Will be more precise, original post was too much of a splurge. It's an attempt to link Sellars' account that you've presented with the Myth of the Given thesis. At least, my understanding of both of them.

Is there still a linguistic function for whiteness and other abstract particulars? Do they still have some mechanism? I get the intuition that a complete de-substantialisation of all abstract particulars is a bit too strong, but I'm not sure Sellars is actually doing that from what you've written.

De-substantialisation might better be phrased as a closure of language use under any additional realization of language use. No other types of entities are generated or implicated from word use alone. This simultaneously undercuts concepts as abstract objects distinct from how they are used and transposes concepts as patterns of inherited language use.

Concepts aren't things, patterns in word use are, previous patterns promote words following other words causally - like discussing a topic and staying on topic. Nothing more is brought to bear on the word meanings other than their usage patterns - there's no instantiation from beyond speech except from what accompanies speech and remains unspoken.

What I'm interested in is do abstract objects still have some kind of function, or is it better interpreted as an abstracting process that somehow follows a real one. Also how do patterns of usage play a role in the theory - a 'pattern of usage' is a definite thing, 'patterns of usage' are not.

But ideally, I imagine, there is some kind of possible inheritance from a 'patterns of usage' to a 'pattern of usage'. The link between the two could be interpreted in a closed, 'flattened' way where 'patterns of usage' are only ever (negotiated, literally) demarcations between what can sensibly follow on from any given use of words and what cannot. The material basis of word use is what causes word to follow word, and this whole process - including the unspoken accompaniment which underpins words as contextualised islands of sense - loosely the 'meaning in the head' or the interpretation, or regularities in what regularities to apply... language is closed under this recursion and recombinant matching of what is part of use, and always-already part of use.

Or it could be interpreted in a 'bifurcated' way, where the play of abstract objects have their own distinct 'process' and constraints on sensible expression. Some kind of idealism or Platonism in the broad sense. If it's a 'subprocess' - this then names a game we play to organise and reference other games.

EG, when Devin Townsend screams 'Love is about control' as part of the song Love, it's quite clear what is conveyed, despite any metaphysical subtleties. We can also understand reifying word use dealing with abstract objects as concrete things. EG red implies coloured. No matter if this is a proxy for some other talk, the 'game of proxies' - of rule following for user interface specification to transpose into @csalisbury's analogy. I read you as suggesting Sellars has this flattened view, and there's some closure principle whereby words never 'summon' something beyond (like redness) into being through instantiation. This is a way of rendering language as a material process which is closed under operations of abstraction. Another analogy - a Kantian transcendental argument reveals something about (in broad terms) our mind because the kind of possibility dealt with is of impossibility to conceive otherwise. This is ok in some regards, but this can't play the role of a constraint on our minds, just a constraint on generation of concepts about it if done sensibly.

Sellars' arguments are conceptual themselves- so we have to be able to understand what is nominalised and why, and also what it would mean to speak contrariwise to this nominalism even when Sellars' account is true. Which means there should be some role for the dynamics of concepts to play - and I think this dynamism along with the flatness of language undercut the traditional role of the a-priori - you can't sneak up on language to get its back and take the a priori from behind, you're generating aspects of a priori by working through concepts philosophically, and this is just a special case of the closure of language use under abstractions of rule following. So arguments about conceptual dynamics are still conceptual dynamics, and take their cues from what patterns of language use have been about them before. So when Sellars says:

The history of philosophy is the lingua franca which makes communication between philosophers, at least of different points of view, possible. Philosophy without the history of philosophy if not empty or blind is at least dumb.

my bolding, I think Sellars' is giving an account of how a historical a-priori localises and is modified contextually. Background from Sparknotes' page on Foucault's 'The Archaeology of Knowledge' for those unfamiliar with the idea:

historical a priori - The positivities (see above) that constitute discursive formations and relations form a 'historical a priori, a level of historical language which other modes of analysis depend on but fail to address. Discourse functions at the level of 'things said;' thus, any analysis of the formal structure, hidden meaning, or psychological traces of discourse take the level of discourse itself for granted, as a kind of raw material that is difficult to recognize due to its operation at the level of existence itself. It is important to note that the historical a priori constituted by the positivity of discourse is not an a priori in the usual sense of a formal philosophical principle. Instead, the historical a priori is simply a feature of the level of discourse as opposed to other levels of analysis; it does not remain stable as a single principle with a single content, but rather shifts with the transformations of the positivities themselves.

and positivities:

positivity - In the chapter entitled 'Rarity, Exteriority, Accumulation' (see section eleven), Foucault begins to use the term 'positivity' to designate an approach to discourse that excludes anything lying beneath it or hidden within it. For archeology, discourse is to be described only on the level of its basic, operative existence, its existence as a set of emerging and transforming statements (and relations between statements). In this sense, archeology addresses only the 'positivities' of discourse. Further on, Foucault uses 'positivity' almost always in noun form, as a catch-all term for statements, discursive formations, or sub-formations like sciences; any one of these (or any set of relations between them) is a positivity

How do you account for agreement without abstract objects? We don't agree on sounds or scribbles. Agreement as some sort of nodding behavior?

In the context of this thread, I'm thinking that abstract objects are at most part of discursive practices - stuff we do with language. Steps linking each abstract object to each other are moves in games with well known but modifiable rules and scoping contexts. The abstract objects themselves are nothing but their roles in the game, and reference to one is a kind of summary of its roles.

Archetypal abstract object - a group of symmetries of a square, what is it? Well, it's a bunch of interacting terms that let you rotate and mirror the square in a few ways. Where does that leave the square's area? Richer context - the area's invariant when you rotate and mirror it. Why's the area invariant when you rotate it? A bunch of theorems relating codifications of size of something (measures) with possible ways of changing the object (functions and derived actions). Why is the square a square? Eventually it comes down to how we've set it up and nothing more. It's a sufficiently stable and well demarcated bunch of roles to be a general thing - stuff hangs together. It's so stable that a square is formally a model of the symmetry group of a square, so the object doesn't have to come first once it's sufficiently well described - it becomes a satisfier of various patterns and roles.

The properties of the square might be 'out there', but they're 'out there' in terms of how we can sensibly play with notions of the square and make symbol follow symbol. Analogously, word follow word, exposition follow exposition.

This is a completely different question from how does the square in the above sense mirror 'real' squares, like blocks of flats in inner city grid iron. Part of that is that we built it that way. The thread topic might undermine word corresponding to world, like 'red' corresponding to redness or 'square' corresponding to square-properties, but there's probably another way of accounting for this mapping between what's out there and what's in here... An account of that mapping would still be in here, interestingly.

If I'm not speaking total garbage, anyway. :)

In the context of this thread, I'm thinking that abstract objects are at most part of discursive practices - stuff we do with language. Steps linking each abstract object to each other are moves in games with well known but modifiable rules and scoping contexts. The abstract objects themselves are nothing but their roles in the game, and reference to one is a kind of summary of its roles. — fdrake

To be consistent, you'd have to say that all of the above is also true of concrete objects. Jupiter is nothing but a role. Or is it that "Jupiter" is part of a language game, but Jupiter is not? "The set of all non-elephants" is part of a game, but what about the set of all non-elephants?

Or am I speaking total garbage?

They're probably part of games in a different way. Real life is surprising, novel, resistant and unexpectedly crap or good.

Real life is surprising, novel, resistant and unexpectedly crap or good. — fdrake

So is Julie Taymor's work. Her Titus is an abstract object.

Doesn't a thing have to be linguistic in order to play a role in a language game? Abstract objects aren't linguistic.

Why is the square a square? Eventually it comes down to how we've set it up and nothing more. It's a sufficiently stable and well demarcated bunch of roles to be a general thing - stuff hangs together. It's so stable that a square is formally a model of the symmetry group of a square, so the object doesn't have to come first once it's sufficiently well described - it becomes a satisfier of various patterns and roles. — fdrake

Nice. The square is a manifestation of a symmetry-breaking. It is an abstract object in the sense of existing as a limit state. If we are going to tile a flat plane with regular (maximally symmetric) polygons, then - Platonically - there are only triangles, squares and hexagons that will satisfy that constraint.

So now I would draw attention to the difference between abstract objects - or emergent limit states - that we might deem natural and fundamental, vs those that are contingent or complex.

The Platonic puzzle is that both squares and horses could be considered as ideals or perfect forms - abstracta in Platonia. Yet clearly there is also some critical difference between mathematically general patterns or forms, and the kind of biological or cultural forms that seem perhaps archetypal, yet not in a fundamental way.

This is where pan-semiosis or an information theoretic perspective comes in.

The kind of abstracta that have fundamental force - that have true universal existence as limit states - would be the patterns of nature that involve the least structural information. Or in your terms, the rules of their games are simply the most general and inescapable that could be imagined.

So simpler than tiling a plane (which is a little bit special really) would be a universal object like a vortex. The universe at its most naked is a desire to entropify. And nature arranges itself so as to always maximise that outcome. The second law is the rule, and least action is the object of the game. A vortex emerges rather universally as the simplest form that can achieve that result. Among an infinity of possible flow patterns, the vortex is the limit state abstract object that does the job of satisfying this constraint the best.

Well, it gets more complex as nature is hierarchical in spatiotemporal scale. As when hexagonal convection currents first erupt to speed the cooling of a thin oil film - a Benard cell - the vortex is simply turbulence seen on a confined single scale of being. A bath drains with a spiral because as a physical system, there is already other fixed constraints impinging on its free dynamism. There is just the one little plughole a large body of water has to gurgle through.

But a system with minimal information, minimal fixed context, will express turbulent flow over all its possible scales of being. The system will become chaotic. Fractal. Scalefree. Its fluctuations will so lack constraint that those fluctuations no longer have any typical scale.

So when we get down to it, a square is still a fairly high level abstract object in having fixed constraints concerning its scale. A least constrained state - the state where an abstract object stands for some emergent Platonic limit on form - would be more like this kind of fractal notion of "cubic space tiling" ...



So if we want to talk about abstracta as being real, then symmetry maths is our best "game". It is the way we drill down through a story of contextual constraints, stripping away all the superficial or contingent ones - like the kind that might produce a horse - to arrive at the bare minimum of information needed to generate stable order.

Platonism works because there really is some fundamental basis to the very playing of "games of constraint". If objects are the inverse of their contexts - the emergent order that puts a concrete limit to the scope for disorder - then vortexes, fractal branching, and other dissipative patterns are the actual bedrock of physical existence. They are as near as it gets to "bare materiality" in terms of there being "necessary order".

So we have a baseline for abstracta. The patterns generated with Platonic inevitablity in dynamic situations with the least imaginable constraints. The games with the fewest given rules.

And from there - pan-semiotically - we build our way back up to contingent objects like horses and castles.

Horses and castles are also still - at the deepest physical level - just dissipative structures. Horses are nature's way of turning oats into shit, producing at least 80% waste heat along the way. Even castles require great effort and thus great friction and dissipation. As a focus for battles, they become a real magnet for entropic action - a man-made vortex for energy and materials.

But horses and castles are abstract objects - ideal limit state forms - in terms of what is now a complex environment. They are the inverse reflections of a world with the kind of history that has accumulated much information - like grassy, oaty, ecosystems; or feudal human cultures regularly in local conflict.

So what we have is an ontology that is dualistic in information theoretic fashion. The world is its material flows. But also its informational constraints. Reality emerges pan-semiotically because both information and entropy are completely, equally, real. One is not imaginary, the other the proper deal. And physics now makes that pan-semiotic fact centre stage.

Take a tornado - a vortex ripping across the prarie. The information part of the equation is the context that fixes its particular set of constraints in place. Or to put it more simply, everything that is a fact about the recent history of the weather.

Conventionally speaking, the tornado exists in the present. The critical instability that roars away right now is the "material object", the thing that we grant substantial ontic reality. Again conventionally, the past is no longer real as it is dead and gone. And even the future isn't real as it hasn't happened.

But the larger information theoretic view sees past and future as part of the triadic whole, and so also just as real. The past is real in that it actually shapes the current context in its every detail ... and the tornado is simply the limit state object that expresses the violent weatherbomb game which has been set up.

Likewise the future is real in the sense that it contains the entropic goal. Overall, the future is going to be the past left now in a more degraded or entropic state. In informational terms, a store of information is going to get dissipated. A world that was momentarily more complex - having built up some informational density in terms of a weatherbomb temperature gradient - will be left more simple, having got rid of the information of those very constraints.

If there was a town standing in the way of the tornado, that simplication will be evident in its materials winding up being more fractally distributed across the landscape. The man-made returned to a more natural symmetry.

So abstract objects are a story about contextual constraints. Constraints are information that produce material patterns. They produce the regularities of form that are stable material being - instabilty reduced to its dynamical limits.

And as such, there is a sliding scale from the universally necessary to the locally contingent.

Some forms - like vortexes and fractals - are so simple that they will appear everywhere. The most minimal information, or material history, is needed for them to be the manifest case.

While others like horses and castles still reflect these kinds of global symmetry-breaking games - principally the mandate of the second law. However they also are the product of far more elaborated histories - the contexts represented by ecosystems or cultures. They become real abstracta - optimal limit state answers - only in that more highly evolved or highly specified sense.

(All this, by the way, is why Stan Salthe had a dualistic stories on hierarchies. I earlier described the semiotics of hierarchies of entities. This is now the more sophisticated model that is a specification or subsumptive hierarchy in Salthe's jargon. This is now the infodynamic view.)

In the context of this thread, I'm thinking that abstract objects are at most part of discursive practices - stuff we do with language. Steps linking each abstract object to each other are moves in games with well known but modifiable rules and scoping contexts. The abstract objects themselves are nothing but their roles in the game, and reference to one is a kind of summary of its roles. — fdrake

I think this is basically exactly it. One way I like to think of it is that all 'definitions' - whether of words, names, concepts or whathave you - are, at the end of the day, stipulative. This being the case even when we appeal to historical precedent, as when we say, 'this word means such and such because that's how it's always been used': the fact that we appeal to historical use is itself a stipulation: 'this is how I want you to treat the word/concept'. As you say, 'it comes down to how we've set it up and nothing more'.

And this is perhaps nowhere more true than in philosophy itself, which can perhaps be called the ars conceptualis par excellance, in that one generates concepts which allows one - or rather commits one - to parsing the world in such and such a manner, and milking that parsing to see what falls out, as it were. And this is of a piece with Sellars' basic move in his rejection of the given, which is basically the idea that the sensual order has intelligible or propositional form. In rejecting this idea, the question is then how then to track aspects of the real using a process (i.e. language) which does not mirror that real. And it's the recourse to stipulation - with whatever attendant commitments that follow from any such stipulation - that allows one to do that.

I don't know. Golf and sex are similar because one should never confuse holes.

And it's the recourse to stipulation - with whatever attendant commitments that follow from any such stipulation - that allows one to do that. — StreetlightX

How does more stipulation do that?

This may be off-topic to some extent, but is there a link here to the position in the philsophy of mind called adverbialism? From what I gather, the idea is that natural language leads us to think that statements such as "John saw a red afterimage" are to be treated relationally, linking two things, John and his afterimage, and then we start asking questions about what kind of curious things afterimages are. However, if we recast the statement (which is the move that adverbialists recommend) into the form: John senses redly, all we need in the world is John and his properties, and no strange afterimages. My problem with adverbialsim, and it may also have some bite against Sellars jumblese idea, is that even if you can recast the form of a statement in such a way, the question will always remain as to what makes the statement true, and if John senses redly is made true in the same way that "John sees a red afterimage" is made true, then we are still at liberty to think that the adverbialist's statements are made true by the existence of strange objects called afterimages. Do we need a theory of truth before we can decide if jumblese makes sense as an idea?

Similarly, with respect to your point, I think the rejoinder will be: we need 'sentences', yes, but not sentencehood; 'above', yes, but not above-ness. Having winnowed away what he calls abstract singular terms (anything which can have a suffix like '-ity,' ' -hood,' ' -ness,' ' -dom,' and '-cy'), the challenge is then to show that we can treat 'sentences' and 'above' in the nominalistic manner so outlined in the OP. That is, he answers the dangling question above in the negative: no, we don't need expressions which are names of non-particulars: we need expressions which are linguistic objects, which cannot in turn be treated as attributes with ontological standing. That types must be admitted is unavoidable, but - to put it cheekily - what kind of types? — StreetlightX

No, that's not what I had in mind at all. But let me rephrase the whole argument in order to make it clearer.

The first thing to notice is that the existence of "Jumblese" is not an argument for nominalism, since the mere existence of a language with certain features can't be considered decisive when choosing between rival ontologies, as, presumably, these rival ontologists could all craft a language suited to their needs (so, e.g., someone who did not believe in objects, but only in properties, could use Quine's predicate functor language). Hence, there must be a further argument as to why we should think that Jumblese is better suited to our ontological needs.

One such an argument is that its (supposed) ontological commitments are more parsimonious. So theories couched in Jumblese would be more "economical" than theories couched in a more expressive language, say the first-order predicate calculus. Of course, parsimony, as a virtue, does not trump all other considerations. We want to, say, do science in such a language. Is that possible at all? I contend that it's not.

For one, notice that Jumblese is very good at translating atomic predicates. So, given a (finite?) list of atomic predicates, we could in principle introduce a new graphical convention to express each predicate in the list. But we don't want to work with only atomic predicates: there are also predicates defined by complex logical expressions. A typical example is continuity: a function f is continuous at a point b iff for every e>0, there is d such that for every x in the domain of f, if |x-b|<d, then |f(x) - f(b)| < e. Notice the triple quantification and the use of the conditional in the definition of this predicate; how can Jumblese deal with these? Of course, you could introduce a graphical convention corresponding to the symbol, say, "continuous", but the graphical convention would be unable to express the logical relationships that are crucial in the definition of the predicate. And this is just a rather simple mathematical predicate: how can we do chemistry, biology, etc., in Jumblese?

This is a typical challenge to the defender of a nominalist language: to show that it is adequate not just for run-of-the-mill atomic predicates or sentences, but that it can also capture complex scientific language. As far as I know, the only philosopher who took that challenge seriously was Hartry Field, in Science Without Numbers. There, he showed how to nominalize Newtonian mechanics; his nominalization involved an ontology of continuum many spatio-temporal points and many logical resources, as well as "platonistic" resources in proving that the non-nominalistic theory is conservative over his nominalist one. I'm not entirely sure what is the advantage of trading an ontology of abstract objects and properties for continuum many spatio-temporal points. Regardless, notice that he was able to do that solely for Newtonian mechanics. He didn't even attempt to face the challenge of developing a similar nominalization for quantum mechanics, and as far as I know most people are skeptical that this is possible.

Of course, one can then simply say: well, so much the worse for our scientific theories! If they do not employ a nominalistically acceptable language (if they are not formulated in Jumblese), then they do not accurately reflect our preferred ontology and, in spite of their usefulness, they should be taken with a grain of salt, to say the least. But then comes my argument: the nominalist herself is not employing a nominalistically acceptable language, when, e.g., formulating Jumblese. Notice that Sellars, for instance, talks about sentence types when setting up the translation of "X is above Y" in Jumblese---presumably, he is not talking about a translation of a particular inscription of "X is above Y", but a translation of the sentence itself. And that is my point: although perhaps Jumblese itself is free from commitment to properties, our metalanguage when talking about Jumblese is not. So the only way of avoiding reference to types is to use Jumblese itself as its own metalanguage. But I don't see anyone doing this.

But language is a much messier affair than this. In a language such as English, there is a considerable range of sounds that count as a given phoneme. Not just anything, but also not all that sharply circumscribed because we change what will count based on context. There are allophones allowable when singing that would seem strange in everyday conversation. Toddlers utter sentences in which the prosody is right and just a couple of the phonemes are close to standard, and that counts. You use different allophones when whispering or screaming, and so on. — Srap Tasmaner

Exactly, that was part of my point. It is because language is this messy that reference to types is unavoidable. A typical nominalist strategy to do away with types is to employ a resemblance relation between the tokens, and explain reference to types as really being reference to a resemblance between particulars. As you yourself noted, however, this is impossible, because many tokens of the type bear little resemblance at all to each other. So the nominalist's explanaton is implausible.

Incidentally, I don't disagree with anything else in our post.

Hence, there must be a further argument as to why we should think that Jumblese is better suited to our ontological needs. — Nagase

I think there's a misunderstanding here. It is not the case that jumbelese is better suited to our ontological needs. Ordinary language is fine enough. All jumblese is is a pedagogical tool - Sellars uses it to show what is already at work in expressions like f(a) or [Apple is red]. Jumblese isn't doing anything that ordinary language isn't already doing, it just makes what it is doing more obvious. Let's use Sellars' own example(s). He asks us to consider two expressions, both of which express the same thing, the first in ordinary language, the second in jumbelese:

(1) Red a
(2) A

Here is Sellars: "it must be stressed that nothing in or about (2) is doing the job done in (1) by 'red.' Obviously the fact that (2) is in a certain angular style is essential to the semantical role that it is playing. But that fact does not do the job done in (1) by 'red.' Rather it does the job which is done in (1) by the fact that 'a' is concatenated to the left with the token of the word 'red.'" (my bolding). That is, even in (1), the predicate qua predicate isn't doing anything. Jumblese simply makes clear what is already going on in expressions with predicates. Perhaps to really understand what's going on, it's worth briefly going through Sellars' theory of meaning, which expressly invokes both types and metalanguage... in a particular way. Here is an expression:

(3) 'Rouge' means red.

How does Sellars read this? He reads this as correlating the function of an unfamiliar word ('rouge' in French) with the function of a familiar word ('red' in English). The focus on functions is crucial and tells us that 'red' in (3) is not being used in a normal way, but in a metalinguistic manner: it is functioning as what Sellars calls a 'illustrative sortal', where a sortal is, roughly, a 'count word'. To make this clearer, Sellars will reformulate (3) as:

(4) 'Rouge's' (in F) are 'red''s (in E).

(3) and (4) exhibit and show how 'rouge' functions, it does not say the meaning of 'rouge'. So much for 'red'. 'Rouge', in turn, is also functioning in a metalinguistic manner, but instead of an illustrating sortal, it functions as what Sellars refers to as a 'distributive singular term' (DST). A DST functions like the expression 'the lion' in the sentence 'the lion is dignified': the singular term 'the lion' refers distributively to particular lions existing in space and time: hence, a distributive singular term. So what you have with (3/4) is a correlation of two types of metalinguistic functions: the correlation of a distributive singular term ('rouge') with an illustrating sortal ('red'):

(5) DST :: Illustrating Sortal

The purpose of all this wrangling is to show that what are being correlated here are particular linguistic tokenings rather than abstract linguistic types. There is, in other words, a kind of short-circuit between types and tokens, insofar as meaning is a matter of illustrating functions 'all the way down'. At every point you simply have exemplars. Functions are exemplified by other functions, and at no point do you reach a 'hard-core' of 'fact'; instead you simply have (particular) linguistic objects correlated to other (particular) linguistic objects and whose rules of correlation are themselves functions of uniformities of behaviour by language using animals.

I'm apologize for the density of this presentation, but I've tried to fit a theory of meaning in three paragraphs! The point of all this wrangling is that for Sellars, language already functions in the way that jumbelese does: it is already free from commitment to properties. Jumbelse just makes it easier to 'see'.

A DST functions like the expression 'the lion' in the sentence 'the lion is dignified': the singular term 'the lion' refers distributively to particular lions existing in space and time: hence, a distributive singular term. — StreetlightX

That looks a whole lot like what others would call the extension of the predicate "... is a lion."

I wonder if there's a place here for the medieval distinction Lewis revives in Convention:

If I expect every driver to keep right, in sensu composito, then I have one expectation with general content. I expect that every driver will keep right. It does not follow that if Jones is a driver, I expect that he will keep right, for I might not realize that he is a driver. Indeed, I might even realize that Jones is a driver and still not expect that he will keep right, for I might fail to draw the proper conclusion from my general expectation. If, on the other hand, I expect every driver to keep right, in sensu diviso, that I have many expectation, each with nongeneral content. I expect of Jones, a driver, that he will keep right. Of Morgan, too. And so on, for all the drivers there are. I need not know that Jones, Morgan, and the rest are all the drivers there are; I might falsely believe there are other drivers who do not keep right. Or I might altogether lack the general concept of a driver. Generality in sensu composito and generality in sensu diviso are compatible and often coexist; but it is possible to have either one without the other.

(Lewis will argue that the expectations that underwrite convention are primarily general in sensu diviso.)

I'm apologize for the density of this presentation, but I've tried to fit a theory of meaning in three paragraphs! The point of all this wrangling is that for Sellars, language already functions in the way that jumbelese does: it is already free from commitment to properties. Jumbelse just makes it easier to 'see'. — StreetlightX

And this is where we disagree. As I said, Jumbelese can (perhaps) handle simple translations for atomic properties, but what about logically complex properties? How do you represent the property of "for every e>0 there is d such that for every x if |x-a| < d then |f(x) - f(a)| < e"? That is, how do you represent the iterated quantifiers and the implication sign?

In other words, in the case of "a is red", it may be the case that, as you say, the predicate is not doing any job. But what about in cases in which it is doing a job, such as in the case above? Or even in cases in which we quantify over properties, such as (to use a random internet example) "Alice is everything that Bill hopes to be"?

The purpose of all this wrangling is to show that what are being correlated here are particular linguistic tokenings rather than abstract linguistic types. There is, in other words, a kind of short-circuit between types and tokens, insofar as meaning is a matter of illustrating functions 'all the way down'. At every point you simply have exemplars. Functions are exemplified by other functions, and at no point do you reach a 'hard-core' of 'fact'; instead you simply have (particular) linguistic objects correlated to other (particular) linguistic objects and whose rules of correlation are themselves functions of uniformities of behaviour by language using animals. — StreetlightX

But here you end up with the problem I pointed out before. What is it that makes it the case that this particular inscription is a token of, say, rouge? What binds all the tokens of rouge together in a single class? Notice that, if you are a nominalist about properties, you can't even invoke any property that all the tokens share; are we supposed to just take that as a brute fact?

What is it that makes it the case that this particular inscription is a token of, say, rouge? — Nagase

But what role does the type play in determining whether two given inscriptions are (intended to be) tokens of the same type? We can imagine an effective procedure for comparing two inscriptions directly and determining whether (following some community standard, ignoring differences of typeface, for instance) they're intended to be the same.

Type plays no role in the comparison. How could it? If it were necessary instead to compare each inscription to an abstract type, rather than comparing them directly to each other, then we would seem to need some meta-type to enable comparing the given token to a type. We'll never get there.

The upshot of the above was supposed to be this: whatever types are for, it can't be for deciding whether two objects count as the same sort of thing.

That just leaves the examples that involve talking about things in some general way. Some of the standard examples can be readily dealt with as a kind of shorthand (where we're in essence just talking about extensions), and eliminated, at least for countable domains. That just leaves the mathematical examples that even Quine, great foe of second-order logic, thought required sets as first-class objects.

Math is always the odd case.

Whatever all the objects on the table might be, we're rarely tempted to count as objects, just like those, the various sets of objects we could conjure. (So that instead of three objects there would be eight?) Whatever sets are, they're different.

My problem with adverbialsim, and it may also have some bite against Sellars jumblese idea, is that even if you can recast the form of a statement in such a way, the question will always remain as to what makes the statement true, and if John senses redly is made true in the same way that "John sees a red afterimage" is made true, then we are still at liberty to think that the adverbialist's statements are made true by the existence of strange objects called afterimages. Do we need a theory of truth before we can decide if jumblese makes sense as an idea? — jkg20

Hey, sorry, I didn't mean to ignore this, I just literally only had time to make one reply the other day! As an immediate point I think yes, any attempt to treat the language-world relation in the way Sellars does would require - I'd prefer maybe to say entail - a particular theory of truth. Sellars only deals with truth in a relatively schematic way in the book I'm referring to (I'm not super familiar with his work outside of it, although I am reading Science, Preception, and Reality right now!), so I can only sketch an approach.

As far as I understand - which is not far - the very concept of truth for Sellars cannot be thought of outside of the normative rules that govern what might be called 'games of truth'. At the very least this implies that the truth of a statement is not only given by the fact that it corresponds to some state-of-affairs (as he puts it: "This connection of features of 'a is triangular' with ought-to-bes suggest that the truth of 'a is triangular' is itself an ought-to-be"). There needs to be something 'in language' as well (and not just 'in the world') which enables statements to be true. This 'something' is what - I think - Sellars calls 'semantic assertibility' where "the specific varieties of truth-in-L, e.g., true atomic sentence of L, would arise from the varieties of criteria for the semantical assertibility of specific kinds of sentence in L".

Exactly how to think about semantic assertibility and it's role in enabling truth is something I'm somewhat fuzzy on right now. At best though, I just want to say that truth is definitely at issue here, and it isn't foreclosed by a nomianlist approach to predicates.

And this is where we disagree. As I said, Jumbelese can (perhaps) handle simple translations for atomic properties, but what about logically complex properties? How do you represent the property of (S) [my addition - SX] "for every e>0 there is d such that for every x if |x-a| < d then |f(x) - f(a)| < e"? That is, how do you represent the iterated quantifiers and the implication sign? — Nagase

I suppose I don't quite understand how (S) is a property, at least in the sense that 'redness' or 'triangularity' might be a property. I honestly mean this out of sheer ignorance - what is the subject of that property (the iterability is confusing me! - I'm much better at natural language than math)? How do you make sense of (S) as a property?

But here you end up with the problem I pointed out before. What is it that makes it the case that this particular inscription is a token of, say, rouge? What binds all the tokens of rouge together in a single class? Notice that, if you are a nominalist about properties, you can't even invoke any property that all the tokens share; are we supposed to just take that as a brute fact? — Nagase

Surely it's the fact of it being asserted to be so. This might be a disappointing answer but I really think that's it: consider the case of one misspelling (as I used to do alot!) rogue and rouge, where I meant to say rouge. Where someone to call me out on it, where it's obvious that I mean to use rouge (esp. in the context of 'rogue [sic] is red'), my immediate response would be something like 'oh shut up you pedant and deal with the point at hand'.

This is why I've insisted so strongly upon the fact of exemplarity at work here: examples are neither tokens nor types, but are, as it were, tokens that assert their own typicality. To put it in a strong manner: everything is exemplary: the very capacity to assert something as token or type is parasitic or derivative upon exemplifying a token as a token or type as type (each typically in relation to each other of course...). This is why I particularly like Sellars' example of { 'und' (in German) means 'and' } where the first thing he points out is that 'and' is obviously not functioning here as a sentential connective, before going on to point out that this sentence "doesn't merely tell us that 'und' and 'and' have the same meaning; it in some sense gives the meaning." In truth I think that even thinking in terms of tokens and types as anything other than useful shorthand or tools for conceptual organisation is philosophically dangerous and should be kept to a minimum.

Thanks, but no need to apologise, my question was probably a little too basic for this technical thread anyway, so I started another one specifically on adverbialism. As for Sellars and theories of truth, I can see a motivation for the idea that a theory of truth has at some point to find a place to deal with our language forms themselves, in addition to the non-linguistic world and any suppposed relations (e.g. 'correspondence') there may be between that world and the ways we have of expressing facts about it. However, I guess what interests me most is that with perception (which is where adverbialism applies) we (at least seem) to be as close as we can get to a non-linguistic contact with reality, and so perception might have a role to play also in deciding which forms of language should be preferred. Anyway, I've started up another thread on adverbialism to discuss that issue, and I'll leave this thread to discussing the deeper technical issues with predication.

However, I guess what interests me most is that with perception (which is where adverbialism applies) we (at least seem) to be as close as we can get to a non-linguistic contact with reality, and so perception might have a role to play also in deciding which forms of language should be preferred. — jkg20

One interesting thing about Sellars, in this regard, is that - again, as far as I understand it, and I'm still working through it - he actually takes perception to be modelled after lingustic categories. So to perceive something as something, is already to operate in the space of reason and conceptuality, and thus in a cognitive or intentional capacity. Thus Sellars distinguishes sharply - in a Kantian manner - between perceiving and sensing, where only the former belongs to the conceptual order. Like truth then, I think Sellars will argue that our very perceptual forms will in-form what it is that we perceive in a way that is not just 'out there' So there's definitely a connection to your concerns here, although I can only trace it somewhat elliptically.

How do you represent the property of "for every e>0 there is d such that for every x if |x-a| < d then |f(x) - f(a)| < e

This is an interesting example, as the formulation of the epsilon-delta definition of continuity was, historically, an answer to various problems about limits.

Initially, limits were implicit in Newton and Leibniz in their treatment of differentials - fluxions and the dy we know today both manifest as limiting phenomena. At this phase of conceptual development they were just implicit, and famously criticised by Berkeley (and less famously criticised by Marx in the mathematical manuscripts). Treated as a quantity which is 0 at some points in a derivation and nonzero at other points.

After this, while the level of mathematical precision required for pure mathematics still allowed definitions in plain text, you end up with things like this:

“But (which for us here suffices) they continually approach more closely to
the required ratio, in such a way that at length the difference becomes less than any
assignable quantity”

Euler's understanding of continuity is now equivalent to the intermediate value property - the old idea that a continuous function is a function which can be drawn without lifting the pen from the page.

The modern one is Weirstrass', as you posted. Darboux proved that the intermediate value property does not imply continuity by constructing a pathological counterexample. See Darboux functions. This level of precision then allowed the construction of the modern notion of continuity - as an instance of topological continuity. There's thus a construction like P(x) for continuity of x, which while being equivalent to x being continuous in the sense you wrote (Weirstrass'), you can now simply write:

$P(x) \Leftrightarrow x \in \boldsymbol{C}(\mathbb{R})$

to cast it in that form. I imagine a similar trick would work for every logically complex property - by transposing its logical vocabulary into set form (which is always possible up to the objects being too big).

If the difficulty you're highlighting is with regard to predicates requiring higher order quantification, I imagine that this is an obstacle in terms of details rather than one which refutes the central idea Street's been expositing.

Reference on the history of limits which tells roughly this story with greater historical refinement

The point of giving all that historical detail is to illustrate that math, especially math, is just so because it's how we made it just so.

I suppose I don't quite understand how (S) is a property, at least in the sense that 'redness' or 'triangularity' might be a property. I honestly mean this out of sheer ignorance - what is the subject of that property (the iterability is confusing me! - I'm much better at natural language than math)? How do you make sense of (S) as a property? — StreetlightX

The subject of the property in question ("being continuous at point a") is a (real valued) function, say f. Continuity at a point is a property of functions, and a rather important one at that. Be that as it may, my point was the following. Jumblese can handle well simple properties, which are generally represented by atomic predicates. But there are other kinds of properties, complex properties, which are not represented by atomic predicates. A more prosaic example may be the following: x is soluble iff if x is put into water, then x dissolves (this is a very rough characterization of solubility---a more exact approach would need to use counterfactuals and ceteris paribus clauses, but bear with me for the moment). The property of being soluble is not an atomic property, but a complex one, since it is structured. My point is: Jumblese cannot capture this internal structure of the property.

Surely it's the fact of it being asserted to be so. This might be a disappointing answer but I really think that's it: consider the case of one misspelling (as I used to do alot!) rogue and rouge, where I meant to say rouge. Where someone to call me out on it, where it's obvious that I mean to use rouge (esp. in the context of 'rogue [sic] is red'), my immediate response would be something like 'oh shut up you pedant and deal with the point at hand'. — StreetlightX

But in the example at hand, you're grounding the type-token relation on the intention of the speaker/writer to use the relevant type. So the type is (again) explanatory prior to token, and in fact it must exist, for how else would you intend to write it? You can't intend to write a non-existent thing!

This is why I've insisted so strongly upon the fact of exemplarity at work here: examples are neither tokens nor types, but are, as it were, tokens that assert their own typicality. To put it in a strong manner: everything is exemplary: the very capacity to assert something as token or type is parasitic or derivative upon exemplifying a token as a token or type as type (each typically in relation to each other of course...). This is why I particularly like Sellars' example of { 'und' (in German) means 'and' } where the first thing he points out is that 'and' is obviously not functioning here as a sentential connective, before going on to point out that this sentence "doesn't merely tell us that 'und' and 'and' have the same meaning; it in some sense gives the meaning." In truth I think that even thinking in terms of tokens and types as anything other than useful shorthand or tools for conceptual organisation is philosophically dangerous and should be kept to a minimum. — StreetlightX

Well, I'm of the complete opposite opinion: I think types, and abstract objects more generally, are indispensable and that nominalism is a bankrupt approach.

But what role does the type play in determining whether two given inscriptions are (intended to be) tokens of the same type? We can imagine an effective procedure for comparing two inscriptions directly and determining whether (following some community standard, ignoring differences of typeface, for instance) they're intended to be the same.

Type plays no role in the comparison. How could it? If it were necessary instead to compare each inscription to an abstract type, rather than comparing them directly to each other, then we would seem to need some meta-type to enable comparing the given token to a type. We'll never get there. — Srap Tasmaner

I think you're misreading the problem here. The point is not that the type itself explains the relationship between its tokens. Rather, it is that in order to explain the relationship between the tokens, we will generally have recourse to some type, though not necessarily the type of which they are tokens. More generally, we will need at the very least to invoke some properties (of the token, of the linguistic system, of the community, whatever) to explain this relationship, so I don't think a nominalist about properties can get around this challenge.

The point of giving all that historical detail is to illustrate that math, especially math, is just so because it's how we made it just so — fdrake

I strongly disagree with this statement. I actually think the opposite is true: by paying attention to the history of mathematical concepts, we see that they emerged not because we "made it just so", but were rather forced on us by the nature of the entities in question and the problems surrounding them. To my mind, mathematical entities form natural kinds, and the most fruitful mathematical definitions (such as continuity) capture the structure of those kinds.

I imagine a similar trick would work for every logically complex property - by transposing its logical vocabulary into set form (which is always possible up to the objects being too big).

If the difficulty you're highlighting is with regard to predicates requiring higher order quantification, I imagine that this is an obstacle in terms of details rather than one which refutes the central idea Street's been expositing. — fdrake

That's not the difficulty I'm highlighting. Yes, we can use "tricks" to introduce atomic predicates to stand for logically complex one---but that has nothing to do with the complexity of the properties in question. In fact, my point was in the opposite direction: a property does not become less complex just because you can symbolize it with a simple expedient. Notice that this has nothing to do with higher order quantification.

The point is not that the type itself explains the relationship between its tokens. Rather, it is that in order to explain the relationship between the tokens, we will generally have recourse to some type, though not necessarily the type of which they are tokens. — Nagase

Can you take another run at this? This says that to explain the relationship between tokens we will generally have recourse to something that does not itself explain the relationship. The only sense I can make of that is that objects don't talk, people do.

Well, I'm of the complete opposite opinion: I think types, and abstract objects more generally, are indispensable and that nominalism is a bankrupt approach. — Nagase

What would you say about the ontology of abstract objects? Why is math a valuable tool for describing the world?