Ontological Vagueness: Why It’s Impossible, and Why the Ontological and Semantic Consequences are Severe

	Among philosophers who work in metaphysics or semantics or both, it is widely—but certainly not universally—believed that there is no such thing as ontological vagueness, and that vagueness is therefore entirely a feature of thought and language. (Those who take this view often embrace David Lewis’s contention that vagueness is entirely a matter of “semantic indecision.”) We two authors maintain that there is a compelling case to be made for the claim that ontological vagueness is outright impossible; and of course, if it is indeed impossible then it is certainly not actual. We also maintain that the non-reality of ontological vagueness has radical consequences for both ontology and semantics—consequences whose severity has thusfar gone largely unappreciated in philosophy. Considered in themselves, these radical consequences might reasonably serve as grounds for a modus tollens argument against the denial of ontological vagueness—and thus as an argument in favor of it. But, since ontological vagueness is demonstrably impossible, those radical consequences instead must be accepted and embraced.
	We will begin by briefly setting forth a conception of vagueness that we claim is so compelling, once articulated and contemplated, that it is rightly regarded as a priori correct. We will then explain why this conception entails that ontological vagueness is impossible. We will devote the bulk of this paper to articulating the semantical and ontological consequences, and to describing the meta-metaphysical import of accepting those consequences as lessons to be learned in philosophy. Along the way we will describe a new metaphysical problem that arises in the wake of these lessons, and we will sketch a proposed solution to that problem.

1.	The Transvaluationist Conception of Vagueness
	In this section we will summarize some key aspects of the treatment of vagueness we call transvaluationism, which we elsewhere have articulated and defended at some length (see, e.g., Horgan 1995, 1998, 2010, Horgan and Potrč 2008, 2012, Potrč 2002). When one focuses directly on certain obvious-looking features of vagueness, we maintain—rather than becoming too quickly distracted by various potential formal-semantic approaches to the topic—one will find these features well nigh impossible to deny. Indeed, these features—which together constitute the transvaluationist conception of vagueness—are so compellingly obvious that transvaluationism is rightly regarded as a priori correct.
	Vagueness essentially involves sorites-susceptibility. I.e., for any vague constituent in language or thought, and for any putatively vague object or property or relation, there is a sorites sequence directly involving that item—a progression of statements, or of states of affairs (actual or possible), that generate a sorites-paradoxical argument. A second essential feature is what Mark Sainsbury (1990) calls boundarylessness—which involves the simultaneous applicability, to a sorites sequence, of the following two conditions:

The Difference Condition: Initially in the sorites sequence there are items with a specific vague status, and every predecessor of an item with this status has the same status. Eventually in the sequence there are items with the polar-opposite status, and every successor of an item with this status has the same status. No item in the sequence has both the initial status and the polar-opposite status.

The Transition Condition: There is no determinate fact of the matter about status-transitions in the sorites sequence.

	The items mentioned in the Difference Condition might be statements, for instance; and the corresponding statuses might be features like truth, falsity, definite truth, definite falsity, borderline truth/falsity, etc. Or the items might instead be individuals that differ only very slightly from their immediate neighbors in some specific respect (e.g., men each of whose immediate successor has one less hair on his head, or heaps of sand where each results from its predecessor by removal of one grain), and the statuses might be first-order attributes like being bald or being a heap.
	The Transition Condition involves, essentially, two conceptual aspects, one individualistic and the other collectivistic:

The Individualistic Same-Status Principle (ISS Principle): Each item in a sorites sequence has the same vague status as its immediate neighbors.

The Collectivistic Status-Indeterminacy Principle (CSI Principle): There is no correct overall distribution of vague statuses to the items in the sequence.

Given all this, vagueness thereby exhibits a certain specific kind of logical incoherence: viz., the mutual unsatisfiability of the operative principles (the Difference Condition, the ISS Principle, and the CSI Principle). The Difference Condition and the ISS Principle are pairwise incompatible; also, the CSI Principle and the ISS principle are pairwise incompatible if—as the Difference Condition requires—some items in the sorites sequence have a specific status.
	These status-principles, despite being mutually unsatisfiable, exert normative governance over semantically correct affirmatory practice in language and thought. Such normative governance involves two key aspects. First, proper use of vague words and concepts must conform to the following two prohibitory practice-standards for semantically correct affirmations—standards that prohibit one from assigning statuses in ways that would violate the ISS Principle or the CSI Principle:

The Individualistic Status-Attribution Prohibition (ISA Prohibition): Never attribute a specific vague status to an item in a sorites sequence and also attribute a different, incompatible, vague status to its immediate neighbor.

The Collectivistic Status-Attribution Prohibition (CSA Prohibition): Never affirm any determinate overall assignment of vague statuses to the items in a sorites sequence.

Second, the two prohibitory practice-standards are grounded not epistemologically, but rather semantically: not in ignorance of sharp boundaries (there are no sharp boundaries for vague statuses!), but rather in the ISS and CSI principles themselves. These status-principles are semantically “in force,” even though they cannot be mutually satisfied by the respective items in a sorites sequence. They are in force in the sense that it would be semantically incorrect to engage in judgmental/affirmatory practice that violates them. Such status-assignment practice would be semantically incorrect because that assignment would be a violation of the ISS Principle and/or the CSI Principle.
	For vagueness to exist in thought or language, the Difference Condition and the Transition Condition both must be honored in affirmatory practice. Honoring the Difference Condition is something one does actively in one’s affirmings—viz., in one’s assignments of vagueness-involving statuses to some, but not all, of the items in a sorites sequence. Honoring the Transition Condition, on the other hand, is something one does passively—viz., by refraining from assigning any statuses at all to some of the mid-range items in the sequence (in accordance with the CSA prohibition), and also refraining from ever assigning incompatible statuses to immediately adjacent items (in accordance with the ISA prohibition). In short, vagueness in thought and language is possible and actual because people can, and do, engage in vagueness-involving affirmatory practice that is normatively governed by the Transition Condition and the Difference Condition—notwithstanding the fact that vagueness harbors an inherent form of logical incoherence, involving mutually unsatisfiable status-principles.
	Transvaluationism about vagueness comprises the various claims we have made thusfar in this section. Those claims, when contemplated directly, are extremely difficult to deny; rather, upon reflection they recommend themselves a priori—as articulating conceptually necessary truths about vagueness. Admittedly, it is jarring to realize, and to recognize as a priori knowable, that vagueness harbors a form of logical incoherence. And most philosophers who have written about vagueness have managed to avoid coming to this realization-cum-recognition—usually, we suspect, because of some combination of the following tendencies: (i) failing to distinguish between (a) the (generic) kind of logical incoherence constituted by mutually unsatisfiable status principles and (b) the familiar kind of logical incoherence that consists in logical commitment to rampant contradictions, (ii) implicitly presupposing that logical incoherence can be completely avoided by eschewing both classical logic and classical two-valued semantics, (iii) becoming distracted by various formal-semantic techniques, (iv) succumbing to the seductively comforting connotations of the expression ‘semantic indecision’ (for those who contend that vagueness is entirely semantic, and never ontological), and (v) failing to appreciate that status principles that are mutually unsatisfiable can nonetheless ground mutually obeyable affirmatory-practice standards.
	An important corollary of transvaluationism (cf. Horgan Potrč 2008, Horgan 2010)—the first of various philosophical lessons we seek to emphasize in this paper—is this (labeled ‘L1’ for ‘Lesson 1’):

L1.	Any theoretically adequate approach to the logic and semantics of vagueness—any approach that thoroughly avoids commitment to arbitrary sharp boundaries among semantic statuses in a sorites sequence—must really be, not an alternative to the transvaluationist conception of vagueness, but rather an implementation of it.

In particular, this is true of what we call “iterated supervaluationism”—the kind of supervaluationism that treats its own metalinguistic categories as vague (and hence as themselves subject to supervaluationist semantics in a second-order metalanguage), and the semantic categories in the second-order metalanguage as vague, and so on ad infinitum, up through the metalinguistic hierarchy. Given L1, there is no hope of avoiding the inherent logical incoherence at the heart of vagueness, via some sort of fancy formal machinery. Rather, the best that can be sought from an adequate formal-semantic approach—an approach that thoroughly accommodates the boundarylessness of vagueness, and hence avoids positing any sharp boundaries among mutually incompatible semantic statuses in a sorites sequence—is that the formalism will quarantine the inherent logical incoherence, preventing it from tolerating unacceptable forms of inference such as sorites arguments.

2.	Why Ontological Vagueness is Impossible
	Another important corollary of transvaluationism, the second lesson for philosophy, is this:

L2.	Ontological vagueness is impossible.

The argument goes as follows. Although semantic vagueness is both possible and actual because vague affirmatory practice in language and thought can, and does, honor both the Difference Condition and the Transition Condition by being normatively guided by those mutually unsatisfiable requirements, ontological vagueness would require the outright satisfaction, by putative vague objects and/or putative vague properties and relations, of the Difference Condition plus the two constitutive components of the Transition Condition (viz., the ISS Principle and the CSI Principle). Consider, for instance, a sorites sequence involving a putative vague property F. In order for the Difference Condition and the ISS Principle to be jointly satisfied, initial items in the sequence would have to possess F, final items in the sequence would have to possess the polar-opposite property ¬F, no item could possess both F and ¬F, and each item possessing F would have to be such that its immediate neighbors also possess F—all of which is jointly impossible. In addition (to accommodate the CSI Principle), it further would have to be the case that not every item has some F-involving status—which just compounds the impossibility. Therefore, ontological vagueness is impossible: there cannot be vague objects, vague properties, or vague relations in the right ontology.

3.	Supervaluationism and Ontological Regimentation: Semantics in the Ontology Room?
	Metaphysicians have often pursued versions of what Quine called “regimentation.” Roughly and generically, the idea is this. Take some claim that one would like to treat as true, which in its surface grammatical form seems to posit certain objects, properties, or relations that one does not wish to recognize. Give some account of why and how the statement is true, an account that itself eschews positing the offending putative entities. This can be done in the object language, by proposed paraphrase. Or it can be done via what Quine called “semantic ascent,” by articulating truth conditions in a way that avoids positing the offending entities. When this is being done specifically for an ontological purpose—being applied to discourse that appears to posit entities one seeks not to admit into the correct ontology, where the preferred regimentation only posits entities to which the theorist is ontologically committed—we will call it ontological regimentation.
	Recently, metaphysicians have sometimes distinguished between claims that are legitimate in various contexts of ordinary discourse and claims that are legitimate “in the ontology room.” We will adopt here the useful idiom of the ontology room. On our usage, to regard a claim as legitimate in the ontology room is to construe it (i) as genuinely ontologically committed to whatever items (objects, properties, relations, states of affairs) it appears ontologically committed to by virtue of its surface grammar, and (ii) as true when so construed. Ontological regimentation is thus a semantical project that one pursues in the ontology room. It is a way of accommodating as true, from within the ontology room, various claims that one would not regard as true if one construed them as being ontologically committed to the items to which they appear committed by their surface grammar.
	As we said at the outset, it is widely believed among contemporary metaphysicians that there is no such thing as ontological vagueness. Many who take this view, we suspect, are inclined to think that vague discourse and vague thought-content can be smoothly reconciled with the denial of ontological vagueness, via ontological regimentation. More specifically, we suspect, many think that such ontological regimentation can proceed by way of deploying supervaluationist semantics in the ontology room—where the items over which one supervaluates are non-vague entities that are regarded as belonging to the right ontology, such as non-vague physical objects, non-vague properties, and non-vague relations.
	But, given that ontological vagueness is impossible, the project of ontological regimentation of vague discourse via supervaluationist semantics cannot be carried out. And the point is fully generalizable: the project of ontological regimentation of vague discourse cannot be carried out any other way either. Let us elaborate. The argument takes the form of a dilemma.
	First Horn. Suppose one formulates supervaluationist semantics for vague discourse within a metalanguage governed by classical logic and classical two-valued semantics, and also in a way that posits only non-vague objects, properties, relations, candidate-referents for singular terms, and candidate-extensions for predicates—all of which are items that one regards as belonging to the correct ontology. Semantics articulated in this way would indeed constitute a form of ontological regimentation. However, it would run afoul of lesson L1 above: it would posit sharp transitions between the semantic statuses it posits, and thereby would fail to accommodate the status-boundarylessness inherent to genuine vagueness. (Although this approach would posit a semantic status other than truth or falsity—viz., the status neither true nor false—it also would be committed to two sharp semantic status-transitions, in any sorites sequence of vague statements: a sharp transition between the true ones and those that are neither true nor false, and another sharp transition between these latter and the false ones.)
	Second Horn. Suppose instead that one embraces iterated supervaluationism: one formulates supervaluationist semantics within a metalanguage whose key semantical claims are themselves construed as vague, and hence as reflexively requiring supervaluationist truth conditions themselves within a second-order metalanguage—and likewise for each successive level in the metalinguistic hierarchy, ad infinitum. Semantics articulated in this way can accommodate lesson L1; i.e., such semantics can aptly be regarded as an implementation of transvaluationism, and thereby as merely quarantining the inherent, generic, logical incoherence of vagueness—rather than somehow eliminating that form of logical incoherence. (Quarantining the logical incoherence is a matter of blocking reasoning that could lead to rampant contradictions, such as sorites arguments.) Given the impossibility of ontological vagueness, however, iterated-supervaluationist semantics cannot be correctly affirmed in the ontology room. For, even if the ur-elements posited by such semantics are non-vague items that one regards as belonging to the correct ontology (e.g., perfectly precise objects, or perfectly precise properties and relations) the semantics would also need to deploy vague expressions whose surface grammar carries apparent commitment to putative vague entities—expressions like ‘the set of eligible candidate-referents of the singular term “Tibbles”’, and ‘the set of eligible candidate-extensions of the predicate “cat”’. Metalinguistic statements that deploy such vague locutions, and that appear in their surface grammar to be positing vague items, putatively denoted by such locutions, cannot themselves be true when affirmed in the ontology room.
	Although the preceding argument is directed specifically at iterated supervaluationism (for purposes of specificity), the argument generalizes straightforwardly: any theoretically adequate semantical treatment of vagueness must apply iterative to itself at the metalinguistic level and on upward through the whole infinite metalinguistic hierarchy, since otherwise the account will end up going contrary to the essential nature of vagueness by positing sharp semantic status-boundaries; so, since any such iterative account must deploy vague language at every level in the metalinguistic hierarchy, no such account can constitute an ontological-vagueness eschewing ontological regimentation of vague discourse. We thus have arrived at a third lesson of transvaluationism:

L.3. No theoretically adequate approach to the logic and semantics of vagueness can constitute an ontological-vagueness eschewing ontological regimentation of vague discourse.

	We should emphasize that we do not regard L.3 as an objection to reflexively iterative semantical accounts of vagueness, or an objection to iterated supervaluationism in particular. Some such account is apt to be important and valuable for various theoretical purposes. Indeed, such an account is apt to be useful for certain purposes in metaphysics—a theme to which we return below. Nonetheless, there is no hope of deploying such an account to provide an ontological regimentation of vague discourse.

4.	Three Species of Truth: Direct Correspondence, Ontologically Regimentable Indirect Correspondence, and Ontologically Non-Regimentable Indirect Correspondence
	Truth, understood generically, is a correspondence relation: a relation between an intentional/representational item (a proposition, a statement, a thought-content, or some such) and the world. The intentional/representational item constrains the range of potential ways the world might be that constitute potential truth-making ways, vis-à-vis that item. The item is in fact true just in case the actual way the world is belongs to that range or potential truth-making ways the world might be.
	In the ontology room, where the surface grammar of one’s discourse signals genuine ontological commitment, truth is always direct correspondence. An atomic statement of the form ‘Fa’ directly corresponds to the world just in case there exist a unique object o in the correct ontology, and a unique property P in the correct ontology, ‘a’ denotes o, ‘P’ expresses F, and o instantiates P; the corresponding statement of the form ‘~Fa’ directly corresponds to the world just in case there exist a unique object o in the correct ontology, and a unique property P in the correct ontology, such that ‘a’ denotes o, ‘P’ expresses F, and o does not instantiate P; and so forth. In short, direct correspondence is the species of truth that arises when the truth-making ways the world might be involve items in the correct ontology that are directly picked out or quantified over by a statement’s grammatical “positing apparatus”—e.g., singular terms, predicates, and quantifiers.
	Statements that deploy positing apparatus that does not carry genuine ontological commitment to the apparently-posited items, and that are subject to ontological regimentation, also are sometimes true. Their species of truth is not direct correspondence, however, because there do not exist items in the right ontology answering to all of the singular terms, predicates, and quantifiers in such a statement. Rather, their truth is a form of indirect correspondence to the world—where this correspondence is explicable via a regimentation that itself deploys language that itself corresponds to the world directly. We will call this species of truth ontologically regimental indirect correspondence (for short, “OR indirect correspondence”).
	Suppose, for instance, that one were to propose an ontological regimentation of vague discourse via standard, non-iterative supervaluationism. (One’s metalanguage would be governed by classical logic and classical two-valued semantics, one would deploy only non-vague terminology in one’s metalanguage, and one would quantify in one’s metalanguage only over non-vague items that one regards as belonging to the correct ontology—e.g., non-vague objects, non-vague properties and relations, and non-vague sets built from these.) Under such an ontological-regimentation program, what would constitute the truth of (for example) the statement ‘Tibbles is a cat’? Presumably, the putative individual Tibbles, if it were itself an item in the right ontology, would be vague in certain respects—e.g., with respect to synchronic composition, and with respect to diachronic spatiotemporal boundaries. Likewise, the putative property being a cat, if it were itself an item in the right ontology, also would be vague in certain respects—e.g., with respect to range of instantiation. (Think of various creatures in the evolutionary ancestry of contemporary cats.) Thus, given that ontological vagueness is impossible, the truth of ‘Tibbles is a cat’ cannot consist in direct correspondence to the world; ‘Tibbles is a cat’ could not be correctly affirmed in the ontology room. Rather, this statement’s truth would be a matter of ontologically regimental indirect correspondence, consisting in the putative fact (supposedly articulable in the ontology room) that under every eligible assignment A of referents to ‘Tibbles’ and ‘is a cat’—where the eligible referents all are non-vague individuals or non-vague properties that belong to the correct ontology—the statement is true-under- A.
	As we argued in section 3, however, standard supervaluationism is not a theoretically adequate semantical approach to vagueness, because it is committed to sharp semantic-status transitions—e.g., between the status true and the status neither true nor false, and between the latter and the status false. This goes contrary to the essential boundarylessness of vagueness. Moreover, as we also argued in section 3, lesson L.3 of transvaluationism obtains: no theoretically adequate semantical approach to vagueness can deliver ontological regimentations for statements deploying vague constituents.
	Well, then, can such statements ever be true? And if so, in what does their truth consist? One might try taking a radical, hard-line, nihilistic position on these questions by insisting that vague statements are simply never true. However, given the near-ubiquity of vagueness in human thought and human language—including much scientific thought and language—this hard-line position would be tantamount to claiming that almost nothing that humans have ever thought or said is true. We ourselves find such an approach repugnant. We much prefer to seek a way to “save the phenomena”—in this case, the phenomena concerning the numerous truth-attributions that are normally regarded as unproblematic.
	The appropriate alternative course is not far to seek, given that a viable and important distinction has already emerged between two species of truth, direct correspondence and ontologically regimental indirect correspondence. The alternative course is to recognize yet a third species of truth that is applicable to some statements—viz., a form of indirect correspondence with these three features: (1) the statement deploys positing apparatus that does not directly correspond to any items in the correct ontology, (2) the statement is not susceptible to ontological regimentation, and yet nonetheless (3) the statement is correctly affirmable under contextually operative semantic-affirmability standards. We will call this species of truth ontologically non-regimental indirect correspondence (for short, “ONR indirect correspondence”).
	Certain philosophical questions arise about what role(s) are played by items in the correct ontology, with respect to truthmaking in cases of ONR indirect correspondence. Questions also arise about whether the notion can successfully avoid potential threats of conceptual incoherence, vicious theoretical circularity, and the like. We will address such questions shortly. First, however, let us make some remarks by way of elaboration of, and further motivation for, the notion of ONR indirect correspondence as a species of truth.
	First, the third of the above three features that jointly delimit ONR indirect correspondence—viz., correct affirmability under contextually operative semantic-affirmability standards—is a feature common to all three species of the generic notion of truth; thus, it is exhibited too by both direct correspondence and OR indirect correspondence. By contrast, feature (1) is exhibited by both OR indirect correspondence and ONR indirect correspondence (but not direct correspondence), whereas feature (2) is exhibited by OR correspondence but not by either direct correspondence, or ONR indirect correspondence.
	Second, although it takes a certain amount of philosophical reflection about the nature of vagueness to come (perhaps reluctantly) to the conclusion that numerous “ordinary objects” do not belong to the correct ontology because they would be ontologically vague if they did—e.g., tables, chairs, persons—it is much more natural, and much more pre-theoretically plausible, to adopt this stance with respect to the posits of certain other familiar kinds of discourse—for instance, “social entities” like nations, corporations, universities, and the like. It also is much more natural, and much more pre-theoretically plausible, to think that discourse positing items like social entities is not susceptible to—and need not be susceptible to—ontological regimentation. Consider, for instance, the statement ‘The state of Arizona has exactly three public universities’. Prima facie, it is not especially plausible either (i) that the right ontology includes entities like states of the Union or public universities, or (ii) that statements positing such putative entities are subject to ontological regimentations that posit only items that arguably do belong to the correct ontology (say, certain non-vague physical objects and non-vague physical properties and relations). On the contrary, it is much more plausible that truth, for statements of this sort, amounts to the kind of semantically correct affirmability that we are calling ONR indirect correspondence.
	Third, there is certainly no apparent reason to think that humans are incapable of mastering semantic-affirmability standards, for various forms of discourse, that would underwrite ONR indirect correspondence as the species of truth exhibited by statements in such discourse. Various subtle kinds of social-entity positing discourse, for example, are easily mastered by folks of ordinary intelligence. Those who would insist that assertoric discourse cannot work this way bear a heavy burden of proof, in the face of lots of apparent evidence to the contrary.
	Finally, fourth, the oddness of regarding such discourse as exhibiting either direct correspondence or OR indirect correspondence can be underscored by considering what would be the reaction not only of ordinary folks, but even of most members of one’s Philosophy Department, were the department metaphysician to opine, with a worried look, “Are there really such entities as corporations, universities, or philosophy departments? And if not, don’t we need a way of ontologically regimenting all talk that posits such entities?” The expected reaction, even among the others in the Philosophy Department, would be amusement. On its face, such a worry by this hypothetical department metaphysician seems rather silly. Such seeming silliness cries out for explanation; and the natural explanation is that the discourse in question is governed by contextually operative semantic-affirmability standards under which truth, for such discourse, is ONR indirect correspondence.

5. 	Non-Regimental Ontological Anchoring: Semantics in the Doorway of the Ontology Room?
Given that ontological vagueness is impossible, a question arises about semantic ontological anchoring. We ask about non-regimental ontological anchoring, which is trust to us by lessons from the part of the nature of vagueness: boundarylessness needs to be preserved and ontological regimentation programs cannot be viable, given the way the phenomenon of vagueness is construed. Considering this, one is confronted with a ubiquitous presence of vagueness in language and thought. The question about non-regimental ontological anchoring cannot be asked in the ontology room, because vagueness cannot be part and parcel of the ultimate ontology. But some ontological anchoring of vague discourse is needed. The question about non-regimental ontological semantic anchoring is a wide take upon the more specific question about the possibility of vague content to be there in a non-vague world that we will address subsequently.
1.	Lots and lots of serious theorizing deploys vague notions, and seemingly does so essentially and unavoidably. None the worse for that, we claim, even though (a) ontological vagueness is impossible and (b) vagueness does harbor a specific kind of logical incoherence.
	Given that vagueness is a mark of language and thought, it is not surprising to find vague notions in theorizing activities. Vagueness, we take it, is not a feature to be expelled from serious theorizing, but the one that contributes to its richness and persuasive power. Notice that theorizing in theoretical physics, just to take an example, many times happens to be supported by pictures and imagination, which may be non-vague in concrete Einstein’s experience, allowing for an adjusting metaphorical space as the basis for elaboration of the theory. The essential vagueness of serious theorizing imagination and of its notions enables the subsequent fruitful elaboration of the theory. 
	One may also be struck by the fact that serious theorizing deploys vague notions, and by the nature of vagueness that seems to go against basics of serious theorizing. Namely, ontological vagueness being impossible –  how can this accord with the serious theorizing vague notions being there in the world, having an impact in theory? Logical incoherence that is there in the nature of vagueness seems to be incompatible with serious theorizing that certainly appears jarred by any form of incoherence. Here we should just make attentive at the fact that any serious theorizing that happens to be productive has to have some wiggle room for different interpretations, and that it also arises from intellectual tension that may be dubbed incoherence. Notice that the incoherence here allowing for various interpretations is not the strong form of logical incoherence, but a viable form of normative fruitful discrepancies kind of incoherence.
2.	The same is true for lots of philosophical theorizing, and for theorizing that is at least partly philosophical.
	Similarly as in sciences such as physics, also the philosophical theorizing is vague, and it profits from normative incoherence allowing for various interpretations, which is the fruitfulness the philosophers’ job depends upon and from where it takes its inspiration. This begins with partly philosophical theorizing that also trades upon the weak normative incoherence.
3.	It’s certainly true for semantical theorizing about vagueness. An adequate semantical approach needs to iteratively deploy vague notions, and thus can’t be pursued in the ontology room.
	Semantic theorizing about vagueness itself deploys vague notions, possibly opened to various interpretations. The constitutive characteristics of vagueness are normative. They include principles and prohibitions, each of which has not fully determinate range of application. These vague notions do not make it possible for an inquiry into vagueness to succeed in the ontology room.
4.	The notion of ONR indirect correspondence is itself vague. This notion too, important and theoretically legitimate though it is, can’t be deployed in the ontology room. And the right ontology doesn’t, and can’t, include any such putative relation as ONR indirect correspondence.
	Let us turn now to the notion of ONR (ontological non-regimental) indirect correspondence. Non-regimentation means that there cannot be any ontological handling of truth, or in a wider sense semantic status of concepts by the help of non-vague plethora of candidates. ONR indirect correspondence notion is important in order to provide a viable semantic account of metaphysically lightweight posits first such as universities and symposia and then of middle sized dry goods, such as cats or tables. There being an indirect correspondence account of truth means that semantic value of statements or thoughts should not be keyed to ontologically non-vague entities, but rather to the actual state of the complex world to which one refers. Absence of regimentation means that there cannot be any plethora of non-vague candidates in the world. 
	Specifically, the right ontology just cannot involve any such ontologically non-vague relation as is the putative ONR indirect correspondence relation. For it is normatively grounded and therefore vague.
4.5.	Indeed, it may well be that the notion of semantic vagueness is itself a vague notion, in which case there can be no legitimate deployment of this notion in the ontology room. (Cf. Sorensen on the vagueness of ‘vague’.)
	The very notion of semantic vagueness may very well be vague notion itself. But if this is the case, then the notion of semantic vagueness cannot be deployed in ontology room which allows just for entities that are there in the ultimate ontology, and that are therefore non-vague. Sorensen has pointed out the vague nature of the notion of vagueness itself.
5.	A certain philosophical problematic arises, in light of these observations. In the present section we offer a somewhat preliminary, somewhat tentative, characterization of this problematic. This problematic is what we’re labeling non-regimental ontological anchoring.
	The problematic that arises is keyed to the impossibility of ontological vagueness. Issues of truth are proper to semantics. We distinguished between truth as direct correspondence, truth as ontologically regimented indirect correspondence, and truth as ontologically non-regimented indirect correspondence. In respect to truth as direct correspondence the ontological posits referred to in vague assertions (for assertions and thoughts, we presumed, are vague) such as cats or tables should be non-vague. But this would then presumably involve a plethora of non-vague entities, such as cat-candidates or table-candidates – for cats and tables as observed in ontology room would not be able to pass the test of their ultimate ontological existence, due to their vagueness, precisely. This last trial would already be proposal of indirect correspondence, for instead of cats and tables (which may be presumably vague entities and thus incompatible with their nature, given the impossibility of ontological vagueness) one would look for regimental anchoring in direction of a plethora of non-vague cat-candidates or table-candidates. This proposal would then amount to truth construed as indirect correspondence and as an ontologically regimental version of it. It would be a way to anchor ontologically the semantic hook-ups for vague terms that appear in language and thought. But the proposal does not seem to have a lot of chance because of the lesson which we pointed out earlier, namely that you cannot simply dominate vague items in submitting them to ontologically non-vague situation, which would be the case for ontologically regimental indirect correspondence truth construal. If this one is not viable, then there is ontologically non-regimental indirect correspondence as a truth construal on offer. It seems that just ontologically non-regimental indirect correspondence as a construal of truth is really available. In this case one would not subscribe to ultimately ontological directly corresponding candidates as semantical anchors in the world, nor to a plethora of non-vague candidates for each semantically vague term, as goes proposal of ontologically regimental indirect correspondence. In the remaining case no regimentation would be offered, and truth would be construed as indirect correspondence. But one may wonder then what exactly would be the non-regimental ontological anchoring. This is a general question that we will pursue in the follow-up as the question about how vague content, a semantic feature, is possible in an ontologically non-vague world. The problematic of non-regimental ontological anchoring is thus somehow tentative and preliminary.
6.	Broadly speaking, the problematic involves matters ontological. It involves questions about items in the right ontology. It also involves vagueness in language and thought, semantic vagueness.
	The problematic that we are concerned with here involves a possible intersection between two areas: semantic and ontology. If one would take a direct correspondence approach to truth one would have possibility to look for ultimate ontological entities corresponding to what is referred to in language or thought. The relation between the semantic items and ontological items would then be cashed-in along causal or teleological lines, as direct referential relation. But given that semantic features are vague, it is then a question what directly would correspond to them in the ontological world that does not allow for ontological vagueness. Are there items in the right ontology that would correspond to vague semantic notions, features? The first answer is that, if there are such items, they would not offer correspondence in a direct manner. Then, doubt also would turn over to any means about achieving correspondence semantic relation through regimentation procedures. Our problematic, as said, involves matters ontological, matters semantical, and their relation.
7.	An initial pass, useful albeit somewhat metaphorical: How is semantic vagueness ontologically anchored?
	A way to begin formulating the question with the hope of eventually further on answering it is to find out what the ontological anchoring would be like for semantic vagueness. Notice that semantics is vague, for it is a feature involving language and thought, and that the world is non-vague. What may be the relation between these? A clue coming to mind is that such a relation will not be direct, non-vague itself, but that it may well be vague, for it would depend upon normative features. At least, one may say that the relation between vague semantics and between the non-vague world will not be direct, thus probably mediated, and accordingly vague itself. The question about anchoring of semantic vagueness is somehow metaphorical, but it is a trial nevertheless to propose candidates for relation between semantics and ontology, between notions or expressions in language and thought, and between the world, where the first of these relata is vague and the second one is non-vague. Anchoring means that there is some hook-up.
8.	There’s a certain reflexivity in the problematic. What sort of semantic standards are at work when the question itself gets posed, and doesn’t the question reflexively apply to those very standards themselves?
	Ontological anchoring is reflexive in the following sense. The question is about anchoring of semantic ingredients. These are guided by normatively underpinned semantic standards. But these standards themselves may require ontological anchoring. So the question about what is the basis of semantic normative standards turns out to be subjected to the same kind of scrutiny: how are these very standards anchored?
9.	The motivating thought is that there must be something about the items in the correct ontology in virtue of which the phenomenon of semantic vagueness exists, and in virtue of which ONR indirect correspondence obtains with respect to thought and language.
	Ontological non-regimental indirect correspondence (ONR IC) still needs to be hooked to the world, or to the correct ontology. There is impossibility of ontological vagueness. So despite that ONR does not buy regimentation, as its title says, there has to be some kind of relation of semantics to the correct ontology, to the world. Items in the world or in the correct ontology are supposed to give some support for semantics. But semantics of language and thought is compatible with vagueness, whereas correct ontology is not.
10.	Delicate reflexivity enters in here, because one can’t legitimately posit ONR indirect correspondence in the ontology room, and perhaps one can’t posit a phenomenon of semantic vagueness either. (Cf. Sorensen)
	ONR IC (ontological non-regimental indirect correspondence) cannot be in power in ontology room because of its normative and vague nature. Even the phenomenon of semantic vagueness cannot be posited in the ontology room, for the simple reason that ontology room does not allow for vagueness, given that there is impossibility of ontological vagueness. As Sorensen claims, semantic vagueness is a vague phenomenon itself.
11.	The question looks to pertain to ontology, even though it looks as though it probably can’t be answered, or indeed even asked (given its posits) from within the ontology room.
	The question of semantic anchoring seems to be an ontological question, because anchoring should succeed in the world, and so it has an ontological side to it. But semantics because of its normative nature is vague, which goes contrary to ontological room that does not allow for ontological vagueness. The posits of the semantic anchoring pertain to language and thought and so they are vague. So they cannot be posed and answered in the ontology room.
12.	One dimension of the problematic concerns the threat of debilitating incoherence; the worry is that any attempt at an answer might exhibit some kind of deeply problematic form of incoherence—e.g., commitment to rampant contradictions, commitment to a self-defeating infinite regress, or something of the sort. (Some kind of incoherence over and above the kind of logical incoherence that we already know is an essential feature of vagueness.)
	Given that semantics according to its language and thought side is prone to vagueness, and that vagueness is marked by incoherence, although a benign and generic kind of incoherence, the question of non-regimental semantic anchoring may itself exhibit some form of incoherence. One possibility is that rampant contradiction will emerge from the trial to establish semantic anchoring in the world. Or again, the phenomenon of infinite regress may come upon the stage, so that each trial to establish a hook-up will be delayed to a subsequent level. But the incoherence that is typical for vagueness actually resides in its normative nature, involving vagueness supporting conditions and principles. The incoherence in question is thus not necessarily that of the contradictions involving logical kind. 
13.	Seeking a certain kind of conceptually stable theoretical understanding of what it is about the right ontology that constitutes the ontological basis of vagueness in language and thought. The understanding might very well need to deploy vague notions itself, but needs to do so in a conceptually stable way. Using vague notions to address a question that involves matters ontological, and doing so in a conceptually stable way.
	We look for stable theoretical understanding of what exactly is in right ontology that offers the ontological basis for language and thought. As just said, this should be stable understanding, although the notions that it will use may well be vague themselves. In fact, we can use vague notions to address the question about what involves matters ontological. The requirement is that we pose this question and try to answer it in a conceptually stable manner.

6. 	Ontology and Phenomenal Intentionality: Vague Mental Content in a Non-Vague World
The problem of non-regimental ontological anchoring is a generic problem in respect to the question about the possibility for vague content to be there in a non-vague world, the question that we will try to articulate now. We propose to tackle this question which is actually about the relation of semantics and of its ontological basis through the primacy of the phenomenal intentionality.
1.	We propose to approach the problem of non-regimental ontological anchoring by asking this question: Are there any items in the right ontology that exhibit semantic vagueness?
	Non-regimental ontological anchoring has the following characteristics: it should be anchoring to the world, i.e. ontological anchoring. Also, it should not be regimental, in the manner that some entities would be posited in the right ontology that would satisfy a kind of translation from the surface semantic statements figuring non-desirable entities. The anchoring would be ontological though, so that it would be directed to the world, say, that is ontological but does not support ontological vagueness. The problem may be posed in the following manner. Linguistic and mental content is vague, due to the vagueness inherent to language and thought. But the world, as we stated, just cannot be vague, due to the nature of vagueness. Now, on the other hand it would be difficult to escape conclusion that vague content, linguistic or mental, is there in the world. For where else would language and thought be supposed to happen? If the world is conceived as harboring the right ontology, the question is now whether there are items in the right ontology that exhibit semantic vagueness. But this is then supposed to mean that there is vagueness in the world, despite our claim that ontological vagueness is impossible. Thus, how should one tackle the just spelled out problem?
2.	This question itself might very well be one asked from the doorstep, because exhibiting semantic vagueness is arguably a vague notion, and thus arguably not a property one could posit as itself part of the right ontology.
	Wait a minute though. The question about possible items in the right ontology that exhibit ontological vagueness might not be fitting for the ontology room environment. Because exhibiting semantic vagueness is, as we have said (Sorensen) vague notion itself, and so it cannot be posited as a part of the right ontology. As the right ontology is the domain of the ontology room, the question about semantic anchoring then becomes the one that cannot be asked from the ontology room with its strict contextual normative requirements, but from the doorstep of the ontology room.
3.	Say something about phenomenal intentionality, and about the case for it being made elsewhere.
	Phenomenal intentionality, we hold it, is the basic kind of intentionality. In this, we subscribe to the phenomenology of intentionality and intentionality of phenomenology thesis (Horgan Tienson 2002), which is directed against separatism, this one treating intentional directedness as happening without phenomenology as its constitutive ingredient, or again treating phenomenology as not constitutively supported by the intentional relation. The thesis aims for intertwining of the phenomenology and of the intentional. It also goes against ascribing priority to any of these, as we will briefly specify later on. This is all compatible though with the thesis that phenomenal intentionality, as we just said, is a basic kind of intentionality. 
4.	Our proposal: Determinate phenomenal-intentional mental properties belong to the right ontology. These are ontologically non-vague, in three specific ways. First, with respect to location of instantiation. (Location of instantiation of the minimal physical supervenience-base property.) Second, with respect to phenomenal character. (Any change in phenomenal what-it’s-like-ness yields a new, different, determinate, phenomenal property.) Third, with respect to the range of actual and potential instantiation. (Not sorites susceptible via slight phenomenal variations, because any phenomenal variation makes for a distinct phenomenal determinate-property.) Fourth, with respect to phenomenal character.
	Here is our proposal, in basic points, how to answer the question about the possibility of vague content being there in a non-vague world, and thereby the more generic question about the ontological non-regimental anchoring of semantic items.
	First, we distinguish between determinable properties, and between determinate properties. Whereas the first ones, determinable properties, are abstract in the sense that they still need specification, such as color red in its general conceptual form, the second ones are concrete specific properties. By the way, you can see that thereby we allow properties into our ontology. Now, we claim that determinate phenomenal-intentional mental properties belong to the right ontology. This is not the case though with determinable properties. Determinate phenomenal-intentional mental properties now again, are just the semantic vague properties that we use in our starting question that needs to be answered. These properties are intentional, but by having their constitutive phenomenology they are also phenomenal. In fact they are determinate phenomenal-intentional mental properties, as we have announced them.
	Determinate phenomenal-intentional mental properties, we now claim, are ontologically non-vague, in three specific ways. First, they are non-vague with respect to the location of their instantiation. We aim here at the location of instantiation of the minimal physical supervenience-base property in question. Second, they are non-vague with respect to the phenomenal character. Namely we hold it that any change in phenomenal what-it’s-like-ness of such a property yields a new, different, determinate, phenomenal property. So they are unique, a point that deserves to be elaborated, and it will be briefly elaborated here in direction of phenomenology-intentionality identity that we subscribe to. Third, phenomenal-intentional mental properties are non-vague with respect to the range of actual and potential instantiation. They are namely not sorites susceptible via slight phenomenal variations, because any phenomenal variation makes for a distinct phenomenal determinate-property. Fourth, phenomenal-intentional mental properties are non-vague with respect to phenomenal character. If all these characteristics of phenomenal-intentional mental properties hold, then a way is open of recognizing the possibility of non-regimental ontological anchoring, and before of that of the possibility that there is a vague content in a non-vague world indeed. But where has the vagueness gone, for these properties are still vague, we suppose, although they may be the inhabitants of the non-vague world?
5.	These ontologically non-vague properties typically are semantically vague. Their phenomenal character is inherently intentional, and the intentional content of a determinate phenomenal-intentional property is usually, maybe always, semantically vague content.
	Here is the answer to the question where vagueness of semantics items stays despite that they may be recognized as inhabitants of an ontologically non-vague world. The answer is that the ontologically non-vague properties that we mention are semantically vague, which accords with the fact that vagueness is proper to the realms of language and thought. Following the phenomenology of intentionality and intentionality of phenomenology thesis, we can say that phenomenal character of semantically vague properties is inherently intentional. Despite this, the content, i.e. intentional content of a determinate phenomenal property is usually, and perhaps always, semantically vague content. The understanding of this last point would profit from an illustration.
6.	Give the visual field analogy. Sharp at the focal/foveal point in the visual field, progressively less sharp at progressively greater degrees of arc from the foveal point, phenomenally determinate degrees of blurriness at each point in the visual field. Likewise, the presentational contents of one’s current visual experience get progressively less determinate as the degree of arc gets greater.
	Consider the visual field analogy. Whatever is there in the focal/foveal point of your visual field becomes progressively less sharp if you advance along progressively greater degrees of arc from the foveal point, so that there are phenomenally determinate degrees of blurriness at each point in the visual field. In a similar manner, the presentational contents of one’s current visual experience get progressively less determinate as the degree of arc gets greater. You have phenomenologically non-vague experience, but with progressively vague content.
7.	Analogously, the intentional categories built into phenomenology typically have prototype structure. Something counts as falling under the category provided that it is sufficiently relevantly similar to paradigmatic or prototypical instances of the category.
	We have presumed that intentional categories are phenomenologically constitutively supported. These intentional categories though, qua intentional, have their prototype structure, not lastly because of their practical adaptability to cover a range of situations in the world (dogs, say, come in various shapes and sizes, yet they still belong to the prototype of a dog or to the dog category). Something will fall under category provided that it is sufficiently relevantly similar to paradigmatic instances of that category. Similarity of this category vague adaptation along prototypic structure has its vicinity to the visual field metaphor spelled out earlier.
8.	This semantic vagueness, as a feature of ontologically non-vague determinate mental properties, is metaphysically the fundamental kind of semantic vagueness (with phenomenal intentionality being metaphysically the most fundamental kind of intentionality).
	Semantic vagueness is thus a feature of ontologically non-vague determinate mental properties. It is metaphysically the fundamental kind of semantic vagueness. Thus, it is the kind of semantic vagueness that is anchored in the non-vague world, because of the characteristics that we have given. As we say that phenomenal intentionality is metaphysically the most fundamental kind of intentionality, we mean to say that this is the basic intentionality that comes about in the world. It is a vague intentional content with non-vague phenomenological ontological basis.
9.	Semantic normativity is built right in. Ontologically, the truth-makers are non-vague ways the world might be. The semantic normativity has prototype structure: a given determinate way the world might be is a truth-making way, in relation to the intentional content of a given determinate phenomenal-intentional mental property, provided the given way the world might be is sufficiently relevantly similar to ways the world might be that are prototypical truth-makers with respect to that content. (Roughly, anyway.)
	Given that there is semantic vagueness in the content of properties that ontologically are non-vague phenomenal properties succeeding in the world, we can conclude that semantic normativity as well is built right into that vague content, by the fact that vagueness is normatively constituted. On the side of the world, ontologically, the truth-makers are non-vague ways the world might be. The semantic normativity which is in business to put categories upon whatever it encounters, semantically or categorically in the non-vague world, has prototype structure. A given determinate way the world might be is a truth-making way, in relation to the intentional content of a given determinate phenomenal-intentional mental property, provided the given way the world might be is sufficiently relevantly similar to ways the world might be that are prototypical truth-makers with respect to that content. This is at least roughly the case anyway, following perhaps vague nature of categories and prototypes as whatever cognizer projects upon the richly dynamical non-vague world.
10.	Public language, governed by ONR indirect-correspondence semantic standards, gets up and running when enough of these ontologically determinate mental properties are getting instantiated in the world, and are pertinently similar to one another. The pattern of instantiation of determinate, ontologically non-vague phenomenal-intentional mental properties is what ontologically anchors the ONR indirect-correspondence semantic standards that govern most all uses of public language.
	How is communication between several parties engaged into it possible? This is a question about the possibility of public language. Such public language, which is governed by ontologically non-regimental (ONR) indirect-correspondence semantic standards, gets up and running when enough of these ontologically determinate mental properties are getting instantiated in the world, and are pertinently similar to one another. Notice that explanation here takes off with concrete phenomenal intentional features in the world. But there is also the power of semantic prototypical generalization. The pattern of instantiation of determinate, ontologically non-vague phenomenal-intentional mental properties is what ontologically anchors the ONR indirect-correspondence semantic standards that govern most all uses of public language. So we need sufficient amount of the unique phenomenal-intentional cases, which eventually come to the situation where a pattern involving category gets recognized. Then, there is ontological anchoring present, without that regimentation would be necessary in order to get the hook-up between vague content and whatever is there in non-vague world that supports pattern categorization and thereby the possibility of public language.

7. 	Transcendental Idealism Revived
Our ontological non-regimental project of semantic construal of truth as indirect correspondence may be served as a revival of transcendental idealism. The main idea is that there are vague semantic content involving properties that are hooked-up, anchored in the non-vague patterns in the world, empirically real, which the content related categories recognize.
1.	Kant held that various objects posited in common sense and in science, although “empirically real,” are also “transcendentally ideal.”
	There is a story that objects posited by common sense and by science are empirically real. A cat, considered in this manner, is empirically real, it has certain specific characteristics, such as a certain specific weight. Notice that such a cat, being specifically there in non-vague world, by its very concreteness, may be called unique. But cat is also transcendentally ideal, in the sense where we talk about it in a manner of vague semantic category, where we look in non-vague world for patterns that we may recognize and order under the category of the cat.
2.	Semantics, done in the doorway of the ontology room to address the task of non-regimental ontological anchoring, can usefully adopt this Kantian terminology, and can offer a specific way of glossing it.
	We have introduced semantics for which we recognized that it is vague, and so we had to situate it not outright in non-vagueness strictly observing ontology room, but in the doorway of the ontology room. In this manner we aimed to address the task of non-regimental ontological anchoring, i.e. of ontological anchoring that retains an autonomous semantic sphere despite of being hooked-up to the non-vague world, in its semantic categorical patterns recognizing manner. Such a semantic can now usefully adopt the “empirically real-transcendentally ideal” terminology, and it can offer a specific way of glossing it. As we have indicated, empirically real refers to the unique kind of basis in the non-vague world, whereas transcendentally ideal allows for vague categorically detached semantic patterns.
3.	Most of the posits of both common sense and science are “transcendentally ideal” in this sense: they are not items that belong to the correct ontology. They are posits of thought and language which itself is governed by ONR indirect-correspondence semantic standards.
	Here we extend our gloss. The posits of common sense and science, such as cats or atoms, are mostly “transcendentally ideal” in the sense that they do not belong to the right ontology, to the ultimate non-vague ontology, which has its proper place in the ontology room. Being posits, they are in this semantic sense vague creatures belonging to the realm of mind and language. These posits are governed by ONR indirect correspondence semantic standards, which underlines their vague nature.
4.	Many of these posits are “empirically real” in this sense: Claims entailing their existence are true, under ONR indirect-correspondence semantic standards that govern them in typical contexts of use.
	But when semantic posit cat appears in a statement which happens to be true at a certain occasion, such as “The cat is on the mat”, we can say that at such an occasion the posit in question is empirically real. Empirical reality, here, comes from the very fact that semantic vague content fits to ONR indirect correspondence semantic standards that typically govern its use in contexts.
5.	It is noteworthy that Kant argued for his transcendental idealism in ways that relied heavily on certain putative antinomies that arise when reason goes suitably self-critical; thus his critique of pure reason.
	Kant transcendental idealism relies heavily on a range of antinomies that are tackled in a reflexive critical manner, which happens to amount, say, to the critique of pure reason. Notice the parallel here with our austere realism (Horgan Potrč 2008) project, where we start with posits of common sense, proceed to the claim that common sense itself gets critical at the antithetic phase as some antinomic kind of hurdles are recognized by it in its previous thetic manner of positing things. Finally, we claim that following such reflexive experience common sense itself is ready to embrace truth as indirect correspondence, which in the here used lingo would mean that empirically real anchoring to non-vague world is accommodated by transcendentally ideal ONR indirect correspondence contextual standards.
6.	Our own approach to vagueness amounts to a certain way of implementing such a critique. When one carefully attends to aspects of the phenomenon of vagueness that seem a priori undeniable once brought into focus, one is driven to transvaluationism. This in turn generates the conclusion that ontological vagueness is impossible, and underwrites the claim that in most contexts of thought and language, truth amounts to NOR indirect correspondence. Which, in turn, leads to the conclusion that most of the posits of both common sense and science are indeed transcendentally ideal, albeit empirically real—with these ideas glossed as explained above.
	We now turn our attention to the question of ontological vagueness. We take it that the phenomenon of vagueness is captured by the transvaluationist approach in an a priori correct manner. A follow-up of transvaluationism however is that ontological vagueness is impossible. From here, one has to recognize that in most contexts of use truth needs to be indirect correspondence, adopting “transcendentally ideal” semantically vague attitude. Following this, most of posits of common sense will be transcendentally ideal besides to being empirically real.
7.	This is quite a far cry from the kind of unvarnished scientific naturalism that regards all truth as direct correspondence, regards at least some of the posits of common sense (tables, chairs, persons, middle sized dry goods) as genuine denizens of the right ontology, and that regards many of the posits of science as genuine denizens of the right ontology.
	Our itinerary to ONR indirect correspondence construal of semantic truth now goes against semantic accounts that try to reduce intentional relation to causal (Dretske, Kripke) or teleological (Millikan) facts. Against all these, our argument would start with the basic phenomenal intentionality. Once ONR indirect correspondence construal of truth is adopted, the posits of common sense cannot be held anymore to be denizens of the right ontology and inhabiting ontology room. This has the consequence that such items must be recognized as semantically vague in repsect to their constitution and thus as transcendentally ideal. 
8.	But, one must follow the vagueness-based critique where it forces one to go.
	Our accent here is in respect to semantic content vague anchoring in the non-vague world. Following the dialectics of common sense, one realizes that, now, vagueness based critique has to be followed wherever it leads. Common sense starts with empirically real last ontology inhabiting posits, then it goes into reflexive antinomic mood, and finally buys semantic transcendentally ideal vague form of such posits, i.e. ONR indirect correspondence as an adequate semantical rendering.

8. 	Ontological and Non-Ontological Metaphysics
Following our inquiry into ONR indirect correspondence anchoring of semantic content in the non-vague world, we have inadvertently also tackled some lessons concerning metaphysics. There is ontological, and there is also non-ontological metaphysics. As Brentano, just to deliver an example, takes categories to belong to the metaphysical inquiry, we would say that this is a case of non-ontological metaphysics, for categories in their semantical sense must be non-vague and so they do not belong to the ultimate ontology.
1.	If one accepts what we’ve been arguing above, then one apparent consequence will be that some issues discussed in metaphysics—perhaps quite a few of them—turn out not to be issues pertaining to which items belong to the right ontology.
	In respect to what we claim about ONR indirect correspondence, we can realize that many issues that are known as genuinely ontological ones really cannot belong to ontology, for serious ontology requires ontology room, but many times posits that come forward in discussion really appear in the doorway of ontology room, perhaps.
2.	For example: What’s the relation between a statue and the lump of clay from which it is composed? Well, both statue and lump of clay, were they items in the right ontology, would be vague in certain ways—e.g., temporal boundaries, synchronic microphysical composition. So, given the impossibility of ontological vagueness, neither belongs to the right ontology.
	One nice example of a problem that appears to be ontological in the sense just specified, is not ontological at all. This is the discussion pertaining to the explanation of relation between a statue and between the lump of clay from which the statue is composed. It happens that neither of these can inhabit the ontology room or be a denizen of the ultimate ontology, because both of these are vague. So they have to be semantic and not ontological posits. And indeed, both statue and lump of clay are vague according to several parameters, such as their synchronic or diachronic composition. Indeed, none of these belongs to the right ontology, given that ontological vagueness is impossible.
3.	Which makes it look like the issue really is a matter involving ONR indirect correspondence semantic standards that govern—or arguably should govern—thought and discourse about statues and about lumps of clay.
	The discussion about the relation between statue and the lump of clay therefore involves ONR indirect correspondence. At least, following our study of vagueness and anchoring relation of semantic features, truth as direct correspondence cannot be the right departure for the statue and lump of clay discussion. We deal with vague posits and not with denizens of ultimate ontology.
4.	Maybe there’s a fact of the matter thus, based on pre-existing ONR indirect correspondence semantic standards that govern such talk and thought, in ordinary contexts. But if so, not a fact about how certain items in the right ontology are related to one another.
	Indeed, as philosophers discuss about the relation that is there between statue and lump of clay out of which it is composed, they already buy ONR indirect correspondence semantic standards, which govern thought and talk about such items in ordinary contexts. This shows that we do not have to do with matters that succeed in the right ontology or in the ontology room which is opposed to normatively based indirect correspondence construal of truth.
5. 	Or maybe pre-existing ONR indirect correspondence semantic standards, in respective ordinary contexts of thought and talk about, respectively, statues and lumps of clay, are somewhat indeterminate—enough so that they don’t actually fix any determinate answer to questions like “What’s the relation between a statue and the lump of clay that composes it?”
	Perhaps ONR indirect correspondence semantic standards governing statue and lump of clay talk in ordinary contexts are to some extent indeterminate, so that the question concerning their relation can actually not be fixed at all.
6. 	If that’s the case, then the issue looks even more different than it does when construed as an ontological issue. Something like: What’s the best way to choose to talk and think, when considering such questions.
	If the above is the case, then statue and lump of clay issue is not really about ultimate ontology. It is rather an issue about which kind of talk or thought to choose at the time one discusses it.
7.	And one possibility is that there isn’t any single best way to do so, although given more specific contextual purposes, there might be one.
	Having different ways of thought and talk as the choice to the kind of statue-lump of clay issues, one may realize that there are different manners of thinking and talking, that there are different senses, as one could state in a somewhat Fregean manner. This is then definitely not an issue involving ultimate ontology, however.
8.	An instructive illustration of this latter kind of thing—one that nicely ties back to vagueness, is Lewis’s treatment of the 1001 cats, construed as not being about items in the right ontology. Cf. our discussion of that in our “Existence Monism Trumps Priority Monism,” some of which we might want to repeat here.
	Applying the above insight to the vagueness talk, and specifically perhaps to OR indirect correspondence truth semantic talk, one can use Lewis’s treatment of 1001 cats as candidates for regimented ontological approach to the semantic of cat. But vagueness, as one lesson goes, cannot be expelled in this or in any related manner.

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