INVASIVE WEEDS IN PARMENIDES'S GARDEN Olga Ramírez Calle Abstract The paper attempts to conciliate the important distinction between what-is, or exists, and what-is-not _thereby supporting Russell's existential analysis _with some Meinongian insights. For this purpose, it surveys the varied inhabitants of the realm of 'non-being' and tries to clarify their diverse statuses. The position that results makes it possible to rescue them back in surprising but non-threatening form, leaving our ontology safe from contradiction. Keywords: Meinong, non-existents, fictions, possibles, impossibles, numbers 1. Entering the goddess's forbidden path The world of non-existence is surprisingly overpopulated: from fictions to pure non-existents, quasi-existents, and non-actuals, to thick and thin universals, poems and maybe symphonies, maybe numbers, and the whole troop of the impossibles. These 'homeless objects'1are all lodged in realms that we know to be in some sense different from the real experiential world, but, somehow, there too. Giving an account of how they can be there in their peculiar, non-existent way is a longstanding puzzle. To work our way into this ghostly 'jungle' it will be helpful to first distinguish the different sub-species from each other. This can be achieved, for example, by considering the diverse ways in which they relate to what we can 3 characterise as 'ordinary existence' in the actual world. For the sake of drawing the line – which we ex-ante assume to be drawable, or else we would not make sense of the problem, nor be discussing it at all – I will specify what I mean by 'ordinary existence'. No entity can be said to exist in the actual world in an ordinary sense if it is not possible to have some kind of experiential acquaintance with it. This need not be understood, of course, in literal Russellian terms, but it sets indeed a requirement to prove that the experiential conditions of application of corresponding statements are satisfied in order to make them true.2 Therefore, no entity can be said to exist in the actual world if a) it is not possible to access some spatio-temporal experience that would make claims about it true (if it cannot be said to take place at a given point of time and in a given situation), b) if we cannot regard judgments about it as being actually true on some such basis; c) if it is not possible to reidentify3 it through different judgements in alternative contexts and d) if it can have no causal impact on other such entities. Correspondingly, if an entity satisfies the opposite requirements to a), b), c) and d), we would agree that it exists. For exposition purposes, though, I will allow talk of 'non-ordinary' ways of existence in describing how entities are said to be there other than in the sense described. With these clarifications, let us start our surveillance of non-beings. a. Fictions (Sherlock Holmes, Pegasus, etc.). These would denote individuals who are invented and taken to exist in invented worlds. They will never exist in the real actual world, nor will their defining properties be instantiated in it. Some real experiential individual might exhibit resemblances to Sherlock Holmes, but he would not be him. 4 b. Pure non-existents (the alien captured by NASA, Vulcano, Phlogiston, etc.). These so denoted guys, unlike Sherlock Holmes or Darth Vader (who were never postulated as potential experiential candidates), were described as existent in the actual world, but we found proof that they do not. Thus, they actually have no existence at all, not even in fiction,4 nor did they exist and pass away. A sub-sort of them, however, about whose existence or nonexistence we have no proof (they might already exist or come to existence some time), might be characterised as: b.1. Potential existents (an engineered rational being resulting from the combination of canine and human DNA, a super-intelligent human being with telepathic capacities, unbelievable sorts of superpowerful robots, etc.) could be species of such. Their ambition is to, at some point, have ordinary existence, but they do not. c. Quasi-existents5 (individual witches, shamans, saints, etc.). These are peculiar folks, since while they make it possible to identify some real existent beings as their denotation, they mislead us into thinking that what we have identified is a being with properties beyond those which the ordinary existent being actually has. For example, experiencing a person seemingly in trance, claiming to access the spiritual world, acting as a healing figure, using ailments and other non-standard procedures in treating others' illnesses, made it possible to identify a 'Shaman', but on such experiential basis further extraordinary powers were attributed to him.6 Quasi-existents, thus, never properly existed, but there was a specific experience on whose behalf they were identified. As such an experience it is not merely meant some causal effects in the experiential world that made 5 it possible to presume their existence, as with some theoretical entities; in this sense they differ from pure, exposed, non-existents too. Their relation to ordinary existence can therefore be characterised as misleading. d. Non-actuals (Socrates; Napoleon; Cervantes; Tolong – the dog I someday will have already been baptised by my niece). These comprise individuals who have been or, predictably, will be, ordinary existent beings, but are actually not such. Their relation to ordinary existence can be characterised as transient. e. Generalia. Here I will include, in an uncritical way, conceptual meanings and, more generally, the so-called 'universals'. The actual existent world might exemplify them, but they themselves would not have ordinary existence as such and never will. If they exist, they do so in some other realm. f. Subject-dependents (symphonies, poems, tastes, pains, etc.). Whether these should be considered in this enumeration is much more questionable, but since other authors make a case about them, I will include them too. They would exist in ordinary reality as much as our bodily feelings in general do; their existence requires our existence, but they are also experientable just the same as all other beings that constitute what we consider standard cases of ordinary existence. They depend upon experiences that we conceptually capture, locally7 and in a timely manner. This aspect differentiates them from fictions and other non-existents, since the latter are not experienced as such. There is a difference between the thinking process and what the process is about. We can be said to experience thinking but not to experience the entity that Sherlock Holmes is supposed to be. Poems, though, have a 6 mixed character, in the sense that they partially belong to the fictional and, to some extent, the generalia groups, but full grasp of them requires experiencing their musicality too. g. Impossibles (the round square, the simultaneously red and green all over book). Clearly, they are not and will never be part of ordinary existence; furthermore, ordinary existence absolutely abhors them. Among all of the non-existent folks, these are by far the most radically threatening ones. This can be for logical or empirical reasons. The above are impossible for logical reasons, but there is an empirical sub-sort: g.1. Empirically impossibles (human beings who do not breath, stars made out of cotton). These are impossible according to what we know about natural laws. Their impossibility to take place in ordinary existence depends on how right we are in our knowledge about natural world laws. They would differ from what I have called 'potential existents' in that, according to our actual knowledge, the latter do not exist, but what we know about the world does not make their coming into being completely impossible. h. Numbers (0 and the rest). These are as numerous as one wishes, up to infinity, although some of the others could also parallel this capacity. Their relation to ordinary existence is the most intriguing one. Although they do not exist in the experiential world, and never will, they appear to be somehow essential to it too. Unlike pure non-existents, they were never postulated as real standard existent individuals, and like fictions and generalia, their existence, if at all, would be in some other realm. 7 With this, I think I have a fair taxonomy to start with and to try to make sense of their diverse statuses and of their status as a whole. 2. Meinognian objects or Russellian impostors: Do we have to choose? Russell's (1905) analysis of non-denoting expressions in terms of definite descriptions was thought of as a measure to debunk deceiving ontological proliferations of the Meinognian type. This also allowed him to provide a better solution to the problem of negative existential sentences, with which he had earlier struggled. Russell's achievement was, I believe, a huge step towards clarifying when we should be legitimised to assume the existence of what we talk about and when we should not, and how we should conduct a corresponding proof. This is a position abounded upon by Quine (1953) in his critique of Meinong-like views. Indeed, we can easily be misled by linguistic appearances, assuming the ordinary existence of the presumed referents of our denoting terms. With this, I want to make clear where I stand in this regard, in case what I have to say in what follows should raise any doubt. To expand our ontology, as Meinong (1888) does, to say that with 'the present King of France' we are referring to an 'object' of a peculiar non-being8 sort, which is already pre-given and is logically prior to our judgement about its existence or non-existence (has 'external Being', Aubersein: §4) and constitutes some more basic 'grade of Being', is completely uneconomic and confusing. Consider the following quotes Should I judge of an object that it is not, so it seems that I have to have apprehended it first to say from it that it doesn't exist (Meinong 1988: 10, §4 'On the Externality (Aubersein) of the pure object'). We have to do with a Being, that has neither existence nor subsistence (Bestand), but just to the extent that to both, if one can put it so, as grades of Being, existence and subsistence, a third grade is to be added. This Being would then belong to each object as such. (ibidem: 10).9 8 The idea, therefore, is that in considering, for example, 'the present King of France', we might judge 'that the present king of France does not exist'. The that-clause constitutes what he calls an 'Objective', by which we are apprehending an object not merely a representation of it (Meinong 1988: 9)10 that has Being (in the third grade of our last quote) and which we judge as not existing. Such an ontology, which embraces all kinds of non-beings, possibles, and impossibles (for which this 'pre-given way of Being as 'Aubersein' holds too), would seem to betray the very sense of the term ontology and its allusion to 'what there is' as opposed to 'what is not there'. Meinong's introduced 'So-sein-objects' (to refer to their having 'a given way of being' even if they do not exist) which he wants to distinguish from 'existent objects' are already more than mere descriptions. They are understood as what the description is about and, therefore, as having Being. This is, for him, the case with both non-existent objects and possibilities, and also with fictions (such as the golden mountain, which is golden and a mountain even if it does not exist). The difference with 'real Being' is something which he wants to make palatable by using the contrast between 'Sosein' and 'Sein' – a distinction that, strictly speaking, would work if the former, as the term expresses, is understood as a mere predication, a mere description of a specific way of being. But it rather amounts to seeing the description (which with Russell's procedure would come out as unsaturated) as already concerning an object with a peculiar degraded way of being of the 'non-being sort'. He then can be said to split this elementary Being into the existent and the non-existent (Sosein) types. Thus, we arrive at a conception that to avoid paradox separates the notion of Being from that of Existence, as just seen, and splits then Being into two sorts (existent and non-existent). However, the resource of saying that something is 9 (has some objectual pre-given grade of Being) but does not exist strikes one as some kind of prestidigitation trick, not far from the claim that 'what-is-not is', which already set all alarms by Parmenides centuries ago. Such talk attracted equally harsh critique from Russell, who sharply noticed that even the predication of existence had to be allowed in Meinong's picture of the non-existent objects: but the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction. It is contended, for example, that the existent present King of France exists, and also does not exist; that the round square is round, and also not round, etc. But this is intolerable; and if any theory can be found to avoid this result, it is to be preferred (Russell 1905: 483). By way of such a reconstruction, Russell attempted to show, in Meinong's own terms, as Bourgeois (1981) argues, the incorrectness of a theory that makes it possible to predicate existence of an object that does not exist and make further contradictory claims. Meinong's attempt to distinguish 'being existent' (as a mere predication) from 'exist' in his reply to Russell (Meinong 1907: §3, 1910: §20) was, in Russell's eyes, just an artificial manoeuvre that disguised one and the same thing (Russell 1907: 439) as two different ones. Notably, even some who, like Bourgeois (1981: 665), tried to make sense of Meinong's response, concluded finding his proposed solution unable to surmount the core of Russell's objection; the objection allowed being reformulated using 'exists' itself as a predication and attributing it to an object that does not exist. Finally, I do not think the nuclear/extranuclear differentiation helps any better to make sense of Meinong's distinction, which Parsons (1974: 574) tried to apply to 'existent golden Mountain'. Nuclear properties are those that according to the description constitute the object, 'being golden', 'being existent', extranuclear ones those that are dependent upon external factors such as existence or non-existence. The distinction could be said to 10 achieve some clarification of the Meinongian position, maybe, but at the price of acknowledging a predicative mode of existence that ends up being devoid of its very sense, making its attribution worthless. The alternative proposed by Jacquette (1996: 81) to consider existence an extranuclear property and, thus, not to allow its nuclear use, could work better but, as some have pointed out, might require too strong a skimming of the theory for its own liking. Given such a picture, to conclude that 'the present King of France' is simply a description of ours, for which there is no reference, and no object at all, is a relief. It would unmistakably separate out when what we say is asserted about something that is independently there in an ordinary experiential way, and just then has Being and Existence, and when not. Nevertheless, this convoluted world of Meinong's appears to have something to it too. This explains why a good array of authors, including Chisholm (1973), Parsons (1974), the Routleys (1973), and Jaquette (1982, 1996) or Lambert (1974), to name a few, have defended or logically elaborated consonant views, as well as its recent resurrection in the form of more or less watered down contemporary Neo-Meinongian positions, for example, Priest (2005), Berto (2008), Crane (2012), Eklund (2005). The difficulty is how to place some Meinongian insights so that it is worth all the efforts of his 'ontology' in a helpful way, without making us say what we should not be saying. My purpose, thus, is to try to make sense of this comprehensive picture of beings of the beyond, in such a way that it allows us to keep the gains of Russell s work. In doing so, I am not going to concentrate directly on Meinong s proposals, but will proceed rather freely in analysing the different modalities of 'non-existents' above independently. 11 3. From fictions to 'reals' and back again I will initiate my journey into the realm of Not-Being by considering first 'the fictionals'. I am going to use a little star to distinguish these 'beings'* from those belonging to the realm of Being in some ordinary experiential sense (those that would correspond in Meinong's own ontology to 'objects that have real Being'). The * is not meant here to suggest that we have to do with a specific way of being, of the sort that 'is not', as in Meinong, but in the sense that it is not meant literally. Since, as should have become clear, the separation between Being and Existence (or 'there being objects that have no Being') is, in my view, utterly confusing. The peculiarity of such fictional, so-called 'beings'*, is that they actually could not be unmasked through a Russellian analysis, since they never wore a mask, so to speak. According to Russell s analysis, the term 'Sherlock Holmes' in sentences such as (1) 'Sherlock Holmes played the violin', is to be seen as a definite description (recording the main features attributed to Sherlock Holmes in Doyle's novels). We would then prove that there is no such experiential individual that satisfies it. Without entering the difficulties that such a descriptive account of proper names is seen to have in the later discussion,11 I would say that the real issue here is a different one. Let us reconstruct the sentence above in Russellian terms, where SH stands for Sherlock Homes and V for 'plays the violin'. (1) ∃(x)'SH(x) ∧ V(x), ∧	∀y	('SH(y) ∧ V(y), ↔ (x = y)) The second part of the sentence expresses the uniqueness and identity of the sodescribed 'being'*. What is the problem then? In the non-fictional case of 'the present King of France', or, for a change, 'the first female President of Russia', a Russellian reconstruction makes clear that there is no experiential individual 12 satisfying the description and therefore no such real existent being we are talking about. However, it might be that these sentences uttered in some other moment of history come out true. It is possible that we might, on some occasion, find an individual who corresponds to the description. So, here we take the sentence 'the first female President of Russia has a dog', where the FFPR stands for the subject and D for the predicate. (2) ∃(x)(FFPR(x) ∧ D(x) ∧	∀(y)((FFPR(y) ∧ D(y)) ↔ (x = y)) We expect this sentence to be satisfied by an existent actual being that exhibits those properties if we are to find the sentence true. Comparing this now with the sentence (1) above, we see that although it has the same form, the peculiarity of (1) is not that it is not satisfied by any existent individual having the characteristics attributed to the assumed Sherlock, but, rather, that it could not be. Why? Not because there could be many, as Kripke once argued (1980: 58), but because, as the second part of the sentence makes clear, there is only one such being, and even if we should find another satisfying most of the characteristics of Holmes, it could not be him. It is a characteristic of the authentic and unique Sherlock Holmes that he is fictional, and an ordinary existent one would not have such a character. Therefore, while sentence (1) does presume the existence of an individual we are talking about, it is not open for saturation. It is rather already satisfied by our fictional individual. This means that in speaking about Sherlock Holmes, we do not have a normal unsaturated sentence but an already saturated one. In contrast, sentence (2) is and should remain unsaturated by any positive object, as long as no existential 13 individual satisfies it. However, if we reconstruct our sentence (1) in the following way, including F as a predicate for fictionality, (1) * ∃(x)%F(x) ∧ SH(x) ∧ V(x), ∧	∀y	(%F(y) ∧ SH(y) ∧ V(y), ↔ (x = y)) and then we take ourselves to have a fictional being named 'Sherlock Holmes' satisfying the sentence, we fall back into the contradictory claim that there is (or exists) a being (without star, since we are talking about existence without qualification) such that he has the extra property of being fictitious. Then, since 'fictitious' means 'not really existent', or so we take it to mean, we obtain our paradox. We actually go directly to what Russell found 'intolerable' in Meinong's view of the idea of 'objects that do not have existence', objects that are graspable, and in a way are externally there but do not exist.12 But if we reconstruct the sentence as in (1) ** Fic Ex%(SH(x) ∧ V(x), ∧	∀y	%(SH(y) ∧ V(y), ↔ (x = y))) using a fictional operator to apply it to the existential quantifier and all that follows, then both the description and its saturation by our presumed existent unique individual come out as fictitious. Being fictional is not here predicated of a pregiven object, but through the operator Fic it is meant to characterise existence itself and all that is attributed to it (the objects that are part of existence, their properties, and their relations). Existence is not a property but a presumption and, therefore, merely fictional. Furthermore, we should separate out here too the existential claim (the existentially quantified sentence) and the existential presumption that there would really be* a unique object that saturates it: the presumption of an individual, 14 call it Fica, that does satisfy (1)**. That is, we need not just say that such and such exists, but to represent it to some extent as an existent individual who would, for example, occupy a different spatio-temporal point than the other individuals in a fictional play, and picture his continuity and spatial moves along the story, his interactions with others, and so on. The proposal, therefore, departs from the nuclear/extranuclear distinction or the encoding/exemplifying view, since it does not amount to acknowledging a merely predicative mode of existence. To some extent, the reconstruction presented in (1)** might conform more likely with certain forms of pretence accounts (such as Walton 1990). But, for now, I would not want to commit myself to any label until the complete contours and implications of the position I shall be defending are in place. The specific formulation chosen in (1)**, regardless of possible coincidences with other proposals too,13 is thought to serve the interests of the view I am leading to and should be read in the terms proposed. Interesting here, from my perspective, is the perfect analogy of the structure of fictional discourse, whose definite descriptions are already satisfied by a unique individual, with respect to the standard practice where ordinary existent individuals are assigned to corresponding existential sentences. What makes Sherlock Holmes more than a mere description is precisely the (fictional) presumption of a unique individual who would exist and who satisfies the description. Mere possibilities (potential existents), such as 'the individual who is a combination of human and canine DNA' or 'the golden pencil on my table', are not presumed to have any individual satisfying corresponding descriptions. As we put it at the outset, 'possibilities' aspire to ordinary existential satisfaction; correspondingly, their existential sentences would only be fulfilled if, for example, a real golden pencil is 15 to be found on my desk, turning the possibility into a reality and the sentence into a true one. If we, therefore, subject them to proof in the Russellian experiential sense, we find corresponding descriptions to be empty. It is thus important not to attribute non-saturated definite descriptions positive denotation (contrary to what Meinong does with his So-seins in direct predications) and to trace a clear distinction between such merely possible statements and fictions. This distances my proposal too, I believe, from Meinongian-based free logic accounts (Lambert 1960), since I do want to keep differences regarding commitments to existence. Now, the case of 'non-actuals' brings particularly interesting aspects to the problem. While it is easier to assimilate future beings to mere possibilities and understand them along the same lines, past individuals raise interesting questions. It seems to me very weird to think of my deceased father as a mere description. I actually consider myself as being able to refer back to him, to refer to the individual who was there. But how can that be? Kripkean 'causal chains' tell a story of me referring back to the individual who was baptised 'XYZ', and whom I call 'my father'. But the above does not say much about how this is possible, nor does it amount to any commitment regarding the acquired status of the referred object. Actually, if we look at it, the whole past itself does not exist at all! For all that is said, he could perfectly well be counted as a Meinognian object with non-existence. If, on the other hand, I use Russell's procedure, a corresponding existential sentence would come out false. There is (unfortunately) no such person to be encountered anymore. But now what has suddenly struck me as strange is how I have been referring to him all along... as he was there. What has really changed? First, there were times when I was away for a long period and could not continuously check on him. He could have not even been there, and I would have kept referring to him just 16 the same. My knowledge of his past existence is no warranty that I am referring to an existent being. More worryingly still, the problem expands when considering that we have in fact no warranty at all; neither can we be said to be referring to an existent being if all we have is the past. The whole issue ignites then when thinking that this does not just happen with my father, but with all and everything else. How do I keep referring to it all, if my presumed existent beings are not literally existent for me after they pass my surveillance – my experience of them? Testimony can occasionally serve this purpose, but I do not keep reconfirming through others the persistence in Being of my objects of reference either. What about whole cities and oceans and my very past infancy with its populated ingredients, places, and encounters? This is a real black hole in our tidy permanent picture of world stability – one we will inescapably have to deal with. On the other hand, while sentences about 'the golden pencil on my desk' would be satisfied by finding a unique golden pencil on my desk, no future found individual could satisfy the description of my father. He is a complete individual (in Meinong's terms)14 in a way 'the golden pencil on my desk' is not (despite the unique character of the definite description). He is also complete in a way Sherlock Holmes isn't. No new individual could, therefore, take his place. In this sense, nonactual past beings clearly differ from mere possibles and fictions; of whose 'existence' we merely now as much as the description states. But this uniqueness and the once-and-for-all saturated character of descriptions of my father by him do not solve the question of non-actuality, which, as we just saw, expands also to ordinary existent beings of which we just have past experience. Actually, if we consider this problem in its threatening radicality, there appears to be no way to give an account of the existential stability of our referents, the stability we 17 experience them as having for us, by attributing ourselves a capacity to 'keep them present'. To keep, actually, our whole world present beyond the continuously fluent and transient character of our experiences. That is, to maintain something like an imaginative representation of our world while it decays - one where the different real interacting objects are attributed, at a representational level, different noncolliding positions in space and are expected to have a continuity through time and mobility consistent with that of our own. If this is how we experience it, we must be able to situate these objects and their moves and relations as if in some sort of land cart. This stable 'representation' that carries its complete non-actual referential objects as something more than mere descriptions15 (and in that literal sense I mean the word) would very much resemble the kind of representation we reconstructed for the fictional case, where it was already suggested that making sense of fictional claims implies already a similar figuring capacity. This is especially striking in today's virtual games, where we interestingly develop exactly that diagramming in a visually 3D representational way through which we put down our own way of conceiving it. However, maybe we should rather consider that if we can come to such a representational picture in fiction, it is because we already have at our disposal those representational capacities, since we need them to constitute what we consider our referential 'reality'. Put differently, that reality, our reality, is fiction! This means that what we would be referring to when speaking of an existent being such as that referred to by 'the ex-President Obama' in the sentence 'the exPresident Obama is married' should be reconstructed along similar lines to (1) **. With XPO standing for ex-President Obama and M for married, we would obtain: 18 (3) ∗∗ Fic∃(x)'XPO(x) ∧ M(x), ∧	∀y	('XPO(y) ∧ M(y), ↔ (x = y)) where existence is postulated again at a representational level and presumed. Presumed too is the existence of a corresponding object satisfying the statement, as ex-President Obama himself is. Of course, I cannot literally mean that there is no difference between reality and fiction, and I do not. What I am saying is that referring to reals requires such a representation too (in the alluded literal sense of representation, beyond the mere putting into words or, counterpart, thoughts), though not alone. Therefore, since I am proposing a common reconstruction for reals and for fictions, I will change the fictional modifier Fic of the existential sentence above into a presumption modifier Press. Correspondingly, (3) ** turns into (3) ∗∗∗ "#$%% ∃x	(XPO(x)... ). Moreover, (1) ** turns into (1) ∗∗ ∗	"#$%% ∃x	(SH(x)... ). The notion of 'presumption', unlike, for example, 'pretence', implies not the faking of something, but the taking of it for granted, which I think is not the same.16 Actually, I think that in his talk of the 'parafictional' Recanati (2000) would be acknowledging this difference.17 According to Recanati, in parafictional uses of language we are not pretending but rather taking for true. This is akin to what I mean with 'presumption'. We presume existence at the representational level. We presume that these beings exist throughout time, and we keep them represented as doing so, while this would just be (most of the time) a mere presumption. This is also the case in fiction, since our attitude in fiction is not that of mere supposing, but the attitude of something being the case, being true. Therefore, it is important to specify that with the term 'presumption' I am implying the idea of treating the corresponding individuals as real, postulating it to be the case, as opposed to merely supposing or entertaining a possibility that we do not 19 treat as true. But, if 'ordinary existence' is to be seen as a presumption in this sense, then how do we tell the difference between fictions and ordinary existents? Well, we should ask Russell. As he says, this is a matter of acquaintance, of the origin of the representation being based in direct acquaintance. Not understood literally in the sense Russell meant the notion of acquaintance, as we said, but just the idea that it is a form of experiential encounter that gives us grounds to claim that there is a correlation between our stable representation of the individual with something out there. We have, therefore, to do with a well-grounded presumption, which is what we call 'real existence'. That is, the difference between the fictional and the real case is not at the level of the type of representation but is due to the grounding, or lack of it, of the representation. It is the mixed character of the real, perfectly experiential, on the one hand, and representational, on the other, that makes the difference. So, if the representation, in (6) below, goes for both fiction and real existence, where our picture is kept stable throughout a lifespan (until we are told or experience otherwise), real existence departs from a prior time-fugitive originating grounding layer (5). (5) tfugitive (6) tstable 20 At the experiential level in (5) at t2, our object is not there for us anymore, but at the representational level in (6) it remains in representational form as our referential object. The time-limited real experience of ex-President Obama builds the wellgrounded claim that our stable representation of him is real, as long as we (or someone else, in which case knowledge of direct experience is obtained by testimony) have a new experience to the contrary. Therefore, if we subject our claim to the Russellian proof at the experiential level: (3) ∃(x)'XPO(x) ∧ M(x), ∧	∀y	('XPO(y) ∧ M(y), ↔ (x = y)) It comes out positive as soon as we can provide an acquaintance experience or wellgrounded testimony of such. But the stable further existence of our referent, when considering it in the modified form of (3)***, allows confirmation in the presumed modus too. Therefore, a claim of existence on the basis of such a stable representation, while it is a presumption, is a well-grounded one, since at some points of time we did have existential satisfaction in the Russellian sense. To put it differently, at the level of experience, where we situate ourselves, the very existential aspect of our claim in (3)*** Press∃xists	18 finds sufficient confirmation in (3) ∃xists,19 when satisfied by an individual a, while the satisfied existential claim in (1)*** does not have a parallel confirmation in (1). Therefore, our representation in (1)*** is known to us from the very beginning, not to be of the experiential reality. It is just our representational attitude that is of the same kind. In a sense, it is as if our Press∃xists	quantifier	acquires the status of a place holder, that is of a higher order 'quantifier-variable' of existence itself, that can be saturated or not by the real ∃xists	quantifier. 21 On the other hand, the type of justification for our claim in (3)*** is not just based on encounters, although it primarily is, but also a matter of knowledge. The knowledge is that unless there is a sudden decease, living beings continue to exist as we ourselves do. I am absolutely not pretending, though, that we would be doing all this labour of deduction consciously. It is more a necessary condition of possibility to be able to refer in a non-discontinuous way and also plan action and interactions with others towards the future. But in becoming aware of this, we can explain that we are well justified in doing so, keeping the representational stability of existence through the procedures mentioned. In some cases, where our experiential confirmation is really a continuous presential one, paved through continuous encounters and reconfirmations of existence, the presumption is almost equal to experiential reality, as happens with our own self, whose past we keep stable too and whose present existence we continuously experience. In the case of deceased non-actual beings, what we become is proof of their ceased existence. What we have is a (well-grounded) presumption of existence whose continuity is truncated up to a given point. Therefore, representational reference to the past, since stability makes it possible to refer back and forth to an individual, is still of the real existent kind, as it alludes to a time when there was still the grounded level of proof. But nothing of the sort is possible anymore in a present or future form. Notice that the proposal here is an epistemological one. It does not limit itself to say in the case of real existence, that there is an individual out there we take our semantics to refer to, as some authors have argued (for example, Parsons 1974). The idea is more radical in the sense that of necessity, the real existent object is just stable as a such for us through a representation. This means that we are not referring 22 to an existent individual in the experiential world all along and then we give a semantic account of it. But, rather, that our experience merely delivers a punctual basis and the representation is required for stability. 4. Numbers As Frege (1884) well saw, counting unities requires separating them out through a concept.20 This, I believe, need not mean literally that we need 'linguistic concepts' to distinguish unities, as in some direct realist positions. 21 It also allows for a more basic pre-conceptual reading according to which there is no counting that is not done from a given perspective, by distinguishing some particular aspect on whose behalf individuals can be separated out from their surroundings. However, for the sake of simplicity, I will be referring to the 'conceptual' sorting out of unities. Yet, if we are to consciously become aware of what it is that we do in this process, we would be representing to ourselves this very operation (the conceptual detachment of a unity) in general terms, a procedure through which we figuratively capture our own activity. That is, we do not cognitively appraise it, as if it would be some further occurrence or experienceable phenomenon in our epistemic world, but rather we reconstruct what (we think) must be taking place through our own performance. In doing so, two aspects should be distinguished: the very conceptual individuation and the real individual that results. Now, as I have argued elsewhere (Ramírez 2020a:160,168), I believe that, contrary to what Frege ended up capturing, it is the latter that constitutes the proper numerical unity. It is not the formal conceptual aspect, something that certainly would be equivalent to a class, but the corresponding representation of a real individual or a real object cut off from an extended background. To put it differently, it is the very stable representation of a (non-further saturable) real individual that constitutes the numerical unity. It is a 23 representation, but a representation of a reality. This is precisely, I think, the same kind of individual, of a singled-out object, we refer to, in both fiction and our representation of reality – not concepts, not classes, not mere descriptions, but the representation of the reality that satisfies our quantoren, and that is exactly the same as the numerical unity. While Frege, I believe, was initially orientated towards this, he shied away, since this would have brought him beyond the mere formal, analytical account to a representational one (more akin to the Kantian representation in Intuition).22 He miscalculated in thinking that the concept of the unity itself (or of a class of them) could be a substitution instance of further existential sentences, with the known disappointing consequences.23 However, what results out of the considerations made, to put it concisely, is that Sherlock Holmes, after all, is just...a number – nothing we should wonder about, since he always was a master of disguise. But we should not feel too superior either, since, at the end of the day, we are a number too! But one of a mixed sort: half ghost, half real. Nevertheless, there are still 'others' in our list that might have it worse. 5. Pure non-existents What are we to say of the family of 'Vulcano' and the like? We cannot presume their existence, since what we are presuming is that they have none; not even fictional. Giving an account of their predicated 'non-existence' has always been especially problematic. In Meinong's ontology, we are saying of an 'external object', Vulcano, that non-existence is attributable to it. We obtain, therefore, the contradiction that there is something, we are denoting some object, that is not. Russell's alternative reconstruction dispelled the puzzle, showing that it was simply 24 a non-satisfied description. So, we have an existential quantified sentence that proves to be non-saturated at the experiential level; just as in the case of Jupiter, we have one that is. A reconstruction of such sentences as if they would nevertheless be denoting some (low grade Being) objects, while posing no problem in fiction and by the stable representation of real existent objects when they are not present, is here to be avoided. It would block their capability of being saturated at the experiential level, which is the only one that could satisfy the kind of existential claim made through a statement postulating the existence of a corresponding planet. According to our knowledge at such a level, the sentence would be empty and, if we consider our proof of non-existence to be definite, then the very possibility considered would be denied. If this is the case, then we should conclude that: it is not possible that there is the object such and so. But what happens when we have no proof one way or the other? What happens when we merely entertain the possible existence of an entity such as 'the nearest by planet containing other intelligent beings'? These are finally the 'possible beings' we have alluded to but not yet directly treated. As opposed to real existence and fiction, we are not representationally taking for granted their actual reality. That is not what we want to presume. We know there are no well-grounded reasons to claim real existence (nor to claim the contrary), and as opposed to fiction, we are not presuming them to be objects at the representational level either. Nevertheless, here too, we want to have the opportunity to consider them at the representational level, we actually do, in order to be able to talk about and operate with them, to consider future interactions with others or further consequences that their existence, actions, or reactions could have for us in our world. This is like if we would keep a chess game board and consider moves back and forth to analyse 25 what their consequences would be. In considering their possible real existence, we are entertaining not their actual reality but some possible alternative or future one. But how are we to do this without providing such sentences with a denotation, which, if at all, they ought to have (corresponding to the claim made) at the level of experiential reality? We cannot merely represent such an object as a presumption of existence, well-grounded or not, because that would confound it with real existents or fictions. Therefore, at the representational level, this must be reconstructed differently. That is, at the representational level, we pictured the resulting unities of conceptual individuation (those of saturated existential Russellian sentences) as being what we assume to be stable (well-grounded) realities. These are taken to have a corresponding experiential grounded level. Fictions, we said, differ in terms of their lack of this mixed character and grounding source. They are mere representations of existence. But we do just the same as we would if they were there, it is just that we are aware of their merely presumed character. This cannot be equally reconstructed in the 'entertaining future or alternative reality' cases, since we are in no way representing actual existence.24 We are, in fact, representing lack of existence, lack of object, since possibilities define themselves by 'not being taken to be the case'.25 But how can that be? Here we have our puzzle back. This was, I guess, the difficulty with which Meinong was confronted. Although he saw in this sense no essential difference between fictions and possibilities, the quandary was to picture something that-is-not as if it would be. Yet, before, when giving an account of what it is that we represent when we depict an individual as existent, I argued that, ultimately, we had to do with numerical unities. If we say there are three cups on the shelf, we distinguish each cup through the concept and obtain 26 three unities of the sort. What remains outside conceptual individuation has no existence 'as cup', so it is nothing from the perspective of the concept.26 If we picture the existent unities of the cups, like in (4) a), below, and if we want to entertain possible cups that do not exist, this would amount to representing them in the territory of non-existence in (b), but relative to the concept of 'cup'. So, if we entertain the possibility of there being two cups on the shelf, for example, that means presuming the non-existence of corresponding objects (to remain consistent with possibilities not being existent).27 However, in the sense that there are no objects of the sort and, thus, being consistent with Russell's claim that such denoting expressions are not saturated, what we are doing is representing them like in (4)* above, as non-existent objects but as cups. Notice that there is a difference between saying: (i) 'there is an object that does not exist', and (ii) 'an object does not exist'. We are saying (ii) and in this sense we talk of non-existent objects or non-existent cups, while Meinong was seduced to talk about (i). Now, if, as I stated previously, the general representation of numerical unities amounts to the representation of the application of a concept to some reality, what are these ghostly unities of non-existence? Well, I have argued (Ramirez 2020a, 2020b) that they are (4)* 27 the negative numbers. Negative numbers are absences: minus 1, minus 2, minus 3 objects, which might be cups or whatever, if what we are considering is the nonexistence but possibility of three cups on the shelf, for example. This mere representing of the lack of cups is interesting from the perspective of searching for their reality. After all, it is just through a concept, as Frege stated, that we can distinguish unities, and it is through the concept of 'cup' that we are making 'wholes for cups in the emptiness' so to speak, that are nevertheless not to be counted 'as cups' and can be counted as cups not being there, and thus negative cups. In this way we can accommodate Meinong's notion that the cups are 'so-seins', that is, they have the predicative form of 'being cups' and, as he argued, 'you can count what doesn t exist' (1988: 5). There are two negative numbers of cups on the shelf. If we assume this is right and go back to our Vulcano case, what is the difference between Vulcano of whose non-existence we have proof and the possibilities just considered? If we pay attention, the difference between both parallels with the distinction before between fictions and realities. At the representational level, they are the same, but at the grounding level, we have a difference. Correspondingly, in the Vulcano case, we would be representing it just the same as by possible negative existents, with the difference that here we have a well-grounded proof of nonexistence, the non-saturated Russellian sentence at the experiential level, in addition to proof of its non-existence. We can thereby make sense of the 'negative number' Vulcano, which we can say does not have real existence on the basis of a proof according to the Russellian method. The mixed character of the representation – half experiential (proof of absence at the experiential level), half ghost (negative number) so to speak – applies here too. However, if the proof is definitive, as we 28 stated previously, we can simply deny Not −	∃xistent"#$%%, that is, the negative existential presupposition as a whole. I am not going to enter much into the realm of the quasi-reals, since actually an explicit Russellian sentence at the experiential level would exhibit the purported satisfier as a hoax. Therefore, the status of 'quasi-real' would thereby have to be abandoned, and we could turn the corresponding individuals into fictions, attribute them a non-literal sense, or make them disappear. Although understanding how such terms come into being and their deceiving force is quite interesting, in our context they do not add much new. The case of generalia, however, I will leave for a future occasion, since although they would behave as reals in being partially well grounded, they pose a particularity of their own. A different issue is with the impossible, which raises much perplexity. As opposed to pure non-existents, with impossibles it is not that we have proof of their non-existence. It is that we need not even try, since we know in advance that no proof could be found. One option would be to see impossibles as irrational numbers, which do express the impossibility of a numerical distribution in any conclusive numerical terms, obtaining a number that, in some sense, is not a countable number at the same time. It is a magnitude not capturable by one unity or the other, not expressively by any discrete counting, since whenever one splits a continuum, one originates a difference between the unities and the continuum. This is often irrelevant, but sometimes it is not. So, if an extension is a continuum between two discrete unities – call them 'a' and 'b' (which can also be understood as parts and parts of parts of unities) – there is always a difference between the numerical division and the 'notnumerically divided', and therefore something in between the split parts. Since it 29 has no presence as any kind of countable unity that can be considered 'something' (it is no expressible number), it does not have existence as either the one or the other; or, alternatively, it could be included in either. In a sense, it can be considered both 'a' and 'b', but paradoxically 'a' defines itself by 'not being b', from which it has been detached. So, it could not be 'b' but, at the same time, it is not something 'other than b', and so it can also be 'b'. But, then again, 'b' defines itself by not being 'a', and so it cannot be 'a'. However, since it is not 'something other than a', it can also be 'a'. So, we obtain this contradictory result that it is 'a' and 'b', but if it is the one it could not be the other. Just the same as the 'round square', we figure out something in the middle of the opposition between round and square – something that actually cannot be, since if it is round it is not square, and vice versa. Even at a predicative level, and even as a 'so-sein' in Meinongnian terms, it is contradictory, since it is so and not so at the same time. Is it not precisely this position we are somehow imagining? Could that do? I will leave it here, since I am aware this might strike one as slightly strange but do please give it thought. With this, I believe we have ordered our ontological picture without doing wrong to the extremely important distinction between the existent and the nonexistent in Russellian experiential terms, while at the same time making room for some of the Meinongian insights. Meinong's non-existents (including fictions, possibles, pure non-existents, and impossibles) do not have room in our ontology, for which experientiality, as both Russell and Kant claimed, is the basic requirement. Their presumed existential quantor is a non-saturated one, as we might put it. Unlike Meinong, who explicitly denied we had to do with representations (1988: §4, p.9) 28, we assigned them a place at the representational level, where picturing what is not part of the experiential world and distinguishing it from what 30 is, is not absurd; furthermore, we came to conclude that even the stability of our actual referential world owes much to such a representational level too. Reality, as we understand it, would not be the reality it is without it. 6. Final thoughts The picture that emerges from the deliberations above is one in which our representational thinking about objects – real or fictive, possible, impossible, or non-existent – which both Meinong and Frege (with the exception of the impossible in the last case) took to be objective, shares the same basic structure as our dealing with mathematical numbers. That is, in thinking about some such individual, we would be applying a certain formal structure to some units that are made available in representational modus as something external, and we are ultimately operating with numbers.29 In addition, the other way around, when we do mathematics, we are, at the end of the day, thinking about reality and its possibilities, or even impossibilities, to better understand it. Pretending that with our rational reconstruction of such a representational level (which we take for granted but do not experience as such epistemically) we would have to do with an enhancement of the world of experience amounts to the same kind of failure Kant so carefully separated away in his Critique of Pure Reason. The confusion is between transcendental reconstruction and transcendent knowledge beyond the realm of experience. In the first case, we are not acquiring any real knowledge. We are rather reconstructing what has to be the case for this cognitive activity, characteristic of our knowledge and thinking about the world, to be the way we experience it. Moreover, we do this in the cognitive terms we understand, figuring out the conditions that would make it possible, just as we try 31 to figure out the likely forces behind some events in the world. Of course, we ourselves belong to that experiential world, as does our brain, but we cannot properly acquire experiential knowledge about how we think. Thinking is an experience, but how it occurs is not30, just as are experiences those of other internal events, such as pains, pressures, or emotions, not our capturing of them. We can have second-order thoughts about our speaking and thinking or our emotions of which we are aware, as some have suggested,31 but there is no experience of how we come to do so. This is more a matter of inferring that we must have done it, since we are aware of them. The representational structure of our thinking about existent and non-existent objects or numbers is something we would become aware of in an inferential sense: it must be like that. We know we think in such a way, but how we manage to do so is a later re-enactment. If we are thereby right, it does take place, but our knowledge of it is no direct experience, and we cannot claim to know it to be. Therefore, it is not true that there are any such external objects or numbers, the weeds ought to be purged in this sense, not merely domestically arranged. But it is true that we must represent them as being (or as lacking). Finally, it might be claimed that our own representational forces are part of the world, and they indiscriminately are so, just as any other forces we exert, but they generate no further realities beyond themselves. 7. Literature Berto, Francesco, 2008, "Modal Meinongianism for Fictional Objects," Metaphysica, 9: 205–218. Bourgeois, V.W. 1981. "Beyond Russell and Meinong." Canadian Journal of Philosophy 11 (4): 653-666. 32 Chisholm, R. 1973. "Homeless Objects." Revue Internationale de Philosophie 27: 207-223. Crane, T. 2013, The Objects of Thought. Oxford: Oxford University Press. Frege, G. 1884. Grundlangen der Arithmethik. Hamburg: Felix Meiner Verlag. Frege, G. 1884. Foundations of Arithmetic. 2nd ed. New York: Harper & Brothers Harper Torchwoods (1953). Jaquette, D. 1982. "Meinong's Theory of Defective Objects." Grazer Philosophische Studien 15: 1-19. Jaquette, D. 1996. Meinongian Logic. The Semantics of Existence and Nonexistence. Perspectives in Analytical Philosophy 11: Berlin–New York: de Gruyter. Kant, I. 1781. Critique of Pure Reason. Cambridge: The Cambridge Ed. of the Works of E. Kant (1998). Kaplan, D. 2005. "Reading 'On Denoting' on its Centenary." Mind 114 (456): 933-1003. Kripke, S. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press. Lambert, K.1974. "Impossible objects." Inquiry 17: 303–14. Lambert, K. 1960. "The Definition of E! in Free Logic." Abstracts: The International Congress for Logic, Methodology and Philosophy of Science. Stanford: Stanford University Press. Meinong, A. 1888. Über Gegenstandstheorie Selbstdarstellung. Hamburg: Felix Meiner Verlag. 33 Parsons, P. "A Prolegomena to Meinongian Semantics." Journal of Philosophy 71(16): 561-580 Priest, G., 2005. Towards Non-Being. The Logic and Metaphysics of Intentionality. Oxford: Clarendon. Quine, W. v. O. 1953. "On What there is." From a Logical Point of View: 1-20. Harvard: Harvard University Press. Ramírez, O. 2012. "Boghossian's Blind-Reasoning Conditionalization and Thick Ethical Concepts." Ethics in Progress 3(1):31-52 Ramírez, O. 2018. "Between Witches, Angels and Unicorns. The Possibilities of Expanding Russell's Existential Analysis." ELogos 25(1): 4–15. Ramírez, O. 2020a. "Numbers, Empiricism and the A Priori." Logos and Episteme. 11(2): 149-177. Ramírez, O. 2020b. "I do not believe in Meigas but there are such." E-Logos 27(1): 4-20. Recanati, F. 2000. Oratio Obliqua, Oratio Recta. Cambridge MA: MIT Press. Recanati, F. (2018) "Fictional, Metafictional, Parafictional." Proceedings of the Aristotelian Society 128(1): 25-54. Routley R. and V. 1973. "Rehabilitating Meinong's Theory of Objects." Revue Internationale de Philosophie 27: 224–54. Russell, B. 1905. "On Denoting." Mind New Series 14: 479-93. Russell, B. 1918. "The Philosophy of Logical Atomism". The Monist 29: 190222. Walton, K. 1990. Mimesis as Make-Believe: On the Foundations of the Representational Arts. Cambridge MA: Harvard University Press. 34 1 The expression 'Heimatlose Gegenstände' is Meinong's own. See Meinong 1907. 2 This requirement, of course, requires some care since non-harmonic concepts (among which are the quasi-existences mentioned later) characterise themselves, precisely, by an imbalance between their introduction and elimination rules that would appear to justify illegitimate existential claims. 3 The identity requirement, pressed emphatically by both Frege (1884) and Quine (1969), as well as the spatio-temporal condition, that Quine underwrites too, are here necessary though not sufficient conditions, since numbers, for example, would not appear in my account (following criteria a), b) c)) as entities ordinarily taken to exist. 4 Note that the difference between Phlogiston and a fictional entity is that (unlike our notions of Darth Vader or Madame Bovary) our very idea of Phlogiston considered it to be a chemical substance that was part of the experiential world. That is, it was expected to be experientially detectable (at least at some point and time) and thought to have already a causal impact on the world. Once this is proven wrong, the kind of entity we meant with Phlogiston ceases to exist. Someone might indeed invent a story in which a fictional chemical substance with the name 'Phlogiston' is taken to exist (in the fiction) but, since it would no longer have the pretence to be part of the experiential world, it would not be the same. Such 'pure non-existents' also differ from 'Quasiexistents' in the fact that there is no specific identifiable experience any more on whose behalf they are considered indirectly proven. 5 With this term, I clearly do not refer to what Meinong (1988:10-11) characterised as 'quasi-beings' (Quasisein). I am, actually, not following any given characterisation at all, but referring to a distinction previously made in Ramírez (2018: 5) 6 Ramírez (2018, 2012) 7 Some have argued that music, for example, is a merely temporal experience, but this is disputable since sound waves do seem to be present in some locations. 8 I will use 'Being' and 'Non-Being' capitalized when used as substantives, such as in 'has Being or has Non-Being'. Otherwise I will use the non-capitalized 'being' or 'non-being' both as adjectives in "an object of the non-being sort" or to speak of individual 'beings'. 9 These are my own translations from the original German text. 10 That he does not mean merely existence in the representation; see passages such as this: (...) that the object possibly needs the representation 'not to exist', just as little as to exists, and even that, just to the extent as it should require of 'being represented' maximum an existence existence in the representation, that is 'pseudo-existence'as a result (Meinong 2018: §4, 9). 11 Actually, I am not interested at present in the difficulties of determining which description would be the adequate reconstruction of a proper name, or how it is that individuals with differing 35 information manage to refer to the same individual. Rather, my focus is on how we prove whether the individual who we are attempting to refer to by some, call it, 'ideal description' is there or not. Of course, there can be differences in the particular aspects being proved by certain individuals depending on the information they have. Nevertheless, the way they are proved, in general, by human beings, can be the same. This is so even in the limited case where all someone might have as a description is that there was someone baptised as 'Holmes'. 12 Such a formulation might suit the case where an existential claim is made that describes an apple with such and such properties, and we then saturate the empty space with a fake apple as the unique one satisfying the specific characteristics of the description. Such an 'apple' could be seen as really existent though as a fake. It might be supposed that regarding a painted picture of Sherlock, put in place of the description could do for its existence as well, we could pretend it is the individual we are referring to. But since the paper figure would not satisfy the descriptions attributed to Sherlock Holmes, it would not do either. 13 For example, other defenders of the pretence view, such as Recanati (2000). 14 According to Meinong, while real individuals are complete, fictional individuals and possible ones are not. We just have as complete a characterization as the description goes and that leaves many informational gaps: did Sherlock have an ant? Was he ever in Albacete? There can be no true or false answer to that. 15 I found Recanati's (2000) proposal to solve this problem by appealing to descriptive files very interesting, and he is probably right that we store files that way too. However, I think his proposal is not enough for several reasons. First, such files need not imply taking for existent and referring all along to the individual the file is about, the one satisfying the corresponding descriptions. Second, referring to such an individual as existent requires us making sense of its position and its possible further moves, possible future encounters with ourselves or others in other places in a consistent and timely manner. This requires, I believe, activating some spatio-temporal representational coordinates. Therefore, this position might be complementary to his. Actually, Recanati (2018), in discussing parafictional discourse, poses precisely the problem I allude to in defence of a 'presumption' instead of a 'pretence' view. The parafictional use possibly allows a better appreciation of the point. As Recanati stated, in parafictional uses, we are not pretending; we are taking the claims to be true about a given object, for whose purpose the representational object in my picture very well serves. Of course, since we move at the representational level, neither objects nor properties are real, but just in representational modus. Actually, Recanati (2000) mentioned a proposal that defends the existence of 'dot objects.' I do not know enough about that position, but maybe it comes closer to what I am proposing. 16 In my account we are not simply linguistically pretending that there is an individual such and so, and pretending sentences about it to be true, but we are actually literally representing some such individual occupying a given space, having a continuity through time, etc. and truly referring to it. 17 See footnote above on Recanati. 18 Kaplan (2005) considered that Russell's analysis implied no ontological commitment and could be applied to non-existents. I believe that goes completely against Russell's very idea. Nevertheless, I have been applying it at both the representational level and the experiential level, not at all because it indifferently applies to both in equal form, but because if we apply the Press modifier to existence, a Press modified version of Russell's sentence lends itself to be used in this context too. 19 This mixed character explains why at the experiential level in the moment of acquaintance we can directly refer a lá Kripke to 'Gödel', for example, while later on any explanation of who we mean, at that level, for those who lack direct acquaintance, must be in descriptive terms, even if the description reduces to the individual that was named Gödel at tn in place p. At the same time, though, we have a sense that we can keep on directly referring to him, because at the representational level, in keeping a corresponding representative of Gödel, we do. 20 'Denn der Begriff, dem die Zahl beigelegt wird, grenzt im Allgemeinen das unter ihn Fallende in bestimmter Weise ab. Der Begriff „Buchstabe des Wortes Zahl" grenzt das Z gegen das a, dieses gegen das h, u. s. w. ab.' (Frege 1884: § 54, 42). 21 To this point too Ramírez (2020a:160, footnote 27) 22 I use 'Intuition' with a capital I to refer to the Kantian notion, to separate it out from the mere idea of 'intuition' as a presumed alternative way of acquiring knowledge. 23 Ramírez 2020a:161-168 24 Unfortunately, I cannot enter to comment on the differences of my account here with the modal proposals offered by Berto (2008) and Priest (2005), but I guess they will be apparent. 25 We can distinguish epistemological and ontological uses of 'possibility'. This can be due to our knowledge: something possibly exists, but we do not know. Or it can be an ontological matter: 36 something does not exist, but it possibly could. The claim affects surely the second case. However, since we are the ones who represent reality according to our knowledge, at the practical level ignorance of whether something is the case amounts to not counting it as real either. 26 I am basing myself in this section in both, Ramírez 2020a and 2020b, here specifically in 2020a:169-170). 27 Compare with Ramirez (2020b:18-19) 28 Text quoted in footnote 10. 29 I would not want to commit to fictionalism in mathematics, since this representational aspect is not simply pretence, but belongs to the very constitutive way of our knowledge of the world. 30 A similar line of reasoning concerning this point is to be found in Ramírez (2020a:176-177) 31 In a sense, Recanati (2000) captures this idea through his notion of 'metarepresentation'. However, I am not completely sure if he understands it the same way. To be sure, the notion of representation in this paper, more akin to the Kantian representation in Intuition, is different from that in Recanati's picture.