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What exists in the theory of descriptions?

  1. Sep 28, 2009 #1
    Actually, I'm more interested in the proper use of the word "existence" than trying to think up a list of things that exist. In Bertrand Russell's A History of Western Philosophy, in the chapter on the Philosophy of Logical Analysis, Russell has this to say about the proper use of the word:

    In his theory of descriptions, the real meaning of a sentence such as "The author of Waverley exists (or existed or will exist)" is "There is an entity c such that the statement 'x wrote Waverley' is true if x is c and false otherwise."

    It seems to me the point of this is to avoid the confusion that is caused by treating existence as a predicate, as in Anselm's proof that God exists. That is, you don't say that a certain thing has the properties of blueness, roundess, hardness, awesomeness, premature balditude, and existence. Modern logic makes it clear that that last one is an error. But what is wrong with taking "Scott exists" to mean "There exists x such that statement 'x is Scott' is true." The theory of descriptions makes essential use of statements of identity, so I don't see why it wouldn't apply here.
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  3. Sep 28, 2009 #2
    Haven't read the book, but I'm guessing it goes something like this...

    Given names are just labels or referents.
    Saying 'x exists' really doesn't say anything at all.

    Like saying x is x, is not so much true or false, as it is redundant, a definition.
  4. Sep 29, 2009 #3
    Yes, that's probably what he's getting at. But then I wonder how do you say that a certain name has a referent? Some names don't have a referent. Santa Claus is a common example. Unless I'm misunderstanding Russell, it sounds like you would first have to come up with a description of Santa Claus (jolly, red-suited, bearded guy who lives at the north pole, etc.) before you could say that he doesn't exist. Maybe that's how it should be, though. As you said, names are labels for things. And unless you have a description in mind, I guess it really doesn't say anything about the world to say, "There is no referent for the name Santa Claus." Because until you associate a description with that name, it is just an empty place-holder. Do I have it right?

    Edit: I think I have gotten confused by my recent attempt to study predicate logic with identity (PLI). In that system there is the theorem

    [tex]\exists x (x=x)[/tex]

    which is interpreted as "There is an individual x such that x is x." Admittedly, that doesn't tell us much about x, but it does seem to say that something exists. So in PLI, it seems perfectly natural to say something like "Santa Claus exists."

    [tex]\exists x(x= \mbox{Santa Claus})[/tex]
    Last edited: Sep 29, 2009
  5. Sep 29, 2009 #4


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    The general issue here is that Russell was trying to create a fundamental atomistic version of logic. So all things could be talked about successfully as an additive collection of particulars. Exactly the same principle as behind modern information theoretic thinking where reality is reduced to digital bits.

    But logic, like reality, needs to be triadic to capture the full story.

    So the two other dimensions that Russell was trying to eliminate from the modelling were vagueness and generality.

    With Santa Claus for example, this could be taken as a general idea or a particular instance. So both would "exist", but in quite different ways.

    The general idea of Santa Claus would act as a constraining form. It would be saying that some instance of being would have to conform to this universal template to qualify as "a Santa Claus". Inserted as an "x" into a logical statement, it would act as a boundary constraint.

    And then there would be the opposite case of a specific instance of a Santa Claus. Some actual located substantial being. Here the logical structure becomes additive or constructing. If we saw a lot of Santa Clauses and summed over their variety, we would get a sharper general notion of Santa Claus-ness.

    Now obviously Santa Claus is chosen as a paradoxical example here because like God and the Emperor of Germany, these seem like one-shot examples. But Santa Claus is a concept clearly derived as a sum over variety, a generalisation, of notions of twinkly-eyed old grandad types in anglo culture.

    So the particular~general dichotomy is one of the complexities of reality that Russell was famously trying to reduce to a monadic, atomistic, story of just particulars.

    Vagueness was a second dichotomy he was trying to eliminate - the crisp~vague dichotomy. He was trying to eliminate the idea of vagueness so that there only remained the crisp.

    So with Santa Claus, Russell would argue that any uncertainty or fuzziness surrounding some particular instance of a Santa Claus would be a semantic vagueness (the sorities paradox approach). And then semantic vagueness could actually be eliminated with atomistic logical approaches.

    But while Russell was singing the mainstream uber-reductionist hymn, CS Peirce was working in considerable obscurity on a fully triadic approach to logic, one that retained the three essential elements of the particular, the general, and the vague.

    Russell is actually a great philosopher because he took a particular reductionist approach about as far as it would go - all the way until it broke down. But people have never really reacted to that outcome in the way you might expect (just as Godelian incompleteness and Zeno's paradoxes generally are misread for what they actually are telling us).

    It is like the mainstream walked until it reached the edge of a great cliff - the point at which the reductionist road finally gave way - and have spent ever since wandering bemusedly along the fracture kind of hoping that the breach will one day miraculously heal itself and the journey can be picked up again.

    Some 99% of posts to this forum, for example, are expressions of mystification at finding the royal road of standard logic hits this abrupt limit. But all you have to do is turn around and note the two dimensions that have been left behind in chasing the "crisp particular", the holy bit. And these two dimensions are global generality and foundational vagueness.
  6. Sep 30, 2009 #5

    You covered a lot of interesting points in your post, and it will take me a while to digest it and ask intelligent questions about it. In the meantime, can you tell me what is the actual significance of Godelian incompleteness that people generally miss? I am trying to learn about that very subject now. I'd also like to hear what you have to say about Zeno's paradox.

    Russell may have relaxed his logical atomism in later years. He held that we give names to 'things' as a convenient way of bundling together certain events. Inspired by modern physics, he took events to be the fundamental stuff of the material world. I don't know if that still counts as logical atomism or not, but at least it is not a very naive form of it, as in medieval philosophies.
  7. Sep 30, 2009 #6


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    On Godel...about my favourite "post-incompleteness" book is Rosen's Essays on Life Itself.

    Basically Godel can be taking as a baseline position on how all modelling operates instead of as indictment of maths' ultimate failure. So how the glass is 99% full rather than 1% empty.

    On Zeno.....Zeno should return us to dichotomous thinking. So instead of trying to argue that reality either is continuous, or it is discrete, we should learn to see how these two extremes are the limits that bound what actually can exist.

    Mainstream thought wants always to be monadic - to reduce everything to some single essence. But dualities always present themselves (they doing it again in string theory, category theory, QM theory, whatever...). But dualism (thinking that both opposing extremes actually exist) is then the wrong alternative. The correct response is to see dualities as the limits - and therefore precisely what cannot in themselves, in some complete and isolate fashion, exist.

    So draw a line to bound a circle, and then throw the line away as it is not part of what is actually real, just our convenient model of the limit.

    On Russell....Russell's events approach is to me much more realistic. Partly because it is atomism done properly.

    To talk about things that exist - which are confined at a location but then have infinite or unbounded extension in time - is obviously a weak form of locality. A strong form of locality - the strongest, the limit indeed - is spatiotemporal locality. That is a 0D point within a 4D context. So an "event".

    Of course, getting Peircean now, an event is really normally the sign of an interaction, some dyad. So should we treat events as primal or interactions?

    And then we can think about punctate change vs smooth change. An event is a sharply-located-in-spacetime change (that is, sharply detectable because of a smoothly existing or persisting context - now we are talking Peircean triads).

    So is punctate change more fundamental than smooth change? I think so, but these are the kinds of questions that arise.
  8. Sep 30, 2009 #7


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    A description has meaning only within some context, no? To say something "exists" can be meaningful only if there's a context to which its existence (in whatever sense) is relevant.

    Contexts, it seems to me, are made of interactions... so this concept seems ontologically fundamental. Something can be said to exist IFF it participates in an interaction-context that makes its existence relevant to something else.

    Change, on the other hand -- whether conceived as continuous or as made of point-events -- doesn't have this fundamental character. To describe a change, you need to be able to describe what exists, i.e participates in some interaction-context that makes meaningful what it is and what changes about it, over time.

    In physics, point-events are a mathematical artifice, and continuous change is only a "classical" approximation, while everything that actually happens is an interaction.
  9. Sep 30, 2009 #8
    I'm interested in biology from a systems theory approach, so I will have to learn more about Robert Rosen.

    Okay. It's nice to hear a sane assessment instead of the usual reckless, overreaching conclusions. Godel's first incompleteness theorem says that in any formal system that includes elementary arithmetic, there will be at least one arithmetical statement that is neither provable nor refutable. So if the system is known to be sound (correct), there is a true statement that is unprovable (or equivalently, a false statement that is unrefutable). Nothing about the Theory of Everything or the existence of God, etc. Godel's result is plenty damn interesting itself, and there's no reason for it to be sensationalized.

    That's probably true. However, even if reality isn't continuous, I don't think Zeno successfully disproved continuity. If we are talking about his treatment of the arrow in flight, it is not surprising that he arrives at a paradox when he simultaneously treats the motion as continuous and discontinuous. If there were really a "next" instant in continuous time, then it would be a problem that the arrow is static at that instant, no different from an arrow at rest. But there is no "next" instant, as there is in discrete time. Zeno just didn't have a very good mathematical model of the continuum. That's hardly a mark against him, considering that nobody did until people like Weierstrass and Cantor came on the scene.

    As for the rest of the discussion, please carry on. It is very interesting stuff. I don't understand the bit about how events are really dyadic. Maybe that could be elaborated on. Perhaps either apeiron or ConradDJ could answer this: does the contention that everything is based on interaction have anything to do with the fundamental nature of the observer/observed relation in modern physics?

    Also, anyone who has anything to add about the original topic, the theory of descriptions...feel free to join in.
  10. Sep 30, 2009 #9

    There is no Zeno paradox in the Brukner-Zeilinger information interpretation. There are no time-related paradoxes either(backwards causality, arrow of time, subjectivity of time, abscence of universal moment NOW). There is no space-related paradox either(the disappearance of space under certain circumastances, the universe's boundery conditions, entanglement and FTL signalling, something out of nothing, the finely tuned initial conditions, the existence of physical laws, etc). Essentially, there are no paradoxes at all, except maybe the source of it all.

    Last edited: Sep 30, 2009
  11. Sep 30, 2009 #10


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    That wasn't what I meant. Rather that he was successfully demonstrating the unreality of these mutually complementary ideas - continuity and discreteness. Take them as being real, rather than limits, and paradox results.

    But modern maths shows that using unreal ideas like pure discreteness, or pure continuity, is not a problem. In fact it is better to model with completely "clean", unrealistically simple, concepts.

    It only becomes a problem when we try to map the concepts back onto physical reality. For example, the huge debate in physics about how to map continuous GR on to discrete QM. That is when we need to pay attention to the simplifications being made in our ontic concepts.

    So neither actual discreteness nor actual continuity can exist in reality (as to actually have one would destroy the logically necessary existence of the other). However, it is quite possible to have both these extremes as the limits on what exists. Indeed, that is what seems to be logically necessary.

    The answers quickly get complicated. If you are into biology and systems theory, perhaps you should check out biosemiosis - a modern attempt to apply the triadic logic of CS Peirce.

    There are actually varieties of dyadic relations.

    Dyadic: I take this to mean a simple symmetrical interaction - one across a single scale. So two particles can have an interaction, whether it is a collision or exchange. They are of the same size. They are like two ends, the terminating points, of a relationship.

    Dichotomistic: Now this is an asymmetric interaction. One that crosses scale. So now, as Conrad stresses, it is about events and their contexts. Figure and ground. A much richer and more interesting situation. But less well modelled in maths or physics. Newtonian mechanics captured the essence of dyadic interactions, but dichotomistic interactions are not generally understood. They are like symmetry breakings and phase transitions. But the maths here is poorly developed.

    I would be cautious of saying "everything is based on interaction" because that is a monadic kind of statement. All things boil down to a one-ness of some kind.

    Interaction is meant to allude to the dyads that result in triads - the dichotomies that produce hierarchies. So interaction may need to be further unpacked to make plain that a dyadic relation is being asserted as basic.

    For example, I would talk about the process of differentiation~integration. A form of relating that is going in two directions at once. This more precisely captures the ideas at the heart of the "all is interactions" viewpoint.

    But I meant to answer your query on observers. Yes, if you believe that dichotomies - interactions with scale - are what is fundamental, then event~context is going to be a basic duality. Observers would be the contexts that globally shape (or more correctly, form the boundary constraints) to the observed, the events that are found locally to occur.

    Again, Peirce's semiotics is tentatively being extended to cover physics. So from biosemiosis, we can expand to pansemiosis.
  12. Oct 1, 2009 #11


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    Rosen’s work does look very interesting – and has directly to do with the question about observers. But I haven’t yet had time to learn much about it, since I just learned about him recently from apeiron. Here’s a link.


    As to physics – there’s a strong indication in quantum theory that entities can have definite existence and possess determinate characteristics only to the extent that some context of relationships makes their existence physically meaningful. Things exist to the extent that they make a difference to other things that exist.

    This interests me very much, because it poses such a philosophical challenge – to come up with fundamental ontological concepts that make sense of this situation. And at the same time, so much is known about physics, and its foundations are so thoroughly analyzed, that there’s a tremendous amount of information to work with in developing these ideas.

    At bottom, Planck’s “quantum of action” itself is a very strong indication that whatever happens in the world, always occurs in discrete, momentary events... Planck called them at one point, “atoms of happening”. And the structure of particle physics makes it appear that these “atoms” are in every case interactions – things that happen between things.

    So one way we might try to work out a new ontology would be to start from the “between” rather than from “things”, as fundamental -- to try to imagine things as made out of their relationships, in some sense. (Including ourselves, as made out of all our relationships – physical, biological and personal). I think this is the basic thought behind the “systems science” apeiron talks about.

    It’s not at all clear how to formulate the concepts we need for this... how to understand the structure of what happens in relationships, at a fundamental level. What happens in physical relationships seems to be essentially the communication of information about what exists – the “observer/observed” relationship. I tried to develop some ideas about this in another thread --


    So yes, in short, the notions of “interaction” and “observation” both point to the same question about the fundamental structure of the “between” in physics.
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  13. Oct 1, 2009 #12


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    If you read Relativity theory, "events" are not dyadic... they're essentially "point-events" located someplace in spacetime. This makes the classical assumption that things -- and events -- are well-defined "in themselves" and just "exist" in an absolute sense.

    So Quantum Mechanics and particle physics is where the dyadic aspect of events comes to the forefront. But even there it's not well conceptualized. The word "interaction" occurs everywhere in physics, but like "observation" or "measurement" it's almost an undefined term.
  14. Oct 1, 2009 #13

    I don't understand how the existence of one (an instance of something discrete) would destroy the existence of the other. Are we still confining ourselves to the question of the continuity of motion? How could either discreteness or continuity be logically necessary? Even in the case of motion, there seems to be the possibility of simply discontinuous (as opposed to discrete) motion, i.e. motion that is continuous for a while but experiences jumps. Or was that exactly what you were trying to say? It sounds like that's what you were getting at when you said that continuity and discreteness are merely limits of what is possible.

    I will look up biosemiosis. I should not have given the impression that I already know something about biology and systems theory. It's just that I'm interested in learning :). I think life, even (especially?) the most basic forms of it, is the most fascinating stuff there is.

    I have to admit I'm out of my depth here. Is there a particular work of Peirce's that would serve as a good introduction to his triadic approach? I pretty much only know his name and that he is the founder of a particular brand of pragmatism, distinct from William James' or John Dewey's.
  15. Oct 1, 2009 #14

    Thank you for the links. I have looked a little at the Robert Rosen website. It looks interesting but over my head. I'm not just saying that to be lazy. Rather, I really need to learn about what he's criticizing (attempts to extend thermodynamics to open systems, for example) before I can understand his criticisms. A while back I started reading Prigigone's From Being to Becoming but didn't finish it. I have a whole long list of "things I intend to learn about," which includes dynamical systems, stat. mech., and the like, but it will be a while before I get to it. I will, however, read through that thread you linked to.

    Yes, that's exactly how I was thinking of events...as mathematical points, between which there is an invariant interval. But I see from what you say that that is not quite the picture in particle physics. An event implies some exchange or interaction.
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  16. Oct 1, 2009 #15


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    This comes back to the logic of dichotomies - the foundation of philosophy. Thesis and anti-thesis. Socratic dialogue. To be able to suggest one thing as true always creates the matching possibility of its opposite. So then you have to opposing - or complementary? - extremes. And do you chose one as true, the other false, or accept both as true (as the complementary bounding limits to reality).

    So to be able to have the continuous, there must also be the anti-thesis of discreteness. But then neither can actually exist because then the other would have been in reality eliminated.

    One polar extreme cannot be true, because then the other would have to be false (or emergent, or have some other secondary status). But both extremes can be "true" in the sense they are true limits - and boundaries then don't actually themselves exist.

    That's all right. You have been asking good questions. Biosemiosis is still pretty new and wild. I wouldn't recommend the literature as a starting point.

    A good pop book might be Eric D. Schneider and Dorion Sagan's Into the Cool


    (not biosemiosis but about dissipative structure - a better framework of analysis really)

    Actually this is a real problem. The story on Peirce was that he was so brilliant/awkward that few understood him at the time, he got bumped by Harvard and spent his life writing largely unpublished screeds in poverty. He was rediscovered around a decade ago or so ago and there has been an effort to make sense of his legacy. But there are no handy pop introductions, you have to read the man himself.

    You can get a glimpse of him in a pop book on the pragmatists - The Metaphysical Club by Louis Menand. While that is good at showing how he was the centre of his circle, it does not really get into his systems thinking.

    If you are interested in a set of key readings that help define the terrain here, there is this list....

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  17. Oct 2, 2009 #16
    Well, I certainly agree with the principle of contradiction; namely, that a particular motion cannot be simultaneously continuous and non-continuous (discontinuous). But I'm using the word "continuous" to predicate particular instances of motion. It sounds like you are saying that predicates must predicate reality as a whole. I have trouble following this. If you'll permit me a crude example, I think it's okay to say "this is a green apple" and "that is a red apple" without the greeness of one apple destroying the redness of the other apple. But reality as a whole is neither green nor red, nor any other color as far as I know. Please forgive me if I misunderstand you.

    Also, thank you for the reading suggestions. I have at least heard of the term "dissipative structure," but don't know what it is yet. And I recognize a few authors on the list you linked to, but most of them are new to me. There is so much to learn and so little time!
  18. Oct 2, 2009 #17


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    I'm talking here about philosophy's attempt to find the ousia or essence of reality. The most fundamental or universal categories. So colours and apples are not general enough to be metaphysical categories. But a number of dichotomies such as stasis~flux, substance~form, chance~necessity, atom~void, and discrete~continuous were identified in ancient greek thought, and have proved robust even into modern times.

    So my argument only concerns these kinds of ultimate dichotomies - metaphysics' search for a ToE.
  19. Oct 3, 2009 #18
    Ah, okay. Thanks for clearing that up. Coming back to Russell's theory of descriptions, I don't know if he was aiming for a theory of reality. In fact, he explicitly says that the aims of logical analysis were less ambitious than those of traditional philosophy. Then again, that could just be a rationalization after failing to answer all the problems of philosophy. He and Whitehead were ambitious when it came to mathematics, but I'm pretty sure Russell was always aware that mathematical knowledge is of a different nature than factual knowledge about the world.
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