How Things 'Become': The Infinity of Definition
March 13, 2008 9:18 AM   Subscribe

I am looking for writings on the infinity of definition.

I am interested in the exponentially divergent curve that is definition.

We create writings and art to better define the world, yet true definition is infinite.

We mediate the universe by erecting borders of definition, i.e. all striped, four-legged, hooved mammals are probably zebras. We categorise the universe into hierarchies, but the more we examine the more pronounced and expansive these hierarchies become.

Language is our greatest defining tool. Yet, the metaphors we evolve to expand the potential of language can themselves only be made to refer back to the language which created them. An infinite loop emerges in most definition.

As new technology emerges we use it to 'add' meaning to artifacts which are already partly defined. By looking at the world with ever more refined microscopes we bring reality into greater clarity. This metaphor can be expanded to refer to texts, art, archaeology, culture etc.

Who has written on the problem of definition? What critical theory has been written on the emergence of infinity?

This question adds on to past questions I have asked at MeFi including (in reverse order):

- Art and artifacts experienced through technology
- The mimetic and narrative capacities of artefacts
- Examples of 'The Infinite' in Myth and Their Effect on Conditions of Truth

Here's hoping you have some ideas...
posted by 0bvious to Writing & Language (32 answers total) 11 users marked this as a favorite
Best answer: Metaphors we Live By (Lackoff and Johnson): This is a good resource, but it really only addresses the ways in which language is metaphorical. Not just metaphorical at the surface (consciously), but deeply metaphorical (only seen on deeper meditation).

Kant and the Platypus (Umberto Eco): Treatment of categories, natural and otherwise. Also, hilarious and great book.

Having Thought: Essays on the Metaphysics of Mind (John Haugeland): A philosopher of meaning and also of technology. So it might be a good place to start in on the ideas about what "understanding" does for us. It's vaguely in the phenomenological tradition (as far as I understand it...), so you could also jump into the Dewey, Pierce, pragamists too, which were interested in how knowing is related to doing (action in the world).
posted by zpousman at 9:55 AM on March 13, 2008 [3 favorites]

Mod note: removed link to your own blog post, put it in your profile if you want people to read it
posted by jessamyn (staff) at 9:56 AM on March 13, 2008

"Definition" is a form of truth, so you might want to do some reading and research on the evolving nature of truth. The first thing that comes to mind is some Derrida and deconstruction pointing to the malleable influences on any instance of a concept (like "truth"). He also has plenty to say on the nature of language and how it figures into a lack (or not...) of fixed meaning. Beyond this I'm sure someone can pipe up with some semiotics recommendations, but getting some Literary Criticism readers could go a long way here. All of this is to generalize on your question, since I'm reading it not as specifically about "infinity" and "definition," but about the ways language is used to express these ideas in whatever context they are brought up.
posted by rhizome at 10:11 AM on March 13, 2008

We create writings and art to better define the world, yet true definition is infinite.

Sounds like you are referring obliquely to Gödel's Incompleteness Theorems.
posted by monju_bosatsu at 10:13 AM on March 13, 2008

Best answer: Oh, and just a word of philosophical terminology that might help your research on this topic.

When you say "the infinity of definition" you could mean one of two things. Firstly, you might mean the "infinite regression" of definitions, where definitions lead to other definitions which lead to other definitions, which are all stuck in the dictionary. So how do all those definitions ever get out into the *real* world? Second, you might mean the multiplicity or multi-facets of definitions, which rhizome points out is part of truth. If this is your interest (and a very quick skim of your blog post seems to imply that this is your core interest), then I would read this as a primer on the topics of whether the social world is real (and what stance sociologists take on that world):

Burrell, G. and Morgan, G. Sociological Paradigms and Organizational Analysis. Ashgate Publishing 1979.
posted by zpousman at 10:25 AM on March 13, 2008 [1 favorite]

Best answer: Following up on what rhizome said, the sorts of questions you're asking here are similar to those that concerned Derrida in a lot of his writings (see Of Grammatology and Writing and Difference). I'm more familiar with Foucault, who touches on this sort of things from a structuralist point of view in The Order of Things and from a post-structuralist point of view in The Archeology of Knowledge.

This idea of the endlessness of definition (how one word leads to another and on to another, without really contacting anything but other words) is the subject of a lot of postmodern fiction. Taking up that angle, you might enjoy Linda Hutcheon's A Poetics of Postmodernism.

But, rather than get caught up in all of that, I prefer to stick with the pragmatists and see language as an imperfect but useful tool for understanding things. If you want to side-step most of the continental theorists and look at it from that side, grab anything by Richard Rorty and branch out from there. You'll find connections between his work and that of Derrida and Foucault, but his point of view is quite different.
posted by wheat at 10:37 AM on March 13, 2008 [1 favorite]

Best answer: Douglas Hofstadter's Gödel, Escher, Bach talks about recursive definitions, meaning in general, and the paradoxes that come from both. (Also music theory, art history, early AI research, fractals, the history of formal logic, talking animals and Lewis Carroll. It's a hell of a book.)
posted by nebulawindphone at 10:40 AM on March 13, 2008 [1 favorite]

Response by poster: Much thanks so far...

I am definitely most interested in 'the multiplicity or multi-facets of definition'. In a sense, I use the word definition as it is used to describe digital photography, i.e. the greater the pixel count the higher the definition. TRUE, PERFECT definition in this sense, can be understood as a digital image with an infinite number of pixels. The only model than can describe the world is the world itself.

I want to uncover the fractal-like capacity of language, metaphor and definition, most specifically in the archaeological examination of texts, writing, books etc. Reality is infinite. How can we ever refer to it without referencing infinity?

All artefacts are palimpsests with infinite layers. At least, that's the metaphor I intend to explore.
posted by 0bvious at 10:45 AM on March 13, 2008

In a sense, I use the word definition as it is used to describe digital photography, i.e. the greater the pixel count the higher the definition. TRUE, PERFECT definition in this sense, can be understood as a digital image with an infinite number of pixels.

The word most commonly used to refer to this is "resolution", not "definition".

It sounds like you're interested in the difference between continuous and discrete descriptions of reality.
posted by mr_roboto at 10:50 AM on March 13, 2008

Response by poster: I chose not to use the word resolution because of its connotations, although once applied to the study of language, texts and meaning either word will suffice.
posted by 0bvious at 10:56 AM on March 13, 2008

Also note that an infinite number of pixels does not necessarily imply a continuous mapping: infinite countable sets are not necessarily continuous (consider the integers vs. the reals).
posted by mr_roboto at 10:58 AM on March 13, 2008

Well, "definition" has connotations that make your question extremely ambiguous and confusing. Hence all the answers you received that clearly didn't understand your meaning.
posted by mr_roboto at 10:59 AM on March 13, 2008

Best answer: MetaTalk
posted by OmieWise at 11:01 AM on March 13, 2008

Also, I'm not sure why you refer to "definition" or "resolution" as "exponentially divergent". Shouldn't it scale as a power law (i.e. as length^2 in two dimensions, length^3 in 3D, etc.)?
posted by mr_roboto at 11:03 AM on March 13, 2008

You are making an argument that definition is infinite, and asking for writings that support this definition. I don't think this argument is sound. Definitions change because people don't understand the nature of the thing they are defining, or because the thing defined changes in its relationship to the world. This is not an infinite process. Take iridium.

If I were to rephrase your question to one I might provide an answer on: Why is our understanding evolving past and out-dating so many of our definitions?

This isn't your question, but if it was your question I would suggest that the old standbys are best: The Dialogues of Plato, and Analects of Confucius. These works, in my experience, lay bare as well as anything what motivates us to avoid precision, and our purposes in defining things - which are not to understand the things themselves. In as much as we define for other reasons than to understand the thing as it is, we are doomed to produce flawed definitions.
posted by ewkpates at 11:05 AM on March 13, 2008 [1 favorite]

Seconding that you should read some Derrida. You should also read some semiotics to ground yourself a bit more in the sort of philosophy you seem to be discussing here (here is a previous question seeking an introduction to semiotics). You may also be interested in Frege's ideas about language (Sinn und Bedeutung, or Sense and Reference).

Reality is infinite.

This is a common enough idea in philosophy, but we don't really know that it is true. Maybe reality is just really, really big. In either case, a bit of set theory might interest you. Gödel, Escher, Bach is indeed a very interesting book and you might want to pair it with David Foster Wallace's Everything and More which gives a fairly easy to follow explanation of the idea of infinity both within and outside the bounds of set theory. You'll want to pay particular attention to his discussion of Cantor's different infinities.

Please don't take this the wrong way, but you may have better luck with these sorts of questions if you do a little more background research and learn to use philosophical terms correctly. I think I know what you are getting at, but it is a bit difficult to tease out the ideas behind what you write when you use a lot of terms that are used in philosophy and critical theory in non-standard ways. Alternatively, if you aren't familiar with the subject area that you want to learn about, it may be better to state your question in the simplest everyday language possible to avoid confusion.
posted by ssg at 11:21 AM on March 13, 2008 [4 favorites]

I could be wrong, but upon reading your question I immediately thought, Once I understand chair, I also understand the extrapolation of chairness and all therein that can be applied.

Try reading some Wittgenstein. He opines on things that can be expressed through words, and other concepts that can only be shown in order to be understood (and the differences between the two, which can be difficult to write about in absolutes).

I took a class on metaphysics in grad school that addressed some of the issues and authors mentioned above, but found Wittgenstein to be both frustrating and enlightening on such subjects.
posted by Unicorn on the cob at 11:25 AM on March 13, 2008

You need to read Wittgenstein. (wiki) The picture theory of language is closest to what you're talking about.
posted by kpmcguire at 11:31 AM on March 13, 2008

Best answer: This is a common enough idea in philosophy, but we don't really know that it is true

I think he's talking infinity the other way, not the expanse of space, but the infinite possibilities or divisibilities of each thing - the endless indefiniteness of reality as compared with our attempts to define it simply through symbols.

Emerson had some good essays on that. Merleau-Ponty, Heidegger, all the language stuff of the early 20th c... Derrida, Barthes, Lakoff... I dunno though, I think you're making a basic error with the understanding of definition itself as infinite - it's precisely by using a finite symbol to try to track an infinite substance that language is imperfect and always changing, but it's not infinite itself, because it's abstract. Abstraction is the one place where straight lines can be drawn.

--or you can be a pragmatist, and acknowledge that straight lines in real life are "straight enough" for our purposes if we're careful, as many contemporary language theorists do - that our definitions may not be exact in some absolute sense, but as I think Robert Brandom puts it "language has a downtown".
posted by mdn at 11:54 AM on March 13, 2008

Response by poster: Once again, thanks...

To clarify myself, I am not so much offering my own definition as asking a question in enough ways to provoke various levels of response. I welcome positive and negative answers in equal measure.

My question is cross-disciplinary, hence the mix of words. I am pretty well versed in the works of Bataille, Barthes, Bakhtin and their ilk, and more recently have come to wallow in the wonder that is Susan Stewart.

Thus, a semiotic approach to the archaeology of meaning is kind of my aim, with leanings towards the evolutionary origins and forms that meaning has.

ewkpates: Although I agree that 'definitions change ... because the thing defined changes in its relationship to the world', I do believe that there is a contradiction in what you have said. When the relationship something has with the world shifts we are left with at least two levels of definition, the original and the new. The new definition is not removed completely from the old, the new contains the old within it. To truly understand the Morning and the Evening star, in all its glorious philosophical history, we need to acknowledge:

1. The morning star is the evening star
2. People used to believe that they were different
3. Why people believed this

Without all three levels of definition (and a whole heap more) we have moved nowhere. All definition therefore is accumulative, and exponential. The more ways we have to look the more we will see. I doubt anyone here would claim that we will stop being better able to define the world around us.
posted by 0bvious at 12:09 PM on March 13, 2008

It sounds to me like you will not find research on exactly this topic because it is not a topic at all, really.

Definitions can be made more or less precise to an unspecified degree, but an "infinity" and "an exponentially divergent curve" is your idiosyncratic way of picturing this; it is not a fact about definition. You should consider, for example, why you chose the word "exponential" -- did you actually discover something exponential in the nature of definition, or is this just a part of a picture that charms you?

You should read Wittgenstein, starting with the Philosophical Investigations; he talks a lot about language and criteria of definition and also about being caught in a picture and the effect this has on philosophizing. Or, if you are interested in the degress of precision of nature -- is the universe at some level discrete, or can you always find smaller and smaller pieces -- you are interested in a debate going back to the ancient Greeks. Leibniz talks a lot about this in Monadology. Analytic philosophy dealing with "natural kinds" might interest you. If, after all, nature turns out to be discrete, then definition also will probably face a natural limit at some point. Or, if you wish to stick with the picture of the curve that you have fabricated, you can just write freely about it; but since it is a picture of your invention, I doubt you will find it covered somewhere else.
posted by creasy boy at 12:24 PM on March 13, 2008

0bvious: While the eventual aim of whatever project you want to embark on may very well be cross-disciplinary, the question you are asking here seems to be more or less within the bounds of the philosophy of language. Learn the theory well first, then you can apply it to other subjects. For example, Barthes, as I'm sure you know, is often tossed around a lot in critical theory. A lot of what Barthes wrote was an application of ideas from the philosophy of language to particular subjects. Trying to divine the ideas that Barthes is working with from their application is a lot harder than learning about the ideas directly. Once you understand the background, then it is much easier to see what Barthes is adding to those ideas. You'll find this kind of relationship between philosophy and critical theory is quite common and you will often find it fruitful to study a bit more of the background. I know that critical theory students often find rigorous philosophy boring (Foucault is sexy, Frege is not), but sometimes you need to do the boring things to be able to do the exciting things well.
posted by ssg at 12:37 PM on March 13, 2008 [2 favorites]

Response by poster: Maybe I should move away from the word 'infinite'. It seems that without that I can still make a vaild point.

Whether you agree with my meanderings or not, I thank you for your input so far. I come to AskMeFi to expand my reading list. However many professors I visit for advice and ideas I can only trawl so many sources and perspectives. Metafilter opens the possibilities up a little. So thanks.

My questions on here have been vague mainly because I am following a kind of hunch. The MA course in critical theory I attend is very experimental and open in its approach. It allows me to respond to theory from a creative position. I apologise if this creative approach blurs my questions.

Meaning will tend to explode occasionally.
posted by 0bvious at 1:03 PM on March 13, 2008

Best answer: Check out morphological, semantic, or cognitive psychology articles on Prototype Theory.

Lakoff (the linguist) is a good starting point for this.
posted by whimsicalnymph at 2:24 PM on March 13, 2008

Best answer: To me, it sounds like you have a bunch of different ideas all crowded together, and would do well to separate them so you can read up on the vast literature produced in the 20th century on all of them. Try to think about your questions in the least jargonny way possible, and you will have an easier time separating out your questions.
Partly you're asking about how we understand the world (concepts, representations), partly you're asking about the nature of language and its role in shaping our understanding of the world (reference, Sapir-Whorf, metaphor), and partly you're asking about the world itself (categories). Those things in parentheses are the keywords I would point you to. If you make up your own terms for these things, you'll make it harder to converse with others and you'll make it harder for yourself to understand what other people have written on this stuff.

You want to look into [the Stanford Encyclopedia of Philosophy will give you a little overview and bibliography to get started with each topic.]
-later Wittgenstein (Philosophical Investigations). I promise you will dig him.

-reference (how does the word "cat" come to refer to actual cats in the world? what is it to "refer"? can a word succeed in referring to a nonexistent object like a unicorn? etc)

-representation (all representations will be merely partial. how can we judge what makes one better than another? how can we pursue complete knowledge of the world when any representation we have in our minds will need to leave some aspects of the world out?)

-concepts (what are concepts? what makes something like a penguin fall under a concept like 'bird'?)

-categories of things in the world.

Final bit of advice: One could easily spend an entire academic career on any one of these topics. So don't design a MA project for yourself that will require 50 years to finish. Remember to think of your thesis topic in terms of a manageable project that can be accomplished in the time you have. Better to pick a narrow topic (one aspect of the thing you're interested in) and do it well than to pick a huge topic and do it badly.
posted by LobsterMitten at 2:33 PM on March 13, 2008 [1 favorite]

This Carroll "story" reproduced at the beginning of GEB is relevant, I think, and tremendously deep.
posted by grobstein at 6:29 PM on March 13, 2008

Infinity and the Mind by Rudy Rucker is a fun read. It's more about the definition of infinity than the reverse, but he approaches it from mathematical and philosophical sides.
Zen also deals with the nature objectness and thingness, and how the mind characterizes experience. The (very long and detailed) forward to Mind in Tibetan Buddhism is really interesting, it describes the the flow of consciousness through the brain. Not strictly speaking Zen obviously but it's good.
posted by doctor_negative at 6:44 PM on March 13, 2008 [1 favorite]

Best answer: Firstly: I suggest that in thinking about this topic, you drop the word 'definition'. 'Definition' is ambiguous. Among other things, it can mean (1) resolution (as of a digital picture), (2) meaning (as of a word), or (3) the act of stipulating a new meaning for a word. It's not clear which of these you are interested in. In your original question, it's pretty obvious that you were focusing on meaning, but your in-thread responses, you use the word to mean resolution. It's easy to see how you got confused: it sounds like you're interested in theories of meaning in which meanings have no atomic or primitive constituents. I guess you could say that if you keep zooming in on the constituents of a word meaning and you never get to the bottom, then the "resolution" of the meaning is infinite -- that is, the definition has infinite definition. But c'mon, that's confusing to everyone.

Secondly: The sense of 'definition' you're most interested in is (2), I think. But semantic meaning is a property of words, languages, or other representational systems. In your original question, you claim that we "define the world", and language is a tool that helps us do this. We can define words like 'table' and 'chair': but how can we define tables and chairs? Avoid use-mention errors; do not confuse semantics with metaphysics.

OK. I'm going to try to reformulate the question that I think you were asking, using terminology that should be more familiar to analytic philosophers. I hope this is helpful.

Q: The semantic meaning of any word can be decomposed into constituent meanings. For example, "vixen" can plausibly be decomposed into "female fox". But now the words in the definiens need to be decomposed, and a regress looms. Whenever you've got a regress looming, there are three options. You can go foundationalist and claim that there's a stopping point, you can go holist and claim that things circle back in upon themselves, or you can go infinitist and claim that the chain runs on forever. Are any infinitist theories of meaning?

A: No, none that I know of.

Most theorists in linguistics and philosophy argue for a type of foundationalism. They think that there are atomic meanings. In fact, quite a few readings that people in this thread have suggested are actually of this sort. Lakoff and Johnson, for instance, think that nearly all language is metaphorical, but they also believe that some bits of language are non-metaphorical -- words like 'up' that refer to our proprioceptive bodily states -- and these words ground the rest of our language. Bertrand Russell and a whole swack of logical positivists thought everything petered out in sensory experience. Another view sometimes held is that almost all lexical meanings are atomic. On this view, 'bachelor' does not derive its cognitive meaning from 'unmarried man', even though we can use the latter phrase to help someone learn what the word 'bachelor' refers to.

But forget that. What should really interest you, I think, is meaning holism -- the view that chains of meaning determination circle back in upon themselves, so that the meaning of a term is determined by its relations to many or all of the other terms in a language. It's also sometimes called semantic holism or concept holism. W. V. O. Quine is the guy to look at here: take a look at his "Two Dogmas of Empiricism", which many consider to be the single most influential paper in analytic philosophy of the last century. It'll probably be a tough slog at first (you might want to look up some material on the analytic/synthetic distinction), but it's a must-read if you're interested in this topic. (And it's got stuff in it about semantic revision, too; there's this great bit at the end comparing the posits of modern physics to the gods of Homer that I think you'll like a lot.)
posted by painquale at 9:08 PM on March 13, 2008 [3 favorites]

It's enjoyable to see all the linguistic / semiotic approaches to answering this, but I see it more as a token of a type of metaphysics - ie the relationship between the particular & the abstract.

The OP writes, "We mediate the universe by erecting borders of definition, i.e. all striped, four-legged, hooved mammals are probably zebras. We categorise the universe into hierarchies, but the more we examine the more pronounced and expansive these hierarchies become"

And later, "I am definitely most interested in 'the multiplicity or multi-facets of definition'. In a sense, I use the word definition as it is used to describe digital photography, i.e. the greater the pixel count the higher the definition. TRUE, PERFECT definition in this sense, can be understood as a digital image with an infinite number of pixels. The only model than can describe the world is the world itself."

Of course, if you had the patience & the need or desire, you could stop referring to zebras in general, and start talking about "my pet zebra, Zed, who has three white hairs in his left nostril, and then describe the exact placement, cellular structure, dimensions etc of those hairs until you finally had an (almost) infinitely precise definition of that zebra.

However, he then seems to conflate the concept of the infinitely precise ontological definition of the universe with a confusingly similar-sounding, but entirely different issue - the infinite chain of semiotic signification, whereby signifiers refer to signifieds which are themselves only signifiers pointing to further signifieds; a seemingly endless chain that never appears to escape language & come into contact with material "reality", whatever that might be.

And yet, I remember one of my professors of semiotics pointing out that no matter how nihilistic this might sound - linguistic signifiers never grounding themselves absolutely in material signifieds - you can still go to a restaurant, ask for a plate of beans, then happily devour it, so it's not all that bad, after all.
posted by UbuRoivas at 10:04 PM on March 13, 2008

(IMHO, though, phenomenology pretty much undermines the ontological exercise, but I'm bored of this topic & heading off elsewhere now. Read some Merleau-Ponty as a starting point, then work your way to post-structuralism & deconstruction. Try to get totally lost on the way, it's more fun)
posted by UbuRoivas at 10:21 PM on March 13, 2008

I reflected that even in the languages of humans there is no proposition that does not imply the entire universe; to say "the jaguar" is to say all the jaguars that engendered it, the deer and turtles it has devoured, the grass that fed the deer, the earth that was mother to the grass, the sky that gave light to the earth. I reflected that in the language of a god every word would speak that infinite concatenation of events, and not implicitly but explicitly, and not linearly but instantaneously.
From "The Writing of the God" by Jorge Luis Borges. He gets at this sort of thing quite a lot in his fiction.
posted by ludwig_van at 11:24 AM on March 14, 2008 [1 favorite]

Best answer: Have you seen this previous question ("How do we jump into a closed set") ?
posted by tomcooke at 3:02 PM on March 14, 2008

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