Well, it looks like I’m going to have to break my moratorium on posting about OOO again, given that Levi has just thrown down the gauntlet on his blog (here), specifically challenging us Sellarsians/Brandomians to account for the paradoxes of material implication. Moreover, he’s done it in the context of resurrecting the first debate between himself and I, concerning the reality of fictional objects (all of the appropriate references to which should be trackable from here).
I’ll say up front that I don’t think what Levi’s written poses any problems for either me or anyone else he references (including Brandom, Sellars, Ladyman and Ross, and Ray Brassier (given the reference to ‘eliminative materialists’, ‘scientism’, and his explicit remarks in the comments)). I don’t think it poses any problems for me because it completely misses my own position on the nature of reality (in the sense of ‘realness’ – it can also be read as a substantive, roughly synonymous with ‘the world’, or ‘the universe’, but I tend to call that ‘the Real’) and thus what it is for fictional objects to lack it. I don’t think it poses any problems for anyone else because it’s not clear what consequences Levi is trying to draw from the paradoxes of material implication. I’ll tackle these points in turn, along with a number of others along the way.
This is another long post, so be warned. If you’re only interested in my own account of fiction, try sections 1 & 2. If you’re only interested in my criticisms of Levi’s thoughts on logic, try sections 3 & 4. If you’re only interested in my interpretation of Brandom, try sections 5-7. And if you’re only interested in my brief comments on how this applies to Ray (which will be hard to read in isolation), read section 8. Now, on with the show.
[Update: Anyone who wants a more concise analysis of the problems with Levi’s appeals to logic should look at Zachary Luke Fraser‘s comments on the original post (here), and David Roden’s post on his blog (here). As I’ve noted before, brevity is not one of my virtues.]
1. Truth and Reality
The major point that Levi implicitly appeals to in his post is that there is an important link between something’s being real and there being things one can say about it that are true. The relevant quote seems to be this:-
Ontologically fictions should be treated as real (not true) precisely because they are capable of producing truths despite being false.
We’ll leave the question of what it is to ‘produce truths despite being false’ till the final section. For now, the important point is that Levi doesn’t explicate this link between truth and reality. This is to some extent forgivable because there is a really strong intuitive link between these two notions. It’s a link which features heavily in Heidegger’s philosophy (following the influence of the neo-Kantians), and pops up explicitly in a few other places.
However, if there is one idea that my Essay on Transcendental Realism is dedicated to explicating, and working out the consequences of, it’s this link between the notions of truth and reality. In fact, I not only try to elaborate the connection between the reality of objects and there being true things we can say about them (which is originally touched on by Quine), but I attempt to develop a broader notion of reality that can also apply to predicates, and to other aspects of the world (e.g., modality). Levi’s idea that the fact that there are true claims that can be made about fictional objects somehow forces us (his presumed interlocutors) to acknowledge their reality is so strange precisely because this is one of the principal problems that motivates the whole account of truth developed in the Essay.
To re-explain my position in brief, the connection is not between reality and truth simpliciter, but between reality and objective truth, defined as that species of truth whose prevalence is absolutely independent of our attitudes about it. Claims about fictional entities are the paradigm case of claims whose truth is attitude-dependent. The claim that ‘Harry Potter is a Wizard’ is true, as is the claim that ‘Thor is the son of Odin’, but neither of them are objectively true. Harry Potter and Thor aren’t real because although there are true claims about them, there are no objectively true claims about them. This is because in the former case, the attitudes of J.K. Rowling are specially authoritative in determining the truth of claims about Harry Potter (e.g., ‘Harry Potter has a secret half-sister’), and in the latter case, the attitudes of the norse people (though not necessarily any specific norse person) are specially authoritative in determining the truth of claims about Thor. The different kinds of truth correspond to different forms of argument (the game of giving and asking for reasons) because it just is the process through which the truth of claims is assessed. The objects of thought (i.e., that which is over-against us as subjects) can only be entities (i.e. genuinely have Being) insofar as they are genuinely independent of our thought about them (i.e., real), and this means insofar as we can engage in very specific kinds of thought about them (i.e., one susceptible to a specific kind of objective assessment), namely, empirical discourse (as exemplified by the natural sciences).
The strategy I take here is the opposite of a very common approach to the relation between epistemology and ontology, where the aim is to understand how it is we think about different kinds of object (epistemology) on the basis of a prior account of the mode of Being those objects possess (ontology). By contrast, my aim is to make sense of the ontological differences between objects on the basis of epistemological differences between the ways we think (or talk) about them. It turns out that the ontological difference between fictional objects and real objects is that between having no ontological status whatsoever and having some such status. I won’t get into the tricky question of mathematical objects here, but read the Essay itself if you’re interested.
2. Varieties of Fiction
Much of the original (and seemingly sustained) disagreement between myself and Levi on the status of fictional objects stems from the fact that Levi is often ambiguous about precisely what he takes fictional objects to be. Take the following quote:-
What I wish to claim, with my flat ontology, is that fictions are every bit as real as, for example, Popeye (or better yet, Twilight). This follows from my ontic principle developed in my article for The Speculative Turn. There I argue that any difference that makes a difference has a claim to reality. Clearly, when I’m claiming this, I’m not arguing that there is a physical entity like Popeye that eats, can punch people, gets strong when he eats spinach, etc. Popeye is real qua fictions. Nonetheless, Popeye the fiction is a real entity insofar as this fictional entity produces real differences within the world. In the case of Twilight, young women might model their amorous relations on these fictions. As a consequence, these fictions have real ontological efficacy in the world. They produce real differences. And honestly, why would we go to the trouble of critiquing so much myth and ideology if myths and ideologies were not genuinely efficacious in the world?
Now, leaving aside my continued perplexity over whether ‘the production of differences’ is anything more than causal efficacy (which hopefully will be cleared up by Levi’s forthcoming book), the question is what it means to say that Popeye is real ‘qua fictions’. Levi glosses this by claiming that the fictional is a species (indeed the paradigm case of) the symbolic. This simply ups the stakes in the debate over whether we can make sense of his account of the fictional.
As far as Levi is concerned, Popeye qua Popeye has effects within the world, without thereby being physical, i.e., without eating spinach or getting in fights. The problem is, how can Popeye be Popeye without having those properties (and doing those things) that supposedly make him Popeye? Why aren’t we just talking about something other than Popeye here? Surely, if there is no thing that is both real and gains amazing strength when it eats spinach, and Popeye gains amazing strength when he eats spinach, then Popeye can’t be real?
I think these confusions emerge from an overlap between different ways we have of talking about fictions. In order to describe these it’s important to make a distinction between fictions in the sense of stories or narratives, and fictions in the sense of the elements of these narratives. The former correspond to fictional worlds, and the latter to the fictional objects, properties and other things that are contained in them. Given this distinction, I think we can differentiate between three distinct ways of talking about fictions:-
i) Internal Talk: This way of talking about fictions treats them from within the perspective of the fictional world that they are or are contained within. Internal talk about fictional objects essentially treats the fictional world as if it were the actual world for the purposes of working out the consequences of (and assessing the truth of) claims about that world and its objects. So, when we say that “Bruce Wayne’s parents were killed when he was a child” we say it in the same way we say “Bertrand Russell’s parents died when he was a child”, the difference being that we implicitly differentiate the context of other claims that they are to be interpreted in relation to (i.e., between our claims about the fictional world of the DC Batman continuity (which is admittedly difficult to keep track of), and our claims about the actual world). This implicit differentiation can be made explicit by the use of sentential operators like ‘…is true in the DC Batman Continuity’ and ‘…is actually true’.
ii) Quasi-Internal Talk: This way of talking about fictions treats them from the perspective of the actual world, which is to say, it treats them as fictions. This means we talk about the DC Universe as an overarching (or perhaps sprawling) narrative, rather than as a world, and we talk about Batman as a character, rather than as a person. The important features of this kind of talk is that characters (or other narrative elements) can have properties which the corresponding people cannot have within the narrative treated as world. For instance, Batman is a protagonist, which is a specifically narrative property that he can’t possess from within the perspective of the story itself. Similarly, he has the property of being a trademark of DC comics, which is not a specifically narrative property, and although it could be had by things within the story (because there can be fictions within fictions), couldn’t be possessed by Batman qua person in the story.
Another very interesting feature of quasi-internal talk is that it allows for indeterminacy in a way that internal talk doesn’t. For instance, when we treat Batman as a person within a world, we act as if there is an answer to every question one could ask about Batman, even if we do not know that answer. So, we act as if there are determinate facts of the matter as to precisely how thick the fabric of his cowl is, as to what the name of his great-great-great-great-great grandmother on his mother’s side is, and as to whether he has a preference between semi-skimmed or full fat milk. But from the quasi-internal perspective, we can recognise that there are a plenty of holes in the narrative that have yet to be filled in. This idea bares an interesting relation to Michael Dummett’s ideas about anti-realism in fictional discourse, insofar as it suggests that the phenomenon of truth-value gaps may have nothing to do with the underlying logic.
iii) External Talk: This way of talking about fictions takes a further step back, and treats them from the perspective of the discursive processes that produce and sustain them. To understand this we’ve got to further contrast it with quasi-internal discourse. The thing which makes quasi-internal talk quasi-internal is that it’s truth is still assessed relative to the attitudes of some privileged individual or group. This can be seen if we look at the way our talk is often ambiguous between the internal and quasi-internal mode. For instance, we can interpret our earlier statement about ‘Bruce Wayne’ either as “In the story, Bruce Wayne (the person) has the property of having had his parents killed when he was a child” or as “In the actual world, Bruce Wayne (the character) has the property of having had his parents killed when he was a child (in the story)”. Often we simply fail to distinguish between which mode of speech we’re deploying, and this has few consequences, but it’s still important to understand. This is because there is an important relation between Bruce Wayne (the character) having an in-the-story-property, and Bruce Wayne (the person) having a property in the story. The truth of claims about both is dependent upon the attitudes of the authors of Batman, as filtered through the editing process of DC Comics. This holds equally for claims about what we called narrative properties above, insofar as Batman’s being a protagonist supervenes upon the actual content of the story, and thus the other decisions that have been made by its authors.
All this means that quasi-internal discourse is not objective. However, there can be objective discourse about the processes through which the attitudes of some individual or group come to determine what is non-objectively true. For instance, we can describe the structure of the process of creation, control, and editing at DC Comics, and the way it deploys the established canon of Batman comics. This is to describe the process underlying the creation and perpetuation of the attitudes we have towards Batman, both as person (internal) and as character (quasi-internal). I think that we can talk about similar, but much more distributed processes underlying the maintenance and change of all concepts, which insist in the normative attitudes underlying the ways we reason. This is the major part of what in the TR Essay I called the secondary dimension of conceptual content. Of course, we need some quite complicated theoretical resources in order to talk about these kinds of processes (and that’s something I’m working on on the side), so I can’t go into this in any detail right now.
Now, given this threefold distinction, we’ve got three candidates for what Popeye could be qua fiction: a person (physical object), talked about from the perspective of some fictional world, a character (symbolic object?), talked about in a non-objective fashion from the perspective of the actual world, and a discursive process, talked about in an objective fashion, in terms of the ways it systematically affects our attitudes towards either of the other two. I think that Levi denies that Popeye qua fiction is a person, but I think he conflates between the character and the discursive process. I also think that the only reason he can talk about the character/process as being Popeye (and not something else entirely) is because of the way our language involves systematic ambiguity between internal and quasi-internal talk. Once we understand that ambiguity, we should recognise that Popeye the person and Popeye the character aren’t strictly the same, much in the way that a concept and the thing it picks out strictly aren’t the same.
To close this section, it’s helpful to remember that the other major project of the Essay was to work out a way of rigorously distinguishing between various kinds of dependence relation. This was principally in order to formulate the claim that the structure of the world can be epistemologically dependent (sense-dependent) upon the structure of thought without thereby being ontologically dependent upon it (reference dependent), but it has wider applications than this. For instance, it allows us describe things that are ontologically dependent upon our attitudes about them, without the truth of claims about these things being dependent upon those attitudes, which is kind of epistemological independence other than sense-independence. For instance, it enables us to recognise that economic systems can be ontologically dependent upon the attitudes the agents involved in those systems have toward them, without thereby being epistemologically dependent upon the content of those attitudes. Indeed, in a commodity bubble, it is crucial to the existence and persistence of the bubble that the majority of those involved in it have beliefs about the state of the market that are largely incorrect.
Being able to make these distinctions, and thus to describe the relevant social phenomena adequately (i.e., without lapsing into what I’ve elsewhere called quasi-empirical terms), means getting clear about the relation between epistemology and ontology, thought and Being, and not simply collapsing one into the other.
3. From a Logical Point of View
Before turning to Levi’s claims about material implication, I think it’s necessary to frame the issue properly for those who might not be familiar with symbolic logic. I am by no means an expert myself, and so more experienced logicians should feel free to correct me, but I’ll endeavour to provide a little bit of background on material implication. As Levi notes, material implication is the closest thing to the English ‘if… then… ‘, or conditional connectives that can be reconstructed in the truth-functional framework of classical propositional logic (CPL).
In this framework, logical connectives are understood as functions that take the truth-values (these are boolean: 1=true, 0=false) of propositions they operate on as arguments and return a single truth-value as their value (i.e., the truth-value of the proposition they compose with of the propositions they operate on). The simplest example is obviously negation, which is a unitary operator (meaning it only operates on a single proposition) that returns the opposite truth-value (so, the falsity of P (P=0) produces the truth of not P (-P=1). The connectives of CPL can thus all be exhaustively characterised in terms of truth-tables, which specify which truth-value is produced for every possible combination of the relevant arguments (i.e., every possible combination of truth and falsity of the propositions the connective operates on).
The important point to remember though is that although the material conditional is the closest we can get to ‘if… then… ‘ in CPL, that doesn’t mean that it gives us the meaning of English conditionals. Indeed, not only are there a bunch of different ways we use conditional constructions in English (the most infamous being the difference between indicative and subjunctive conditionals), but none of them seem to correspond exactly to the material conditional of CPL. The ways in which the material conditional deviates from our intuitive understanding of conditionals get referred to collectively as the paradoxes of material implication. It’s important to note that the fact that a false antecedent always produces a true conditional is only one of these paradoxes. It’s also important to note that these aren’t paradoxical because they are intuitive assumptions that lead to contradictions (as Russell’s paradox does), but rather because they are results that defy our intuitions. Material implication is perfectly consistent, and as Levi points out, is largely indispensable given the role it has played in the development of mathematics and symbolic logic. However, this does not mean that material implication is the only game in town.
The most famous alternative is intuitionistic implication, the formalisation of which (intuitionistic logic) was developed in order to underwrite the intuitionist program in mathematics, which refused to accept the validity of nonconstructive proofs (those which allow double negation elimination (i.e., – -P = P)). Intuitionistic implication remains important insofar as it is the most natural kind of implication viewed from a proof-theoretic perspective, i.e., from a perspective that tries to understand the nature of logic on the basis of the ways in which we actually prove statements, rather than on the basis of accounts of the (often abstract) objects these statements refer to (the model-theoretic perspective). This claim to naturalness doesn’t exclude material implication, as there has been good work done on reconstructing material implication from this perspective, it simply indicates that we can learn much about the nature of logic from the differences and relations between material and intuitionistic forms of implication. As a side note on this point, Levi seemed to imply that Brandom endorses a “truth-functional” conception of reason in his post (a strange turn of phrase), and this is false for precisely the reason that Brandom has developed an alternative characterisation of the connectives of CPL (plus modal operators) on the basis of the more proof-theoretic notion of incompatibility (though some would say it is insufficiently proof-theoretic).
There have then been various attempts to respond directly to the paradoxes of material implication. The first (and simplest) of these is C.I. Lewis’ development of strict implication, which adds a modal necessity operator (which is not truth-functional, and thus not part of CPL) to the material conditional (i.e., ‘P strictly implies Q’ is read as ‘necessarily (P implies Q)’). This has the effect of making the strict conditional true if and only if the corresponding material conditional is true in all possible worlds (at least on the standard semantics for modal operators). So, when a conditional like ‘If Charles Windsor is King, then the moon is made of cheese’ is true (counter-intuitively) when interpreted as a material conditional, it is false when interpreted as a strict conditional, because it is possible that Charles could be king and the moon not made of green cheese. This seems more intuitive, but it has it’s own problems. For instance, conditionals with impossible antecedents (e.g., ‘if 2+2=5, then the moon is made of green cheese’), and conditionals with necessary consequents (e.g., ‘if David Cameron is prime minister, then 2+2=4’) always come out true.
These kinds of issues motivated the creation of relevance logic, and the corresponding notion of relevant implication. This is one of the forms of substructural logic (along with linear logic), wherein some of the so-called meta-rules that characterise classical logic (formulated by Gentzen) get suspended. I’m not going to explain these in detail, and if you want to know more, you can read the Stanford Encyclopedia of Philosophy article on it, which is very good (here). The basic idea underlying relevant implication is that there must be some kind of connection between the antecedent of a conditional and the consequent of the conditional, or that they must be relevant to one another (like the claims ‘Rex is a dog’ and ‘Rex is a mammal’, and unlike the claims ‘David Cameron is prime minister’ and ‘2+2=4’). The ways in which these connections are established and tracked is a tricky business, and it makes for much more complicated natural deduction procedures. It’s also worth noting that relevance logics are forms of paraconsistent logic, in that they don’t validate the principle of explosion (i.e., that a contradiction entails everything), which is itself one of the paradoxes of material implication. Various forms of paraconsistent logic have been built in order to model contradiction tolerant reasoning, but I don’t know enough about them to be able to say anything useful.
Finally, it’s worth mentioning non-monotonic logic, and the corresponding notion of non-monotonic implication (which in Brandom’s system is known as permissive entailment, or that which underlies entitlement-preserving inference). I’ve briefly explained this before (here in section 3), but it’s worth mentioning again. Implication is monotonic if it cannot be undermined by the addition of additional premises. So, the inference from ‘Rex is a dog’ to ‘Rex is a mammal’ is monotonic insofar as we can add any additional premises we like (e.g., ‘Rex is my favourite pet’, ‘David Cameron is Prime Minister’, ‘2+2=4’, etc.) without it becoming a bad inference. However, the inference from ‘My Dad’s car is in the drive’ to ‘My Dad is at home’ can be undermined by the addition of further premises (called defeasors) such as ‘My Dad took the bus today’, or ‘The car’s rear axel is broken’. The vast majority of our reasoning is non-monotonic (also called probative, or defeasible), and thus being able to account for it is very important. Again, the resources necessary to do so are more complex than those of the CPL framework (and Brandom has done a good job of building a basic pragmatic framework in which to make sense of it).
What all of this shows is that there has been a truly phenomenal amount of work done on material implication and its paradoxes, within the context of the overarching logical project of trying to understand the nature of inference and consequence (and the relation between the two). This is about as competent a summary as I can muster on short notice, but it does indicate that even if we restrict ourselves to understanding reasoning in purely formal-mathematical terms, there’s a lot more to it than what material conditionals make explicit. If we’re willing to reach deeper into the pragmatics of reasoning, I think we can find an even richer philosophical semantics than even these formal tools let us articulate. I’m attempting forays into this work on the side (while I write the last bits of the thesis), and the level of rigour required makes it difficult work. I must try to avoid rigorous posing though, as it’s bad for my posture.
4. Producing Truth or a False Power?
So, finally, I can turn to the consequences Levi draws from the nature of material implication. It’s best to quote the relevant section of his post in full before examining it in detail:-
Now here’s what’s interesting about material conditionals: The only circumstance in which a material conditional is false is that circumstance in which its antecedent (P) is true and it’s consequent (Q) is false. In all other circumstances, material conditionals are true. Thus if the antecedent (P) is false and the antecedent is true the material conditional (P —> Q) is true. Likewise, if the antecedent of a material conditional is false and the consequent of a material conditional is false, then the material conditional as a whole (P —> Q) is true. I won’t bore you with all the details of why this is the case, as it involves a lot of logical equivalences between propositions. For the moment I will take it as face value.
So far so good. Onto the consequences:-
Now there are a couple of points that follow from these points about material conditionals. First, the truth-functional logic that follows from the logic of material conditionals gives, at least, epistemological grounds for treating fictions as real. Ontologically fictions should be treated as real (not true) precisely because they are capable of producing truths despite being false. This entails that ideologies, delusions, fictions (works of art, narratives, novels, myths, religions) have a capacity to produce truth even though they are false. My second point is that this, in my view, calls into question the project of representational realism, eliminative materialism, or scientism where realist ontology is concerned. The representationalist, scientistic, or eliminativist wants to claim that truth can only be produced if the antecedent of a material conditional is true. If the truth produced by a literary work or a political movement based on fictional ideology, mythology, or religion (Martin Luther King’s religious belief for example) is false, the representational realist is necessarily committed to the thesis that such a political or ethical transformation can have no truth.
So here’s what I want to say: If the representational realist, the eliminative materialist, or the scientistic philosopher is truly committed to such a thesis, I want to see the thorough revision of symbolic logic that they develop to account for such a metaphysical position.
Oh boy, are there some problems here. I’ll try to take them one at a time.
First of all, it’s important to notice that Levi has subtly shifted what he’s talking about in talking about fictions here. Originally he was principally talking about fictional objects, such as Popeye or Eldorado, but now he’s talking about fictions as collections of statements, more like the story of Popeye or the myth of Eldorado. He must make this transition insofar as he takes them to be susceptible to assessment of truth and falsity, and he seems to imply that fictions are by definition false. Note that this is already something I would dispute, insofar as I think there is a good sense in which fictions can be true, i.e., insofar as they are qualified using the appropriate sentential operators (e.g., ‘In the DC Universe, Batman is Bruce Wayne’). I’m happy for there to be fictions in the broad sense, such as propositions, norms, and similar objects, that we can make unqualified truth claims about (e.g., ‘The proposition Ray just expressed is true’, ‘All norms are either transcendental or socially instituted’, etc.), as long as we recognise that the kind of truth they have is not objective truth. All of this is important insofar as fictional objects cannot themselves be the antecedents (or consequents) of conditionals, only statements about them can be.
Second, precisely what kinds of truth are these falsities producing? Well, they’re producing conditionals of the form ‘If Eldorado is a city of gold, then grass is green’ and ‘If Popeye exists, then I am the greatest swordman who has ever lived’. Profound truths, no? Given a couple false propositions and the material conditional I’ll give you an infinite number of truths, but they’ll all be completely trivial, or worse, irrelevant (in the technical logical sense). Is this something we need to be worried about? I’d suggest this is just a corollary of our capacity to produce an infinite number of sentences that have never been used before. Given this capacity, it’s hardly surprising that a vast number, if not the majority of these sentences will be distinctly uninteresting. That some of them should be both true and uninteresting is neither here nor there.
Third, precisely what is it to produce a truth? This relates to the first point, insofar as we’d traditionally think of objects (or entities) as having capacities to produce effects, and we certainly wouldn’t consider truth as an effect produced in time, although a statement describing an effect happening at a certain time is in a certain sense made true by that effect happening at that time (though I have absolutely no sympathy for truth-maker theory). I suspect what we have here is another ambiguity, this time between the vehicles (e.g., assertions, sentences, beliefs, etc.) and the contents (i.e., the propositions they express) of discursive representations (something I’ve discussed before, here). Truths understood as vehicles for true contents (e.g., Martin Luther King’s belief states), rather than the true contents themselves (e.g., what Martin Luther King believed), could be taken to have capacities, and changes in their states could be taken to be effects. This way of talking allows one to talk about one persons false beliefs or assertions causing them (or others) to develop true beliefs (or make true assertions). The problem is that these causal relationships between vehicles have nothing, I repeat, nothing, to do with the logical relationships between the contents they bear. I cannot stress that last point enough. That Martin Luther King’s belief in the existence of God played a causal role in the development of the now widely held commitment to the fundamental rightness of tolerance and racial equality has no bearing on the truth or falsity of either, nor on the inferential relations between them. It is indeed the case that causal relations are correctly described by conditionals of a certain kind (i.e., counterfactually robust, or subjunctive conditionals), i.e., that causal relations underwrite inferential relations, but this doesn’t mean that inferential relations are causal relations.
One should thus be able to see that the above passage from Levi contains a quite frightening non-sequitur. This is not just a shift from talking about implication relations between propositions to causal relations between their vehicles (and perhaps even the ‘things’, such as Popeye, which they are about), but it is also a shift from talking about the truth of the conditional as a whole being implied/produced by the falsity of the antecedent, to talking about the truth of the consequent being implied/produced by the falsity of the antecedent. I’ll let that sink in for a moment. It amounts to holding that, at least some of the time, the consequent of a conditional is true because it’s antecedent is false. Again, I cannot stress how wrong this is. I might go so far as to characterise it as ingeniously fallacious.
Now, I think it’s possible to salvage something marginally more reasonable from Levi’s remarks given a little reconstruction. If we ignore the non-sequitur, then it’s possible to reconfigure the initial problem in a way that becomes surprisingly familiar. The issue was that for every false proposition we can make many true conditional propositions. We can simplify this by ignoring the material conditional entirely and focusing on a much simpler connective, namely, negation. As we explained above, one can make a true proposition out of any false proposition plus the negation operator. This is very intuitive, and lets us look at the problem much more directly. What could possibly be objectionable about the fact that false claims license the creation of true negative claims?
Well, this is precisely the problem that some have with the idea of negative facts. This is problematic for Russellians and others who try to account for propositions in metaphysical terms, by making them a special kind of entity composed of the entities they are about. On this approach facts just are true propositions, and this truth is understood in terms of the internal composition of the proposition. So, for instance, the claim that ‘Pete’s back is uncooperative’ is true just in case the proposition it expresses is composed of an object (my back) and a universal property (uncooperativeness), and the two are correctly connected. Leaving aside the question of what this connection consists in (the problem of the unity of the proposition), the simple problem for this position whether or not the fact that ‘It is not the case that Pete’s back is cooperative’ expresses the same fact as ‘Pete’s back is uncooperative’. This is a very crude version of Russellianism, which has subsequently been developed in many ways. Moreover, I’m well aware that Levi endorses nothing like it, but it’s useful for introducing a deeper point.
This point is that problems with negative facts lead very directly to problems with negative existentials. For instance, how are we to understand claims like ‘Pegasus is a winged horse’, if Pegasus doesn’t exist? This is the root of the famous disagreement between Meinong and Russell, the former endorsing the idea that non-existent objects must have some kind of Being (subsistence) in order for claims to be true of them, and the latter developing his famous theory of descriptions in order to deny this. Abstracting from all of the metaphysical machinery of Russell and Meinong, the simplest way of phrasing this problem is this: how is it possible to deny existence to something without thereby presupposing that there is something which doesn’t exist? This is the problem Quine called Plato’s Beard (in ‘On What There Is’, which is one of the classic papers of 20th Century philosophy), in contrast to Occam’s Razor (which tries to shave it off). I think this is really the underlying problem that Levi is aiming for, and it seems to be a repeated theme in the debate between OOO and us partisans of science, namely, the choice between ontological liberalism (or outright promiscuity) and ontological conservativism, or between Meinong’s pluriverse of objects and Quine’s taste for desert landscapes.
The idea seems to be that if claims about fictional objects are strictly false, then these falsities can be used to create truths (using negation and the material conditional) that must in some way depend upon these objects for their truth, therefore granting these objects some kind of ontological status. I’ve pointed out affinities between Graham’s position and Meinong’s before (here), though I’ve never followed it up in depth, but there’s an important disanalogy between both of these positions and the position Levi seemingly advocates. This is that while Graham and Meinong allow for two distinct kinds of object, only one of which is real in the relevant sense, Levi wants fictional objects to be real in a much more full blooded sense. Given that Plato’s Beard hinges on the possibility of drawing such a distinction, this means that even this more reasonable reconstruction of Levi’s claims is not entirely consistent. Whether or not Levi can produce a distinction between the fictional and non-fictional strong enough to underwrite the Beard while nonetheless being weak enough for him to allow fictional objects to engage in full fledged causal relations remains to be seen, but I’m doubtful.
5. Dimensions of Representation
The ultimate question then is whether or not Plato’s Beard actually causes a problem for any of the positions Levi gestured at in his post (eliminative materialism, Sellarsianism, Brandomian inferentialism, ontic structural realism, etc.). I won’t pretend to speak for everyone here, so I’ll just confine myself to my own broadly Brandomian commitments. On this front, the answer is, unsurprisingly, no. In order to explain why this is the case, I’m going to go over the task Brandom sets himself in providing an account of representation, and in doing so I’ll also go over the problem with the opposing Meinongian approach to representation in a bit more detail.
Brandom has a very complex account of representation, which he requires precisely because he commits himself to explaining it in terms of inference. He’s not allowed any representational primitives, and must explain everything in terms that are amenable to the pragmatics of language, or how words are used to refer to things. One of the constraints he places on this account is that it must explain both representational purport (or intending to pick out an object) and representational success (actually picking out an object), without collapsing one into the other (e.g., the difference between talking about ‘the city of gold’ and actually picking out an object that meets that description).
Brandom takes it that the Meinongian approach accounts for representational purport by collapsing it into representational success, by explaining intending an object in terms of the object intended. This demands that for any intentional relation, there must be an intended object, which in the case of an unsuccessful intentional relation must simply be a special kind of object, namely, an unreal one. I’ll quote Brandom at a bit more length, as this is a wonderful passage:-
The trouble with taking it that there is something that is successfully represented by every purported representing is not just that it involves commitment to a luxuriant ontology; ontological self-indulgence is a comparatively harmless vice. But it can be symptomatic of a failure to shoulder an explanatory burden. In this case it evidently (and ultimately unhelpfully) transforms the demand for an account of the relation between correct and incorrect, unfulfilled or merely purported and actually successful representing, into a demand for an account of the relation between the statuses of what is represented in the two cases: between mere subsistence and robust existence. Ontological postulation can no more provide an explanation by itself in this case than it could in the one just considered, where the issues was an account of the relation between the sense in which singular terms are representationally contentful and the sense in which sentences are [basically, a critique of the Russellian account of propositions discussed above].
Now, I will have more to say about how harmless a vice ontological self-indulgence is, but I think the point that it is a symptom of a deeper vice, namely, of shirking the commitment to explain representation, is decisive. I’ve said that this is a serious problem for OOO before, both for Graham’s more closely Meinongian approach (here, here, and here, in section 4), and for Levi’s more scattered account of representation (in this series of posts 1, 2, and 3). There is in fact a legitimate question as to whether Levi’s own account of representation is sufficient to underwrite the beard argument, and thus the criticism we’ve managed to reconstruct, but I’ll ignore this. The challenge is instead to show the corresponding virtue in Brandom’s approach, by sketching how it shoulders this explanatory burden, and in thereby undercuts the account of representation that motivates the beard argument. I can’t explain this in great detail without explaining Brandom’s inferentialist philosophy of language in full, so I’ll try to present the most schematic overview I can. I’m going to skip over the basics of Brandom’s scorekeeping pragmatics, and the account of inferential relations it underpins, as I’ve already explained most of it elsewhere (see here and here, among other places), but if you want details read chapters 1-4 of MIE. For those of you who don’t want to wade through the internal workings of Brandom’s system, this a good point to skip straight to the conclusion.
First, it’s important to understand that Brandom accounts for the content of subsentential expressions (i.e., words and phrases), including singular terms (e.g., ‘Bob’, ‘the fattest man in the world’, etc.) and predicate expressions (e.g., ‘…is red’, ‘…is a dog’, ‘…is between… and… ‘, etc.), in terms of the contribution they make to the material inferential role of the sentences they compose (i.e., to the sentences from which they can be inferred and those which can be inferred from them). Brandom accounts for this in terms of the idea of substitution inferences, wherein one expression is substituted for another expression of the same syntactic type within a sentence (e.g., substituting ‘mammal’ for ‘dog’ in ‘Rex is a dog’, producing the inference to ‘ is a mammal’). Expressions determine the inferential roles of the sentences the expressions they compose insofar as they are associated with set of general patterns of inference (e.g., from ‘x is a dog’ to ‘x is a mammal’, ‘x is a dog’ to ‘x has four legs’, and ‘x is a dachshund’ to ‘x is a dog’, etc.). Brandom calls this set the expression’s SMSICs (or Simple Material Substitution Inferential Commitments). This is what underwrites the compositionality of language (its productivity and systematicity), albeit in a weak form (see Brandom’s debate with Fodor and Lepore for details). All this is covered in chapter 6 of MIE.
Second, Brandom has an account of how the various syntactic types of expressions are differentiated on this basis. We first classify singular terms as those expressions that are principally substituted for one another, and predicates as the substitution frames that result from the former kinds of substitution (e.g., ‘…is red’, ‘…is between… and… ‘, etc.), these are what these are their Substitution-Structural Roles (SSRs). We then classify singular terms as those expressions whose substitution is essentially symmetric (e.g., if one can substitute ‘Clark Kent’ for ‘Superman’ then one can also substitute ‘Superman’ for ‘Clark Kent’), and predicate expressions as those whose substitution is essentially asymmetric (e.g., one can’t substitute ‘mammal’ for ‘dog’ – the inference from ‘x is a mammal’ to ‘x is a dog’ is not a good one), these are their Semantic-Inferential Significances (SISs). There are a few complications with this account (quantifiers and indefinite descriptions (Jon Cogburn), relations (Fodor and Lepore), and non-extensional contexts (McCullagh), but I think they can be dealt with. Moreover, this basic picture allows one to generate a whole host of other syntactic categories (quantifiers, adverbial modifiers, etc.) on the basis of other kinds of SSRs one can generate out of these basic types, pretty much in line with the kind of classification found in Lewis’ general semantics.
Third, it’s important to understand that Brandom’s approach is essentially neo-Fregean, which is to say that it is based on a form of the distinction between sense and reference, which is to say between that which determines what the singular term represents and that which it represents, respectively. This divides into four parts: an account of definite descriptions along broadly Russellian lines, an account of indexicals and demonstratives that avoids Kaplan’s problems with Fregeanism, an account of proper names that satisfies Kripke’s concerns about rigid designation, and an account of de re representational vocabulary such as ‘of’ and ‘about’ (e.g., ‘Pete is thinking about his brother’, and ‘Pete is thinking of his brother that he is awesome’) that solves Kripke’s puzzle about belief, and incorporates Evans and McDowell’s idea about de re senses. Moreover, these handle not only the representation of objects (i.e., what is represented by singular terms) but also the representation of properties (i.e., what is represented by (monadic) predicates), which can be picked out using definite descriptions (e.g., ‘the property of being both an officer and a gentleman’), picked out indexically and demonstratively (e.g., ‘The style of my hair is the one currently in fashion’, ‘This blue is a lighter shade than that one’), picked out by names (especially important in relation to Putnam’s examples of natural kind terms, e.g., ‘water’, ‘gold’, ‘electron’, etc.), and which we can negotiate different perspectives upon (e.g., ‘Pete claims of the property of being an unmarried man that it applies to some married men’, ‘Rutherford thought of probability waves that they were essentially particulate’, etc.).
Finally, Brandom’s inferentialist semantics is split into three levels, corresponding to different aspects of his scorekeeping pragmatics: Inference, Substitution, and Anaphora (what he calls the ISA model). I personally think there’s a fourth dimension, which I call Compartmentalisation (making for an ISAC model), but I won’t mention that further here. We’ve already seen the basics of the first two levels, but in order to understand how the various dimensions of Brandom’s neo-Fregean picture work it’s necessary to add an additional dimension to the account of substitution, namely, Brandom’s account of existential commitments, and to explain the basics of his account of recurrence commitments, or anaphora (both of these are handled in very accessible terms in chapter 7 of MIE).
6. Existence, Quantification and Identity
The important thing to understand about Brandom’s account of existential commitment is that it effectively completes his account of quantification. Whereas most people interpret the quantifiers objectually, as ranging over domains of objects, Brandom interprets the quantifiers substitutionally, as ranging over domains of names for objects (or predicates, in higher order quantification). Brandom interprets unrestricted quantification (which, as we’ll show, he thinks doesn’t work) as ranging over all names, including not just names we actually have but any we might possibly add (this is necessary in order to overcome certain issues regarding cardinality, although Mark Lance has provided an alternative approach to this that is really excellent). The crucial point is then that Brandom’s quantifiers are so called free quantifiers (free logic is another form of deviant logic not discussed above, insofar as it’s principally concerned with the role of with quantifiers and names, and the ontological neutrality of logic). What this means is that the standard quantifiers are the universal quantifier (e.g., for all x: Fx), which is interpreted as an infinite conjunction of claims produced by substituting all names in the domain into the relevant substitution-frame (e.g., Fa & Fb & Fc… etc., for x: Fx) and the particular quantifier (e.g., for some x: Fx), which is similarly interpreted as an infinite disjunction (e.g., Fa v Fb v Fc… etc., for Ex: Fx). This differs from non-free accounts insofar as the particular quantifier does not have existential import, and this is why it isn’t called the existential quantifier. This is to say that the notions of number and existence are properly dissociated. This explains why Brandom needs a separate account of existential commitment that attaches to his account of quantification.
It’s helpful to explain how Brandom’s account of existential commitment works with direct reference to what we need it for: namely, Brandom’s reconstruction of Russell’s analysis of definite descriptions. As already explained, Russell’s analysis was developed in order to undercut Meinong, who held that definite descriptions such as ‘the King of France is bald’ could only be meaningful if there is a (subsistent) King of France, who nonetheless lacks existence. Russell gets around this by analysing the logical structure of descriptions into three parts, each of which specifies a condition that must be satisfied for the description to be true: there is some x that is King of France (existence), for all y, if y is King of France then y=x (uniqueness), and x is bald (predication). This is also Quine’s recommended solution to Plato’s Beard, because it treats the failure of statements that purport to represent nonexistent objects as garden variety falsehood. Representational success is thereby understood in terms of the existence and uniqueness conditions: if either is unsatisfied, the representation is merely false. Brandom’s analysis concurs with this, but he can’t follow Russell and Quine in understanding the existence condition as a matter of existential quantification.
Instead, Brandom borrows some ideas from Frege and understands it as a special kind of substitutional commitment. We mentioned above that singular terms are essentially characterised by symmetric substitution relations, but what we didn’t explain is that these are made explicit by identity claims (i.e., if a=b then one can substitute ‘a’ for ‘b’ in any extensional context, such as ‘Fa’). Brandom thus takes the existence condition on successfully representing an object to be expressed by a special kind of identity claim, which licenses the substitution of the singular term referring to the object with what he calls a canonical designator. The importance of canonical designators is that they provide a special kind of uniqueness that enables us to co-ordinate other substitutional commitments. The best way to see this is with the paradigm case of canonical designator: the natural numbers. These are specified by means of a succession operator (‘) and a fixed point (0), by means of which we can create an infinite number of names (0′, 0” ,0”’, etc.) which can be exchanged for numerals (1, 2, 3, etc.). In essence, we take a single relation (succession) and use it to create a system of co-ordinates over which there is a well defined criteria of identity: if a and b stand in the same succession relations, then a=b (e.g., if x comes after 1 and before 3, then x must be 2). For Brandom, to exist in the general sense is to be identical to something named by a canonical designator, and to exist in a specific sense is to be identical to something named by a specific kind of canonical designator (e.g., numerical existence).
Brandom then takes it that we can account for various kinds of existence by working out other ways of constructing sets of canonical designators, his principle examples being physical existence (which is based on spatio-temporal co-ordinates) and fictional existence (which is based on narrative co-ordinates). In essence, these kinds of existence are essentially sortal predicates. These are predicates in terms of which identity relations are relativised (e.g., x is the same number as y) and quantifiers are restricted (e.g., for some number x, x is the smallest sum of the square of two primes). These have been described in a number of different ways in the analytic tradition. At minimum they are simply predicates that supply criteria of identity for the things they apply to, and thereby enable us to count that type of things, though some analytic metaphysicians (e.g., David Wiggins and Michael Ayers) have provided more elaborate accounts of them in attempts to revive Aristotle’s notion of secondary substance (and the fourfold categorical distinction that results from the intersection of the substance/accident and universal/particular distinctions). I’ll leave these more elaborate accounts to one side an try to explain sortals by contrasting them with non-sortal predicates.
For example, take the predicate ‘…is red’ (a very traditional non-sortal property, or accident). How many red things are there? That there is no good answer to this question is obvious when we consider that any area of colour could be counted as a red thing, and there are uncountable numbers of overlapping and non-contiguous area even on the red wall in front of me. Even if one asks how many red things there are in this room, there still is no good answer. This is really because there is no good answer to the questions ‘How many things are there?’ and ‘How many things are there in this room?’. We have no way of counting things simpliciter. Words like ‘thing’ and ‘object’ are pseudo-sortals that are always accompanied by some implicit sortal restriction. So, I might ask how many things there are in this room, but we both know roughly what kind of things I mean (e.g., books, CDs, pieces of furniture, and electronics, but not nitrogen molecules, locations where food has been spilt, or sets of spatial points), and can thus count them (at least loosely). This means that in order to count red things, triangular things, and so on, I have to specify a sortal such as ‘flash of light’, ‘triangle’, etc., because there are criteria under which it makes sense to ask ‘Is this the same triangle?’ (i.e., if two triangles share the same internal angles, they’re identical), but not ‘Is this the same triangular thing?’ (i.e., we’re not sure whether we’re counting abstract mathematical objects or spatio-temporal instances).
All this shows that (as we hinted above) explicitly unrestricted quantification doesn’t work, and all quantification must be restricted somehow. Brandom thinks that the same applies to identity, so that all identity must somehow be relativised. This is another debate that tends to come up a lot in analytic metaphysics (e.g., is the statue the same as the lump it was made out of, or is it only the same clay?). A lot of neo-Aristotelians (see Michael Ayers again) argue that identity must be absolute, but restricted to a categorial framework (e.g., distinguishing between substances, collections of substances, and the matter substances are made out of as distinct kinds of thing that can’t be identified). Again, I’m going to leave these arguments alone, but it’s good to point to these as indicating the place where my appropriation of Brandom’s account of representation for my critique of metaphysics (another important notion from the TR Essay) connects up with Aristotelian debates about substance (though on the record, I think the intuitive appeal of substance stems from a misunderstanding the intricacies of quantifiers and identity). What’s important is that regardless of whether one endorses absolute identity, identity claims must be restricted by means of some kind of sortal framework, in precisely the way that quantified claims are. If not, we end up with nonsensical identity claims like ‘Julius Caesar is identical to the number 9’, and ‘the concept of Saturn is identical to Saturn’ (which I’ve discussed before in other contexts).
What all of this shows is that the notions of existence, identity, and quantification are very deeply intertwined. The intuitive notions of unrestricted quantification and unrestricted identity inevitably lead to problems, much as intuitive set theory does. Indeed, if one thinks set theory (and its extensions) is derivative upon higher order quantification over plurals and predicates (as suggested by some of Oystein Linnebo’s work (here), then the latter problems follow from the former. One way of looking at the relation that identity and quantification have to existence is then to see the latter as codifying the ways in which the former are restricted, so as to make them workable. This would be to say that free logic plays a very important role in making explicit the implicit features of our reasoning that make counting and identification possible. However, this is not to say that we should simply embrace free logic and abandon objectual quantification and the finitary variants of substitutional quantification. I really think that Brandom’s account can and should be extended to allow all of these kinds of quantifiers, along with the standard generalised quantifiers (e.g., ‘for most x…’, ‘for a few x…’, ‘for half x…’, etc.). These can all be seen as making explicit different aspects of our practices for reasoning about number. I’ve only begun to scratch the surface of this though, and there’s a lot of work to be done.
One final point worth making is that the idea of an integrated sortal framework restricting identity and quantification corresponds to the traditional concern with modes of Being, which was also very important for the early Heidegger. These modes of Being are essentially supposed to be the highest level sortals, which supposedly ‘carve nature at its joints’. They are thus supposed to correspond to the natural forms of existence, identity, and restricted quantifiers (see the literature on quantifier variance, such as Kris McDaniel’s work). I’ve been very skeptical about the idea of modes of Being in the past, specifically insofar as I endorse Deleuze’s claims about the univocity of Being (here), which is incompatible with a multiplicity of modes. It might seem that in endorsing Brandom’s account of existence that I am thereby violating this commitment, but this is not the case. The strong univocity thesis I endorse denies that there is a division of sortals into those that are ontological (e.g., physical, mathematical, artifactual, living, divine, etc.) and those that are ontic (e.g., electron, dog, economic system, etc.). This is one way of articulating Deleuze’s claim that difference itself is univocal (though I suspect not the only one). This is compatible with Brandom’s account of existence as long as I deny ontological status to all but one of the highest level sortals. This is precisely what is achieved by my account of objectivity and reality. As we saw above, I’m quite happy for there to be fictional existence, it just isn’t a kind of real existence. My endorsement of univocity thus amounts to the claim that although there are different types of existence, there aren’t different types of real existence, and genuine talk about Being is talk about the latter.
7. Sense and Reference
In providing an overview of Brandom’s account of existential commitment, and the way it allows him to adopt Russell’s theory of descriptions, we’ve uncovered the foundation of his account of reference. The rest of this account, and the account of sense that corresponds to it, can only be understood by way of Brandom’s account of what he calls recurrence commitments, or the generalised phenomenon of anaphora. Once we have explained this, we will have the basis of a unified picture of representational purport/success in terms of the way that sense determines successful or unsuccessful reference.
In order to understand the notion of recurrence it’s important to understand the distinction between lexical types and lexical tokens (e.g., when I type ‘artichoke artichoke artichoke’, there is only one word between the quote marks, but three tokens of that word). It’s also important to understand that there can be different concepts that correspond to the same word, which is to say that the expressions that express them are lexically identical, or homonyms (e.g., the ‘bank’ of a river and the ‘bank’ that one takes one’s money out of). Those tokens (or tokenings) of expressions that correspond to the same concept are said to be recurrences of one another. These expressions thus share the same content (i.e., SMSICs). A recurrence commitment is just a commitment to the effect that one expression is a recurrence of another, or loosely, that they mean the same thing.
This all seems very simple at the moment but it becomes more complex when we realise that there are two different kinds recurrence commitment, symmetrical and asymmetrical, and that these combine to create (at least) two different kinds of recurrence structure. A recurrence class is an equivalence class of tokenings, which is to say a set of tokenings whose semantic features are all taken to be the same. No particular tokening is privileged in determining the content of the rest of the tokenings. An anaphoric chain is a sequence of tokenings in which the semantic features of later tokenings are taken to depend upon those of earlier tokenings (in potentially quite complex ways). Anaphoric chains involve the privileging of particular tokens, called anaphoric antecedents, whose features determine the content of the all the tokens in the chain, the rest of which are anaphoric dependents. The most classic example of anaphoric chains are produced by anaphoric pronouns (e.g., ‘he’, ‘she’, ‘it’), such as when I say ‘My mother makes nice cakes, but she just can’t seem to get toffee right’. Here, ‘my mother’ is the antecedent and ‘she’ is the dependent, the latter getting its meaning from the former. Moreover, just as recurrence classes can incorporate tokens from sentences spoken by different people, so can anaphoric chains. It’s possible for one person to start a conversation by referring to someone, and from that point on for no one to use his name, but simply to call him ‘he’. We’re even able to rely on contextual factors to differentiate between different chains running in the same conversation, all using the same pronoun (i.e., when we’ve got multiple ‘he’s’, ‘she’s’, or ‘it’s’). So, whereas recurrence classes are generally made up of lexically co-typical tokens (and often just correspond to lexical types), anaphoric chains are often made up of lexically different tokens, precisely in order to differentiate between their statuses within the chain.
These recurrence structures are Brandom’s equivalent of Frege’s senses, insofar as they determine the reference of the expressions that express them without thereby being reducible to this reference. Moreover, different recurrence structures can determine the same referent (e.g., the senses of ‘the heaviest man in the world’ and ‘the man with the greatest mass’ can be different even if their referents are always the same). This cashes out Frege’s idea of the difference between objects (references) and modes of presentation of objects (senses), and thereby solves Frege’s Puzzle. This is to account for the possibility of informative identity statements, such as ‘the morning star is the evening star’ and ‘Clark Kent is Superman’ (in contrast to trivial ones, such as ‘the morning star is the morning star’ and ‘Clark Kent is Clark Kent’), which is achieved insofar as it is possible for us to grasp the sense of the various expressions (a practical grasp of the recurrence structure) without thereby knowing their referents, or that their referents are identical (correct commitments involving the relevant expressions). To think about this in a different way, recurrence commitments constitute the identity of the names we use to refer to objects (e.g., ‘a’ and ‘b’), and thus make possible substitution commitments between these names (e.g., ‘a=b’).
This brings us to Kripke’s work on proper names. Kripke essentially showed that Russell’s approach to definite descriptions doesn’t work when applied to proper names, because proper names are what he calls rigid designators. What he means by this is that they pick out the same object in all possible worlds. This means that if the meaning of ‘Aristotle’ is a set of descriptive conditions that the actual Aristotle satisfies, such as ‘Aristotle is the most famous student of Plato’, then we can’t make sense of statements like ‘Aristotle might not have been the most famous student of Plato’, or the more literal ‘There is some possible world in which Aristotle is not the most famous student of Plato’. This caused a revival of sorts for Millian theories of names, which take the meaning of a name to simply be its referent. I won’t go into these, as I find them deeply weird, and they require some technical jiggery pokery in order to get around Frege’s Puzzle. What’s it’s important to understand is that Kripke originally took his arguments to apply to Frege, insofar as he took Frege’s notion of sense to be descriptive in Russellian way. This isn’t clear from Frege’s actual writings, and it was actively disputed by a number of neo-Fregeans (Evans and McDowell) who developed accounts of de re senses (i.e., senses that are tied to their objects non-linguistically) as distinct from the de dicto senses of descriptions.
Brandom is part of this neo-Fregean tradition (even if his semantic framework is radically different from the Davidsonian one of Evans and McDowell), and uses his distinction between recurrence classes and anaphoric chains to account for the distinction between de dicto and de re senses, respectively. In essence, he takes it that proper names are governed by anaphoric chains that privilege some initial tokening, from which they take their meaning. This answers Kripke’s challenges very easily, because anaphoric dependents are de jure rigid designators, as can be seen from the sentence ‘Aristotle was a great thinker, but he might not have been the most famous student of Plato’. Brandom’s account thus makes using the same name (say the nickname ‘Geordie’) to refer to the same person over time the same kind of activity as using the same pronoun to refer to something earlier in a conversation. The social enterprise of creating and tracking names differs in degree just insofar as it is more complicated. Those who know Kripke will find this very similar to his causal theory of names, wherein the reference of a name is fixed by an initial event of baptism. The difference is that whereas Kripke is notoriously vague about the precise nature of the causal relation through which reference is inherited, Brandom has a detailed account of inheritance in terms of normative statuses (recurrence commitments) and the practical abilities necessary to keep track of them.
This strategy successfully solves Kripke’s Puzzle, which I won’t explain in detail, but essentially turns around the fact that we can use the same word to refer to the same object in two different cases without realising that we are doing so, and thereby commit ourselves to inconsistent beliefs (e.g., if someone who reads my blog says ‘Pete is a genius’, referring to me as writer of the blog, but who also knows me in person says ‘Pete is a moron’, referring to me as person, without realising the two are one and the same, then they seem to believe both that I am and am not a genius). This is because it’s entirely possible for us to have incorrect recurrence commitments, or to simply falter in keeping track of them (i.e., my reader/associate is either plain wrong in thinking these are two different people, or has temporarily forgotten they’re the same). It also solves Kaplan’s issues with indexicals and demonstratives, which I won’t cover in any detail, because the indexical and demonstrative tokenings function straightforwardly as anaphoric antecedents (e.g., ‘this ice cream is great, it’s got bits in and everything’, or ‘He better get here now‘ and ‘I’m glad he got there then‘, spoken at different times and places).
We’ve thus provided a complete overview of Brandom’s account of representational purport, but we need to explain the last dimension of Brandom’s his account of representational success: his perspectivalism. One of the important bits of Brandom’s account I skipped over at the beginning is his account of deontic scorekeeping (chapter 3, MIE). In essence, Brandom thinks that we’re engaged in a game of giving and asking for reasons (entitlements) for our own positions (commitments), and keeping track of the commitments and entitlements of those that we’re playing with. This means that we’re not only constantly working out the consequences of our own commitments, but that we’re doing the same for those of others. However, because of the way inference works, we have to assess the consequences of a sentence within the context of the other sentences held true, or auxiliary commitments, and we do it using some understanding of what follows from what, or inferential commitments. This means that for every one of another person’s commitments we keep score on, we can keep score on it using their auxiliary and inferential commitments, our auxiliary and inferential commitments, or some combination thereof, and that we always fill in the blanks with our own. This is what Brandom calls double-book scorekeeping, though it’s really massively multi-book in practice. The upshot of this is that whether or not someone’s purported representation is successful is relative to the perspective from which it’s judged (e.g., if I overhear a conversation between two people talking about ‘the man drinking champagne in the corner of the room’, and I know that I’m the only person who could possible meet that description, but that I’m drinking ginger beer and not champagne, then from my perspective they’ve strictly failed to represent, even if they’ve succeeded in practical terms).
This might seem to undermine the whole edifice of Brandom’s semantics, leading to some kind of vulgar relativism. Much ink has been spilled on this point, and much has been written about the infamous chapter 8 of MIE, where all of this is explained. I’m not going to rehearse these debates here, but simply present Brandom’s response to this in as brief a form as possible. In essence, Brandom takes it that this is not the case because we can effectively understand things from one another’s perspectives, and that we can argue about which of our perspectives is correct, so that we are always in a position to genuinely aim at the truth of the matter. There needn’t be a transcendent perspective (i.e., a God’s eye view) in order to make sense of the content of thoughts and concepts, and if one pursued an explanation in these terms, one would violate the link between semantics and pragmatics Brandom places so much importance in, insofar as the way we used words has nothing to do with such a transcendent perspective.
Brandom backs up this answer by showing how representational vocabulary (paradigmatically ‘of’ and ‘about’) allows us to move from implicitly negotiating between one another’s perspectives in practice, to explicitly negotiating them, such that we can argue about not only our commitments but the contents of these commitments (and the concepts that compose them). This works by allowing us to make explicit the perspectival difference between the commitments we undertake and those we attribute to others (e.g., ‘Pete claims of one of the greatest philosophers of all time that his thought is mediocre at best’, said by someone else, ‘Hegel thought about mechanisms that can be described in abstract causal terms that they had some supracausal metaphysical status’). In turn, this is made possible by our ability to keep track of anaphoric chains, because we can agree that the words we use should have the same meaning (agreement over recurrence commitments) while nonetheless disagreeing about what these meanings are (disagreement over other commitments). As Brandom says, the representational dimension of conceptual content is a matter of its social perspectival articulation.
That, my friends, is Brandom’s account of representation in (a fairly large) nutshell.
8. Conclusion: Parsing Parsimony
So, with that fairly large diversion out of the way, let’s return to Levi’s criticisms. I’ll first reiterate the core claim he made:-
The representationalist, scientistic, or eliminativist wants to claim that truth can only be produced if the antecedent of a material conditional is true.
What we showed above is that not only is this not true, but that it’s hard to make any good sense of what it could mean. Nonetheless, we should also assess the criticisms Levi bases on this interpretation. To quote the relevant passage in full:-
So here’s what I want to say: If the representational realist, the eliminative materialist, or the scientistic philosopher is truly committed to such a thesis, I want to see the thorough revision of symbolic logic that they develop to account for such a metaphysical position. In advancing such an argument, let’s remember that the so-called scientistic thinker and eliminative materialist is committed to rational account of inquiry, norms governing discourse, and all the rest. That’s what Brandom, after all, tells us. And this is what their “truth-functional” reason is committed to. So given the key role that material conditionals play in our foundations of mathematics (let’s remember all our Ladyman and Ross, our Sellars, our Brandom and how they wax on about norms and reason) and our sciences, are they willing to sacrifice the material conditional? Have they revised symbolic logic in such a way that they’re willing to sacrifice all the fruitful work that the material conditional and biconditional have accomplished? Will they rise to the challenge of giving us the new symbolic logic that refuses the possibility of a material conditional containing a false antecedent producing a true proposition? Inquiring minds want to know. So far I’ve only seen assertions, peppered with lots of truculent language and obscurantist reasoning (Laruelle) parading in the posture of rigor, but I have not seen this reworking of the basic principles of reason. So where is it?
The main idea here is that somehow eliminativists, Sellarsians, Brandomians, and Ladyman and Ross (who by no means present a united front on these issues) must somehow revise symbolic logic if they wish to deny existence to fictions (which as we’ve seen, not all of them do, given Brandom’s account of fictional existence). The real target underlying Levi’s criticisms here is Ray Brassier, who made a few remarks about the importance of truth and the dismissal of fiction in his most recent interview (here). This is directly relevant to me insofar as Ray recommended my Essay on Transcendental Realism in the interview (much to my surprise and delight). He also made a few somewhat controversial remarks that form the subtext of this engagement (which I commented on briefly here). So, do any of the above thinkers, and specifically Ray or myself have to invent a new symbolic logic in order to underwrite our positions, or rework the very principles of reason itself?
In a word, no. But it’s worth pointing out that this is not just because the basis for Levi’s criticism doesn’t work, but also because, contrary to Levi’s implicit suggestion, we’re not ineluctably bound to a single logic. What I mean by this kind of logical pluralism is precisely not that we can pick and choose between different logical systems as it takes our fancy. Instead, I follow Brandom (and others) in seeing all logical systems as making explicit different facets of the same unified structure of reason. We don’t rework the principles of reason by choosing to study variant forms of implication, but deepen our understanding of them. For those who think this is an empty promise, I recommend taking a look at the excellent, but unpublished draft of Jaroslav Peregrin’s book on inferentialism (here), which develops some of these Brandomian ideas in a slightly different direction than Brandom’s own.
This brings us to the real meat of the debate between OOO, myself, and Ray, at least as they tend to characterise it: the principle of parsimony, or the idea that we should not posit more entities than necessary. Graham and Levi have repeatedly castigated us ‘partisans of science’ for endorsing this principle. In doing so it seems that we spoil everyone’s fun, and live only to stop people from talking about the myriad effervescent existences conjured in their thought and talk. In opposition, OOO paints pictures of ‘flat ontologies’ in which, in some loose sense, everything exists, even if everything isn’t necessarily real in Graham’s sense. OOO invites everyone who wants in to the metaphysical party, no matter what they want to talk about. Given this, the question is why are we such metaphysical party poopers? Well, I won’t speak for Ray, but I imagine he’d be sympathetic to what I’ve got to say for myself. From my perspective, there are essentially three reasons.
First, as I’ve shown, we just can’t make good sense of the idea of unrestricted quantification, and this means that we can’t make precise this loose idea that everything exists. Even if we interpreted it in terms of standard objectual quantification, it becomes trivial (as Quine noted), insofar as everything in the domain of quantification is implicitly assumed to exist. Torn between meaninglessness and triviality, this particular selling point of OOO seems like empty metaphor.
Second, to borrow a turn of phrase from Ray: because I believe in truth. Or rather, because I believe in a specific kind of truth, and the structures of reason that define it. What I mean is that I believe in the ideal of objective truth, and the forms of discourse that are defined by it, namely, mathematical and empirical science. I also believe that the latter is subject to a number of internal constraints that the structures of reason place upon it. I believe that reason demands that we explain empirical phenomena, and that this is guided by the Kantian virtues of economy and systematicity. We aim to have the minimum number of commitments necessary coupled with the maximum number of inferential connections between these commitments possible. In conjunction with the requirement of consistency, these rational virtues drive the process of inquiry. Parsimony is a necessary consequence of these virtues.
Third, I don’t see how this denies anyone (other than unrepentant armchair metaphysicians) their fun. As I’ve shown above, I’ve got absolutely no problem with there being as many existents as anyone could want. Nothing about parsimony should discourage people from writing new and more interesting fictions, or from propagating new and stranger interpretations of old ones. All it denies is that they can claim that these are real, and what this means is that they cannot be used in explaining the phenomena studied by the natural sciences. I not only find this demand eminently reasonable, but it strikes me that it would be truly disastrous to ignore it. However, it seems that this is precisely where OOO finds it’s affinity with Latour, who, as I’ve argued elsewhere (here and here), seems to permit precisely this kind of freeform explanation.
All in all, it comes down to this: I want to say that Popeye exists, but that he isn’t real, and thus has no ontological status; Graham wants to say that Popeye exists, but that he isn’t real, maintaining that unreal (or sensuous) existents do have ontological status; and Levi wants to say that Popeye exists, is real, and has ontological status, although he doesn’t have any of the properties we associate with Popeye. Put another way, Graham thinks that Popeye isn’t real, but he is realish, and Levi holds that Popeye is real but that he isn’t really Popeye. I just don’t think either of these ways of thinking about reality is coherent.