “”A” refers to (a)”, we are betraying our assumption that somebody has got to be doing it right (an “expert”), and that somebody is worth trusting; and for many of our assertions, we only assert them justifiably when we ourselves happen to be experts. (Most of us, presumably, are more or less experts about all kinds of things: our bodies, lives, etc.)

    Well, we do use names and definite descriptions to refer to nonexistent intentional objects, don’t we? And there is clearly a difference between talking or thinking about nothing (i.e. not talking or thinking about anything) and talking or thinking about something nonexistent (fictional/imaginary), isn’t there?

    The intention to refer (and the assumption of successful reference) does not guarantee actually successful reference. So yes, we use names to refer to nonexistent objects, and fail, by virtue of the nonexistence of the object. As for the difference between intentionally failing to refer to anything, and intentionally trying to refer to a non-existent thing — there can certainly be a felt difference in the ways that the failure of reference proceeds. I’m not one of those people who thinks that sense presupposes reference — a sentence can contain sense without a referent. Vacuity can be presented to us in many different ways. Hence, there is no need to posit a referent in mind-space. It means there are informative ways of speaking which are strictly false (and, as it happens, these false ways of speaking can also be used as an instrument to talk about what is true).

    I expect a metaphysical theory of truth to explain (nonpluralistically) what truth is.
    Does “‹p› is true iff p” alone tell me satisfyingly what truth is? I don’t think so.

    This is getting off the terrain of my initial comment, which — I’ll point out again, studious me — included a warning about it being predicated upon a minimalist theory of truth.

    Anyway. Want to abandon minimalism? Fine with me. Pick some kind of coherence theory of truth, then, or perhaps a suitably restrained (non-crazy) version of the pragmatic theory. I see no reason to adopt a ‘correspondence’ theory, here.

    From what I understand, there is nothing about a truth-maker which demands correspondence between the representation and the world. e.g., there are times when trust is a truth-maker, of all things. This is one of the reasons that the correspondence theory has to fail: speech acts with the logical form of declaratives, promises, etc. are truth-apt.

    [Edited for clarity]

  58. BLS Nelson wrote:
    “The intention to refer (and the assumption of successful reference) does not guarantee actually successful reference. So yes, we use names to refer to nonexistent objects, and fail, by virtue of the nonexistence of the object. As for the difference between intentionally failing to refer to anything, and intentionally trying to refer to a non-existent thing — there can certainly be a felt difference in the ways that the failure of reference proceeds.”

    It seems to me that, in the intentionalistic sense, for something to be referred to is simply for it to be thought of or talked about. Then, in this sense, reference isn’t existence-entailing.

    BLS Nelson wrote:
    “I’m not one of those people who thinks that sense presupposes reference — a sentence can contain sense without a referent. Vacuity can be presented to us in many different ways. Hence, there is no need to posit a referent in mind-space. It means there are informative ways of speaking which are strictly false (and, as it happens, these false ways of speaking can also be used as an instrument to talk about what is true).”

    – You’re right. Sense/Meaning is independent of reference or at least reference to existents.

    – As for “vacuity”, we can distinguish between “existential/referential vacuity” and “intentional/semantic vacuity”. Fictional discourse is existentially/referentially vacuous, because fictional objects are nonexistent objects, but it isn’t intentionally/semantically vacuous, because it is meaningful.

    – The name “Pegasus” doesn’t refer to the Pegasus-idea but to Pegasus; and Pegasus doesn’t exist and so doesn’t exist anywhere, while the Pegasus-idea, i.e. mental representations of Pegasus, may be said to exist in our minds.

    “Mathematical fictionalists, while refusing to accept the truth of mathematics, do not reject mathematical discourse.  They do not want mathematicians to stop doing mathematics, or empirical scientists to stop doing mathematically-infused empirical science. Rather, they advocate taking an attitude sometimes called ‘acceptance’ to the utterances of ordinary mathematical discourse.  That is, they advocate making full use of those utterances in one’s theorizing without holding those utterances to be true (an attitude aptly described by Chris Daly (2008, 426) as ‘exploitation’).” – Mary Leng: http://www.iep.utm.edu/mathfict/

    BLS Nelson wrote:
    “Want to abandon minimalism? Fine with me. Pick some kind of coherence theory of truth, then, or perhaps a suitably restrained (non-crazy) version of the pragmatic theory. I see no reason to adopt a ‘correspondence’ theory, here.
    From what I understand, there is nothing about a truth-maker which demands correspondence between the representation and the world. e.g., there are times when trust is a truth-maker, of all things. This is one of the reasons that the correspondence theory has to fail: speech acts with the logical form of declaratives, promises, etc. are truth-apt.”

    A sentence such as “I promise not to betray you” is made true by its utterance. That is, your performing this speech-act makes the sentence true. So this is not a counterexample to truthmaker maximalism, according to which all truths have truthmakers which are ontically distinct from them—except for the small class of sentences which make themselves true, e.g. “This is an English sentence”. (On the other hand, there seems to be an ontic difference between the sentence “This is an English sentence” and the fact that “This is an English sentence” is an English sentence, since sentences aren’t facts.)

    I think that the correspondence theory, particularly in its truthmaker version, captures the basic intuitive idea of truth: Truth is a quality of those representations which represent reality as it really is. And this is not a matter of coherence or consensus but of correspondence (for want of a better term).

    “The idea of a truthmaker for a particular truth, then, is just some existent, some portion of reality, in virtue of which that truth is true. The relation, I think. is a cross-categorial one, one term being an entity or entities in the world, the other being a truth. (I hold that truths are true propositions…) To demand truthmakers for particular truths is to accept a realist theory for these truths. There is something that exists in reality, independent of the proposition in question, which makes the truth true. The ‘making’ here is, of course, not the causal sense of ‘making’. The best formulation of what this making is seems to be given by the phrase ‘in virtue of’. It is in virtue of that independent reality that the proposition is true. What makes the proposition a truth is how it stands to this reality.”

    (Armstrong, D. M. Truth and Truthmakers. Cambridge: Cambridge University Press, 2004. p. 5)

  59. Hey Myron,

    It seems to me that, in the intentionalistic sense, for something to be referred to is simply for it to be thought of or talked about. Then, in this sense, reference isn’t existence-entailing… The name “Pegasus” doesn’t refer to the Pegasus-idea but to Pegasus; and Pegasus doesn’t exist and so doesn’t exist anywhere, while the Pegasus-idea, i.e. mental representations of Pegasus, may be said to exist in our minds.

    I see that that is your position, but that’s what’s being interrogated. Can public words and sentences successfully refer to things that are tokened only privately? Why should we believe that’s the best explanation of what’s going on?

    The realist surely will recognize the distinction between primary intentionality (contents of consciousness) and derived intentionality (the aboutness of words). But the “aboutness” involved in primary intentionality actively indicates real objects presented in a certain light. This is not always justifiable. Sometimes, those “real objects” are merely assumed to exist, as when it comes to fictional discourse. But, in the ideal condition, we suspend disbelief.

    That sounds like fictionalism, and it would be if that were the end of the story. But the thing is, our false sentences can themselves be used in order to be able to form a conceptual scheme, and this conceptual scheme as a whole can be used to form a whole new body of true beliefs. When our conceptual schemes are good enough — say, when they arguably provide a basis for All of Science, as is the case with mathematics — then the fictions (presented in the first-order) are false, but are essential to frame an idiom which is itself used in such a way to state truths. So long as we assume that the conceptual scheme has a set of epistemic goals — that it plays an active part in an institution, say — we may say it is truth-apt. We stop saying it is truth-apt when the institution drops out.

    The first mathematician was but a dreamer. Then, her progeny made up stories of Platonic truths. Then came the engineers, and we stopped worrying about all that irrealist nonsense, because physical statements which made use of the mathematical idiom discovered that they were way too useful to all this to be a coincidence.

    There are deeper worries when it comes to promises, owing to the fact that promises are a borderline case of collective action. This deeper point can be brought to light when we consider another range of cases, where self-fulfilling prophecies can be a feature of collective intentionality. (See here.) That’s what I mean when I say trust is sometimes a truth-maker.

    The fact that it is perfectly natural for use truth-talk about institutions ought to indicate to us that error theory has abandoned the project of explaining truth. Instead, you’re trying to legislate truth — which is something you can’t do from a correspondence theory!

  60. Myron,

    I think we’ve reached an impasse on the subject of language, which I think is the main issue, so I’ll say no more except to ask you to clarify one point, if you care to do so. Earlier I asked you :
    But let me ask whether it would be any more acceptable to you if I said that numbers and dogs exist in different ways, rather than in different senses of ‘exist’?”

    And you responded:
    It is acceptable for me to say that there are two ways or modes of existing: accidental and necessary existence. (But I deny that there can be things which exist logically necessarily.)

    Now you write:
    I think that abstract objects such as numbers do not exist at all, and what doesn’t exist at all doesn’t exist in any way.

    I took your first response to mean that numbers exist in the necessary way/mode and dogs in the accidental way/mode. But it appears you didn’t mean that. Could you please clarify your first response for me?

  61. Ben,

    Richard, but when you say “But, if I’m familiar with his idiosyncracies and understand him, he can still be communicating true information to me”, you’re arguably abandoning the literal meaning of the sentence in order to talk about speaker’s meaning.

    OK. Please treat that sentence as an aside. It wasn’t my main point. I’m sorry my use of it was confusing. I’m certainly not denying that there’s an important distinction between using a sentence in a conventional sense and using it in an unconventional sense. I prefer the word “conventional” to “literal”, as I don’t think the literal/figurative distinction is the most relevant one here.

    In Leo’s case, you originally wrote:

    Whether or not “Dragons exist in mind-space” is a meaningful statement is really the whole issue, my man.

    I assumed that “mind-space” was not a term already familiar to you. If that’s the case then there is no conventional meaning (at least none known to you and me) and so the situation is quite different from the arthritis case. If Leo has coined his own term of art, then we must consider what he meant by it before we can judge whether the statement is meaningful.

    But perhaps I mistook you. Perhaps you were already familiar with the term “mind-space”, and you were questioning the meaningfulness of the statement given your experience of how the term is typically used. That would be a different kettle of fish.

    You went on to write:
    I think he meant something like the ‘space of reasons’.

    I rather doubt that’s what Leo meant, which brings us back to the importance of asking what he did mean. Of course, if your interpretation is based on your prior experience of reading the term, then it may be better founded than mine. But it sounds to me like you had no more basis for your interpretation than I did. Actually, I would say mine had a bit more basis, since it was more faithful to the word “mind” in “mind-space”, and it was more charitable to Leo.

    It seems to me, on reflection, that Leo’s use of the word “space” echoes the use of that word to refer to sets of logical possibilities, as in the mathematical terms “search space” and “sample space”. Similarly, Daniel Dennett uses the term “design space” to refer to the set of all possible designs. And I expect many other writers have used similar terms. On that basis, the best interpretation of “mind-space” would probably be that it means the set of all possible minds. This differs from my original interpretation of Leo, when I interpreted him to mean the set of all minds that exist in reality (or all existing human minds). You could challenge whether it’s coherent/meaningful to talk of the set of all possible minds, but that seems not to have been your point.

    In fact, I don’t think Leo coined the term himself. Google throws up a few relevant prior uses. I think some are best interpreted as referring to a logical space and others as referring to the set of actually existing minds. Most are just too vague or weird to be helpful.

  62. P.S. Myron, on reflection I think you were making a distinction between “necessary” and “logically necessary”. I guess your “necessary existence” excludes things which are logically necessary, including numbers.

    So your short answer to my original question could have been “No”. :wink:

  63. Richard Wein wrote:
    “Earlier I asked you :
    
—But let me ask whether it would be any more acceptable to you if I said that numbers and dogs exist in different ways, rather than in different senses of ‘exist’?—

    And you responded:
    
—It is acceptable for me to say that there are two ways or modes of existing: accidental and necessary existence. (But I deny that there can be things which exist logically necessarily.)—

    Now you write:
—I think that abstract objects such as numbers do not exist at all, and what doesn’t exist at all doesn’t exist in any way.—

    I took your first response to mean that numbers exist in the necessary way/mode and dogs in the accidental way/mode. But it appears you didn’t mean that. Could you please clarify your first response for me?
    P.S. Myron, on reflection I think you were making a distinction between “necessary” and “logically necessary”. I guess your “necessary existence” excludes things which are logically necessary, including numbers.
    So your short answer to my original question could have been “No”.”

    I should have written: There are two concepts of modes of existence, the concepts of accidental existence and necessary existence. For this doesn’t imply that both modes of existence exist, i.e. that there are both things which exist accidentally and things which exist necessarily. The concept of accidental existence is the same as the concept of non-necessary existence, and so the basic concept is “necessary existence”.

    But there is more than one kind of necessity, and so this concept needs to be clarified:
    Is necessary existence logically necessary existence or ontologically necessary existence?
    If the former, I think that “x exists necessarily” is (logically) necessarily false for every x, i.e. the existence of logically necessary existents is logically impossible; and if the latter, I think the concept of ontologically necessary existence is the same as the concept of essentially eternal existence, and that it is an open question whether this concept’s extension is empty.
    If mathematical platonism were true, then, I think, numbers would exist ontologically necessarily in the sense that they would be essentially eternal.

    x is an existentially/ontologically necessary being
    =def
    x is essentially eternal/exists essentially eternally
    =def
    For all possible worlds w, if x exists in w, then there is neither a first nor a last moment of x’s existence, i.e. then x has always existed in w and will always exist in w, i.e. then x is both uncreatable and indestructible in w.

    Existential necessity is called “factual necessity” by Richard Swinburne. The decisive difference between an existentially/factually necessary being and a logically necessary being is that the former is logically contingent in the sense that it does not exist in all logically possible worlds. There are some logically possible worlds where it does not exist.

  64. Hey Richard,

    Please treat that sentence as an aside. It wasn’t my main point. I’m sorry my use of it was confusing. I’m certainly not denying that there’s an important distinction between using a sentence in a conventional sense and using it in an unconventional sense. I prefer the word “conventional” to “literal”, as I don’t think the literal/figurative distinction is the most relevant one here.

    You’re right to suggest that I potentially conflate “sentence meaning” / “literal meaning” with “conventional meaning”. Not everyone does this. For instance, Davidson prefers to think of literal meaning in terms of the person’s first or prior meaning. And I think he is committed to some very strange ideas about the literal. (For Davidson, when you’re speaking to a serial malapropist, “A nice derangement of epitaphs” might literally mean “a nice arrangement of epithets”, even if that usage is self-consciously unconventional.) So I conflate the literal and the conventional only because it strikes me as a superior view. That’s why I qualified my claim above with the term “arguably”.

    So you didn’t do anything wrong. Perhaps you just committed yourself to a Davidsonian sort of view, and there’s nothing wrong with that (as far as this narrow point is concerned). It’s just one of those things that needed to be cleared up.

    I don’t mean to suggest that the term “mind-space” was unfamiliar to me. (I don’t know if it’s the space of reasons, or whatever; it doesn’t really seem to matter, we’ve got the basic idea, that we’re talking about the place where it looks as though ideas are tokened.) I also do not mean to say that the term “mind-space” is meaningless. I suggested that it was meaningless (or, perhaps, always false) in the context of that sentence where it is preceded by “exists in”.

    Now that I think of it, I’d prefer to speak of such expressions as always false than as meaningless. “Meaningless” is very strong and cruel. I picked it up as a force of habit from Russell, but maybe there’s no justification for talking that way.

  65. Myron,

    Thanks for that clarification. I misinterpreted your earlier reply.

    Ben,

    I think the literal/figurative distinction is a particularly fuzzy one. Is “space” being used figuratively when it’s used (as in mathematics) to refer to a set? I don’t think anything of any importance hangs on that question. But I for one would be disinclined to refer to such technical usages as “figurative”.

  66. Richard, I’m inclined to say that it is being used literally in that context, because the language of sets has yielded institutional successes with real things. Those instrumental successes allow us to retrospectively reinterpret the original fiction of sets into the facts of science.

    But you still have to apply this lesson to ‘minds’. And there might be an ambiguity involved here. What are we talking about, if we’re talking about minds? If by ‘mind’ you mean something subjective or private, then there’s no literal mind-space, nor any existing in it. But if you mean to suggest that minds are public, then there’s no literal difference between minds and math, and it makes perfectly good sense to talk about ‘existing in mind-space’. That will involve letting go of any proprietary sense in which you determine what you think, but it’s a plausible enough move.

    My sense is that the conventional meaning of ‘mind’ is something like the former, not the latter. But even if that were so, I don’t suppose it always needs to be that way.

  67. Sorry: “your” not “you’re”.

  68. It seems to me that which can be quantified is that which has quantity to the perception, and existence need not be limited to the senses or imagination of the perceiving party. It becomes a verificationist and positivist point if you do. It is sort of a Witgenstein TLP point.

    However, we can conceive of that which is greater than we can sense or perceive, since we can conceive of that which is less, and are humble enough (sometimes) to concede we are not the arbiter of existence. Though we may need to play language games, and use Thomist analogy to describe such a Perceiver. That is sort of a Witgenstein PI point.

    What you think about the notion of “existence”, existing as a legitimate topic of a valuable philosophical discourse, depends on your position between those two points on Wittgenstein’s ontological journey I suspect.

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