Existence and Logical Form

 

 

There have been two main theories about the logical form of existence statements: the first-order predicate theory and the second-order predicate theory. One theory maintains that “exists” expresses a property that objects have; the other theory maintains that “exists” serves to make a statement about a predicate or concept or property, to the effect that it has instances. Both theories have their attractions and drawbacks, which I won’t discuss; my purpose is to present a new theory.

            I call this theory “the intentional object theory”: it says that an ascription of existence predicates something of an intentional object (an object of thought or other mental representation), not of an ordinary object or a concept. We are talking about an intentional object when we speak of existence not a regular object or a concept (predicate, property); and we are ascribing a certain property to that object. For example, if I say “Sherlock Holmes does not exist” I am saying something about an object of thought—the subject matter of my thought. Similarly, if I say “Mick Jagger exists” I am speaking not of the existent Mick Jagger but of the intentional object corresponding to him—the object of thought I would still have even if he did not exist. I won’t go into the question of the meaning and legitimacy of talk of intentional objects; my aim is to make a proposal about logical form given that we can talk this way.  [1] So let us introduce a piece of notation: we designate an intentional object by placing an asterisk after a name or other singular term for an object (existent or not), as in “Mick Jagger*”, to be read “the intentional object that corresponds to Mick Jagger”. The theory, then, is that statements of existence are about such objects, and only such objects; they are not about ordinary objects such as Sir Mick himself, or about predicates such as “lead singer of the Rolling Stones”.

            But what do such statements say about Mick Jagger*? They say that this intentional object is actualized. So the analysis of “Mick Jagger exists” is “Mick Jagger* is actualized”. I am taking the term “actualized” as primitive but its intuitive meaning should be clear enough (we could also use “realized” or “exemplified”). One thing we must not do is analyze it as “corresponds to an object that exists”, since that introduces existence as a predicate of objects. Instead we are analyzing existence as applied to objects (misleadingly so) in terms of intentional objects being actualized: that is the primitive notion. Suppose we are debating the existence of unicorns, with you a believer and me a disbeliever, and you claim to have seen a unicorn last week: I might reply “That was just a figment of your imagination”. What I am saying is that your intentional object when it seemed to you that you saw a unicorn was not actualized—in contrast to your reported sightings of regular hornless horses. The logical form of my statement is: “Unicorns* are not actualized”. Whenever we think of an object, existent or non-existent, we have of an intentional object in mind, and that object can be said to be actualized or not. One way to conceive such objects is as possible objects (in some sense of “possible”); then we are saying of possible objects whether or not they are actualized (which is not to say “actual”). To put it in a way that is familiar, though potentially misleading, we introduce an ontology of intentional objects and then we analyze existence statements as predications of actualization of entities in this ontology. The metaphysics of this ontology is no doubt tricky and controversial, but I am steering clear of all that in order to make a logical point: existence statements are not about ordinary objects or about concepts; they are about intentional objects. If we use Meinong’s categories, we can put the position by saying that existence statements are always about subsistent entities, which can be said to be either actualized or not actualized, thus giving rise to existence and non-existence.

            It is easy to get lost in the metaphysical fog here, so let me restate the thrust of the position in less fraught terms: existence is to be analyzed by means of a predicate of singular terms, not objects or concepts. When I say, “Mick Jagger exists” I am saying “The name ‘Mick Jagger’ is actualized”. This is not strictly correct, because names cannot be actualized in the sense intended, but it helps to get the logical point across: namely, that we have something else to play with aside from objects and concepts—we have names themselves. Indeed, one view of existence statements precisely is that they ascribe denotation to names, as in “The name ‘Mick Jagger’ denotes”. The intentional object theory is logically similar in that it uses a new predicate in application to something other than objects or concepts–the theory speaks of intentional objects being actualized and not of names denoting. The denotation theory is meta-linguistic; the actualization theory is, so to speak, meta-intentional. It uses an ontology of intentional objects to analyze existence statements by invoking a property of those objects, viz. actualization.

            We thus allow that there is reference shift inside existence statements: names don’t refer to their ordinary reference but to intentional objects (compare Frege on indirect discourse). In “Mick Jagger exists” the name refers not to Sir Mick himself but to the intentional object Mick Jagger*. This solves an old problem: the problem of redundancy and self-contradiction. We are not referring to an object and then saying it exists (redundancy) or that it doesn’t exist (contradiction); we are referring to an intentional object, which is neutral between existence and non-existence, and then saying whether it is actualized or not. Suppose I am the subject of a psychological experiment in which the experimenter is feeding me visual impressions, some of which are veridical and some are not: some are of horses, some are of unicorns. She asks me to say whether I think the impression corresponds to anything real or not; for reasons of experimental protocol she prefers that I answer with the words, “That intentional object is actualized/not actualized”. Thus I explicitly refer to my intentional objects and predicate something of them, thereby expressing my existential beliefs. That is the gist of the theory I am proposing.  [2]

If we try to reconstruct how the concept of existence came to be employed in the first place, the picture is that we noticed that some of our thoughts and percepts correspond to real things and some are about merely imaginary things. We wanted a way to distinguish between the two cases: so we took to saying that some of the things that enter our minds are actualized and some are not. Then we abbreviated this to speak directly of the existence of things, all along really meaning that objects of thought can be actualized (realized, exemplified) or not. Thus logical form became hidden in the simple sentences we use to talk about existence, such as “Mick Jagger exists”. There was always something funny and jarring about that form of words, but it was brief and convenient. The sentence doesn’t seem logically like “Mick Jagger is a good dancer” or “Mick Jagger is English”; and indeed it is really about something other than Mick the man. For Mick to exist is for the intentional object Mick* to be actualized, but nothing like this is true of his dancing ability or nationality. Vernacular statements of existence are misleading as to their true topic.

 

  [1] I have discussed intentional objects in Logical Properties (Oxford: Oxford University Press, 2000), chapter 2, and in “The Objects of Intentionality” in Consciousness and Its Objects (Oxford: Oxford University Press, 2004).

  [2] Imagine you are a brain in a vat: none of the things you experience actually exists, but you have an enormous range of merely intentional objects before your mind. Then to say of each non-existent thing that it does not exist is to say that the corresponding intentional object is not actualized—that it is merely intentional. If we now place the brain in a vat into a normal head so that the world is perceived, we can say that the subject’s intentional objects are actualized.

 

 

The Language of Physics

 

 

Physics employs four denoting terms to cover what are usually referred to as forces: “gravity”, “electromagnetism”, “the weak force”, and “the strong force”. What is the semantics of these terms? Are they names, descriptions, or demonstratives? Do they function like standard natural kind terms?

            It is sometimes said that Einstein’s theory of gravity in General Relativity shows that gravity is not really a force after all. The thought is that by replacing action at a distance with the geometry of space we have abandoned the idea that gravity is a force. There is nothing more to gravity than the structure of space. We used to think that gravity was a type of force acting across space, but it has turned out not to be. On this view, the term “gravity” does not analytically entail “force”. But there are other ways we could react to General Relativity: we could say that gravity has turned out not to exist, since the term does entail being a force and the theory shows that it is not a force; or we could hold that gravity does exist and has turned out to consist in the geometry of space, but it is still a force because force is reducible to geometry. So we have three possible positions: (a) gravity exists but has turned out not to be a force; (b) gravity exists and is a force because relativity theory tells us what this force is; (c) gravity does not exist because relativity shows it is not a force and “gravity” entails “force”. The first thing to say about these options is that it is completely unclear which view we should adopt; the meaning of the term “gravity” seems indeterminate between the three views. We could adopt any of them and not be accused of semantic (or scientific) impropriety.

            Compare “magnetism”: what if we were to conclude that a charged particle distorts the space around it in a similar way to gravity? Should we then say that magnetism has turned out not to be a force? We could equally say that it is still a force but that the force reduces to geometry. Or we could simply announce that magnetism has turned out not to exist (like phlogiston). Again, the term “magnetism” seems too indeterminate to allow of a straightforward resolution; the decision about how to use the term in the light of the new theory seems purely pragmatic. It is easier practically to keep using the term and describing magnetism as a force, but this is hard to defend as the clear truth about the meaning of the term given the alternatives. We could equally declare that magnetism is not really a force after all, or that it doesn’t exist (we would then need a new term for what does exist in magnetic interactions).

            Could there be fool’s gravity or fool’s magnetism? Could there be a Twin Earth that contains a force indistinguishable from gravity that isn’t gravity? That is hard to envisage: what could differentiate real gravity from its fake epistemic counterpart? The case is not like water and H2O, in which we have a clear idea of hidden structure in the shape of chemical composition, to be contrasted with superficial appearance. But if something acts like gravity or magnetism mustn’t it be gravity or magnetism? How could a force obey Newton’s inverse square law and not be gravity? So it is hard to see how the standard arguments apply to these terms of physics; they don’t fit the usual natural kind model. Or at least it is unclear that they do—we can describe hypothetical cases in different ways and not violate their meaning.

            These physical terms are thus not readily classifiable as names or descriptions or demonstratives—that is, they don’t function in such a way as to fall clearly into any of those semantic categories. They are a bit like names, somewhat similar to descriptions, and akin to demonstratives—without being clearly any of the above. Thus we find semantic indeterminacy at the heart of the most exact of sciences.  [1]

 

  [1] Of course, we are only too familiar with epistemic indeterminacy at the quantum level, and possibly ontological indeterminacy. But it is another thing to find that “gravity” is neither a logically proper name of something, nor a definite description of something (“the force that acts at a distance”), nor a demonstrative term for something (“that physical phenomenon”). It seems to float between these alternatives. Thus we can’t say definitively whether Einstein abolished gravity in favor of spatial curvature or told us what gravity is (spatial curvature).

 

 

The Fidelity Theory of Truth

 

 

We are accustomed to deflationary accounts of truth according to which there isn’t much of interest to say about the concept—it’s just a way to avoid repetition, a convenient shorthand, and strictly redundant. We are also accustomed to rigorous technical definitions, geared to formal languages, in which truth is rendered mathematical. The concept has been tamed, dethroned, and demystified—deflated. But maybe it needs to have some air pumped back into it and treated with more reverence—inflated. Maybe truth is more interesting than we have been led to believe, carrying more of a metaphysical wallop. Following that hunch I propose what I call the “fidelity theory of truth”, which can be succinctly stated as follows: A statement S is true if and only if S it is faithful to reality. Clearly the operative notions here are faithfulness and reality, the former being a relational notion and the latter corresponding to an object standing in that relation. The sense in which truth is faithfulness can be illustrated by reference to the concept of a faithful copy of an original: a faithful copy accurately represents or duplicates what it is a copy of. In that way it is true to the original: it has “fidelity”. To be false, then, is to be unfaithful to reality, to lack fidelity.

It is a significant fact that we describe marital fidelity using the word “true”: you may have a “true love” that is “true to” you. These concepts are intertwined: the general idea is that of two entities chained steadfastly together, not diverging or deviating. It is as if a true statement is one that does not “cheat” on reality, which sticks close to reality, not straying from it. This conceptual connection imbues the word “true” with a normative dimension: it is good to speak truly because it is good to be faithful (to be true to something). Truth is fidelity to reality, which is better than succumbing to fantasy. The usual definitions of truth make no effort to capture the normative aspect of truth, but surely this is a non-negotiable feature of the concept, so it is good to build it into the definition. Truth is bonded to reality as people are bonded in marriage (see how inflationary I am being!). We can also use this mode of definition to unify two uses of “true”: as applied to propositions and as applied to pictures. A picture can be described as a “true likeness” and also as “faithful” to its object. Thus we can say: a picture P is a true likeness of an object x if and only if P faithfully depicts x; or P is true to x if and only if it faithfully depicts x. Again there is a whiff of the normative here: it is good to create faithful depictions and bad to create unfaithful depictions.  [1]

Am I then resurrecting the picture theory of meaning and truth? No, because we need a different account of faithfulness in the case of propositional truth, as follows: a statement is faithful to reality if and only if it accurately describes reality. Now we have brought in the concept of accuracy, which also belongs with pictorial truth: a faithful reproduction is precisely an accurate reproduction. Fidelity is defined in terms of accuracy—pictorial or propositional. This allows truth to come in degrees, since representations can be more or less accurate. A given statement might not describe reality with complete accuracy, as when I say of a mostly cloudless sky that it is blue or of the grimy snow in my yard that it is white (the general sentence “snow is white” is not entirely accurate, i.e. not entirely true). We can have accurate description and accurate depiction, as well as the lack of these, and that is what allows the use of “true” in both contexts: the underlying concept is that of accuracy.  [2] What the concept of fidelity adds is the admonition to strive to be faithful to something. Our language clothes the (fairly) neutral concept of accuracy with a virtue-theoretic concept of faithfulness–as if we have a duty to make our statements true. The duty of truthfulness is a duty of fidelity. And there is only one reality (but as many forms of unreality as there are errors and fantasies): we must be faithful to that reality and to it alone—no dalliances with “alternative realities”. Truth demands representational monogamy.

Usually the theorist of truth limits himself to the word “true” (possibly supplemented with “true of”), but we also need to reckon with the locution “true to” and to take into account the broad way in which these words are used—it isn’t all a matter of propositions being true sans phrase. Once we do that we see the link to pictorial truth (“true likeness”) and we glimpse the link to the concept of fidelity. Now our concept of truth is beginning to expand into something more interesting than deflationary accounts would suggest; but we have yet to add the other main component of the theory, viz. reality. The way I formulated the theory has it that a true statement is one that is faithful to reality. One might say “faithful to the facts” in the hope of sounding less portentous, but really this notion of “the facts” is just the notion of reality—the totality of all that is real. It would not do to reformulate the theory as follows: a true statement is one that is faithful to fantasy. Nor would it be right to say that truth is fidelity to human knowledge or to what is useful. We must employ a concept that injects the requisite degree of realism into the definition of truth—and what better concept to do that than the concept of reality (we could even say “mind-independent reality”). Thus the concept of truth is defined by reference to the resounding concept of REALITY: not this or that reality, but reality as such—the whole shebang. Statements must be faithful to the world, to actuality, to how things are. A statement stands in a certain relation to this all-encompassing entity (not just to bits and pieces in it): and it is true or false according as it is faithful or unfaithful to this entity. When we predicate truth we are, according to this pumped-up theory, speaking of the whole world, of everything that is; we are not just speaking of the specific things the statement in question concerns.  [3] Double inflation! This is what we must be true to—this is our marriage partner in the search for truth. We have an obligation to Reality to be faithful to her in our statements and beliefs. This is a far cry from the pared down, “’snow is white’ is true if and only if snow is white”, which says nothing of reality as a whole or of being faithful to her. Our general concept of truth is bound up with our general concept of reality (“how things are”), probably the most general concept we have—a metaphysical concept if ever there was one. To put it pretentiously: Truth is fidelity to the Real.

This accounts for the sense we have that truth is a profound and substantive concept, contrary to the dismissive and trivializing tendencies of the deflationary theory. Predicating truth is asserting a relation between a statement and everything there is, where that relation is heavily infused with normative force. This is why we say such things as, “You are out of touch with reality” when someone says something egregiously false: the speaker has failed in his duty to stand in the faithfulness relation to reality as a whole, as evidenced by this particular lapse. To speak of truth is not merely to speak of statements and what they are about; it is to speak of the wider reality in which everything has being. Thus it is not the case that the sentence, “’snow is white’ is true” means the same as the sentence “snow is white”, contrary to the so-called equivalence thesis: for the latter makes no use of the concepts of fidelity and reality, while the former does (albeit implicitly). The word “true” is bursting with large exciting ideas and is not the dull placeholder it is often reputed to be. To be true is to be true to reality, where truth-to is a matter of being faithful to something.

 

  [1] It is notable that standard theories of truth neglect the locution “true to”, but surely it is desirable to bring it into the picture—consider “true to the facts”. Maybe “true to” is basic, not “true” or “true of”.

  [2] The OED defines “accurate” as “correct in all details” (it defines “correct” as “free from error”). This is not to import the concept of truth itself into the definition, since a picture may be accurate without being true: truth emerges as a special case of this more general notion. Thus the definition is not circular (not that circularity is always a vice, so long as the circle of notions is wide enough).

  [3] One reason we need to formulate the theory using this very broad concept is that different statements concern different kinds of subject-matter and have different kinds of logical form (not every statement is subject-predicate); we need to be able to generalize over every type of statement and every subject-matter. Another reason is simply that the theory is most naturally formulated in this way: it just sounds intuitively right to say, “Truth is faithfulness to reality”.

                                                Concepts of Natural Kinds

 

 

According to the standard model, concepts like water and heat are natural kind concepts subject to Twin Earth cases: they are not “in the head”, they have an “indexical component”, they function as mere “labels”. Alongside these concepts we have another range of “theoretical” concepts, such as H2O and molecular motion: these concepts pick out the same natural kinds as the former concepts, but they are concepts of a different type. They express the “real essence” of the natural kind, what it is intrinsically and necessarily. They are not mere labels, they are not indexical, and they are not subject to Twin Earth cases. Thus, if one of our counterparts on Twin Earth uses the term “H2O”, he refers to H2O (water), even if the water-like liquid on Twin Earth is not H2O but XYZ (so “water” on Twin Earth refers to XYZ while “H2O” refers to H2O). Twin Earth contains both hydrogen and oxygen and speakers refer to these elements with “hydrogen” and “oxygen” (we may suppose), so their phrase means the same as ours, which entails that their words “water” and “H2O” do not refer to the same natural kind. This suggests a general thesis: for any concept like water there is (or could be) a corresponding concept like H2O. For any concept C subject to Twin Earth cases there is a concept C* not subject to Twin Earth cases such that C* refers to the same natural kind as C. If this thesis is correct, then our basic concepts of reality are not natural kind concepts, as conceived by the standard model. Instead, they are analogous to the concepts H2O and molecular motion: descriptive, internal to the conceiving subject, and invariant between Earth and Twin Earth. Concepts of the real essence of natural kinds are not themselves natural kind concepts, as conceived by the standard model.

            An objection may be raised to the thesis: Can’t we create Twin Earth cases for “oxygen” and “hydrogen”? What if Twin Earth does not contain these elements, though it does contain elements that are superficially similar to them: then won’t speakers on Twin Earth mean those elements not the ones we mean with the same terms? So the corresponding concepts will differ on Earth and Twin Earth, thus conforming to the standard model. If so, the concepts corresponding to the constituents of “H2O” will be natural kind concepts, as the standard model conceives them. But now there is a question about whether those concepts fit the thesis we are considering: won’t there be a corresponding concept for oxygen that fails to fit the standard model? Thus we can say that oxygen is the chemical element with atomic number 8, and now the question is whether that concept fits the standard model. It is hard to see how it could, since speakers on Twin Earth will have to mean the same thing we do by “chemical element with atomic number 8” (remember they are internally identical to us). And if that is so, then water will have a corresponding concept that is not itself of the type that water is—not a natural kind concept (though a concept of a natural kind).

            Still, someone might object that even this highly theoretical concept contains constituents that can be made subject to the Twin Earth treatment—say, the concept atom or the concept electron. Couldn’t Twin Earth be bathed, not in electrons, but in some superficially similar kind of particle, indistinguishable from electrons by the inhabitants of Twin Earth? Then won’t they refer to that type of particle not electrons with “electron”? This is now becoming farfetched and difficult to articulate, not like the original intuitive story about “water”: how could there be particles that are superficially just like electrons but are not electrons? But even supposing such a thing to be possible, we can ask about other expressions for electrons—say, “negatively charged particle”. This concept is surely not subject to Twin Earth cases! In the end the chain of terms denoting natural kinds bottoms out in a description that contains no terms that are subject to Twin Earth cases. So reality is not ultimately conceivable onlyby means of concepts that fit the standard model. Natural kind concepts of the type exemplified by water and heatare not the ultimate way we conceive of reality—just as the initial cases suggested. When we conceive of a liquid as water we mentally represent it in a way that differs structurally from the way it is mentally represented by the concept H2O; and the latter type of concept is what is fundamental to representing reality. Natural kind concepts of the type expressed in the vernacular are really a dispensable substitute for more basic “theoretical” concepts. The possibility of Twin Earth cases is not universal to concepts for natural kinds. At the most basic level, our concepts of natural kinds are not natural kind concepts. For the basic concepts of natural kinds, meaning (content) is “in the head”, even if it is not for their vernacular counterparts.

 

Colin McGinn