• Leontiskos
    3.8k
    This is a reading group for Gyula Klima’s paper, “St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding.” The paper is 14 pages long before notes and references, and collects together some of the tangential themes from the recent thread on Quine and reference. Its focal point is St. Anselm’s famous proof for God’s existence, although that proof is not what the paper is ultimately centered on.

    What I want to do is read the paper slowly, section by section. We will start with section 1 but comments on the introduction are also welcome. Let’s try to keep the discussion focused on the content of each section, and then after we finish the final section the thread can enter “free for all” mode, at which point broader comments, criticisms, and tangents can be pursued. I want to move slowly so that even those with limited time will have an opportunity to read and contribute. The sections are as follows:


    (click a heading to go to that part of the thread)

    The paper is freely available:



    (Note that this will be my first time reading the paper as well.)
  • Leontiskos
    3.8k
    Part 1. The Modern vs. the Medieval Conception of Reference

    Russell and reference via quantification -- Quine's slogan -- misinterpretations of Anselm -- intention, medieval reference, and ampliation -- entia rationis -- ontological commitments -- correctly interpreting Anselm

    Here are the first few sentences of the paper:

    Saint Anselm’s proof for God’s existence in his Proslogion, as the label “ontological” retrospectively hung on it indicates, is usually treated as involving some sophisticated problem of, or a much less sophisticated tampering with, the concept of existence. In this paper I intend to approach Saint Anselm’s reasoning from a somewhat different angle.

    First, I will point out that what makes many of our contemporaries think it involves a problem with the concept of existence is our modern conception of reference, intimately tied up with the concept of existence. On the other hand, I also wish to show that the conception of reference that is at work in Saint Anselm’s argument, indeed, that is generally at work in medieval thought, is radically different, not so tied up with the concept of existence, while it is at least as justifiable as the modern conception.
    Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding, 69

    ---

    Edit: I received a PM from someone essentially asking, "What's the fuss?" If you are not familiar with the modern conception of reference stemming largely from Bertrand Russell, and also the way that quantificational logic understands existence via figures like Frege and Quine, then the paper may be somewhat opaque to you. Certainly the first section will be opaque. Nevertheless, the latter sections of the paper might be more accessible even to those who are not familiar with the modern tradition.
  • Count Timothy von Icarus
    3.2k
    I'll just stick to the opening section for now.

    First, I will point out that the distinction between ens reale and ens rationis probably is more important in a realist context. If we're actually capable of abstraction, then it's important to note that composing and dividing in the human intellect doesn't result in a vast multiplicity of new entities.


    From the paper:

    At this point, however, anyone having qualms about “multiplying entities”, indeed, “obscure entities”, should be reminded that the distinction between objects, or beings (entia) simpliciter, and objects of thought, or beings of reason (entia rationis) is not a division of a given class (say the class of objects, or beings, or entities) into two mutually exclusive subclasses. The class of beings or objects is just the class of beings or objects simpliciter, that is, beings without any qualification, of which beings of reason or objects of thought do not form a subclass. Mere beings of reason, therefore, are not beings, and mere objects of thought are not a kind of objects, indeed, not any more than fictitious detectives are a kind of detectives, or fake diamonds are a kind of diamonds.

    Qualifications of this kind are what medieval logicians called determinatio diminuens, which cannot be removed from their determinabile on pain of fallacia secundum quid et simpliciter.11 Accordingly, admitting objects of thought, or beings of reason, as possible objects of reference, does not imply admitting any new objects, or any new kind of beings, so this does not enlarge our ontology.

    At the outset, I will just note that it will probably be unhelpful to think of the ens reale/ens rationis or relationes secundum dici (relations according to speech) / relationes secundum esse (relations according to being), etc. as directly translatable into the terms of the modern mental/physical dualism. This is what I had initially thought on my exposure to these terms, and it led to some confusion.

    Such a framing might suggest a straightforward solution (at least on the ontology side of things) along the lines of: "mental entities can just be reduced to brain states, and so they exist as physical ens reale, just not fundamentally or descriptively." This will not do for capturing how thought is itself related to eidos (form/act) or the phenomenological whatness (quiddity) of things in medieval thought. And it misses the way in which what constitutes being a proper being (as opposed to a heap) is conceived of due to the legacy of Plato, Aristotle, and Neoplatonism.

    I will just note that such an understanding of beings is more convincing than might be supposed, but it'd lead way off topic to discuss it. It will suffice to say that it's probably best to bracket such a reduction as a consideration, because it remains problematic even in systems that have been constructed precisely to try to make such a reduction plausible. The problem that mere mechanism does not seem to capture "how things can be false" is at least as old as Aristotle and still seems to be a great difficulty.

    In logic, we have to work with clear terms and distinct categories, and a binary of ens reale and ens rationis works well enough, but there is often a graduation of being assumed (i.e., e.g. in this thread or in the "Great Chain of Being," although the latter notion is rarely presented well, generally being reduced into a caricature of monarchical propaganda or some such straw man).

    So on this conception Quine’s answer to “the ontological problem”: “What is there?”, namely, “Everything” is true. For on this conception the claim: “Everything exists” (or its stylistic variants: “Everything is” or “Everything is a being” or “Everything is an existent” or “There is/exists everything”) is true.12 Still, “Something that does not exist can be thought of” is also true, where, the subject being ampliated in the context of the intentional predicate, “Something” binds a variable that ranges over mere objects of thought that do not exist.13


    There is an interesting connection here to the idea of the "mind being potentially all things," as well as prime matter being sheer potency, and so in a sense nothing. The mind is a true "microcosm" in this respect, i.e., that it shares a likeness with prime matter while also being act to the greatest degree. To be anything at all is to be something, to have some intelligible whatness, which ties back to Parmenides "the same is for thinking as for being." But this last one can be taken in several senses. "All that is can be thought," does not imply "all that is thought is."

    Modern thought sometimes has more difficulty with this to the extent that it has eliminated a solid understanding of, or ground for, the distinction between act and potency by declaring potency to be suspect due to being "unobservable." The older tradition certainly agrees in some sense, since to be observable is to be something, to have quiddity, and so to be actual, but it maintains the distinction because potency is required to explain change.

    The contrasting options are either to make no distinction between the actual and potential (or hypothetical), leading to an inflated ontology and cosmology (i.e., everything thinkable is), or to go in the opposite direction and declare that only the actual (often as "physical") is. But then there is also the move to declaring that unintelligible being lacking in any whatness can exist (a view made possible if one conceives of consciousness as primarily an accidental representation of being). Sometimes we see these together, for instance, an inflated nominalist ontology combined with the assertion that the completely unintelligible/unthinkable also exists.
  • Leontiskos
    3.8k
    I'll just stick to the opening section for now.Count Timothy von Icarus

    Sounds good. I haven't even read section 2 yet. :cool:

    I think it's probably a good idea to stick to section 1 before moving on to section 2; section 2 before moving on to section 3, etc. It looks like each section will have enough content to sustain its own discussion, questions, confusion, etc. Bite-sized pieces will also make participation easier, for myself included.

    First, I will point out that the distinction...Count Timothy von Icarus

    Great thoughts. I've been on the road all day and need a nap, but I will come back to this. :smile:
  • Count Timothy von Icarus
    3.2k
    A relevant, helpful article on some of the terms: https://plato.stanford.edu/entries/medieval-terms/#Sign

    I might skip past the historical overview because it is very heavy on terminology, but then the full explanations come later.

    Useful context:


    [On signification]

    A twelfth-century commentary on the Perihermeneias reports Porphyry as saying that at the time of Aristotle, there was a great debate over the principal signification of utterances: was it ‘res’ (things) or incorporeal natures (Plato) or sensus (sensations) or imaginationes (representations) or intellectus (concepts)?[9] In fact, medieval philosophers of language were heir to two conflicting semantic theories. According to Aristotle, the greatest authority from the ancient world, words name things by signifying concepts in the mind (Boethius translated Aristotle’s term as passiones animae – affections of the soul) which are likenesses abstracted from them. But Augustine, the greatest of the Church fathers, had held that words signify things by means of those concepts.[10] This led the medievals to the question: do words signify concepts or things? The question had already been asked by Alexander of Aphrodisias and his answer was transmitted to the medievals in Boethius’ second commentary on Aristotle’s Perihermeneias (De Interpretatione): “Alexander asks, if they are the names of things, why has Aristotle said that spoken sounds are in the first place signs of thoughts … But perhaps, he says, he puts it this way because although spoken sounds are the names of things we do not use spoken sounds to signify things, but [to signify] affections of the soul that are produced in us by the things. Then in view of what spoken sounds themselves are used to signify he was right to say they are primarily signs of them” (tr. Smith, pp. 36–37).[11] So words primarily signify concepts.

    But the matter was not settled, other than that whatever view a medieval philosopher took, it had to be made to accord with the authority of Aristotle, perhaps in extremis by reinterpreting Aristotle’s words. Abelard refers to a distinction between significatio intellectuum (signification of concepts) and significatio rei (signification of the thing), more properly called nomination or appellation (see De Rijk, Logica Modernorum, vol. II(1), pp. 192–5). Similarly, the Tractatus de proprietatibus sermonum asks whether words signify concepts or things, and responds: both (intellectum et rem), but primarily a thing via a concept as medium (op.cit . II (2), p. 707)...

    ...Just as signification corresponds most closely – though not exactly – to contemporary ideas of meaning or sense, so supposition corresponds in some ways to modern notions of reference, denotation and extension. The comparison is far from exact, however. One major difference is that the medievals distinguished many different modes (modi) of supposition. Despite the difference between different authors’ semantic theories, particularly as they developed over the centuries, there is a remarkable consistency in the terminology and interrelation of the different modes.

    [For example:]

    Man is the worthiest of creatures
    Socrates is a man
    So Socrates is the worthiest of creatures

    The premises are true and the conclusion false, so wherein lies the fallacy? It is one of equivocation or “four terms”: ‘homo’ (‘man’) has simple supposition in the first premise and personal supposition in the second, so there is no unambiguous middle term to unite the premises.


  • Leontiskos
    3.8k
    "All that is can be thought," does not imply "all that is thought is."Count Timothy von Icarus

    Yes, and I think the quotes you highlight are important:

    At this point, however, anyone having qualms about “multiplying entities”, indeed, “obscure entities”, should be reminded that the distinction between objects, or beings (entia) simpliciter, and objects of thought, or beings of reason (entia rationis) is not a division of a given class (say the class of objects, or beings, or entities) into two mutually exclusive subclasses.Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding - Section 1

    So what is going on here? On the modern scene it is well accepted that a term can refer to beings (entia), such as deer, socks, trees, etc. But then when it is proposed that a term can also refer to beings of reason or objects of thought (entia rationis), the common objection is that this will "multiply entities" and thus transgress Occam's Razor. Specifically there is the idea that it will require two mutually exclusive ontological subclasses, one subclass for beings simpliciter and one subclass for beings of reason.

    We actually saw this play out two days ago in the midst of a discussion on Mario Bunge, who admits of conceptual existence and who treats existence as a first-order predicate. A response was as follows:

    A few notes on treating existence as a predicate. We can of course do this, with some cost. The result is a logic that ranges over things that exist and things that do not exist. That is, it in effect has two domains, one of things that exist and one of things that... do not exist.A Response to Mario Bunge

    (Consider also footnotes 7 and 12. The assumption here derives from Quine's opposition to Alexius Meinong, who posited two ontological subclasses of a sort.)

    That is, the assumption is that Bunge must be working with two mutually exclusive subclasses, at least "in effect." This is the sort of objection that Klima has in his sights. How does he address this objection?

    ...Mere beings of reason, therefore, are not beings, and mere objects of thought are not a kind of objects, indeed, not any more than fictitious detectives are a kind of detectives, or fake diamonds are a kind of diamonds.

    Qualifications of this kind are what medieval logicians called determinatio diminuens, which cannot be removed from their determinabile on pain of fallacia secundum quid et simpliciter.[11] Accordingly, admitting objects of thought, or beings of reason, as possible objects of reference, does not imply admitting any new objects, or any new kind of beings, so this does not enlarge our ontology.
    Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding - Section 1

    First, there are not two ontological subclasses. In an ontological sense there are only beings (entia). But then how do beings of reason (entia rationis) fit in? According to Klima, beings of reason are not beings, but they can still be objects of reference.

    For example, suppose Fido is a dog but Jordan thinks Fido is a cat. Jordan's thought or understanding of Fido as a cat does not refer to any being, given that Jordan is mistaken. Nevertheless, we can still refer to Jordan's cat-Fido thought because it is a being of reason and we can refer to beings of reason. Referring to Jordan's thought, we might tell him, "The way you are thinking about Fido is not correct." We refer to Jordan's thought without granting it ontological status as something that enlarges our ontology (and this is a generic move that can accommodate many different sub-theories).

    Klima's point about "fallacia secundum quid et simpliciter" is effectively that there are rules against reifying beings of reason and shifting them into beings (simpliciter). If you fail to keep track of what is a being and what is a being of reason, or try to "pull a fast one" by swapping out a being of reason and swapping in a being (simpliciter) when no one is looking, then you're committing a fallacy. When beings of reason are allowed as referents new rules are added to make sure we don't mix up the two.

    Modern thought sometimes has more difficulty with this to the extent that it has eliminated a solid understanding of, or ground for, the distinction between act and potency...Count Timothy von Icarus

    I agree. Good point.

    - Good stuff. :up:
  • Leontiskos
    3.8k
    I received a PM from someone essentially asking, "What's the fuss?"Leontiskos

    What is a way into the paper? In footnote 3 Klima points to Frege's Kantian criticism of Anselm's proof. Let's look at that source:

    § 53. By properties which are asserted of a concept I naturally do not mean the characteristics which make up the concept. These latter ate properties of the things which fall under the concept, not of the concept. Thus “rectangular” is not a property of the concept “rectangular triangle’; but the proposition that there exists no rectangular equilateral rectilinear triangle does state a property of the concept “rectangular equilateral rectilinear triangle”; it assigns to it the number nought.

    In this respect existence is analogous to number. Affirmation of existence is in fact nothing but denial of the number nought. Because existence is a property of concepts the ontological argument for the existence of God breaks down. But oneness* is not a component characteristic of the concept “God” any more than existence is. Oneness cannot be used in the definition of this concept any more than the solidity of a house, or its commodiousness or desirability, can be used in building it along with the beams, bricks and mortar...

    * [I.e. the character of being single or unique, called by theologians “unity”.]
    — Frege, The Foundations of Arithmetic, tr. Austin (1960)

    Frege seems to be appealing to some notion of extensionality. He thinks that existence is a property of concepts insofar as number is assigned to concepts. For example, what number is assigned to the concept, "Moons orbiting Earth"? The answer for Frege is '1', and in virtue of this "denial of the number nought" there exists a moon orbiting Earth. Rather, that is what existence means for Frege. Similarly, if Frege wanted to tell us that there do not exist any motorcycles that are orbiting Earth, what he would say is that the concept, "Motorcycles orbiting Earth," is to be assigned the number '0'. Such is his account of existence.

    So when considering Anselm's proof Frege tells us that 'oneness' (namely, the variety of non-noughtness traditionally accorded to God), "is not a component characteristic of the concept 'God'..." That is, the concept "God" does not have an intrinsic property '1'. In Kleine Schriften he will talk about a concept being "not empty." Klima follows Haaparanta in tracing some of this back to Kant, who was a strong influence on Frege and who Frege agrees with vis-a-vis Anselm's proof.

    So on Frege's proto-extensional understanding, Anselm is saying that the concept 'God' has a component characteristic of oneness (which entails that the concept is not nought or not empty, ergo, that it exists). Frege claims that this is false and that the proof therefore fails. He says, "No, Anselm, the concept 'God' is not non-empty qua concept."

    Like I said, I haven't read beyond section 1, and I don't want to go too fast, but this is at least the foil that Klima is using in setting out a medieval approach—in setting out a more accurate way to interpret Anselm's proof.
  • Leontiskos
    3.8k
    The other technical part of this section concerns "ampliation":

    According to this conception, in an appropriate ampliative context we can successfully refer to what we can think of according to the proper meaning of the terms involved. But thinking of something does not imply the existence of what is thought of. Thus, in the same way, referring to something does not imply the existence of what is referred to, or, as the medievals put it, significare (‘to signify’) and supponere (‘to refer’) ampliate their object-terms to nonexistents in the same way as intelligere (‘to think’, ‘to understand’) and other verbs signifying mental acts do.[14]Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding - Section 1

    The idea here is that we can think about something without thinking that it exists, so why can't we signify and refer without presupposing existence? The medievals are very interested in argument and the natural way we use language. If we are to mount compelling arguments we must be able to do in a technical sense what we already do quite naturally in everyday settings, namely we must be able to reference thoughts, theories, suggestions, postulations, etc., in order to apply the rigors of argument and reason.

    In a source from footnote 11 Klima begins with a simple argument:

    (1) Bucephalus is dead
    (2) What is dead does not exist
    Therefore,
    (3) Bucephalus does not exist
    Therefore,
    (4) something does not exist

    In my opinion, this is a conclusive argument for the thesis that something does not exist. As is well-known, however, many philosophers regard this thesis as paradoxical in a way, and, consequently, they would raise several objections to the simple reasoning that led to it above...
    Klima | Existence, Quantification and the Medieval Theory of Ampliation

    "Bucephalus is dead, and therefore does not exist." When we utter such a thing we are abstracting time away from Bucephalus, and thinking of him in a timeless sort of way. He does not exist now, but he did exist in the past, and in talking about him now we are talking about something that does not exist. This is an example of what the medievals called ampliation, and in this case it is ampliation with respect to time. Cf. footnote 14.

    Thoughts?
  • Banno
    26.2k
    The first sentence of section one says:

    On the paradigmatic account of reference in contemporary philosophical semantics, owing in large part to Russell’s Theory of Descriptions, the burden of reference is taken to be carried basically by the bound variables of quantification theory, which supposedly reflects all there is to the universal logical features, or “deep structure” of natural languages.

    The descriptive theory of reference had its heyday in the time prior to Kripke. So this struck me as at best inaccurate. But to check I went to the PhilPapers survey and found support for causal views on reference at 46% and for descriptions at 17%. Hardly "paradigmatic".

    So it seems to me this paper missed it's target by fifty years or so. Mediaeval critique of historical aspects of logic is a pretty fringe market.



    Edit: Copied here from later in the thread, so I don't lose it.

    Summarising my comments on section 2, here are four problems with the argument as it is present.

    1. There is a problem in defining a maximum element in a domain that may have no limits.
    2. There is a sleight of hand from ens rationis to ens reale, somewhat hidden here but brought out in Free Logic by the invalidity of a move from Ti to E!i.
    3. There are four premises to the reductio, any or each of which may be false. That the second assumption is the one that must be rejected is not established.
    4. The argument relies on a substitution within an intensional context, at line (5), that is not justified.

    And finally, (1) and (3) in combination make the assumption that god exists. This explains why the argument is valid, since it amounts to "god exists, therefore god exists". It also makes the argument circular.


    Edit: I placed my summation fo the article here.
  • Tom Storm
    9.4k
    Interesting. Given the interest in nostalgia projects of every kind these days, along with a hatred of modernity, I wouldn't be surprised if Medieval critiques become fashionable again in some circles. :razz:
  • Wayfarer
    23.6k
    So it seems to me this paper missed it's target by fifty years or soBanno

    The relentless grind of progress, eh. Philosophical ideas certainly have short use-by dates in our day and age.
  • fdrake
    6.9k
    Please try to remain exegetical in thread.
  • Count Timothy von Icarus
    3.2k


    Klima's target is how Anselm's ontological argument has been received and analyzed in contemporary thought, and he's referring to reference as it has affected ontology. Try to make it past the first sentence before finding an offending whole two words that "render the paper obsolete."

    First, even if one supposes that Klima, being a medieval specialist, absolutely cannot be well acquainted with modern philosophy of language (dubious), he would no doubt be familiar with how St. Anslem's theory in particular is critiqued in terms of contemporary thought. And the critiques he is pointing to have their genesis in Russell and Frege.

    Second, "paradigmatic" does not mean "popular." No interpretation of quantum mechanics is subject to more regular criticism than the original "two worlds" formulation of the Copenhagen Interpretation, yet it remains the paradigm in that it is the last theory to hold wide sway and remains the jumping off point for a wide range of alternative theories, none of which has become hegemonic. The Routledge Contemporary Introductions to Philosophy of Language (a popular survey text) and Oxford's alternative both dedicate the most time to Russell and Frege, because they are the foundation from which critiques and alternatives (e.g. Grice, etc.) start from. But also because they had a major affect on other areas of philosophy, of relevance ontology, which is the place where theories of reference intersect with Anselm's argument. Reference here is referred to (lol) in terms of how it led to Quine's formulation, which renewed interest in ontology/metaontology, and continues to be popular there.
  • bongo fury
    1.7k
    This account, coupled with the Kantian-Fregean idea of existence as a second-order predicate, i.e., a quantifier, quite naturally leads to Quine’s slogan: “to be is to be a value of a bound variable”.2Klima

    This rang a bell.

    I also am puzzled about the utility and motivation of a second special doctrine which [Geach] puts forward, namely, that quantification is a second-level predicate. He elucidates this doctrine as follows :

    " A first-level predicate can be attached to a name, in order to make an assertion about that which the name stands for ; a second-level predicate can be attached to such a first-level predicate in order to make an assertion about that which it stands for. Quine's misunderstanding of second-level pre-dicates arises from his unwillingness to admit that first-level predicates do stand for anything."

    This doctrine is, as Mr. Geach remarks, to be found in Frege. It is also espoused in my own first book (1934). But neither of these circumstances counts in favour of the doctrine, and Mr. Geach also says nothing to raise the doctrine above the level of a bare pronunciamento. Surely we can understand quantifiers perfectly well with or without classifying them as predicates which make assertions about that which first-level predicates stand for. Nothing is achieved by this move except the creation of an opportunity to talk of first-level predicates as standing for something.
    Quine reply to Geach
  • Leontiskos
    3.8k
    Try to make it past the first sentence before finding an offending whole two words that "render the paper obsolete."Count Timothy von Icarus

    Yes, the Troll hath arrived, as anticipated:

    I will make a thread that includes the topic of intentional reference/identity sometime in at least the next month. It will be a reading group, so trolling will not be tolerated.Leontiskos

    Banno polled the recent fads in Anglo philosophy and found that Kripke is more popular than Russell. If he had managed to read past the first sentence he would have learned that the paper actually spends more time on Kripke than Russell. But for Banno to read a whole sentence is a remarkable event that should be celebrated. Would that philosophy moved beyond fad-following.

    First, even if one supposes that Klima, being a medieval specialist, absolutely cannot be well acquainted with modern philosophy of language (dubious)Count Timothy von Icarus

    Note that the book in which this chapter is contained was published in 2000. Alongside primary sources, Klima's secondary sources for modern views are from the 1980's and early 90's. Which means that he is 10-15 years ahead of the epoch that Banno remains stuck in.

    Gyula Klima is Hungarian, and began his philosophical career in Hungary. Clearly he is more familiar with figures like Kant and Frege, who have a much wider reach than the parochial set of Anglo philosophers from the mid 20th century. But upon moving onto the Anglo-American scene Klima no doubt began to encounter this philosophical descendant of Logical Positivism which encloses Banno's horizon.

    The relentless grind of progress, eh. Philosophical ideas certainly have short use-by dates in our day and age.Wayfarer

    Even old as he is, Banno may live long enough to see all of the philosophers he believes to be so important forgotten in the same way his Hare has been forgotten. Even Banno's big names like Wittgenstein and Kripke are virtually unknown outside of the English-speaking world. So there is more than a little irony here - like the man scoffing at the out-of-date fashion of others while wearing bell-bottoms with a choker.
  • Leontiskos
    3.8k
    - So is the idea that Quine is here implicitly abandoning this doctrine that is "espoused in my own first book"? Is Quine here abandoning his idea that, "to be is to be a value of a bound variable"?
  • Tom Storm
    9.4k
    :up:
    Try to make it past the first sentence before finding an offending whole two words that "render the paper obsolete."Count Timothy von Icarus

    Sorry CT, I have no view on the paper, I was just making a needless quip.
  • Leontiskos
    3.8k
    Part 2: The Proof

    (Here is a link to Anselm's Proslogion for those interested.)

    In this section Klima formulates Anselm's proof according to the principles of the first part of the paper. He gives this formulation in a natural language argument, and then in quantification theory. I will again quote the first paragraph:

    With this understanding of Anselm’s conception of the relationship between existence and reference we can see that his argument constitutes a valid proof of God’s existence without committing him either to an ontology overpopulated with entities of dubious status or to the question-begging assumption that the referent of his description exists. In fact, we can see this even within the framework of standard quantification theory, provided we keep in mind that in the context of Anselm’s argument, this context being an ampliative context, we should interpret our variables as ranging over objects of thought, only some of which are objects simpliciter.Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding - Section 2
  • bongo fury
    1.7k
    Is Quine here abandoning his idea that, "to be is to be a value of a bound variable"?Leontiskos

    No, just the doctrine received from Frege regarding quantifiers as second-order predicates, that is, as attaching to first order predicates in the manner that first order predicates attach to names. This specific doctrine is being dropped.

    Why? Because first order predicates attach to names in a manner that generally assumes the existence of a thing named. Where this is in doubt, the meaningfulness of the sentence is in doubt.

    Quine, as a nominalist, would rather not encourage any similar assumption about a predicate. Let's not have the meaningfulness of a predication depend on the existence of a thing or even a property that the predicate denotes (applies to).

    That would mess up his proposed application of Russell's method of definite descriptions to the task in question, that of asserting an uncontroversially meaningful sentence denying the existence of Pegasus.
  • Leontiskos
    3.8k
    Quine, as a nominalist, would rather not encourage any similar assumption about a predicate.bongo fury

    Right, ergo:

    Consider now Quine's insight, on which the quantifier account is based, that it is bound variables rather than singular terms that carry ontological commitment. To implement this insight, Quine simply eliminated singular terms from the language.Ontological Commitment | SEP

    So back to your original quote of Klima:

    [Russell's] account, coupled with the Kantian-Fregean idea of existence as a second-order predicate, i.e., a quantifier, quite naturally leads to Quine’s slogan: “to be is to be a value of a bound variable”.[2]Gyula Klima, St. Anselm's Proof - Section 1

    My understanding is that you are saying Quine rejects the idea that existence is a second-order predicate, and therefore Klima is mistaken in his claim, "[this] quite naturally leads to Quine's slogan..."

    Now I don't quite see how your quote from Quine substantiates this, for he literally says, "[The doctrine] is also espoused in my own first book." Regardless, it makes sense to me that Quine would not want to call the quantifier a second-order predicate per se, but that he would nevertheless admit that it does bear on existence in a second-order manner. And in any case, Klima has tied "existence as a second-order predicate" to a Kantian-Fregian confluence, not to Quine, so I don't find the claim about Quine in Klima.

    Or am I misunderstanding the motive for your quote? Are you instead affirming Quine's intimation that proposing existence as a second-order predicate lacks coherence?

    Ultimately Klima is going to propose existence as some kind of first-order predicate, and he is going to outline an idea which was very well developed in the medieval period, namely an idea that differs from Quine (but also Meinong) with respect to ontological commitment, and Kripke with respect to reference.
  • bongo fury
    1.7k
    My understanding is that you are saying Quine rejects the idea that existence is a second-order predicate,Leontiskos

    Agreed.

    and therefore Klima is mistaken in his claim, "[this] quite naturally leads to Quine's slogan..."Leontiskos

    Not necessarily, but the claim wants explaining. What is meant to be wrong with the slogan, and what has the doctrine of quantifiers being second order predicates got to do with it?

    Regardless, it makes sense to me that Quine would not want to call the quantifier a second-order predicate per se, but that he would nevertheless admit that it does bear on existence in a second-order manner.Leontiskos

    In what way?
  • Banno
    26.2k
    Banno read the whole paper, which you say you have not yet done, then followed the guidelines you set up in posting about the first section. I was following your instructions.

    Having done so, it is disingenuous for you and Tim to then censure me for it. But that's the trouble with presenting an article for critique when what you desire is agreement.

    But I am happy for you, Leon, to make this thread about me, if that is what you want.


    The alternative to descriptivist theory, from the paragraphs following the one I cited above, is some variation on an intentional theory of reference - "linguistic expressions refer to what their users intend by them to refer to in a given context". Perhaps not quite he Humpty Dumpty theory of meaning, "When I use a word, it means just what I choose it to mean - neither more nor less", since there is an implicit recognition of a community of "users". And an acknowledgement of modality in that one can refer to things that do not "exist", where what it is to "exist" remains obscure.

    In modal terms, there are things in the actual world and things in possible worlds, and we can refer to either. But it might well be closer to the text to use a free logic, in which a singular term - a proper name - maybe used not just for things in the domain, but also for things outside it, hence permitting discussion of "supposita".

    In a free logic there are two domains, one, inner domain for things that are really real, and another outer domain for things that are not so real, but we still want to talk about. So the question Anselm raises is, we have the description "a something a greater than which cannot be conceived"; is it in the outer domain, or is it in the inner domain? And much of this part of the article is concerned with showing that this is not the same as asking if there is a greatest something. Seems fine.

    We should here make a distinction between two different uses of quantification - of "all" and "some". There is the other use of quantification to say that something is an individual in the domain: "There is exactly one thing that is the author of Tom Sawyer". This is the quantification used by Quine in his "to be is to be the value of a bound variable". Then there is the extension of this applied to the descriptive theories of reference, where "There is exactly one thing that is the author of Tom Sawyer, and it is the very same as Mark Twain" supposedly explains how "Mark Twain" manages to refer to Mark Twain. The former is distinct from the latter, and the former provides one way to talk about what it is to exist, the latter is a somewhat discredited philosophical theory.

    Yawn.
  • Banno
    26.2k
    (1) g=dfix.~($y)(M(y)(x))
    (2) I(g)
    (3) ("x)("y)(I(x)&R(y)®M(y)(x)))
    (4) R(g)
    (a) M(g)(g) [2,3,4, UI, &I, MP]
    (b) ($y)(M(y)(g)) [a, EG]
    (5) ($y)(M(y)(ix.~($y)(M(y)(x))) [1,b, SI]

    Damn, that's ugly.
  • Leontiskos
    3.8k
    In what way?bongo fury

    In the way that quantification brings with it ontological commitment.

    Not necessarily, but the claim wants explaining. What is meant to be wrong with the slogan, and what has the doctrine of quantifiers being second order predicates got to do with it?bongo fury

    Quine is meant to be part of the background for common contemporary interpretations of Anselm, but some of the connections get made throughout the first section. See for example footnote 6:

    6 W.V.O. Quine: “On What There Is”, in: Quine, W.V.O. 1971. p. 3. By the way, it is interesting that Quine apparently never asked himself: to whom does the name “Wyman” refer? — nobody? — then how do I know that Wyman is not the same as McX? For despite the fact that nothing in the world “wymanizes”, let alone “mcxizes”, Wyman and McX are quite distinguishable imaginary characters in Quine’s paper: Wyman, e.g., is introduced to us as a “subtler mind”, than McX. As we shall see, these questions are easily answerable on the basis of the theory of reference advanced in this paper. Not so on the basis of Quine’s.Gyula Klima, St. Anselm's Proof - Section 1
  • Leontiskos
    3.8k
    Damn, that's ugly.Banno

    "What Is It Like to Be a Troll?" by Banno with a preface by Thomas Nagel.

    followed the guidelinesBanno

    You haven't engaged with the paper at all, so clearly you're not managing to follow the guidelines.
    Or in other words: you're derailing another thread, like you always do.
  • Banno
    26.2k
    You haven't engaged with the paper at all,Leontiskos
    :rofl:
  • Banno
    26.2k
    (1) g=dfix.~($y)(M(y)(x))

    Seems to be, in a more standard notation, g:=ix¬(∃y)M(y,x). God is defined as the thought object x such that no y may be thought greater than x.

    ix is the definite description operator, read as "The x such that...".

    Notice that the existence (as a thought) of such an individual is here just assumed.

    Why should we make that assumption? In particular, if the definition is self-contradicting, there need be no such individual.

    Consider an analogous argument defining the highest number as that number which is higher than any other number. The definition is fine, except that there is no such highest number.

    A pretty standard response to that part of the Ontological argument.
  • Banno
    26.2k
    That's probably what this is trying to head off:

    As he says: “what if someone were to say that there is something greater than everything there is [...] and [that] something greater than it, although does not exist, can still be thought of?” Evidently, we can think of something greater than the thing greater than everything, unless the thing that is greater than everything is the same as that than which nothing greater can be thought of. But Anselm’s point here is precisely that although, of course, there is nothing greater than the thing greater than everything, which is supposed to exist, something greater than what is greater than everything still can be thought of, if the thing greater than everything is not the same as that than which nothing greater can be thought of. So if the thing greater than everything is not the same as that than which nothing greater can be thought of, then something greater still can be thought of; therefore, that than which nothing greater can be thought of can be thought of, even if it is not supposed to exist.

    What a mess. So god is not the thing greater than everything, but the thing greater than the thing greater than everything.

    Trouble is, that is not what g:=ix¬(∃y)M(y,x) says. God is still a thought object, albeit the greatest thought object.
  • Leontiskos
    3.8k
    - Good. This is what I mean by "engaging the paper." Pontifications from 30,000 feet are something that should only come after we've worked through the paper, in the "free for all" phase.

    ($y)Banno

    As above, Klima gives (∃y), not ($y).

    In fact, much of your quote is a misrepresentation of what Klima writes in the paper. You were presumably copy/pasting without checking to see if the output was accurate. A bit more care would be welcome, given how much people struggle with formal logic even before you start incorporating symbols like $, ", ®.

    Consider an analogous argument defining the highest number as that number which is higher than any other number. The definition is fine, except that there is no such highest number.Banno

    You are saying the number does not exist, but you also require that the thought object of the number does not exist. Is that what you are claiming? That there is no thought object "the highest number"?

    Or: that there is no thought object of God as defined by Klima?
  • Banno
    26.2k
    Good. This is what I mean by "engaging the paper."Leontiskos

    Though shalt engage only in ways expected by Leon.

    In fact, much of your quote is a misrepresentation of what Klima writes in the paper. You were presumably copy/pasting without checking to see if the output was accurate. A bit more care would be welcome, given how much people struggle with formal logic even before you start incorporating symbols like $, ", ®.Leontiskos
    What? Those are the symbols in the HTML text you linked.

    Ok, so are you claiming g:=ix¬(∃y)M(y,x) is not an accurate presentation of (1)? Then what is?

    You are saying the number does not exist, but you also require that the thought object of the number does not exist.Leontiskos
    No. Kids will ask wha the highest number is. Takes them a while to see that there isn't one. Theists similarly ask what the greatest being is. Since they already think they know the answer, the question is disingenuous.
  • Leontiskos
    3.8k
    What? Those are the symbols in the HTML text you linked.Banno

    Maybe check the book chapter version above. Your web interpreter may be misinterpreting the html encodings (although that would be a bit surprising - I still think it is a copy/paste encoding error).
123458
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet
Add a Comment

Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.

×
We use cookies and similar methods to recognize visitors and remember their preferences.