Language is about social co-ordination with respect to mutual projects. The act of 'attempted definition' is itself a pragmatic attempt to agree about such projects. Insofar that humans have much sensory apparatus in common, there is much 'unsaid' agreement, but since perception tends to be active not passive, the dynamics of social interaction can involve the shifting of 'project goals'. This manifests as subsequent semantic drift over the import of 'words'.* Pragmatism is the ultimate decider because it is a call for consenual project goals.

*In the nebulous social goal situation we call 'philosophy', semantic drift equates to what Wittgenstein called 'language on holiday'.

What's odd about W's paradox is that we intuiti that we can define a word with accuracy and completeness, but then appears we can't.

We imagine that the people around us are following the same rules we are, yet there could always be a situation just beyond the horizon that reveals that this isnt true.

This video appeared on reddit recently. It offers some thoughts about whether we can ever go beyond being pragmatic about defining words. Tell me what you think: — frank

Similar skeptical reasoning can be applied to any word of any human language. The power of Kripke's example is that in mathematics the rules for the use of expressions appear to be defined clearly for an infinite number of cases. Kripke doesn't question the validity in mathematics of the '+' function, but rather the meta-linguistic usage of 'plus': what fact can we point to that shows that 'plus' refers to the mathematical function '+'. — Wikipedia

Why doesn't Kripke "question" the validity in mathematics of th the '+' function?

Is the mathematical function '+' so well-defined as to leave no room for doubt, in which case Kripke would be admitting a solution to Wittgenstein's paradox viz. that being able to state the rule is a good indication that a person is following that particular rule.

One argument against this "solution" is that each word sub-unit in a rule is itself subject to the same problem of conforming to multiple interpretations of a rule.

My response is that definitions, traced back to their origins, all start off with the obvious. Nobody will ever make an error in what "water" means or what "pain" means. We begin from the obvious, unquestionable meanings of such words and build our word-empire from there. Let's take the example of a chair, a favorite it seems.

A chair is, "obviously", more complex than its constituents. In the meaning of "chair" the only rule-following error that can be made is to mistake "chair" to mean a component or property of a chair. I mean we may mistake "chair" to mean wood or metal or other simpler constituent property of "chair". This type of error is impossible or highly improbable because the meanings of these simpler components of a chair is already understood - bridges already crossed.

:joke:

We begin from the obvious, unquestionable meanings of such words and build our word-empire from there — TheMadFool

Even if this is true, the Empire is apt to be filled with fudge factor.

That doesnt help us to know by observation of people whether they understand words exactly the same way we do.

Hmm. Every serious effort at communication usually includes a definitions section, for the obvious purpose of helping people understand what's being presented. Examples being textbooks, laws, love letters - and was there ever a love letter that did not set out at length the writer's understanding of the term both abstractly and in application? And has it not always been the case that the recipient could keep his or her own counsel on the matter; and further that they might even arrive at a meeting of the minds?

And communication can also as well be a problem in efficient encoding. In any case, where meaning is important, the "paradox" is avoided by the offering of the possibility of clarification of meaning. In short, not a paradox at all, but a recognition that communication is not always simple or easy, nor simply nor easily achieved.

Readers here on TPF will recognize that most of our disagreements, thereby wasted time and effort, are based in failures to come to at least agreed preliminary definitional understandings, meaning that whatever the discussion is supposed to be in any unitary sense, it cannot be because the interlocutors don't know what they're talking about.

And in terms of the meanings of words, it seems to me less a matter of drilling down to some incontrovertible meaning as bedrock, which the video makes clear is problematic/impossible, than it is a matter of correct focus, outside of which either way, the meaning retreats and withdraws into a blurred ambiguity and then meaninglessness.

No doubt in some calculus of the philosophy of language the paradox has some significance, but beyond being a not-very-useful warning about meanings, I don't see it as of much use or significance for most folks.

And has it not always been the case that the recipient could keep his or her own counsel on the matter; and further that they might even arrive at a meeting of the minds? — tim wood

That's a good question. What fact would you point to to assure yourself that a meeting of minds has taken place?

And in terms of the meanings of words, it seems to me less a matter of drilling down to some incontrovertible meaning as bedrock, which the video makes clear is problematic/impossible, than it is a matter of correct focus, outside of which either way, the meaning retreats and withdraws into a blurred ambiguity and then meaninglessness. — tim wood

Correct focus? What's that and how does it work?

Science seems pretty useful. I guess you meant something else though?

This video appeared on reddit recently. It offers some thoughts about whether we can ever go beyond being pragmatic about defining words. — frank

This problem occurs in natural language, because natural language tries to establish correspondence with the real, physical world.

This problem does not occur in formal languages, because a formal-language sentence does not "mean" anything. It just acquires (or does not) its truth status from other formal-language sentences that already have such status. Example: S1 is true, S2 is true, S3 is false. What is the truth status of S1 and not S2 or S3?

It is a tremendous advantage that S1, S2, and S3 do not mean anything.

Natural language obviously has its applications but is often useless in situations where you should rather use a meaningless formal language. In that case, the solution is simply to strip away all meaning.

What fact would you point to to assure yourself that a meeting of minds has taken place? — frank

The fact of a statement of agreement.

Correct focus? What's that and how does it work? — frank

The idea of establishing meanings relevant to present purpose. If I call this piece of furniture a chair and you say not-so-fast, it's just profoundly empty space with some really, really small particles whizzing around within its outer boundaries, then a) we have not (yet) had a meeting of minds, and b) we need to focus on what we need to mean to have a conversation.

More than that, you're soliciting opinion, and there's no reason to think mine better than yours. What, then, do you say?

We can, and have, set up limited systems within which rigid rules operate. To put forward the ‘chair’ example is to side on the position that there is no exact, but a ‘chair’ isn’t a universal term. Chairs exist in the physical world in numerous forms.

I’ve recently used the game tic-tac-toe as an example. The rules are clear enough, and limited enough, for us to learn without any disagreement about how to play and how to win. For young children there are possible misinterpretations and mistakes because they don’t have the capacity to see all the possibilities in their minds eye. The same goes for us and a ‘chair’. We lack the capacity to see all possibilities of chair because the ‘limit’ chair operates in is ... well, ‘limitless’ as far as we can see.

As we’re able to extend our thought further into time by the facility of ‘language’ we’re able to encapsulate set parameters for our understanding and expand our abstract capacities.

The fallacy is the overextension of rules beyond set parameters. The thing is we’re always, at least partially, inclined to do this. We also do reap the reward of the occasional happy accident of such over-extensions. A so-called ‘cognitive bias’ can prove fruitful in realms no person without such bias would even consider looking. The human ‘flaw’ is necessarily a ‘boon’ in some occasions.

What fact would you point to to assure yourself that a meeting of minds has taken place?
— frank
The fact of a statement of agreement. — tim wood

Ok.

The fallacy is the overextension of rules beyond set parameters. — I like sushi

Yep.

Science seems pretty useful. I guess you meant something else though? — I like sushi

?

The underlying difficulty is we don't know what other minds experience, we attempt to guess it based on how they behave, how they look, how they sound, ...

Some people seem to be able to read people better than others, is it simply that they are very attentive to the clues that the other person gives off, or that in some way they are able to directly experience what the other experiences?

In uttering words we attempt to convey what we experience, to give rise to that experience in others. With some people sometimes it seems that a few words do the job, or even no word and just looking at each other is enough, while with some other people it seems that even after repeated clarification the essence of the experience doesn't get through to the other side.

We can try to be as clear as we can, but then we can't be clearer than that. Sometimes no amount of words or explanations can convey what a picture can convey or what hugging someone can convey. Sometimes people are in a state where they aren't ready to listen or to understand something because they feel in a specific way or because what they are told is in conflict with some deeply held belief.

Words are one tool to communicate, not the only one, so in the situations where that tool doesn't seem to work it seems indeed futile to insist on using it with exactness and hoping that if only we use it precisely enough it will start working.

One example I like to use is that of the dictionary. Even if we all used the exact same dictionary, with all the exact same definitions for each word, we would still have zero guarantee that we would understand one another, because there is a missing link between the words and what experiences the words refer to. A dictionary relates words with one another, not with actual experiences, feelings, perceptions.

Without that link it doesn't help to strive for more exactness by using the same definition of a word, and then the same definitions of the words that make up the definition of the word and so on and so forth, because eventually the original word is defined in terms of itself, circularly. What breaks the circularity is the link between words and experiences, which more precise definitions do not provide.

But we don't have an objective link, each of us has their own personal link, and words alone do not help to clarify these links, rather we need to interact with people in other ways in order to uncover what they experience and to communicate what we experience more precisely. Maybe exactness could be reached, but not through words.

Even if this is true, the Empire is apt to be filled with fudge factor.

That doesnt help us to know by observation of people whether they understand words exactly the same way we do. — frank

I like philosophy and math because of present/claimed rigor. Exactness is great because it allows us to isolate a concept or theory in a sterile room of sorts for better analysis.

However...

I think the great Wittgenstein was aware that language functions a bit differently - it's not just exactitude and precision that it aims for. We have science, philosophy and math for such activities.

Language requires a certain amount of flexibility to minimize an exponential increase in the number of words we need to learn. Everyone knows that words usually have multiple meanings and that's for a very good reason - to prevent memory overload and wasting time over unnecessary hair splitting. I think it's this flexibility that leads to the Wittgenstein paradox.

Very very very well said!

I think it's this flexibility that leads to the Wittgenstein paradox. — TheMadFool

I think you're right. Natural language is in use where experiences vary (as Leo pointed out). It would take time and special personalities to even uncover this.

Doesn’t matter. Appears we do generally agree.

Boring :(

I think you're right. Natural language is in use where experiences vary (as Leo pointed out). It would take time and special personalities to even uncover this. — frank

An error in my post which I hope to "correct"...

It isn't about ambiguity as I thought. Actually it's about multiple disparate rules that concur ONLY in a particular set of instances. The effect being an inability to determine if a given number of people are actually following the same rule or not.

However it doesn't seem so bad because the relationship as in the example of "plus" and "quus" is that of containment. The "quus" rule lies within the "plus" rule. The concurrence between "quus" and "plus" is true in the specified range of numbers.

What I mean is there is no right vs wrong/true vs false in the matter of rules as far as Wittgenstein's paradox is concerned. It's more about degrees of correctness. In our example the "quus" rule isn't wrong/false which would be a real problem. Rather the "plus" rule is more correct than the "quus" rule.

In short there is no error and the difference in the rules is just a question of degrees of correctness.

There is no black and white. Simply shades of grey.

Doesn’t matter. Appears we do generally agree.

Boring — I like sushi

I'm very gratified when I find I'm not the only person on the planet who thinks x. But yea, retract claws, abort missile launch. What's for lunch?

In short there is no error and the difference in the rules is just a question of degrees of correctness. — TheMadFool

Which says that communication can't be rooted in rule-following, though we may be able to note what looks like rule-following.

Have you ever noticed that post-structuralists seem to isolate themselves in a domain of words and phrases? When you ask them what's beyond that realm, they say there is no escaping it. Which makes one wonder: is there really a bubble of words floating around in the universe somewhere?

Rather, human communication is a form of our overall interaction with the world. In the same way we look around asking questions and getting answers just with our senses, we look at each other and encounter something we take to be subjects just like ourselves. I agree that the way we think about ourselves is influenced by language, but I'm saying language itself is a form of sensing that applies only to psyches.

I think that the history of divinity might reveal that we started off thinking of the world as a giant psyche. Praying to the sun was the way we interacted with it. Somewhere in there is the notion that science as we know it is the offspring of religion in a deeper way than some people realize. What if speech is actually a primary way to sensing and interacting for humans?

The paradox is that the whole point of communication is to commune with others in the same way we seek to commune with the world through our senses.

I can conclude that communication never really happens, or that something accounts for the existence of communion that isnt obvious.

There is no black and white. Simply shades of grey. — TheMadFool

Except that one such intermediate shade is sufficient, usually, to facilitate perfectly reliable separation of black and white.

Not that such a separation is possible between the categories designated by "offside" and "not offside", which are assumed to exhaust the domain of football-play-states, and must therefore eventually overlap, however keen the effort and eyesight of referees.

Consideration of which is, I would think, a better use of the example than using it for discussion of Plus and Quus. The definition aspect of offside is an unproblematic equation of "offside" vs. "not offside" with "nearer to the opposing team's goal-line than are the ball and at least all but one of that team's players" vs. "not nearer... etc." Which, as you point out, isn't about induction or generalisation, and isn't what creates disputes.

And not that Plus and Quus aren't fascinating as anything, e.g. Blue and Grue. But they don't depend on necessary vagueness ('open texture') of terms. I.e. on the impossibility of keeping one term separate from another (such as its complement) without a margin for error, an impossibility that does explain the sporting disputes.

What I mean to say is that the problem may not be with language but with the users of language. Might we be mistaking ignorance/incomplete knowledge for a linguistic paradox?

In math there's a similar problem with induction. Suppose we're given only a three numbers in a sequence like so:

A = {1, 4, 8,...}

We're asked to find the next number in the sequence.

There are two possible rules given what we do know:

1) 1 + 3 = 4 and then 4 + 4 = 8

2) 2^0 = 1, 2^2 = 4, 2^3 = 8

As you can see the problem isn't with mathematics <language> but with inadequate data.

As with the off-site rule we need some more more data points to complete our understanding of the rule being applied.

There are two possible rules — TheMadFool

... or as many as you like. I think you're back on Plus/Quus.

Just saying, offside rule disputes may be a good example of a different (interesting) problem, but not this one.

A = {1, 4, 8,...}

We're asked to find the next number in the sequence.

There are two possible rules given what we do know:

1) 1 + 3 = 4 and then 4 + 4 = 8

2) 2^0 = 1, 2^2 = 4, 2^3 = 8

As you can see the problem isn't with mathematics <language> but with inadequate data. — TheMadFool

I think we agree. It's not a problem with mathematics or language. It's that on reflection, we note that there's no way to verify that communication has the clarity and precision we assume it has.

More data wouldn't resolve that. It's similar to the problem of induction.

... or as many as you like. I think you're back on Plus/Quus.

Just saying, offside rule disputes may be a good example of a different (interesting) problem, but not this one. — bongo fury

I think we agree. It's not a problem with mathematics or language. It's that on reflection, we note that there's no way to verify that communication has the clarity and precision we assume it has.

More data wouldn't resolve that. It's similar to the problem of induction. — frank

I guess the example given is insufficient to capture the essence of Wittgenstein's paradox because both the off-side example and the plus-quus example are about acquiring more information.

Could you guys give me a better example? Thanks.

guess the example given is insufficient to capture the essence of Wittgenstein's paradox because both the off-side example and the plus-quus example are about acquiring more information. — TheMadFool

How would you know you have all the required info? What fact would you point to to show that you have it?

I guess the example given is insufficient to capture the essence of Wittgenstein's paradox because both the off-side example and the plus-quus example are about acquiring more information.
Could you guys give me a better example? Thanks. — TheMadFool

Presumably plus-quus isn't in doubt as a case of Kripgenstein, at least? But compare blue-grue if you want another (or very close).

I was questioning offside as a suitable example of (yes) generalising from limited (but presumed non-vague) information, and recommending it instead as a case of vagueness, specifically the ineliminability of vagueness in measurement with no margin of error. (I.e. a case of the futility of insisting on exactness, where the latter is assumed absolute rather than relative to a margin of error.)

How would you know you have all the required info? What fact would you point to to show that you have it? — frank

The required info would be instances where the disagreement arises, thus revealing that different rules are/were in play.

Presumably plus-quus isn't in doubt as a case of Kripgenstein, at least? But compare blue-grue if you want another (or very close).

I was questioning offside as a suitable example of (yes) generalising from limited (but presumed non-vague) information, and recommending it as a case of vagueness, specifically the ineliminability of vagueness in measurement with no margin of error. — bongo fury

I think vagueness requires a continuum to exist in. The classic heap paradox illustrates that quite well I believe. However Wittgenstein's paradox seem to be about clear and distinct rules. No continuum.

I think vagueness requires a continuum to exist in. The classic heap paradox illustrates that quite well I believe. — TheMadFool

Well it illustrates the opposite, because it proceeds step by discrete step. But a continuum can make the vagueness ineliminable, yes.

However Wittgenstein's paradox seems to be about clear and distinct rules. No continuum. — TheMadFool

"No vagueness", and yes, my point exactly.

One example I like to use is that of the dictionary. Even if we all used the exact same dictionary, with all the exact same definitions for each word, we would still have zero guarantee that we would understand one another, because there is a missing link between the words and what experiences the words refer to. A dictionary relates words with one another, not with actual experiences, feelings, perceptions. — leo

If the meaning of words were how they are used, and the the way we are taught the meaning of words is by using them to point to things in the world, not to point to things in our head, or our experiences, then when we use words we would be using them as we've seen others use them and how they taught us to use them. There would be no pointing to our experiences in using words, only pointing to the world outside of our experiences.

When someone says, "I have a stomach ache and feel like I'm going to vomit." How does one to learn how to use those words if we can't see what it is that they are pointing to when using them? I can't see their feelings. I can see their behavior, and it is that I would associate the meaning of the words, not something I can't observe, like their feelings. So when I use that same phrase, would I be pointing to my behavior, or my feelings? How would I know that a person is pointing to their feelings if I can't see their feelings?

If we say that those words point to their actions when using them, or the meaning of the words are how they are using them along with their actions, then I could say I have a stomach ache and hold my stomach as if I appear to be protecting my upset stomach, then I could do that without having the feeling of having a stomach ache, and I'd be wrong in how I'm using it, or I'd be lying.

It seems to me that we all have similar feelings or experiences and it is those similar experiences and feelings that we understand others as having an are pointing to when they speak. Meaning isn't use, or else there would be a lot of misuse going on because we can't always see what a person is pointing to when using them, as in the upset stomach example. Meaning is the relationship between some idea in your head and the words that others know that point to that shared feeling or experience.