segunda-feira, 30 de janeiro de 2017


Corrected draft of the chapter on Frege for the book PHILOSOPHICAL SEMANTICS, to be published in 2017 by the CSP.

11. Existence as a property of concepts
At this point we can turn to Frege’s treatment of the concept of existence. Deepening an idea already present in Kant, he suggested that existence is a property (Eigenschaft) of a concept, namely, the property that at least one object would fall under it (Frege 1884, sec. 53). A similar idea was later advocated by Bertrand Russell in the suggestion that existence is the property of a propositional function to be true for at least one instance (Russell 1994: 232-3, 250-54.).
   Here I will not try to interpret the details of Frege’s often obscure remarks. Using more current terminology, I will follow an explanation taken from John Searle, who with his usual clarity brings us unmistakably to the point (2008: 176). Consider the sentence ‘Horses exist’. This sentence can be analyzed as:

There is at least one ... such that (... is a horse).

As Searle notes, this sentence contains two components. One is expressed by the predicate ‘…is a horse’, symbolically Hx (where we use x instead of ‘…’ and H replaces ‘is a horse’). The other component is the predication of existence expressed by the open sentence ‘there is at least one ... such that ...’. This predication can be symbolically expressed as Ǝx(...) (where Ǝx replaces ‘there is at least one … such that…’, and the last ‘...’ is the gap to be filled by some concept applied to something, now in the usual sense of the word concept, which in this case is the concept horse symbolized as Hx. The result is that the whole sentence ‘Horses exist’ can be symbolized as Ǝx(Hx). This also means that the predication of existence Ǝx(...) is a meta-predication expressing a higher-order concept, a concept of a concept, a meta-concept under which other concepts can fall, in this case (Hx). Thus, a sentence with the form Ǝx(Fxusually expresses a second-order concept applied to a first order concept. In a Fregean way of speaking, what this second-order concept does is to say of the first-order concept that at least one object falls under it, which also means that the first order concept is satisfied or fulfilled by being applied to at least one thing. Existence is in this sense something objective, since this satisfaction is independent of our cognitive grasping of it as the applicability of a concept.
   These last ways of speaking are more interesting to us because they could be paraphrased in accordance with our identification of concepts with senses of predicates (that is, conceptual or semantic-cognitive ascription rules), showing that existence is a property of these rules, namely, the property of being satisfied, fulfilled, or simply applicable. Thus, when I say ‘Horses exist’, I mean that the concept expressed by the predicate ‘…is a horse’ is effectively applicable in a domain of external objects. I add the adverb ‘effectively’ in order to make clear that I do not mean the word ‘applicable’ in a merely subjunctive sense, as referring to something that may be applied, but as referring to something that is applicable for sure. Moreover, as I also pointed out above, the existence or effective applicability of a semantic-cognitive rule is always considered with regard to a certain domain of entities, the fundamental one being the domain of the real empirical world, be it the external (physical) world (Carnap’s thing-world) or the internal (psychological) world. The first case is that of the statement ‘Horses exist’. Thus, what is meant with the predication of existence isn’t the applicability of the ascription rule of a general term as a mere possibility entertained only in our imagination, but also effective applicability of the rule. Moreover, this effective applicability is usually within what we may call its proper domain of entities, which in the case of horses is a domain of external, physical objects (in the case of the Valkyries, by contrast, the proper domain is a fictional one, that of Norse mythology).
   However, there are others higher-order domains and sub-domains of entities in which we apply the predicate of existence, even if only in a very subsidiary sense. One can say, for instance, that the Valkyrie’s horses exist in the fictional domain of Wagner’s opera The Valkyrie in the sense that the ascription rules for these horses are effectively applicable in the fictional domain described in the libretto. So, there are fictional domains in the arts, domains of imaginable and plausible entities, domains of so-called abstract entities and their various sub-domains, like the domain of mathematical entities, of logical entities, etc., and the word ‘existence’ can be applied to concepts belonging to all of them.
   So, according to the view I support, to say that horses, rocks, trees and chairs exist is to confer effective applicability to the ascription rules of the respective concept-words ‘horse’, ‘rock’, ‘tree’ and ‘chair’ in the fundamental domain of material objects belonging to the objectively real external world. To say that thoughts, joys and pains exist is to confer effective applicability to the ascription rules expressed by the concept-words ‘thought’, ‘joy’ and ‘pain’ in the subjectively real mental domain of entities. And to say that ‘totalitarianism’, ‘corruption’ and ‘exploitation’ exist is to affirm the effective applicability of the ascription rules of these concept-words within the psycho-physical domain of social entities. The domain of entities to which such concept-words apply is usually assumed as respectively physical, psychological and social. Finally, to say that an entity exists is, save exceptions, to say that its conceptual rule is effectively applicable in what was in many cases already conventionally established as its most proper domain of application. Thus, to give examples, the most proper domain of application of the conceptual word ‘horse’ is the real external world, while the most proper domain of application of ‘Valkyrie’ is a fictional one.
   As we have already noted, a concept – that is, the semantic-cognitive ascription rule of a predicative expression – is able to generate subjective criterial configurations. Thus, to say that a concept-word is effectively applicable is to say that subjective criterial configurations generated by an ascription rule are satisfied or fulfilled by corresponding objective criterial configurations. These criterial configurations must be configurations of tropes usually belonging to more complex constructions out of tropes called facts – a point I intend to explain and justify in more detail in the last chapter, where the problem of perception receives consideration.
   The parallel between the concept of existence in Frege and the more detailed concept of existence derived from our reconstruction of concepts as senses of predicates understood as ascription rules is straightforward:

     Concept of existence (Frege) =
A higher-order concept that demands for its satisfaction that a lower-order concept has at least one object that falls under it.

     Concept of existence (reconstructed) =
A higher-order conceptual rule that demands for its (effective) application that a first order conceptual (or ascriptive) semantic-cognitive rule is effectively applicable to at least one entity, this entity being a trope or a configuration of tropes, usually in what is conventionally viewed as its proper domain.

In my judgment, the major advantage of this last form of analysis is epistemological: we are able to better scrutinize the nature of our existence-assignments, as will be shown in the answers to objections that follow.

12. Two naive objections
There are two naïve objections to my formulation of the higher-order view of existence, whose answer is revealing. The first naïve objection would be that the concept of effective applicability of a rule is an anthropomorphic one, while things are said to exist in full independence of cognitive beings.
   However, this objection only arises if we confuse the concept of effective applicability (within a certain domain) with the concept of (effective) application. The application of a semantic-cognitive rule is an act or a series of acts, which are essentially mental, though often also inevitably physical, resulting in judgments. The application of the conceptual rule for the identification of the planet Venus, for instance, really demands the existence of cognitive beings able to apply it. Our judgment that our Moon orbits the Earth, for instance, depends on the experience of the application of a verifying rule for the existence of this fact by ourselves or by someone who testifies its application. On the other hand, the concept of (effective) applicability is not anthropomorphic. Even if there were no cognitive beings able to apply the identifying rule for the concept Venus, this planet would continue to exist, since the ascription rule for the identification of Venus would still be effectively applicable to this object in its proper domain. The rule would still be applicable, even if no one had ever applied or even conceived it. The rule would be effectively applicable in a universe without any cognitive beings able to conceive it, since if it existed, it would be effectively applicable. Thus, there is no doubt that the concept of effective applicability is not anthropomorphic.
   This answer makes it easier to refute a second naïve objection that proponents of the idea that existence is a property of things instead of concepts would be tempted to raise against my proposal. It would be the objection that if existence is a property of conceptual rules, then it has nothing to do with the objects that fall under these concepts: existence seems to be something floating above things said to exist. However, this seems odd, since intuitively we think that existence in some way belongs to entities we believe exist!
   The answer to this objection is that there is no contradiction between being a second-order property of an entity and belonging to this entity. We see this when we invert the form of exposition. We can not only say that some ascription rules have the property of being effectively applicable to some entities belonging to a certain domain, but we can also say that some entities have the property of having their own ascription rules effectively applicable to them, meaning by this that these entities exist in their proper domain. That is, when we say that entities such as horses exist, we also mean that at least one of these conceivable kinds of objects has the higher-order property of having its ascription rule effectively applicable to it. In other words, we mean that it has the meta-property of existing in the actual world, and this property is also a property of the object of the kind – even if of a second-order – since it is a property-property at the level of the object’s ascription rule and not intrinsic to it.
   In still other words, according to the higher-order view of existence, the trope of red of this couch exists only insofar as this object (the couch) has the property of falling under the concept of being red in the Fregean way of speaking. But speaking in a more detailed way, we can say that the trope of redness of the indicated couch exists in the sense that the ascription rule of the concept-word ‘red’ has the meta-property of being effectively applicable to the couch’s trope of redness. However, this also means that the couch’s trope of redness secondarily owns the meta-property of its ascription rule of being effectively applicable to it – it has this property property. Now, since this metaproperty of being effectively applicable is the property (or trope) of existence, and this meta-property is applicable to the ascription rule (since it is effectively applicable), this meta-property is indirectly and dependently applicable to the trope of redness belonging to the real empirical world.
   In short: the meta-rule of existence also applies to the trope, even if in a secondary way. Thus, one can argue that it is a peculiar feature of the concept of existence (and certainly of some other concepts) that, being owned by a first order concept effectively applicable to some entity, it must also be owned by the given entity belonging to the chosen domain of entities without being a proper element of this entity.

13. Existence attributed to objects
The idea that existence is a property of concepts concerns not only what is meant by general terms, but also by singular terms, since both kinds of term express senses, and their references can be said to exist. Since singular terms can be divided into definite descriptions, proper names and indexicals, I will briefly consider each of them, beginning with definite descriptions like ‘the inventor of the Maieutic’.
   Applying to the sentence the Russellian treatment of definite descriptions and replacing the predicate ‘…is the inventor of the Maieutic’ with M, the sentence ‘The inventor of the Maieutic existed’ can be analyzed as:

Ǝ[Mx & (y) (My → (y = x)].

In this way, we are affirming the existence of at least one and not more than one inventor of the Maieutic, which means that the ascription rule that constitutes the concept (sense) expressed by the predicate ‘…is inventor of the Maieutic’ has the property of being effectively applicable to only one human being – Socrates – who once existed.[1]
   Consider now the case of proper names. As we have seen, they should also have senses in the form of identifying rules. Considering existence as the effective applicability of a semantic-conceptual rule in a chosen domain, the existence of the object referred to by a proper name should be established by the effective applicability of its identifying rule, usually in a proper contextualized domain, such as the external world.
   Although this issue cannot be properly addressed without a deeper investigation of the nature of proper names, we can begin by making a suggestive defense by applying Russell’s method (not his inadequate metaphysics of meaning) to the foregoing view. In order to do this we transform proper names into predicative expressions applied to only one particular, showing then that the senses of names themselves can be reduced to the conceptual senses of predicative terms. A first step in the attempt to arrive at this is to transform the proper name into a predicate. Thus, ‘Socrates’ in ‘Socrates exists’ can be transformed into a predicate in the sentence ‘There is something that socratizes’, or ‘Ǝx(x socratizes)’, as W. V-O. Quine suggested to use the name Pegasus to form a predicate as ‘the thing that pegagizes’ (1948/9: 27). Taken literally, such suggestions are not only linguistically atrocious, but also defective, since they leave open the possibility that there is more than one Socrates.
   Despite this, I think that ‘Ǝx(x socratizes)’ points in the right direction by suggesting that the existence of a name’s bearer may be asserted by means of the conceptual senses of predicative terms. For the verb ‘to socratize’ can be seen as a kind of abbreviation of the predicative conceptual expressions that are included in those descriptions, supposedly summarized by the proper name ‘Socrates’. This is a reasonable strategy insofar as we take seriously the bundle theory of proper names that was already present in one or another way in the writings of Frege, Russell and Wittgenstein, and made more explicit by P. F. Strawson and John Searle. According to this theory, the whole sense of a proper name is given by a cluster of definite descriptions. To illustrate this, we can assume that the sentence ‘Ǝx(x socratizes)’ is an abbreviation of what could be more extensively and adequately expressed as:

Ǝ{x is inventor of Maieutic, x is mentor of Plato... is Xanthippe's husband}.

Of course, this is still insufficient, since it not only demands that all predicates must be satisfied, but leaves open the possibility that these predicates could be applied to more than one object. However, this fault can be easily remedied by means of the Russellian device of restricting the number of objects of predication to only one:

Ǝ{x and no other person invented the Maieutic, or x and no other person was the mentor of Plato or… or x and no other was the husband of Xanthippe}.

Symbolizing the predicates ‘…is inventor of the Maieutic’ as P1, ‘…is Plato’s mentor’ as P2, and ‘…is husband of Xanthippe’ as Pn, the above sentence can be still symbolically formulated as follows:

Ǝx [(P1x & (y1) (P1y1 → (y1 = x)) ˅ (P2x & (y2) (P2y2 → (y2 = x)) ˅... ˅ (Pnx & (yn) (Pnyn → (yn = x))]

Here the meaning of a proper name is translated into the conceptual-senses of predicative expressions such as P1, P2… Pn, which according to our analysis are nothing but semantic ascription rules expressed by predicates that we expect to be really applicable to one and the same thing. So analyzed, the attribution of existence to the object referred to by a proper name is made by saying that its sense, its identifying rule, effectively applies in the assumed context. As this rule for the identification of the name was here analyzed in terms of a disjunctive set of rules for the application of predicates that must be applied to the same individual, we can easily explain existence. The existence of the bearer of the proper name is the same as the effective applicability of a larger or smaller number of conceptual rules of predicative expressions to one and the same individual.
   Of course, here it could be objected that all these descriptivist attempts to explain the meaning of a proper name are doomed to failure. This must be so, not only because the Russellian device is limited, but also because they amount to some version of the bundle theory of proper names with its well-known difficulties, which were already persuasively pointed out, mainly by Saul Kripke, Keith Donnellan and others.
   However, before we arrive at any conclusion, there are three points that must be considered. The first is that, contrary to a current bias, these objections have few effects against the most explicitly developed versions of descriptivist theories, some of them having already been successfully answered by John. R. Searle with relative success (Searle 1983, Ch. 9). A second point is that Kripke’s alternative solution, the causal-historical view, could never be developed in a satisfactory way. These two first points lead us to the conclusion that the bundle theory hasn’t yet been conclusively refuted, perhaps it just needs a stronger defense.[2]

14. Existence of objects and its identifying rules
The third point to be considered is that the above presented analysis is a crude simplification when seen from the viewpoint of my own much more elaborated version of the bundle theory of proper names. This version has (in my humble opinion) much greater explanatory power than any previous theory, making possible strong defenses against the most diverse counter­examples. Although the theory and its consequences are too complex to be discussed here at length, I have already summarized it in some depth in the appendix to chapter 1.
   Briefly repeating what I said there, my view is the following. The traditional bundle theory of proper names defended by Frege, Russell, Wittgenstein, P. F. Strawson, John Searle and others has a severe limitation that seems to have been overlooked: the bundles have no internal order. The theory does not tell us what description or combination of descriptions have more or less weight and even why some seem to be very important for applying the name, while others are obviously irrelevant for it. Definite descriptions are expressions of rules that should help us to connect the proper name with its reference; they are in this sense description-rules. Regarding all this, my question is whether we cannot find the general form of a rule that if applied to any bundle of descriptions associated with any proper name allows us to know in what ways the satisfaction of these descriptions makes this proper name applicable to some referent.
   When searching for the general form of a rule, the first thing to do is to classify the descriptions. There is a natural ordinary-language method to do this: check how proper names are treated in encyclopedias. If we do that, we will easily distinguish fundamental from merely auxiliary descriptions, which are accidental. If we do this, we will see that proper names are first and foremost attached to two fundamental forms of description, which I call localizing and characterizing description rules. Here is how we can define them:

(A)   Localizing description-rule: This is the description that gives the spatio-temporal location and career of the object referred to by the proper name.
(B)    Characterizing description-rule: This is the description that gives the characteristics of the object that we consider the most relevant to be referred to by the proper name – which gives us the reason to use the name.

Consider, for instance, the name ‘Adolph Hitler.’[3] Here is what is said about him in the first paragraph of a Wikipedia article:

Adolf Hitler (20 April 1889 – 30 April 1945) was born in Braunan an Inn, Austria. Later he was a German politician and leader of the Nazi Party. He was Chancellor of Germany from 1933 to 1945 and Führer of Nazi Germany from 1934 to 1945. As effective dictator of Nazi Germany, Hitler was at the centre of World War II in Europe and the Holocaust.

It is usual in encyclopedias that the first thing we find is an abbreviation of the localizing description rule, followed by an abbreviation of the characterizing description rule, stating the reason why we remember the name. What follows in the Wikipedia article (as in many others) are more or less relevant details and explanations. We find a variety of definite and indefinite descriptions that are more or less irrelevant – the accidental, auxiliary descriptions. For example: Hitler was ‘the lover of Eva Brown’, ‘the son of Alois Hitler and Clara Pölzi’[4], ‘the person called ‘Adolf Hitler’’[5], ‘the boy who was sent by his father Alois to the Realschule in Linz in September 1900’. All this information given by encyclopedias will also be found in extended form in biographies.
You will find the same things if you look at other proper names like ‘New York’, ‘USA’, ‘Eiffel Tower’, ‘Niagara Falls’ or ‘Venus’ in encyclopedias. Of course, there are also the proper names of most people, who are not mentioned in encyclopedias. But the basic mechanism of reference remains the same. It is not difficult to see that the relevant information is given by their localizing descriptions and by the usually much more scattered characterizing descriptions. So, in most cases, if you know who Sam is, you will probably get the relevant information by looking at his identity card, his employment record, his passport, perhaps adding to this the information given by his family and acquaintances about his personality, character, education, interests, relationships, deeds, etc., which are linked together by only one spatio-temporal career.
   Now, my suggestion was that, although a conjunction of the localizing and the characterizing descriptions isn’t required in any possible world, as Kripke has clearly shown (1980: 62), a disjunction of the two fundamental description rules must in some degree be satisfied in order to allow a proper name to refer to its object in any possible world. John Searle has long since noted this point. As he wrote:

…if none of the identifying descriptions believed to be true of some object proved to be true of some independently located object, then that object couldn’t be identical to the bearer of the name. (1969: 169)

Indeed, if we identify a person called Adolf Hitler who was born in Mittelweg and lived in Germany from 1634 to 1689, working as a saddler and having nothing to do with politics, we would say that he wasn’t our Adolf, since he does not satisfy any of the disjunction.
   Moreover, there are two other complementary conditions that need to be added. First, a condition of sufficiency that needs to be satisfied: the disjunction of these two fundamental descriptions must be at least sufficiently satisfied in order to allow a proper name to refer to its object in any possible world. So, you can imagine a possible world where there was no World War II and Hitler was born in 20 April 1889 in Braunan an In, the son of Alois and Clara. However, he had the same career as Adolf Hitler only up to the point where he was not (as really occurred) rejected but accepted in the Vienna Academy of Fine Arts in 1907, becoming a rich painter who tragically died in his early thirties. In this case, we are inclined to say that this person is our Adolph in this counterfactual situation, although he satisfies only the localizing description rule and even this only partially. He satisfies the condition of sufficience.
   The second important condition is that of predominance, demanding that a possible bearer of a proper name should satisfy fundamental descriptions in a more complete manner than any other competitor in the considered possible world, since by definition the bearer of a proper name must be always one unique specified object. Thus, suppose that in a very similar possible world there were twins Adolph and Rudoph Hitler, both born in… 20 April 1889… but only Rudolph went to Berlin, participated to the World War I and led the Nazi Party, being responsible for the World War II and the Holocaust, while Adolph choose to be a farmer in his native Austria. We would tend to think that Rudolph was the true Hitler, despite his different name, since the name Rudolph is associated with the disjunction of conditions belonging to the identifying rule for our Adolph in a much stronger way than the name of his twin brother.
   Finally, it is important to see that the object to be referred to belongs to the nearest relevant class that does not mix with the contents made explicit by the fundamental conditions (for instance, to be a human being – and not a politician – for Adolph Hitler, and to be a celestial body – and not a planet – for Venus).
   Putting all this together, we are able to propose the following general form of the identifying rule for proper names, a form that must be satisfied by any bundle of descriptions associated with a given proper name:

    General form of the identifying rule for proper names:
In any possible world our proper name ‘N’ has a bearer iff it belongs to the nearest relevant class of referents, so that more than any other object it sufficiently at least satisfies the conditions set by (A) its localizing description rule and/or (B) its characterizing description rule. (Auxiliary descriptions may be helpful in the identification).

Now we can apply this form to any well-known bundle of descriptions that we associate with a proper name in order to have its identifying rule. When we associate ‘Adolf Hitler’ with the bundle of descriptions associated with the proper name, we get the following identifying rule:

In any possible world, our proper name ‘Adolf Hitler’ has a bearer
this bearer belongs to the class of human beings, so that more than any other person who sufficiently and more than any other satisfies the following disjunction of conditions:
(A)   being born in 20 April 1889 in… living the last part of his life in Germany… dying in 30 April 1945 in Berlin… and/or
(B)     the condition of (B) being the leader of the Nazi Party… dictator of Nazi Germany from 1934 to 1945… the person most responsible for World War II and the Holocaust.
(He would also very probably satisfy the auxiliary descriptions of being ‘the lover of Eva Braun’, ‘the person called ‘Adolf Hitler’, ‘the son of Alois and Clara’, etc.)

This identifying rule gives us the core meaning of the proper name ‘Adolf Hitler’. If we try to imagine an Adolf Hitler who does not minimally satisfies neither the localizing nor the characterizing condition, we see that this is impossible. This was the case of the Adolph Hitler born in Mittelweg in 1634, who was a saddler and had nothing to do with politics. Surely, he could not be the person in a political socio-historical context whom we unavoidably mean with the name ‘Adolph Hitler’, but some homonymous person.
   This example also outlines the lack of relevance of the auxiliary descriptions. Suppose that the Adolf Hitler born in Mittelweg in 1634 satisfies many of the best-known auxiliary descriptions: he was the lover of Eva Braun, he was the son of Alois Hitler and Clara Pölzi, the person called ‘Adolf Hitler’, the boy who was sent by his father Alois to the Realschule in Linz in September 1900… The feeling elicited by these discoveries would be of puzzlement, not persuasion. For the Eva Braun could not be the well-known Eva Braun who commited suicide in the Bunker… the identity of names of his parents would be a curious coincidence, the Realschule would be another… (He could not, it is true, satisfy the description ‘the author of Mein Kampf; however, this is no auxiliary description, but part of the characterizing description of our Adolf.) Anyway, in no moment will this change our conviction that he is not our Adolf.
   Since so understood the rule of identification simply defines what object among all others owns the proper name by establishing the (definitional) criteria for identification of the bearer of the proper name in any possible world, it also applies in any possible world where the bearer of the name exists, satisfying the main point of the Kripkian definition of what is a rigid designator (1980: 48). The individual definite descriptions belonging to the bundle, on the other hand, being only loosely associated with the identifying rule, can refer to other objects in different possible worlds, being therefore only accidental or flaccid designators.[6]
   Moreover, one can insert a name correctly in a sufficiently vague discourse without knowing more than auxiliary and indefinite descriptions, even when they are wrong, as Kripke realized. This is the case at least as far as these descriptions are convergent (rightly classified), making in this way what we should call a parasitical reference, which can be helpful in several ways. – If someone already knows that Hitler was ‘some dictator’ or thinks erroneously that he was ‘a general’, this person already classifies him correctly as a human being and already can apply the name correctly in sufficiently vague contexts and possibly learn more about him.
   Now, the existence of an object referred to by a proper name is the effective applicability of what can be called the identifying rule of the proper name in its (in most cases proper) context. We know that Hitler existed because we know that his identifying rule was effectively applied in the political-historical context of Europe in the first half of the twentieth century. And as far as the identifying rule for the proper name ‘Hitler’ is concerned, being a conceptual rule, it has the second-order property of being effectively applicable in its proper contextual domain – the domain of human beings belonging to the external world – and we say that the bearer of this name really existed.
   Finally, it is interesting to note that we can try to give a Russellian formulation for the form of the identifying rule. Calling the predicate ‘…satisfies its localizing condition more than any other object’ L and the predicate ‘…satisfies its characterizing condition more than any other object’ C, we can say that a proper name N has a bearer if and only if regarding the nearest relevant class of objects:

   Ǝx [(Lx ˅ Cx) & (y) ((Ly ˅ Cy) → (y = x))]

The difficulty (for the logician) is that this is not a sufficiently adequate formal replacement of the general form of the identifying rule for proper names, since it leaves insufficiently clear the satisfaction of the condition of sufficiency and takes for granted the existence of only one object satisfying the rule. But it is already sufficient to formally show that the existence of the object referred to by a proper name can also be seen as a property of concepts.

15. Existence of spatio-temporal locations: indexicals
Finally, there is the problem of the application of the proposed analysis of existence to the designata of those singular terms that change their reference with the context: the indexicals. I will consider then only very briefly. Take simple statements with indexicals as (pointing) ‘There is a raven’, ‘Here is cold’, ‘It rained yesterday’, ‘I am tired’, ‘I am here now’... What the indexicals essentially do is at least to point to some spatio-temporal location relatively to the speaker. Thus, ‘here’ points to the place where the speaker is, ‘now’ to the moment when he speaks, ‘yesterday’ to the period of time of the day before the day of the speaker’s utterance… There is more than this regarding indexicals like ‘I’, ‘she’, ‘he’, ‘they’. These personal pronouns cover more than the simple spatio-temporal location of the speaker, but this does not matter to us now.
   Consider now the statement ‘There is a raven’. First, there is the spatio-temporal location that can be pointed to by the speaker, which is relative to the spatio-temporal location of the speaker within some context. All this must be assumed in applying the demonstrative ‘there’. The identifying rule for ‘there’ can at least be summarized in the description (i): ‘the spatio-temporal location pointed to (or contextually shown) by the speaker when he utters the word.’ Now, what we call the existence of the spatio-temporal location indicated by the demonstrative ‘there’ must be the effective applicability of this identifying rule of location in the restricted contextual domain established by the speaker when he speaks the sentence. Once we have applied this identifying rule, we are allowed to apply the ascriptive rule of the predicate ‘…is a raven’ to the existing location. Now, how would we symbolize this? Calling the pointed to spatio-temporal location L and the predicate ‘…is a raven’ R, it could be simply Ǝ(Lx & Rx) & (y) [(Ly & Ry) → (y = x)], which means: ‘There is precisely one x spatio-temporally located in L, and this x is R.’ Although the location L figures here as a predicate, the condition of unity (any x) makes its reference an individual.
   There is another way to build indexicals, adding to them a sortal predicate, as in ‘the raven there’ in the sentence ‘The raven there is flying’ or ‘this chair’ in the sentence ‘This chair has two armrests’. In these cases, considering that the phrases ‘the raven there’ and ‘this chair’ refer to only one specific object, distinguishing it from all others, these phrases work as singular terms and must be analyzed as expressing an identifying rule. So, replacing ‘The raven there’ by R and ‘…is flying’ by F, we can formalize the sentence ‘The raven there is flying’ as Ǝx [Rx & (y) (Ry → (y = x)) & Fx].  
   When we use an indexical statement the language, so to speak, touches the world, which makes indexicals the ultimate roots of reference. Because of this, although the sense still determines its reference, there is here a double direction of fit. On the one hand, with the help of our sensory cognitions we create the identifying rules for indexicals when they are for the first time used in a determined context. On the other hand, once formed, these rules determine the spatio-temporal location of the place, the object or both. Now, a new identifying rule can sooner or later be applied again, and may be interpersonally conventionalized by association with new non-indexical terms of our language.

16. Advantages of the higher-order view of existence
There are several advantages in conceiving existence as a higher-order property. One is that it gives a straightforward answer to what seems odd in the traditional forms of the ontological proof of God’s existence. So according to Descartes, if (1) God is the being with all perfections and (2) existence is a perfection, we can conclude (3) that God exists. But if existence is a meta-property of objects and not a proper intrinsic first order property of them, differing in this way from perfections like infinite goodness, omniscience and omnipresence, which should be intrinsic properties of God, the ontological proof is doomed to failure (see Frege 1874, sec. 53).
   However, the greatest advantage of conceiving existence as a higher-order property is that we do not find problems with the denial of existence. Suppose that existence were a first-order property of an object. In this case, in a sentence like ‘Vulcan does not exist’, the negation of existence should be applied to the object itself, and we would first have to identify the object in order to deny that it has the property (or trope) of existence. But since in order to identify the object we first need to admit that it exists, we would be caught in a contradiction: we would have to admit the existence of Vulcan in order to deny its existence.
   Anyway, according to our Fregean view, this conclusion isn’t necessary, because all we do by denying the existence of Vulcan is to admit that the ascription rule that forms the concept of Vulcan doesn’t have the property of being effectively applicable in its proper contextualized domain of a physical object. Using Russellian devices we could analyze the sentence ‘Vulcan does not exist’ as a shorthand way of saying (only to illustrate our point):

(x is a small planet that has an orbit between Mercury and the Sun) & (y) (if y is a small planet with an orbit between Mercury and the Sun, then y = x).

   What falls under the scope of ‘~Ǝx’ are the concepts constitutive of the identifying rule, which in my illustration consists of an ascription rule for a predicate that must be applied to only one and the same object. What ‘~Ǝx’ does is just to deny the property of this rule of being effectively applicable to the corresponding physical object.[7]

17. The ubiquity of existence
The understanding of existence as the effective applicability of conceptual rules allows us to explain the nearly unlimited extensions in the application of this concept. Why, given that existence is primarily attributed to properties and objects of the outside world or of psychological states, are we also allowed to say that supposed entities like hypothetical and merely imaginary ones exist? Some believe that contradictory objects exist. We can even say that everything exists, meaning by this that all that can be conceived does exist, at least as something that can be conceived. And even of existence itself it can be said that it exists. Indeed, it seems that in one way or another everything exists. How can this be possible?
   Concerning supposed entities, there are two mains kinds: hypothetical entities that experience hasn’t yet shown to exist or has shown not to exist, and fictional entities. Beginning with the first ones, it is clear that we can find a sense in which they exist. Although the planet Vulcan has been show not to exist in the real external world, its proper domain, it surely existed in other domains, such as in the minds of many astronomers in the past who searched for it… and it still exists in our minds as a merely imaginary object. This is no problem for the proposed view, because our identifying rules can also be applicable, at least partially, only in the dependent domain of conceivable things that we consider as possible or even plausible candidates for existence in the external world. If I imagine the hypothetical planet Vulcan orbiting the Sun, I apply the identifying rule for that proper name in my imagination (even if in a vague and skeptical way) to a merely conceivable state of affairs. Indeed, the French scientist Le Verrier, who first named the planet, even had a localizing rule according to which Vulcan should be a small planet orbiting close to the Sun at a distance of 21 million km, which he mathematically calculated in order to explain by means of Newtonian mechanics the perihelion precession of Mercury’s orbit. He applied this rule in the domain of what is conceivable, which means that Vulcan existed in the restricted domain of the imagination of Le Verrier and other astronomers of his time, though not in its proper domain – that of a concrete object belonging to the external world.
   Consider now the case of purely fictional entities. Ivan is a character in Dostoyevsky’s philosophical novel The Brothers Karamazov. He never existed in the real world; but he can be said to exist in the fictional world created in this novel, which is from the start fictional. In this domain, Ivan is the son of Fyodor Pavlovich and has two brothers, Dimitri and Alyosha. Ivan is a cerebral, as much as a weak character, taking refuge from the inevitable confrontations of life in contemplation and inaction and creating resentful justifications for this; in the end, under the weight of his own conflicts, he descends into madness. These and other elements form parts of the rule for Ivan’s identification. We say that he exists in the story, insofar as this rule is effectively applicable only to him within this proper fictional domain. In opposition to the case of hypotheses, existence in a fictional world excludes from the start existence in the real world. That Ivan said to Alyosha: ‘let the worms devour one another’ is true in the story, the suggestion was made. But it has no sense or existence in the domain of the real external world, since it was not written to fit in it.
   Saul Kripke gave examples of cases of fictional fictional characters like Gonzago (2013: 250), who is a personage that appears in Shakespeare’s play Hamlet as a fictional character created by Hamlet in his play within a play ‘The Murder of Gonzago’. There is a hierarchy here. We may say that Gonzago exists in a third-order domain, requiring the effective application of a proper identifying rule in this domain, which is supported by the existence of the plot of the fictional play Hamlet in a second-order domain. This play is in turn supported by the identification of some writer and written papers in the first-order domain of our self-sustaining empirical world.
   As with other merely conceived entities like pegasi and unicorns, existence is here affirmed within a domain that is dependent, derivative or extended (Kripke 2013: 81), being supported by the basic form of existence, which concerns the effective applicability of cognitive rules in the domain of the real external (physical) or internal (psychological) world. Existence in these ways of use is parasitic to the fundamental sense, though retaining its basic sense (also Searle 1969: 78-9).
   What about the attribution of existence to contradictory imaginative conceptions like a round square? This case is really too hard to be swallowed. We cannot combine the rule of identification of the square with the rule of identification of a round thing, so that both can identify one and the same thing. We cannot do this even in our imagination. Because of this impossibility, we must recognize that in a literal sense a round square cannot reasonably exist: we cannot have a contradictory combination of rules because it cannot build an applicable rule combination. Since the conceptual ascription rules are what constitute their cognitive meanings, this conclusion agrees with our strongest intuition: contradictions do not exist because they lack cognitive meaning.[8]
   Finally, what about existence? Can we say that existence itself exists? Surely, we know that existence exists in the sense that we know that the concept-word ‘existence’ is effectively applicable to the property of effective applicability of conceptual rules to the most diverse domains, telling us that this property of effective applicability exists. Existence exists in the sense that we can build a meta-meta-rule of existence, whose criterion of application is the effective applicability of our meta-conceptual rules made for the attribution of existence as the property of effective applicability of lower-order conceptual rules. Since these meta-conceptual rules of existence are effectively applicable (since the entities belonging to their varied domains exist), the meta-meta-rule – which demands the applicability of meta-rules to first order conceptual rules – also applies. Consequently, it is safe to conclude that existence itself exists. Well, then, does the existence of existence also exist? Surely, since we can conceive a meta-meta-meta-rule of existence demanding effective applicability of the meta-meta-rule of existence to meta-rules of existence, we can conclude that the meta-meta-meta-rule of existence is also applicable to the foregoing meta-meta-rule, making it consequently existent, and so on in an infinite regress, which is virtuous since stoppable.

17. Answering some objections
According to many present theorists, existence is a first order predicate. A statement like ‘Horses exist’ should be analyzed in a form similar to ‘Horses are animals.’ Since they have developed objections against the traditional view of philosophers like Frege and Russell, I will answer here at least some of them as they were put forward by Collin McGinn (2000b: 21-30). The answers are helpful in clarifying my own view.
   The first one is against Russell’s proposal that to say that something exists is to say that a propositional function – a property, a concept – is true for at least one instance. Roughly stated, the objection is that for one object to instantiate a property this object must already exist, an admission that would make Russell’s view circular, since it must already presuppose the existence of objects instantiating the property. For example, if ‘Mars is a planet’ is true, it presupposes the existence of the planet Mars to instantiate the property expressed by ‘…is a planet’ in order to make the sentence true. In short: there must already be existent objects in order to instantiate the properties ascribed to them by our conceptual words.
   This objection works insofar as one holds a Kripkian view of objects bearing proper names, since for him they cannot be defined by their own properties (1980: 52). Once we have analyzed objects as clusters of tropes displaying compresence, the objection appears to us in a different way. Since not only the ascribing rules of predicative expressions, but also the identifying rules of nominal terms are for us conceptual rules, our position should be generally stated as saying that existence is the effective applicability of semantic-cognitive rules in some chosen domain or context. However, since they also apply to objects as compresent clusters of tropes, this means that we cannot conceive any object as being given – that is, as existing – without simultaneously conceiving its identifying rule as being applicable to it. Thus, for instance, the existence of a concrete object like the planet Mars is nothing but the effective applicability of its identifying rule in its proper physical context. We cannot separate the existence of the object in its proper context from the effective applicability of its identifying rule in the same context, since this is what establishes the existence of the object in any possible world. Now, since it seems that the attribution of truth comes from the applicability of the identifying rule added to the applicability of the ascription rule (Tugendhat & Wolf 1983: 235-6), the attribution of properties and of the object’s existence (e.g. Mars) are simultaneous. As the attribution of truth follows from the first two, it is wrong to demand that the attribution of truth requires the attribution of any property prior to the attribution of existence of this property and the object as a cluster of properties (tropes). Consequently, the flaw in McGinn’s objection is to suppose that we can separate the instantiation of an object from its attribution of existence.
   Now to the second objection: uninstantiated properties are said to exist. But in order to exist, an uninstantiated property must fall under a higher-order property attributing its existence. This higher-order property must also exist, which means that it must fall under a still higher-order property and so on infinitely. Consequently, the attribution of existence as a higher-order property is impossible, because it requires an infinite regress of properties to allow the attribution of existence of a first-order property.
   My answer is that I agree (partially) with the diagnosis, but not with the prognosis. The effective applicability of a semantic-cognitive (conceptual) rule in its proper domain not only endows its reference with existence, but is in itself a second-order property or trope that can also be said to exist. And also a semantic-cognitive rule that is only imaginatively applicable not only endows its reference with existence in an imaginary domain, but can be said to exist by having the second-order property (or trope) effectively applicable in this domain. In any case, the property (or trope) of existence exists, which means that we can say that the applicability of the rule has the property of being applicable, and so on indefinitely. This leads us to an infinite regress, of course. But this is a virtuous infinite regress, since we don’t need to consider all the unlimited applicabilities of applicatilities or existences of existences in order to admit that some higher-order rule is applicable, once its applicability is experienced, attributing in this way existence to some entity. The mark of a virtuous regress is that we may stop it without loss when we feel that we do not need further steps to what we intend to say, and this is just what we have here (see appendix of chapter 3).
   The third objection is that there are statements that resist the traditional paraphrase. First, there are statements ascribing existence to particulars, such as ‘Venus exists’. We have already answered this objection in our treatment of proper names as conceptual identifying rules.
   But there are other objections. Consider the statement ‘Something exists’. Although this is a true statement, McGinn thinks that it is not paraphraseable in terms of the higher-order view, since there is no property to be instantiated here, and if we try to translate into the standard form we get the gibberish ‘Ǝx(…x).’ This answer is too easy. What ‘Something exists’ means is that there is at least one trope or construction out of tropes that exists without a further determination on our side. In other words, we can say that there is some semantic-conceptual rule that is applicable to some domain of entities, even if we do not specify this rule. But this possibility is shown even by our logical symbolism on an elementary level. In logic we symbolize an undetermined property as F. Hence, if we translate ‘Something exists’ symbolically, we get Ǝx(Fx) and not Ǝx(…x). Moreover, there is nothing wrong with Ǝx(Fx). Often we come to this result by applying existential generalizations to singular sentences like ‘Venus exists’. Calling Venus V, if it is true that ‘Ǝx(Vx)’, this implies by existential generalization that some property exists or ‘Ǝx(Fx), namely, that some conceptual rule is effectively applicable. Thus, there is no mystery in accepting the existence of undetermined properties.
   There are also more complicated statements which seem to resist the higher-order understanding of existence, like:

1.     Some cities are purely imaginary.
2.     Some of the things you are talking about do not exist.
3.     There are things that do not exist. …

Nonetheless, we can explain the predication of existence in them easily, insofar as we do not confuse the domains of application of the semantic-cognitive rules involved. Thus (1) can mean that some cities that exist in the imaginary domain exist only in this domain. Thus, the effective application of rules allowing us to identify the imaginary cities of Chloe or Valdrada in the contextual domain of the book The Invisible Cities are proper to a fictional context. Statement (2) can mean that there are things that exist only in the imagination, but not in the external world, that is, there are identifying rules that are effectively applicable only in the ineffective domain of one’s own discourse. Finally, statement (3) means that there are things that may exist only in the mind but not in external reality, that is, the identifying rule of some objects, though effectively applicable in an imaginary fictional domain, are not in the domain of external reality.
   The last of McGinn’s objections is that according to the higher-order view nothing can exist without falling under some property or other, which rules out the existence of a thing that has no properties – a ‘bare existent’. However, our empiricist commitment makes us see this not as a weakness, but rather as a further anti-metaphysical advantage of the higher-order view.

18. Reference of concepts again: a metaphysical excurse
It is instructive to consider what happens when we compare the famous phenomenalist view of J. S. Mill, according to which ‘matter’ or ‘substance’ is nothing but ‘permanent possibilities of sensation’ with our view of existence in terms of the effective applicability of conceptual rules. The results will be no less speculative than Mill’s phenomenalism itself, but they may be telling.
   Mill’s main epistemological question was: If all that is experientially given to us are sensory phenomena, how can we justify our belief in the existence of an external world, an objective world constituted by substance or matter? – An external world that can exist even when there is no observer at all to perceive it?
   Mill’s answer to this question was a development of Berkeley’s unofficial view, according to which things that we know to exist when they are not perceived by us are nothing more than things that we are well aware that would be perceived by us under suitable circumstances.[9] As Berkeley writes:

The table I write on, I say, exists, that is, I see and feel it; and if I were out of my study I should say it existed – meaning thereby that if I was in my study I might perceive it, or that some other spirit actually does perceive it. (Berkeley 1710, I, sec 3)

   According to this view, esse is not only percipi, but also percipi possi. In a more explicit manner, what Mill suggests is that:

Matter or substance is not made up of actual sensations, but of groups of permanent (or guaranteed or certified) possibilities of sensation.

   Mill justifies his identification of matter or substance with permanent possibilities of sensation in the following way. First, these possibilities of sensation are conditional certainties: they are not mere epistemic possibilities, but firm conditional expectations that are or could be based on experience. They are permanent in the sense that, once suitable circumstances are given, they would always be experienced insofar as they are said to exist. And they are guaranteed or certified in the sense that we have reasons – observational or not – to have a firm expectation that under suitable circumstances they will be experienced again. This does not mean that the groups of permanent possibilities of sensations would depend for their existence on our past experience of them, because if that were so, they could not exist without us as subjects of knowledge, and we would fall like Berkeley into some radical form of idealism like his immaterialism. This was not Mill’s intention. As he explains:

We mean [by permanent possibilities of sensation]… something which exists when we are not thinking of it; which existed before we have ever thought of it, and would exist if we were annihilated; and further that things exist that we never saw, touched or otherwise perceived, and things which never have been perceived by man. (Mill 1979, X: 178-177)
Thus, it is clear that Mill wished to avoid idealism: the permanent possibilities of sensations would exist even if cognitive beings able to perceive them never existed!
   These permanent possibilities are for Mill objective, differing from our actual passing sensations, which are subjective. They are objective because they are grounded, he thinks, in our common public world, which makes us able to interpersonally agree on their existence. Even if different persons cannot have access to the same sensations, they can have access to the same possibilities of sensation… As he writes:

The permanent possibilities are common to us and to our fellow creatures, the actual sensations are not… The world of possible sensations succeeding one another according to laws is as much in other beings as it is in me; it has therefore an existence outside me; it is an external world. (Mill 1979, X: 181-2)

This is in summary Mill’s view on the nature of matter – a view that always seemed to me as much deeply suggestive as contentious.
   Nonetheless, I think there is a serious confusion in Mill’s view, which can be made clear when we compare his insights with those of Berkeley. According to the non-official Berkeleyian view, the external world is constituted by sensations whose experience is continually (permanently) possible for us, even if we are not there to experience them. But if this is so, the material objects constituting the external world cannot be reduced to simple ‘groups of permanent possibilities of sensation’, for possibilities as such, permanent or not, cannot be qualitatively distinguished one from the other in the same way as one material object from another. Material objects can be qualitatively very different one from the other, they are multiple and varied, while possibilities are always the same, namely, mere possibilities. Moreover, Mill’s definition of matter leaves the notion of groups of sensations undetermined. Consequently, possibilities (of sensations), permanent or not, cannot be the same as material things. Keeping this in mind, the only feasible way to express the Berkeleyan insight in Mill’s terminology must be the following:

Material objects (or substances) are nothing but groups of sensations whose effective experience is permanently (or guaranteed or certified as) possible.

This would meet the requirement of multiplicity and diversity of material objects, because each material object would be constituted by different groups of sensations that could always be possibly distinctively experienced. But if the permanent possibility is not the material object, what is it?
   I believe it is a way to point to the external existence of the material object. This answer emerges when we consider Mill’s view in the light of our reconstruction of Frege’s concept of existence, according to which existence is the effective applicability of a conceptual or semantic-cognitive rule. If this is so, it seems that the permanent (guaranteed, certified) possibility of groups of sensations could be approximated to the existence of such groups of sensations. Consider the expressions:

1. Permanent (guaranteed, certified) possibilities of groups of sensations.
2. Effectively experienceability of groups of sensations.

Expressions (1) and (2) seem to say the same thing in different words. Now, compare them to the following expressions of existence in our reconstruction of Frege’s view:

3. Effective applicability of a conceptual rule.
4. Effective applicability of a conceptual rule to criterial configurations.
5. Effective applicability of a conceptual rule to groups of sensory contents.

Although (5) is only a case of (3) and (4), it seems clear that when we interpret existence as (5) it is something similar to (2): the effective experienceability of groups of sensations. Since (2) is a different way to say (1), the permanent (guaranteed, certified) possibility is the same as at least a case of existence. That is:

Existence is the permanent (guaranteed, certified) possibility of groups of sensations.

This point is made clearer when we consider the general structure of our conceptual rules of ascription and identification. We already know that these rules have the form of criterial rules that bring us to some (usually pre-reflexive) cognition, given by the satisfaction of variable subjective criterial configurations (supposedly) by means of their match with objective criterial configurations, which should be nothing but configurations of tropes. Now, when we interpret these variable (supposedly objective) criterial configurations as being the same as Mill’s groups of sensations, as we have reconstructed them, we can speak of existence as the effective, guaranteed, certified, permanent possibilities of groups of sensations as consistent with the warranted applicability of the rule. For instance: In order to be applied to a real object the conceptual rule for the concept chair demands the satisfaction of a criterial configuration. This criterial configuration is established by the definition of a chair as a seat with a backrest made for only one person to sit on at a time, which we could decompose in terms of subjective sensory criterial configura­tions that must be satisfied by matching objective criterial configura­tions or configurations of tropes. But the criterial configurations (the subjective, at least) could be reduced to groups of sensations whose experience is permanently (guaranteed, certified as) possible.
   Now, Mill’s insights can help us to deepen our reconstruction of the Fregean concept of existence. A material object exists not only when its conceptual rule is effectively applicable, but also when tropes for the application of its identifying rule can be objectively given to us at least in the form of groups of what we may call contents of sensations whose experienceability is warranted or permanently possible. Moreover, as Mill thought, this experienceability must be (at least in principle) interpersonally accessible by allowing agreement in the description of the experience; it can be more or less directly given; it is (usually) independent of our will; and it is also experienced as following causal laws regarded as typical of things belonging to the external world. We can say that all these things together contribute to building the condition of an effective application of a semantic-cognitive rule in the domain of the external world – they contribute to warranting the attribution of external existence.
   There is, however, an important and seemingly fatal objection to Mill’s view of matter, which is made more acute by the Berkleyan corrections that I have made.[10] It is that the group of sensations or configurations of sensory criteria that satisfy a conceptual rule are by definition psychological. Even sensations that are warranted as permanently possible (sensibilia) must be psychological in a dispositional way. This means that if we follow this path we fall into some kind of idealism in which there is no really objective external world to be contrasted with our subjective world of sensations or sensory criteria, no really non-mental external trope to match the criterial conditions. It is true that, as Mill noted, these possible sensations are independent of our will, that they follow the regularities of nature, even that they seem to be interpersonally accessible under circumstances that warrant their experienceability… But all this seems to be insufficient to perform the magic of making sensations (or even ‘contents of sensations’) be what they aren’t, belonging to a supposed non-mental objective external world. This is a pressing objection, whose answer will be attempted only in the final chapter of this book, as a consequence of our discussion of the correspondence theory of truth in its relation to direct realism.
   Notwithstanding, we can now anticipate something of the way we can deal with the problem. Having in mind our improved views of existence, we can ask: What is, in more conventional language, the existing external material object? One too daring answer would be: the external object (as it is thought) must be the identifying rule in itself, as far as it is applicable; in this way the multiplicity and diversity of objects would be explained by the multiplicity and diversity of identifying rules. However, this cannot be, since a semantic-cognitive rule is something essentially mental, and we are for sure not what Plato called friends of ideas.
   Looking for a less daring answer, we can suggest that the material object is not the semantic-cognitive rule, but is supposed to have the same structure of this rule specularly projected onto the external world. There is a reason for this suggestion: It seems that only something with a structure similar to its semantic-cognitive rule, though inverted, would be able to give unity to the multiple and variable criterial configurations through which external entities are able to give themselves to us in our experience of them. Figuratively speaking, if the semantic-cognitive rule has the form of a tree whose branches end in criterial conditions internal to the rule, then the object of its application as we believe it to be (and not necessarily as it is in itself) must have the structure of an inverted specular tree, whose branches end in objective criterial configurations that (supposedly) should match subjective criterial configurations. Furthermore, these objective criterial configurations should be nothing but tropes and constructions of them (objects, facts). Of course, this objective structure should be putative, so that the rule could be always corrected or improved as an effect of new information regarding its specular objective counterpart.

[1] I ignore the tense, since I regard it as an addition exterior to existence. The time and place in which something exists (existed, will exist) is something additional to the affirmation of its existence.
[2] David Braun and Marga Reimer, two renowned specialists, made a balanced comparison of descriptivist and causal-historic views in their respective articles for the Stanford Encyclopedia of Philosophy. The result was indecidibility.
[3] I felt somewhat uneasy in using this name as an example, but it has the advantage of being well-known.
[4] In some cases, like ‘Queen Elisabeth II’, family origin is part of the localizing description, but this is not necessarily so (see appendix to chapter 2).
[5] What linguistic expression the proper name receives is contingent. What makes this expression necessary is the identifying rule that we attach to it. In a possible world where the name attached to the identifying rule for the name Hitler were attached to the name Hartman, this different name would mean what we mean with the name Hitler. Meta-linguistic theories of proper names equivocally tried to reduce the proper name’s meaning to such auxiliary descriptions (e.g. Katz 1990).
[6] One could object that if we change the rule, it ceases to be a rigid designator. But if we change the rules so that the set of possible worlds to which the proper name applies also changes, you are not applying the same proper name anymore. You may bring changes (normally additions) to the identifying rules insofar as this only determines the identification better, insofar as it does not affect the set of possible worlds to which the proper name applies, insofar as it does not affect its rigidity.
[7] This is again a merely pedagogic simplification (Cf. appendix of chapter 1).
[8] However, if the assertion that there are round squares were merely an equivocal manner of saying that we can syntactically combine the adjectives ‘square’ and ‘round’, that is, a misleading way of saying that there is a syntactic rule allowing the combination of these adjectives, then it makes some sense to attribute existence. But in this case what we are trying to say will be more correctly expressed by the metalinguistic sentence: ‘The rule for constructing the phrase “round square” is applicable, therefore, the phrase “round square” exists as a grammatical construction’. The Meinongian Sosein is reduced here to the recognition of a syntactic triviality.
[9] According with Berkeley’s official view, things that are not actually perceived by us exist because they are continuously being perceived by God (Urmson 1983).
[10] I believe that Mill’s uncomfortable definition of matter was in fact an attempt to evade the objection of idealism that I will expose.

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