The limits of definition

Benj96

What does it really mean to “define”?

For me, definition means to place separations/ delineations, limitations or parameters around a concept or thing which divides it into A “the defined” - the content within the parameters, and B “all other things” ie. “it” and “not it”. Definitions separate things by character or relationship to one another. By “contrast” essentially.

However this immediately leads to some issues especially at the extremes.
If I take the word “everything” how do I define it? You cannot “divide” the concept of “everything” as it is parameterless. Any parameter to u try to place around the set/ content is also included in the set/content.

Similarly you cannot define nothing as it’s contentless. You can’t place a parameter around an empty set.

Another issue I see in defining is the idea of a good definition verses a bad definition.
A good definition is that which describes something discretely, that is to say it doesn’t omit any characteristics about said thing, it perfectly encapsulates the existence of said thing. Nothing is possible for that thing outside of its definition.

This would mean that if we define “shoe” as the Oxford English Dictionary does as “one pair of objects usually made of leather or plastic that you wear on your feet” , a shoe can never be a). something you don’t wear on your feet, b). A non physical object or c) something that doesn’t come in pairs. Do you thing that’s a good definition of a shoe?

Because that definition permits someone to be wearing a pair of plastic watering cans they have never removed from their feet, they’ve always been there, and if they were to lose one they will have violated some law about not being in pairs and the watering-can would reappear magically.

Obviously this is an absurd and overly literal interpretation of “shoe” but it highlights the degree of assumptions we require in order to appreciate a definition correctly. Is a good definition then really one where no assumptions have to made?

It seems that the more specific you make a definition, the more possibilities you omit, that is to say the more inaccurate the definition it gets as most things can be made in an endless myriad of styles, shapes, forms, and even functions and from multiple materials in any number of combinations.

What then do all the millions of shoes in the world have in common? Some are graphics on paper or in media, some are described concepts from peoples minds and some are on your feet but all of them can be defined easily by anyone as a “shoe.”

The most accurate definition of a shoe could be said to be “something”. It’s likely that this definition will indeed contain the set of all possible shoes. However no that the definition is accurate it is completely non-specific.

So it appears that specificity and accuracy in language are inversely related. Definitions can be specific but inaccurate or non-specific and accurate.
Thoughts?

I like sushi

Things are usually understood by how they are used, how they can be used and how they cannot be used. Definitions are not necessary to understand and function in the world.

When I see a table I do not open up some mental definition in my head that defines a table. I move through the environment mostly oblivious to everything around me.

Defining is a habit of atomisation maybe? On forums like this it is often necessary not to assume your take on some seemingly mundane concept/idea is the same as someone else’s. Then it is a matter of playing between being overly pedantic and overly vague. The ‘hits’ you get you know yourself. Sometimes just one hit helps you move forward and sometimes multiple hits just means you are just saying what other people say.

Cuthbert

Do you thing that’s a good definition of a shoe? — Benj96

Not quite. Horse shoes come in fours and you can't wear them on your feet. The brake shoes on your car cannot be worn at all. Cinderella's shoe was not a physical object - it was a fictional creation. Etcetera.

A good definition is that which describes something discretely, that is to say it doesn’t omit any characteristics about said thing, it perfectly encapsulates the existence of said thing. Nothing is possible for that thing outside of its definition. — Benj96

It seems a natural starting point. If you define 'X' well, then your definition should fit all X's and it will fitf nothing else, only X's. It will state all the necessary and sufficient conditions for being an X. Unfortunately, as with 'shoe', there will be quite limited possibilities for defining anything well in that particular sense of 'well'. But we can still define things well in other ways.

Agent Smith

As far as I know, a definition should list ALL SUFFICIENT & NECESSARY conditions for a word to apply to an object, and once this criteria is fulfilled, that object becomes the word's referent.

A shoe is (my own definition), one of a pair of objects one wears on one's foot for protection mostly, but also as a fashion statement (are those shoes that women wear these days? :chin: ).

As you rightly pointed out, no definition is perfect except maybe mathematical and scientific ones and hence the OP I suspect. The issue is in all likelihood more complex than I've presented it in this post; it usually is with philosophical tyros like me!

Furthermore, I've always maintained that Wittgenstein made a mountain out of a molehill by declaring incorrect word usage (breaking the rules of a good definition) as correct ones, but now that you've made clear in the post, is a good definition possible at all? Mathematics & science are quite well-known for the quality of their definitions.

Benj96

Mathematics & science are quite well-known for the quality of their definitions — Agent Smith

I agree that the paradigm of science and maths is establishing truth through consistent laws and rules and in this sense their definitions are more precise than those we use in a linguistic context.
However I think we cannot ignore that definitions even in science and maths are restricted temporally. And as advancements are made, as time progresses and more information is elicited, so too the “best definitions” we have are refined and redefined further.

So really I think definitions are likely to be approximations on any level... as relationships between phenomena are so far not exhaustive. Definitions are relative only to what we know. The future holds many unknowns that will have to be worked into current definitions. Scientific definitions are very different between those of the 1800s and those of the 21st century and many now will be obsolete or over ruled in the next hundreds of years

Agent Smith

↪Benj96

I'm inclined to agree. Just got my new glasses - the optometrist told me I'll need to adapt to it. Could it be that the world is fuzzy and because of that our definitions fall short of the mark. No fault of ours if this is the case, oui?

Relativist

↪Benj96

Words refer to mental concepts - usually fuzzy concepts (e.g. "shoe"). A definition is an attempt to convey the concept associated with the word. Because the concept is fuzzy, there isn't a strict set of properties that unequivocally define it. But the most significant properties are conveyed, based on the most common usage.

T Clark

For me, definition means to place separations/ delineations, limitations or parameters around a concept or thing which divides it into A “the defined” - the content within the parameters, and B “all other things” ie. “it” and “not it”. Definitions separate things by character or relationship to one another. By “contrast” essentially. — Benj96

You're mixing up definitions and distinctions. Definitions apply to words. Distinctions apply to things in general. Mistaking words for the world is a common problem with philosophy. I think I understand the point you're trying to make. We break the unbroken world, everything, into conceptual pieces.

If I take the word “everything” how do I define it? You cannot “divide” the concept of “everything” as it is parameterless. Any parameter to u try to place around the set/ content is also included in the set/content.

Similarly you cannot define nothing as it’s contentless. You can’t place a parameter around an empty set. — Benj96

I'm not sure I get what you're saying. Dividing "everything" is exactly what people do. Taoists have the concept of "Tao," which represents everything, undivided and unspeakable. The minute you speak about it you divide it. Is that what you're getting at?

"Nothing" is easy to define, as long as you're careful what you're trying to mean. It makes sense for me to say that a box has nothing in it, even if it contains air. It makes sense to say that interstellar space contains nothing, even if it contains a few particles per cubic meter and the quantum field.

Taking another tack, scientists see the universe as finite but unbound in three dimensions the way a sphere is unbound in two dimensions.

Another issue I see in defining is the idea of a good definition verses a bad definition.

A good definition is that which describes something discretely, that is to say it doesn’t omit any characteristics about said thing, it perfectly encapsulates the existence of said thing. Nothing is possible for that thing outside of its definition. — Benj96

I don't think that's true. A good definition is one that tells you how to use the word in speech and language in a way that makes you understandable. Words are ambiguous and vague. Definitions don't have to be perfect. Here's a good definition of "shoe" from the web - "A durable covering for the human foot, made of leather or similar material with a rigid sole and heel, usually extending no higher than the ankle." No, it's not perfect, and, yes, there are possible ambiguities. Also, the word has other, related meanings, e.g. horseshoes. But, all in all, it works.

Is a good definition then really one where no assumptions have to made? — Benj96

No.

What then do all the millions of shoes in the world have in common? Some are graphics on paper or in media, some are described concepts from peoples minds and some are on your feet but all of them can be defined easily by anyone as a “shoe.” — Benj96

Graphics on paper are not shoes, they are images. Images of shoes.

The most accurate definition of a shoe could be said to be “something”. — Benj96

In order for words to be useful, we have to be able to use them, but they don't have to be perfect. Language is full of ambiguities and vagueness. We have synonyms, homonyms, homographs, puns, etc. Generally it all works pretty well, which is the best we can expect.

I disagreed with a lot of what you wrote, but it's still an interesting thread about an important subject.

T Clark

On forums like this it is often necessary not to assume your take on some seemingly mundane concept/idea is the same as someone else’s. Then it is a matter of playing between being overly pedantic and overly vague. — I like sushi

Making sure our definitions are clear is especially important on the forum for the reason you note. Unfortunately, it's possible to be overly pedantic and overly vague at the same time.

Hillary

As you rightly pointed out, no definition is perfect except maybe mathematical and scientific ones — Agent Smith

:chin:

Hillary

Defining is a habit of atomisation maybe? On forums like this it is often necessary not to assume your take on some seemingly mundane concept/idea is the same as someone else’s. Then it is a matter of playing between being overly pedantic and overly vague. The ‘hits’ you get you know yourself. Sometimes just one hit helps you move forward and sometimes multiple hits just means you are just saying what other people say. — I like sushi

I'm not sure if atomisation is involved, but I certainly agree that it's false to assume that other people know what you are talking about without further ado. A clear explanation of one's ideas is required, to reach sharpened-pencil-point-like precision.

Benj96

fuzzy and because of that our definitions fall short of the mark. No fault of ours if this is the case, oui? — Agent Smith

It depends what exactly you mean but yes in a general sense I think most things are not clear cut and discrete but rather a more flexible spectrum of transition in which a certain level of bias or interpretation must be made.

For example using the previous example we could say a shoe is a piece of footwear you wear to walk or make a fashion statement. However when one considers repurposing and lateral thinking a shoe can indeed function in many ways - it can be a container for plants, a missile to throw at someone when you’re annoyed, something symbolic like the shoes that hang on telephone wires where drugs are sold, it could be part of a sculpture or art installation in a gallery, or could be worn comically by different animals - cats dogs etc. The list is endless. Yet we can’t afford to spend time defining every possible way a shoe can exist or function even though the possibilities are vast. This applies to most objects and thus yes the world is “fuzzy” indeed.

Benj96

But the most significant properties are conveyed, based on the most common usage. — Relativist

Granted this is true of purpose or utlilitarian based definitions but if we consider all words on the dictionary (all having definitions) there are many that are abstract, metaphysical or don’t have a clear purpose or function in which case this breaks down. There are also circular definitions in which the topic can only be described using words that imply its definition in the first place. For example the word condescending has only ever been described as the act of being condescending or patronising and patronising is defined as condescending in this way no additional information is offered. It’s circular. How then do we convey the property when we must use the property to convey it?

Benj96

Then it is a matter of playing between being overly pedantic and overly vague — I like sushi

Exactly this is the crux for which I started the thread. Definitions deal with specificity and accuracy and is a balance of both, you can be highly specific but it leaves you open to exceptions to the rule or you can be accurate but it leaves the definition much short of anything that conveys precise information

Benj96

Graphics on paper are not shoes, they are images. Images of shoes. — T Clark

Yes but show an image of a shoe to anyone and they will immediately Manifest in the minds eye the functions properties and nature of a shoe or their understanding of what a shoe is. They won’t think of “images” just in the same way that when you see a shoe you don’t think of “vision”. It is the subject not the medium of communication.

Benj96

distinctions — T Clark

Can you define without making distinctions?

Mistaking words for the world is a common problem with philosophy. — T Clark

I know what you’re saying in that language is a projection we apply to objects. We could just as easily call a shoe by any other name as we see in the various languages humans speak. However I don’t see what point there is in clarifying that words are not the real world because if we cannot apply language to the world we cannot gather communal information about anything. If an object doesn’t have a name for its existence then what exactly do we understand it to be? In this way I think distinction and definition is synonymous. TVs have high definition images not high distinction images - although it could be used interchangeably because vision is the ability to “define” contrasts in light perception. To define is to distinguish.

The minute you speak about it you divide it. Is that what you're getting at? — T Clark

In short, yes. And by dividing it we a). Define it and b). Omit possible ways to define it otherwise leading to inaccuracies in our definition. My point was that definitions are limited in that they are decisions we must make about objects that restrict them/ quantify them by character, property or purpose when really their true definition and relationship to other things can never quite be defined linguistically or conceptually. If they could, art, creativity and imagination could not be possible because everything is firmly set in its ways and can’t be redefined otherwise.

I disagreed with a lot of what you wrote, but it's still an interesting thread about an important subject. — T Clark

Feel free to contest anything and everything I say. That’s the purpose of discussion no? Wouldn’t be much use if everyone was unanimous. I’m learning and evaluating what I’ve said based on your input

T Clark

Yes but show an image of a shoe to anyone and they will immediately Manifest in the minds eye the functions properties and nature of a shoe or their understanding of what a shoe is. They won’t think of “images” just in the same way that when you see a shoe you don’t think of “vision”. It is the subject not the medium of communication. — Benj96

I don't understand you're point. There are no two ways about it - a picture of a shoe is not a shoe. The idea of a shoe is not a shoe. "Shoe" is not a shoe.

This is from "What's Up Tiger Lily," a Woody Allen film.

T Clark

Can you define without making distinctions? — Benj96

Here are two definitions of "define" from the web:

Maybe instead of saying that you've mixed up "definition" and "distinction" I should say you have mixed up these two meanings of "define." As it says in the "Tao Te Ching:"

The tao that can be told
is not the eternal Tao
The name that can be named
is not the eternal Name.

The unnamable is the eternally real.
Naming is the origin
of all particular things.

In this sense, it is naming that makes the distinction, not definition. Naming and defining are not the same thing. I don't think that's a nitpicky distinction.

However I don’t see what point there is in clarifying that words are not the real world because if we cannot apply language to the world we cannot gather communal information about anything. — Benj96

Of course we use language to describe and communicate the world to others, but the words aren't actually the world. Words are arrows pointing at the world. They say "See this. Look here."

If an object doesn’t have a name for its existence then what exactly do we understand it to be? In this way I think distinction and definition is synonymous. TVs have high definition images not high distinction images - although it could be used interchangeably because vision is the ability to “define” contrasts in light perception. To define is to distinguish. — Benj96

Again, I think you are mixing up senses of the word "definition."

Agent Smith

As you rightly pointed out, no definition is perfect except maybe mathematical and scientific ones
— Agent Smith — Hillary

There's no ambiguity or vagueness in (say) what a triangle is. Nobody ever gets confused as to what a triangle is, once s/he is edified as to what they (triangles) are, oui? :chin:

Agent Smith

It depends what exactly you mean but yes in a general sense I think most things are not clear cut and discrete but rather a more flexible spectrum of transition in which a certain level of bias or interpretation must be made.

For example using the previous example we could say a shoe is a piece of footwear you wear to walk or make a fashion statement. However when one considers repurposing and lateral thinking a shoe can indeed function in many ways - it can be a container for plants, a missile to throw at someone when you’re annoyed, something symbolic like the shoes that hang on telephone wires where drugs are sold, it could be part of a sculpture or art installation in a gallery, or could be worn comically by different animals - cats dogs etc. The list is endless. Yet we can’t afford to spend time defining every possible way a shoe can exist or function even though the possibilities are vast. This applies to most objects and thus yes the world is “fuzzy” indeed — Benj96

With regard to your example of a shoe, couldn't we make a distinction between primary use(s) (integral to its definition) and secondary use(s) (go hogwild). Wittgenstein should've realized this before shooting his mouth off (meaning is use). :chin:

bert1

The brake shoes on your car cannot be worn at all. — Cuthbert

The brake shoes on my car are very worn. But that is grist to your mill.

Banno

Thoughts? — Benj96

Why do you need a definition of "shoe"? You can already use the word...

Indeed, you presume to be able to say if this or that definition of "shoe" is more or less specific or accurate; but how could you do that unless you were already aware of what a shoe is? How can you tell is a given definition is right unless you already know what a shoe is?

Hence definitions don't tell you anything new. They are overrated.

EricH

Shoes, shoes - is that all you folks can talk about? What about pipes - don't they deserve a seat at the table of this conversation? :razz: ?u=https%3A%2F%2Ftse2.mm.bing.net%2Fth%3Fid%3DOIP.f_Mrh7UgopKDdz9p7YgAwQHaFJ%26pid%3DApi&f=1

?u=https%3A%2F%2Ftse2.mm.bing.net%2Fth%3Fid%3DOIP.f_Mrh7UgopKDdz9p7YgAwQHaFJ%26pid%3DApi&f=1

Skalidris

What's a perfect definition anyway ? We assigned words to concepts and things we see and experience, and these words either represent a category of these or the elements themselves. So we can argue whether an object fits a category, or whether we should expand the category so that the object fits, but arguing if a definition is perfect ? Doesn't make any sense to me.

Linguistic isn't science, it's not meant to understand the world but to make categories of elements in the world so that we can communicate. And since that's the goal, why should we define every word with other words if everyone already understand the concept (eg the word "nothing"). You can teach a child the concept of nothing with toys, and then tell them "this is called nothing". It can't be thought with words, so why should we try to define it "rigorously" ?

Philosophim

Definitions are a combination of three factors.

1. Essential properties - These are properties which are absolutely necessary to the word. A tree is a plant.
2. Accidental properties - Properties that the definition can contain, but are not essential to its identity. "A tree can have branches".
3. Context - A societal or intentional situation that changes the essential and accidental properties of the definition. "That plaster statue is a tree." (It is not essential that a tree be a plant, as we are within the context of artistic representations, and thus plaster).

The difficulty is nailing down the context of the situation. If you note that "Trees are made of plaster" when talking about biological trees, you are wrong. If you note that "Trees are made of plaster" when talking about art, you are correct. Oftentimes people aren't debating the essential or accidental properties of a definition, but the context of it.

Benj96

Hence definitions don't tell you anything new. They are overrated. — Banno

I disagree definitions can definitely tell you something new. If not how ever do we educate ourselves on the world/ nature - it’s characteristic, properties and relationships. If definitions don’t tell us anything knew about things that supposes we are all omniscient.

Also one can write fiction, invent objects that don’t exist and give them names based on their hypothetical purpose or traits. Imagination can define.

That’s not to say definitions don’t require a base knowledge from which we can extrapolate knew concepts or recombine older or other ones. I see your point in that in most cases observation comes before requiring a definition for something just as a person living alone in the wilderness doesn’t really need a language or words at all to survive and use things.

Benj96

1. Essential properties - These are properties which are absolutely necessary to the word. A tree is a plant. — Philosophim

The only issue I have with this is the regression of definitions. Ie. A tree is a plant, a plant is a living thing a living thing is ... at so forth all of which by your reasoning has some previous essential property contained within the next. So what is “thee” essential property in the first place? What property must we have in order to begin with the first definition by which we relativistically base the following ones?

2. Accidental properties - Properties that the definition can contain, but are not essential to its identity. "A tree can have branches". — Philosophim

Are there trees without branches?

Benj96

Linguistic isn't science, it's not meant to understand the world but to make categories of elements in the world so that we can communicate. — Skalidris

Not sure I agree that linguistics or languages don’t exist to understand the world because you cannot remove understanding from communication they’re not mutually exclusive. I would imagine it’s difficult to educate someone in science without using a language of sorts. Perhaps mathematics is an exception however maths is often considered a language - with rules and grammar by which subjects - numbers and letters - are put into relationships and functions and whether you call it programming or learning a language it requires an input of rules by which to manipulate the subject matter.

Also a large part of science is about categorising, structuring or ordering things in a useful and meaningful way just as language is.

Philosophim

↪Benj96

The only issue I have with this is the regression of definitions. Ie. A tree is a plant, a plant is a living thing a living thing is ... at so forth all of which by your reasoning has some previous essential property contained within the next. So what is “thee” essential property in the first place? — Benj96

In terms of biology, likely your first experiences with the plant based on your cultural upbringing. This would be different than for a biologist who has plants categorized down to very exacting definitions and standards.

Are there trees without branches? — Benj96

Yes. If I trim all the branches off of a tree, its a "tree without branches".

Benj96

Yes. If I trim all the branches off of a tree, its a "tree without branches". — Philosophim

A dying one maybe haha

Banno

↪Benj96

And yet we use words without being able to provide suitable definitions.

Consider that a child does not learn to use a word by being told its definition. They learn by imitation, trying out new expressions, getting it wrong and getting it right.

The definition comes only after the word had been used.

The limits of definition

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