© 2015 The Author. Journal compilation © 2015 Institute of Philosophy SAS Organon F 22 (Supplementary Issue) 2015: 19-38 Heidegger's Logico-Semantic Strikeback ALBERTO VOLTOLINI Department of Philosophy and Educational Sciences. University of Turin Via S. Ottavio 20. 10124 Turin. Italy alberto.voltolini@unito.it ABSTRACT: In (1959), Carnap famously attacked Heidegger for having constructed an insane metaphysics based on a misconception of both the logical form and the semantics of ordinary language. In what follows, it will be argued that, once one appropriately (i.e., in a Russellian fashion) reads Heidegger's famous sentence that should paradigmatically exemplify such a misconception, i.e., "the nothing nothings", there is nothing either logically or semantically wrong with it. The real controversy as to how that sentence has to be evaluated-not as to its meaning but as to its truth-lies at the metaphysico-ontological level. For in order for the sentence to be true one has to endorse an ontology of impossibilia and Leibniz's principle of the identity of indiscernibles. KEYWORDS: Impossibilia – logical form – metaphysics – nothing – ontology – possibilia – theory of descriptions. 1. Introduction As is well known, in (1959) Rudolph Carnap took some sentences by Martin Heidegger (1977) to be representative of typical examples of metaphysical pseudosentences, i.e., meaningless sentences that are such not only because they contain subsentential terms that are meaningless, but also because, although they are grammatically well-formed, they are logically illformed, i.e., they violate logical form or syntax. The most interesting case discussed by Carnap is a sentence Carnap ascribes to Heidegger: (1) The nothing nothings 20 A L B E R T O V O L T O L I N I for it paradigmatically exhibits both flaws.1 According to Carnap, (1) indeed is not only meaningless because it contains the meaningless predicate "nothings", but also because from a logical point of view the (quasihomophonous) expression "nothing" occurs in it misleadingly. For as regards logical form, this expression is not used in (1) in the only logically correct way it may be used; namely, as a quantifier, as it occurs in negative existentially quantified sentences of the kind "there is nothing that Fs", "(~∃x)(Fx)". Rather, it pretends to be used as if it were a singular term. Thus, it precisely contributes to yielding a logically ill-formed sentence. From Carnap onwards, in some philosophical quarters that sentence or a close reformulation of it has become the paradigm of a nonsensical sentence.2 1 I say "ascribes" for Heidegger's real sentence is "the nothing itself nothings" [Das Nichts selbst nichtet]. In point of fact, Carnap (1959, 69) includes (1) as the last item in a long list of sentences from Heidegger (1977) that for him should be ranked as metaphysical pseudosentences. Yet the other sentences of the list are less representative than (1) in their being metaphysical pseudosentences. For they allegedly exhibit just the first kind of flaw-i.e., they allegedly violate logical form only. Moreover, the reason why such sentences allegedly violate logical form is for Carnap the same as with (1), i.e., they again contain the expression "nothing" (or some cognate expressions) as illogically used. Thus, the way out of this 'no logical form'-charge it will be here provided for (1) also applies to these other sentences. 2 See for instance the way Dennett (1987, 164) makes reference to the sentence "Nothing noths". In what follows, it will be argued that Carnap was wrong on both counts. That is, it will be first of all claimed not only that (1) may be read in a logically correct way, but also that such a way is its suggested reading. So, once (1) is appropriately understood, there is no problem with its logical form. Moreover, it will be claimed that the predicate "nothings" is definitely meaningful. For the present purposes, this is enough. Yet one may even say that, if one endorses certain metaphysico-ontological views about impossible denotata and their identity, (1) can turn out to be not only meaningful, but also true. Admittedly, these views are rather controversial, as we will see soon below. Yet the controversy on this concern precisely regards metaphysico-ontological preferences, not semantic issues. Carnap's challenge is won if (1) is both logically well-formed and meaningful, regardless of whether it is true. H E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 21 Before starting, a caveat. The present reconstruction of the situation at issue is meant to be theoretical, not historical. First of all, there is no aim to show that the present reconstruction of (1) displays what Heidegger had in mind in uttering it. Heidegger himself might well have endorsed Carnap's remark that, like any other relevant "nothing"-sentence he mobilizes in (1977), (1) lies beyond logic.3 3 As Carnap himself underlies, by quoting again Heidegger (1977). Cf. Carnap (1959, 71). Nevertheless, it may well be the case that Carnap failed to grasp Heidegger's concern with the Nothing in its predicament of what is ruled out by whatever there really is, so that facing such a nothingness is what induces anxiety in human beings. Be that as it may, (1) will be here considered in abstraction from Heidegger's real concern with it. Rather, we will perform a theoretical exercise in order to check whether (1), taken as such, is really illogical and meaningless. Moreover, there is no intention to face the historical problem of whether Carnap might have found plausible the logico-semantic apparatus that will be here mobilized in order to retrieve both logical well-formedness and meaningfulness for (1). In conformity with our theoretical exercise, it will rather be assumed that Carnap raises a theoretical challenge concerning the very sentence (1) (and its cognates). As such, this challenge goes beyond Carnap's own logico-semantic preferences (involving e.g. his dislike for Russell's theory of descriptions). Once again, the question such a challenge raises is the following, rather abstract, one: in itself, is (1) really a logically illformed and meaningless sentence? As a result of this way of putting things, if on behalf of a Heideggeroriented philosopher (a certain fictional character: the Heideggerian, for short) one can show that, qua paradigmatic case of an alleged metaphysical pseudosentence, (1) rather is, once appropriately read, both logically wellformed and utterly meaningful, the burden of the proof is on a Carnaporiented philosopher (another fictional character, although closer than the Heideggerean to the real philosopher that inspires it, Carnap himself: the Carnapian, for short) to show either that, appearances notwithstanding, this is still not the case or that such a reading is either just a mere, rather arbitrary, option or anyway irrelevant. 22 A L B E R T O V O L T O L I N I 2. Logical well-formedness Let me start from the first problem envisaged above. Is it that clear that Heidegger's sentence is meaningless mainly because it is logically illformed? To begin with, suppose the Carnapian claimed that the Heideggerian logically misunderstands a sentence merely beginning with "nothing" in a subject-position by committing the Polyphemousian mistake of taking that expression as a singular term rather than as a quantifier expression. Yet this claim would contain a gross error.4 For note that (1) begins not with the mere nominal syntagm "nothing", but with a definite description containing that syntagm-"the nothing". In terms at least of its surface grammar, this definite description works as any other such description in which a noun is prefixed a definite article (like "the book", "the dog", etc.). Given this predicament, the Carnapian might well address the Heideggerian with a Russellian accusation, namely by charging her to have misleadingly equated (1)'s grammatical form, a subject-predicate form, with its logical form, where that definite description is eliminated away.5 Curiously enough (for what counts: see the Introduction's end), Carnap himself seems not very far from committing the above gross error. For on the one hand, he rightly reports Heidegger's dictum as (1), hence as starting with "the nothing" rather than with "nothing". Yet on the other hand, he addresses Heidegger with the joint accusation of both having produced a logically ill-formed sentence and having mistakenly maintained that "the nothing" works in it as a singular term, in such a way that the logical form of (1) coincides with its grammatical form, a subject-predicate form: "No(no)", as Carnap himself writes. Yet the Carnapian cannot charge the Heideggerian with the accusation of having produced a sentence that is logically ill-formed for it illogically mispresents a quantifier as a singular term. 6 4 As is well known, in the Odissey Ulysses leads the cyclop Polyphemus astray by letting him mean "Nobody blinded me" as a sentence containing "nobody" as a proper name and so forcing him to be misunderstood by his fellows, who correctly take "nobody" as a quantifier. 5 Cf. Russell (1905a). As we will immediately see, however, it would be wrong to address the Heideggerian with this accusation. Instead, one may say that perhaps Meinong (1960), or rather the early Russell (see later), implicitly conceived "the nothing" as a singular term such that (1)'s logical form is its grammatical subject-predicate form. 6 Cf. Carnap (1959, 70). Yet those two things cannot stand toH E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 23 gether. One such joint accusation would be correct only if (1) merely contained the nominal syntagm "nothing", not the definite description "the nothing". But since (1) contains "the nothing", the only accusation that Carnap might have addressed to Heidegger is that he mistook (1)'s logical form by equating it with its grammatical form,7 but not that (1) has no logical form at all.8 To begin with, on behalf of the Heideggerian suppose first that the definite description "the nothing" fits a Russellian account of definite descriptions, as any other such description. Second, suppose that the predicative element of that description expresses the property of being identical with nothing, or in other terms, of being a thing such that there is no thing that is identical with that thing-λx((~∃y)(y = x)). If this is the case, insofar as it figures in that description, "nothing" really serves a quantifying purpose. The above observations can be pursued a bit further. Once the Heideggerian positively endorses that a definite description occurs in subjectposition in (1), she can first of all show that no logical ill-formedness occurs in (1). Moreover, by reconstructing (1)'s proper logical form, she can positively account for the idea that (1) contains an expression in subjectposition that can logically function only insofar as it serves a quantifying purpose. Since this was the idea lurking behind Carnap's main reason for rejecting (1)'s well-formedness, the Heideggerian may well expect that the Carnapian charge that (1) is logically ill-formed is adequately countered. Let us see. 7 That Carnap well acknowledges to (1): cf. Carnap (1959, 69). 8 While reading (1959), it repeatedly seems as if Carnap saw no difference in the fact that the relevant sentence merely contains "nothing" or "the nothing" in subject position. Few paragraphs later, Carnap says that the sentence "the nothing exists" would be meaningless even if it were logically correct that "nothing" in it worked as a singular term (my italics). For that sentence would simultaneously ascribe existence and nonexistence to the entity allegedly denoted by the relevant singular term. As we will see later (cf. fn. 14), once (1) is appropriately understood, there is no problem in yielding "the nothing exists" an appropriate reading as well. Independently of this, however, Carnap was perhaps misled by the fact that Heidegger often capitalizes "nothing" (as we have seen, the German original for (1) is "Das Nichts (selbst) nichtet"); as if Carnap's opponent already considered "nothing" taken in isolation as a singular term, so that prefixing it by the definite article were for him simply a way to stress again that consideration. (In point of fact, we will later see that whenever a proper name "N" is prefixed by a definite article so as to get the nominal description "the N", its semantic value changes. But let us put this aside.) 24 A L B E R T O V O L T O L I N I Yet this is not the purpose "nothing" fulfils when it occurs alone as a nominal syntagm in any sentence of the kind "nothing Fs", namely, the purpose of letting that sentence say that there is no thing that instantiates the property expressed by the predicate "F". Rather, the quantifying purpose in (1) shows itself in the fact that the predicate in terms of which the description "the nothing" is Russelleanly analyzed contains a negated existential quantifier, so as to express the property of being a thing such, that there is no thing that is identical with that thing. So, when that description is analysed à la Russell, (1) turns out to be equivalent with: (1R) What is identical with nothing nothings. This formally becomes: (1FR) (∃x)((~∃y)(y=x) ∧ (∀z)((~∃y)(y=z) → (z=x)) ∧ Nx) where the quantifying purpose served by "nothing" is given by the second existential quantifier-"∃y"-in the formalized sentence, the quantifier contained in the predicate by means of which the definite description "the nothing" is eliminated away. Now, once (1) is analyzed as (1FR), no mistake in logical form arises. Thus, Carnap's first claim that Heidegger's sentence is logically ill-formed appears to be ungrounded. The Carnapian might here wonder why, even if she acknowledges that (1) contains the definite description "the nothing" rather than the mere nominal syntagm "nothing", she has to read that description as "the thing that is identical with nothing" and then to take (1) as equivalent with (1R), hence with (1FR). More explicitly, the Carnapian might reply as follows. Let us concede that (1) may be read as (1FR). The problem is, why should it be read as such. Although superficially "nothing" is a noun, logically speaking it expresses a quantifier. So, the alleged description "the nothing" is logically ill-formed. For it impossibly tries to form a nominal syntagm, "the nothing", to be accordingly analyzed à la Russell, out of a quantifier, "nothing", i.e., a second-order predicate, rather than out of a genuine noun, which in Russell's analysis disappears in favour (inter alia) of a firstorder predicate. Yet reading (1) as (1FR) is definitely not an ad hoc move. First of all, we may expect that the account here given for "the nothing" generalizes to other similar cases of definite descriptions involving quantifying expressions. Which is precisely the case. Consider the description "the someH E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 25 thing". Its quantifying purpose may well be accounted for by taking it as a shorthand for "the thing that is identical with something". Thus: (2) The something somethings may well be read as: (2R) What is identical with something somethings hence formally as: (2FR) (∃x)((∃y)(y=x) ∧ (∀z)((∃y)(y=z) → (z=x)) ∧ Sx). Moreover, the Carnapian should provide a justification for the thesis she implicitly assumes in her reply that an expression's contribution to the logical form of sentence in which it figures remains always the same, regardless of the syntactic position in which it occurs. For such a thesis grounds her claim that in the (for her logically ill-formed) description "the nothing", "nothing" works as a quantifier, as in any sentence of the form "Nothing F-s". Yet there are many cases in which an expression's contribution to the logical form of the sentence in which it figures changes according to its syntactic position in such a sentence. Consider a proper name "N". If friends of direct reference are correct, whenever it occurs in subject position, "N"'s contribution to the logical form of the sentence in which so figures is that of an individual constant. Yet when the definite article is prefixed to "N" so as to yield the definite description "the N", the name does not logically work as an individual constant, but as a predicate, typically expressing the property of being called 'N'. So, if we form a definite description by prefixing the definite article to a proper name, say, if we take "Obama" and by prefixing to it the definite article we get the definite description "the Obama", once we insert that description in a sentence it is not simply the case that we may read that description as a shorthand for "the individual who is called 'Obama'". Rather, this is its most plausible reading.9 9 Some say that one such description is what the corresponding proper name abbreviates. Yet there will be here no attempt at checking whether the so-called nominal description theory of proper names (cf. e.g. Bach 1987) is the correct semantic account of such expressions. Mutatis mutandis, therefore, the same will hold for any sentence containing the description "the nothing". 26 A L B E R T O V O L T O L I N I At this point, absent a problem with (1)'s logical form, the Heideggerian can even wonder whether that description, contextually defined à la Russell, has a Russellian denotation, i.e., an entity that uniquely satisfies it. Surprisingly enough, the answer is far from being straightforwardly negative. First, the existential import of (1R) may well be satisfied, once one understands the existential quantifier in a non-existentially loaded way, that is, as a mere particular quantifier. As many have stressed, in order for a Russellian analysis of definite descriptions to work, one does not have to require the existential quantifier involved in that analysis to range over things that exist in a substantial sense.10 By "substantial sense" one here means that the existence involved here is a property that makes a difference for the individuals having it. As many people believing in such a property claim, this property is a non-universal first-order property, i.e., a property that, like any other genuine first-order property, divides the overall domain of what there is into entities that have it and entities that fail to have it.11 Now, in Russell's account, to say that there is something that Fs merely means that the property of being F is instantiated. This says nothing as to whether in order for that property to be instantiated, whatever instantiates it must exist in a substantial sense-that is, whether the property must be an existence-entailing property, in the terminology inaugurated by Cocchiarella (1982). Now, this is the case precisely as regards the property of being identical with nothing. In order for this property to be instantiated, whatever instantiates it does not have to exist in any substantial sense. Thus, once one accepts an ontology that allows for things that do not exist in a substantial sense, it may well turn out that the existential import of (1R) is satisfied.12 Second, one may argue that the uniqueness import of (1R) is also satisfied. For suppose that there were more than one entity that had the property of being identical with nothing; that is, suppose that the property λx((~∃y)(y=x)) had multiple instances. Suppose further that such a property were the only property that qualifies such entities-the other features 10 As we will see soon below, Kaplan (2005) is one of the late supporters of this existential neutrality of Russell's theory of descriptions. 11 For this substantial sense of existence, cf. e.g. McGinn (2000). Substantial existence is what Williamson (2002) labels "existence in physical sense". If one rather sympathizes with Meinong (1960), this is the property of having direct or indirect causal powers. 12 Many people have claimed that identity properties are not existence-entailing properties: cf. again McGinn (2000), Williamson (1990). H E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 27 allegedly qualifying them merely amounting to mere different descriptions that make no real difference between such entities. This indeed is a plausible supposition, for it is hard to see how entities that differ from everything, themselves included, may have other properties.13 Granted, in order for this argument to be really convincing, one has to endorse a Leibnizian principle of the identity of the indiscernibles. In other terms, one has to assume that for any property F, if entity x has it iff entity y has it, then x and y are the very same entity. Given that (apart from selfidentity: see soon later) being identical with nothing is the only property such alleged entities possess, then Leibniz's principle indeed forces such entities to be the same thing. Now, it is well known that Leibniz's principle is controversial: why couldn't x and y share all their properties and nevertheless be two numerically distinct things? Be that as it may, if both the existential and the uniqueness import of (1R) were satisfied, it would turn out that the description "the nothing" has a Russellian denotation. If this were the case, those entities would no longer be distinct. How many entities can there be that differ from everything, themselves included, if this is the only property that allegedly qualifies such entities? 14 To begin with, in order for the property of being identical with nothing to be uniquely instantiated viz. for that description to have a Russellian denotation, that denotation must be an impossible entity. For in order for that property to be (uniquely) instantiated, even assuming a broad domain of possibilia is not enough. Any merely possible entity, that is, any entity which does not substantially exist but which might have done so, does not instantiate the property of being identical with nothing. For it will instead instantiate the opposite property of being identical with something- For the present purposes, however, one can remain neutral not only on whether that argument is convincing, so that the uniqueness import of (1FR) is satisfied, but also on whether the existential import of (1FR) is satisfied, so that "the nothing" denotes. 13 Apart, as we will immediately see, the property of being identical with something. Consider e.g. the description "the nothing that I like". As many claim, since this description involves the intentional predicate "to like", the fact that one applies this description to x yet fails to apply it to y does not entail that x is not y. 14 As a result, far from being meaningless because of its contradictoriety as Carnap claims (cf. fn. 8), the further Heideggerian sentence "the nothing exists" turns out to be true, once meaning "There is [in an existentially unloaded way] only one thing that is identical with nothing". 28 A L B E R T O V O L T O L I N I λx((∃y)(y=x)). The merely possible offspring of (a certain sperm of) Brad Pitt and (a certain egg of) Penelope Cruz, for instance, who does not substantially exist but might have done so, is not such that there is nothing that is identical with him; trivially, he is identical with himself. Yet consider now impossible entities, that is, entities that not only fail to substantially exist but also could not have done so. Well, only an impossibile can instantiate the property of being identical with nothing. For one such entity will be something that is made impossible precisely by the fact that it instantiates not only the property of being identical with nothing, but also, like any other entity whatsoever, the property of being identical with something. As stated before, this is not such a big problem for the Heideggerian once she accepts a non-existentially loaded reading of the particular quantifier, or in other terms, once she accepts that the overall domain of what there is also contains entities that do not exist in a substantial sense. Yet the Heideggerian has to face a more serious problem. If the alleged impossible denotation of the description "the nothing" also instantiates, like any other entity, the property of being identical with something, then it is not the case that it instantiates the property of being identical with nothing. For if our entity is identical with something, then in point of fact it is not the case that there is nothing it is identical with! Or, if you like, it is true both that such a thing is such that nothing is identical with it and that such a thing is such that something (namely, that very thing) is identical with it. So, how can one say that "the nothing" has a denotation, let alone an impossible one, if the existential import of the Russellian paraphrase involving the description is far from being satisfied, or if you like, it is both satisfied and not satisfied? As one may easily see, this critique is reminiscent of Russell's famous criticism against Meinong to the effect that Meinongian nonexistent objects are to be ruled out of the overall ontological domain insofar as they violate the Law of Non-contradiction. Consider two paradigmatic examples of such objects, namely the square that is not a square and the existent present king of France. The former is such that it is both the case that it is a square and that it is not a square. The latter is such that it is both the case that it exists and that it does not exist. As they violate the Law of Non-contradiction, they are no genuine entities.15 15 Cf. Russell (1905a,b). As is well known, Russell's original example involved the case of the round square. Yet in order to avoid the problem of whether the fact that the So according to the criH E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 29 tique in question, the same holds of the thing that is such that both it is the case that nothing is identical with it and it is not the case that nothing is identical with it. For something is identical with it, namely itself. As said before, there is here no particular interest in holding that "the nothing" has a denotation. On behalf of the Heideggerian, one merely has to stick to the idea that sentences containing that description, like (1), are logically well-formed. Yet the problem the above critique arises may be successfully dealt with by slightly amending the Russellian account of (1) put forward before. This amendment can be endorsed by a Heideggerian who adopts the usual device Meinongians use to dispense with Russell's criticism: an impossible entity is ontologically contradictory-for some pair of property P and its complement non-P, it possesses both-but it is not propositionally contradictory-it does not involve that both a sentence "p" and its negation "~p" are true. Let us see.16 Like Russell's criticism to Meinong, the above critique presupposes, as we have done here all along, that the negation involved in mobilizing the expression "being identical with nothing" is propositional and not predicative: that is, it attaches to sentences rather than to predicates. Yet, as Meinongians do to Russell, the Heideggerian may well respond to the above critique that, as far as impossible objects are concerned, the negation there involved is the predicative and not the propositional one. So, Meinongians say, the square that is not a square is not something such that it is both the case that it is a square and that it is not a square. Rather, it is something that is both a square and a non-square. Analogously, the Heideggerian may say, "the nothing" still has an impossible denotation. For it is not the case both that nothing is identical with such a denotation and that something is identical with it (i.e., it is not the case that nothing is identical with it). Rather, that denotation is something that is both identical with something and non-(identical with something), i.e., non-identical with everything. In this respect, like any impossibile for Meinong, the impossible denotation of "the nothing" violates the objectual version of the Law of Non-contra- round square contains incompatible determinations really makes it a contradictory object, Russell's example is reformulated in terms of a case of a Meinongian object that really is in some sense (as we will see immediately below, an objectual rather than a propositional one) a contradictory object. For this common policy, cf. e.g. Thrush (2001, 160). 16 For this Meinongian move cf. e.g. Simons (1990). 30 A L B E R T O V O L T O L I N I diction-for any property P and its complement non-P, an object cannot have both-but not the propositional version of that Law-for any sentence "p" and its negation "~p", both cannot be true, as the Russell-like critique instead presupposes. In other terms, the description "the nothing" may still denote an object, let alone an impossible one. For such an entity is impossible not because it is both the case that nothing is identical with it and that something is identical with it, but merely because it has both a property- being identical with something, λx((∃y)(y=x))-and its complement-being non-(identical with something), i.e., being non-identical with everything, λx((∀y)(y≠x)). This response requires some adjustments in what the description "the nothing" is a shorthand for, hence in the Russellian paraphrase of (1). Once it is read à la Russell, the description "the nothing" has to mean the same as "the thing that is non-identical with everything" instead of "the thing that is such that it is not the case that something is identical with it". In other terms, in the relevant predicate that contributes to eliminate away the description, the negation is not attached to an existential quantifier, as it has been supposed with the Heideggerian all along-"(~∃y)"-but rather to the sub-predicate "identical to something", "(∃y)(x=y)", so as to generate the complementary predicate "non-(identical to something)", i.e., "nonidentical to everything", "(∀y)(y≠x)". Thus, the quantifying import of "nothing" in that description turns out to be ascribed to a universal quantifier-"(∀y)". Putting all this together, for the Heideggerian that adopts the Meinongian distinction between predicative and propositional negation (1R) comes out true when read not as (1FR), but rather as: (1FRMH) (∃x)((∀y)(y≠x) ∧ (∀z)((∀y)(y≠z) → (z=x)) ∧ Nx). For according to such a Meinongianized Heideggerian there is just one thing that is non-identical with everything, a thing which is objectually impossible for it is also identical with something, and that thing nothings. Granted, even once the Meinongian distinction is adopted, not only endorsing the Leibnizian principle of the identity of the indiscernibles, but also allowing for impossibilia so as to get a Russellian denotatum for a description such as "the nothing" is hard to swallow. But, to stress the point once again, the problem now is no longer logical, let alone semantic; it is purely metaphysico-ontological. For the purposes of logical form, to read (1) as (1FRMH) is enough. Remember that the challenge against the Heideggerian is to show that (1) is both logically well-formed and meaningful, H E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 31 not to show that it is true-for which, a necessary condition is that "the nothing" has a Russellian denotation. Yet if on the behalf of the Heideggerian one has an ontological argument in favour of impossibilia-as some claim they have17 Once again, let us put aside what the real Heidegger had in mind. Yet first of all, if in this concern by "genuine singular term" the Carnapian -then there is no reason not to admit impossibilia into the overall domain of what there is. If moreover on the same behalf one also endorses the Leibnizian principle, there is no reason not to admit an impossibile to be the unique instantiator of the property of being non-identical with everything, hence to be the denotation of the description "the nothing". As David Kaplan magistrally claimed: In fact, although Russell's theory of descriptions is often described as a model for avoiding ontological commitments, it is essentially neutral with respect to ontological commitment. This, I think, is one of its virtues. Meinong believed that there is a nonexistent object that is both round and square. Russell didn't. This is an ontological dispute. If Meinong is right, and nothing else is round and square, then the definite description 'the round square' denotes, and there is no way of using Russell's theory of descriptions to remove this object from the ontology. If Meinong is wrong, then the definite description doesn't denote, and that's the end of it. (Kaplan 2005, 975-976) At this point, the Carnapian may try to launch a final attack against the Heideggerian with respect to (1)'s logicality. Let us concede, she might say, that Heidegger did not commit the Polyphemousian error of mistaking a quantifying expression-"nothing"-for a singular term. Yet, the Carnapian might go on saying, even if Heidegger deliberately mobilized a definite description-"the nothing"-this does not mean that the Heideggerian reading of it conforms to Russell's theory of descriptions. For what counts, Heidegger quite likely meant "the nothing" as a genuine singular term. But if the Heideggerian maintained that "the nothing" is a genuine singular term, then a logical mistake can still be ascribed to her with respect to (1); namely, the logical mistake Russell ascribed to anyone taking (1)'s subjectpredicate grammatical form to be identical with its logical form. 17 Cf. for instance Priest (2005), Iacona (2007). 32 A L B E R T O V O L T O L I N I means a Fregean singular term,18 Moreover, suppose that by "genuine singular term" the Carnapian instead means a directly referential device, i.e., a term that extinguishes its truth-conditional contribution in its referent-as logically proper names were for Russell and the early Wittgenstein, and proper names in general are for contemporary sustainers of the post-Kripkean new theory of reference. the accusation bounces back against the Carnapian herself. Suppose that "the nothing" is a definite description and moreover that a definite description, as Frege (1980) wanted, has not to be eliminated away à la Russell, for it logically is a singular term as much as a proper name. But then, not only "the nothing" turns out to be a genuine singular term, but also (1) is logically perfect. For its logical form turns out to be a subject-predicate form, as Frege claimed for any sentence containing a definite description in subject-position. 19 But then to accuse the Heideggerian of mistaking that definite description for a genuine singular term is rather unfair. If somebody must be charged with this accusation, this precisely is Russell himself: not the 1905 Russell of the theory of descriptions, but the 1903 Russell of the Principles of Mathematics. At that time, Russell explicitly took the expression "nothing" as directly referring20 to a certain denoting concept, [NOTHING].21 18 As a loyal Carnapian should do, given Carnap's (1949) intention of precisifying Frege's semantics. In point of fact, it would be very strange that a loyal Carnapian addressed this criticism to the Heideggerian. 19 To be sure, a loyal Carnapian could not take a genuine singular term as a directly referential device; she should take it in a way that does not distinguish between proper names and rigid definite descriptions, namely, as a singular term having qua its intension a constant function from possible worlds to individuals. But let us put this complication aside. 20 As is well known, Russell tends to use the term "to indicate" in order to speak of the relation between an expression and its denoting concept (1903, §51). Yet this is the same term he uses to speak of the standing-for relation that holds between a name and its designatum. Thus, following Salmon (2005) the indication relation may well be taken as a relation of direct reference between the expression and the item it indicates. 21 Cf. Russell (1903, §73). Curiously enough, in that very complicated paragraph of the book Russell puts forward the apparently contradictory theses that i) unlike most denoting concepts, the denoting concept [NOTHING] has no denotation and ii) that denoting concept is not nothing, i.e., it is not identical with its denotation (literally, it is not what itself denotes: for Russell, this is what the sentence "Nothing is not nothing", or better the proposition that sentence signifies, means). That tension may be removed H E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 33 Thus, one may well take (that) Russell also to hold that the definite description "the nothing", like any other definite description, directly refers to another denoting concept, one having uniqueness embedded in it: a determinative denoting concept, [THE [NOTHING]].22 That is, pretty much as for the 1903 Russell the definite description "the present Queen of England" directly refers to the determinative denoting concept [THE [PRESENT & QUEEN_OF_ENGLAND]], while the definite description "the present King of France" directly refers to the determinative denoting concept [THE [PRESENT & KING_OF_FRANCE]], so according to that Russell the description "the nothing" has to directly refer to the determinative denoting concept [THE [NOTHING]]-whatever that concept really amounts to.23 Now, if reading "the nothing" as a directly referential term entails endorsing the 1903 Russell's theory of denoting concepts, then the Heideggerian may well say that she declines to endorse that theory for the well known problems it raises in general-that is, also with respect to 'ordinary' determinative denoting concepts such as the two above [THE [PRESENT & QUEEN_OF_ENGLAND]] and [THE [PRESENT & KING_OF_FRANCE]]. 24 if one takes i) and ii) as respectively saying that such a denoting concept has no possible denotation and that such a concept does not coincide with its impossible denotation. Mutatis mutandis, the same would hold of the determinative denoting concept [THE [NOTHING]] that "the nothing" indicates. So, one may tentatively conclude that Russell at least adumbrated the idea, which I have hitherto reformulated in the context of his later theory of definite descriptions, according to which if the description "the nothing" had a denotation, it would be an impossible one. 22 The phrase "determinative denoting concept" comes from Orilia (2006, 195). See again Orilia (2003) for the notational convention I use in order to speak of denoting concepts. 23 Of course, this denoting concept does not come out as an absurd application of the import of the definite article to the denoting concept indicated by "nothing". Rather, that concept is something the description "the nothing" elliptically indicates. Pretty much as the denoting concept indicated by a description of the kind "the N.N.", where "N.N." stands for a proper name, which would be something like [THE [CALLED_'N.N.']]. 24 For the purposes of this paper, the well known controversy on whether Russell (1905a) criticism of his own previous theory of denoting concepts is sound may be set apart. For that theory has the preliminary problem that, appearances notwithstanding, it prevents one from speaking of the denotation of a denoting concept by using a description that directly refers to that concept. As a result, the Heideggerian may well be inclined to espouse Russell's later 34 A L B E R T O V O L T O L I N I theory of descriptions. Which is precisely what the Heideggerian has been ascribed here all along, by supplying her with a reading of (1) as (1R) taken as (1FR), or better, in terms of the previous adjustment, as (1FRHM). 3. Meaningfulness At this point, the Carnapian may put forward again his second claim against (1). That is, she may remark that in order for (1) to be true, it is not enough to allow the description "the nothing" to have a denotation, it must also be the case that such a denotation satisfies the predicate "nothings" contained in the sentence. But this can hardly be the case, for that predicate means nothing! Which was the second, admittedly weaker, reason, to deny (1) meaningfulness (the first reason being its alleged violation of logical form). Apparently, the Heideggerian may have an easy reply here. It is rather curious that the same philosophical quarters that deny meaningfulness to an apparently ad hoc predicate such as "nothings" have admitted meaningfulness to clearly ad hoc predicates like "pegasizes", or even "carnapizes" and "heideggerizes", which have been invoked to yield a systematic descriptivist theory of proper names. As is well known, Quine (1961) assumed that a proper name "N.N." is synonymous with the description "the N.N.-izer", i.e., "the thing that N.N.-izes". Once such a description is available, one can form a sentence out of it in which the predicate explicitly contained in the Russellian paraphrase of such a sentence that 'eliminates away' that description also figures with the same interpretation in the properly predicative part of the sentence, as follows: (3) The N.N.-izer N.N.-izes (∃x)(Nx ∧ ((∀y)(Ny → y=x) ∧ Nx) So why not allow for the meaningfulness of a predicate such as "nothings" along the same line or similar ones? Yet it would be wiser for the Heideggerian to reject this easy reply. First of all, as we have seen the Heideggerian never commits to the Polyphemousian idea that "nothing" works as a proper name in (1), so it would be odd for her to construe a predicate such as "nothings" out of a proper name, as "pegasizes" and the other infamous predicates are. Second, as far as I know, there can be only one reasonable non question-begging inH E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 35 terpretation of all the predicates of the same kind as "to N.N.-ize",25 according to which those predicates respectively express certain monadic properties of the individuals they are truly predicated of; typically, monadic individual essences, i.e., non-relational properties those individuals uniquely and necessarily possess.26 In this vein, the Heideggerian might say that the predicate "nothings" expresses a monadic individual essence of the thing the description "the nothing" denotes. Yet this would amount to explain obscura by obscuriora. There are many doubts as to what an individual essence in general is, that is, also as regards bona fide individuals like Carnap and Heidegger, Meinong and Russell, let alone a monadic individual essence.27 25 For a criticism to an interpretation reading a predicate of the kind "N.N.-izes" as "being identical with N.N.", which obviously does not explain away the name "N.N." Quine intended to get rid of, cf. Leonardi and Napoli (1995). 26 Notoriously, Kaplan (1975, 722-3) proposed haecceities as relational individual essences like the property of being identical with O such that a certain object O is its only possible possessor. One such property however presupposes that we already have its unique instantiator at our disposal. 27 The only plausible candidates for individual essences are relational non questionbegging properties like world-indexed individual properties (cf. Plantinga 1974), or actualia-dependent individual properties (cf. Rosenkrantz 1984). To grasp what is a monadic individual essence of an impossible entity is definitely an even harder enterprise. As a matter of fact, the Heideggerian has an alternative and more plausible reply at her disposal. Once the description "the nothing" is taken to mean the same as "the thing that is non-identical with everything", the predicate "nothings" may be analogously paraphrased as "is non-identical with everything", which is formally to be read as: "x is such that every y is non-identical with it". In other terms, (1FRHM) may be further analyzed as: (1FRHM′) (∃x)((∀y)(y≠x) ∧ (∀z)((∀y)(y≠z) → (z=x)) ∧ (∀y)(y≠x)). So, the whole sentence may be read as saying that the only thing that is such that everything is non-identical with it is also such that everything is non-identical with it. In point of fact, this is the most plausible interpretation of the predicate "nothings". An (admittedly colloquial) way of rephrasing Heidegger's sentence is: 36 A L B E R T O V O L T O L I N I (1′) The nothing is a nothing whose surface grammar is of the form "The F is an F". As any sentence of this form requires that the very same predicate with the same interpretation occurs throughout it, this is the case with (1′), hence with (1). In terms of the (admittedly controversial) hypothesis that "the nothing" denotes, this move yields a statement that is not only logically well-formed and meaningful, but also true. Granted, that truth is rather trivial-as when one says that the zip inventor is a zip inventor. Yet the Heideggerian may also read (1FRHM′) in a more interesting way, by treating the last occurrence of the universal quantifier "(∀y)" occurring in it as contextually restricted to the mere subdomain of possibilia. By means of this adjustment, the sentence would say that the only thing that is such that everything is non-identical with it, is also such that everything possible is non-identical with it. Incidentally, it is likely that such a reading would be welcome to a Heideggerian that insisted, in a very Heideggerian way, that what one talks about via "the nothing" is not a res, it is beyond the realm of the Seiende. In this reading, in fact, that insistence would not be a Heideggerian clumsiness. For it would express something rather clear: insofar as the thing that is non-identical with everything is no possible thing, it evaporates from the only reality that counts-the subdomain of possibilia-it nullifies itself. The nothing itself nihilates, as Heidegger's dictum is nowadays alternatively translated.28 To sum up. If what has been said here is right, then "the nothing nothings" is, pace Carnap, neither logically ill-formed nor anyway meaningless because of the meaninglessness of some of its subsentential components, notably its predicate expression. It may also turn out that the description "the nothing", once it is supplied with a Russellian account, has a Russellian denotation, provided i) one accepts a Meinongian distinction between predicative and propositional negation and moreover ii) she endorses the richest possible ontology one may conceive of, i.e., an ontology also of impossibilia, as well as iii) Leibniz's metaphysical principle of the identity of indiscernibles. But while appealing to i)–iii) goes toward show- 28 Cf. Heidegger (1977). H E I D E G G E R ' S L O G I C O S E M A N T I C S T R I K E B A C K 37 ing that (1) is true, it is not essential in order for Heidegger's vituperated sentence to regain a highly respectable status.29 29 Let us thank Francesco Berto, Andrea Iacona, Fred Kroon, Francesco Orilia, and Elisa Paganini for various important comments to previous versions of this paper. References BACH, K. (1987): Thought and Reference. Oxford: Clarendon Press. CARNAP, R. (1949): Meaning and Necessity. Chicago: University of Chicago Press. CARNAP, R. (1959): The Elimination of Metaphysics through Logical Analysis of Language. In: Ayer, A.J. (ed.): Logical Positivism. (Transl. from the 1932 German original by A. Pap.) Glencoe, IL: The Free Press, 60-81. COCCHIARELLA, N.B. (1982): Meinong Reconstructed Versus Early Russell Reconstructed. Journal of Philosophical Logic 11, 183-214. DENNETT, D. (1987): The Intentional Stance. Cambridge MA: The MIT Press. FREGE, G. (1980): On Sense and Denotation. In: Geach, P.T. – Black, M. (eds.): Translations from the Philosophical Writings of Gottlob Frege. (Transl. from the 1892 German original by M. Black.) Oxford: Blackwell, 56-78. HEIDEGGER, M. (1977): What is Metaphysics? In: Basic Writings. (Transl. from the 1929 German original by D.F. Krell.) New York: Harper & Row, 89-110. IACONA, A. (2007): Not Everything is Possible. Logic Journal of IGPL 15, 233-237. KAPLAN, D. (1975): How to Russell a Frege-Church. The Journal of Philosophy 72, 716729. KAPLAN, D. (2005): Reading 'On Denoting' on its Centenary. Mind 114, 933-1003. LEONARDI, P. – NAPOLI, E. (1995). On Naming. In: Leonardi, P. – Santambrogio, M. (eds.): On Quine. Cambridge: Cambridge University Press, 251-266. MCGINN, C. (2000): Logical Properties. Oxford: Clarendon Press. MEINONG, A. (1960): On the Theory of Objects. In: Chisholm, R. (ed.): Realism and the Background of Phenomenology. (Transl. from the 1904 German original by I. Levi, D.B. Terrell, and R.M. Chisholm.) New York: Free Press, 76-117. ORILIA, F. (2003): A Description Theory of Singular Reference. Dialectica 57, 7-40. ORILIA, F. (2006): Identity across Time and Stories. In: Bottani, A. – Davies, R. (eds.): Modes of Existence. Munich: Ontos Verlag, 191-220. PLANTINGA, A. (1974): The Nature of Necessity. Oxford: Clarendon Press. PRIEST, G. (2005): Towards Non-Being: The Logic and Metaphysics of Intentionality. Oxford: Clarendon Press. QUINE, W.V.O. (1961): On What There Is. In: From a Logical Point of View. New York: Harper & Row, 1-19. ROSENKRANTZ, G. (1984): Nonexistent Possibles and Their Individuation. Grazer Philosophische Studien 22, 127-147. 38 A L B E R T O V O L T O L I N I RUSSELL, B. (1903): The Principles of Mathematics. Cambridge: Cambridge U.P. RUSSELL, B. (1905a). On Denoting. Mind 14, 473-493. RUSSELL, B. (1905b): Critical Notice of: A. Meinong, Untersuchungen zur Gegenstandtheorie und Psychologie. Mind 14, 530-538. SALMON, N. (2005): On Designating. Mind 114, 1069-1133. SIMONS, P. (1990): On What There Isn't: The Meinong-Russell Dispute. In: Philosophy and Logic in Central Europe from Bolzano to Tarski. Dordrecht: Kluwer, 159-181. THRUSH, M. (2001): Do Meinong's Impossible Objects Entail Contradictions? Grazer Philosophische Studien 62, 157-173. WILLIAMSON T, (1990): Necessary Identity and Necessary Existence. In: Haller, R. – Brandl, J. (eds.): Wittgenstein: Towards a Re-Evaluation I. Vienna: Hölder-PichlerTempsky, 168-175. WILLIAMSON, T (2002): Necessary Existents. In: O'Hear, A. (ed.): Logic, Thought and Language. Cambridge: Cambridge University Press, 233-251.