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.
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.
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.
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
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
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
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
And it's the recourse to stipulation - with whatever attendant commitments that follow from any such stipulation - that allows one to do that. — StreetlightX
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
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
Hence, there must be a further argument as to why we should think that Jumblese is better suited to our ontological needs. — Nagase
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
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.
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
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
What is it that makes it the case that this particular inscription is a token of, say, rouge? — Nagase
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
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
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
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
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
“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”
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
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
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
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
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 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
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
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