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A paradox about borders.

Paralogism September 05, 2019 at 13:57 9325 views 56 comments
China and Pakistan share a border - on this everyone agrees. But the border's rightful location is disputed (untrue since 1963, but just suppose it for the sake of argument) and there is no undisputed portion of it. If China is correct, then the border is in one location, but if Pakistan is correct, then it is in another. So if possibility (A) is true, they share a border, and if possibility (B) is true, they still share one. From this we can conclude that China and Pakistan necessarily share a border.

However, when we make the claim that something exists, it seems evident that we ought to be able to point to that entity, to define it. So if we withhold judgment about which claim is true, then it seems that there is no existent border - it isn't both at once, but could be either one, like a superposition. Without some criteria for favoring one over the other, we are unable to say that any real border exists at all.

This paradox arises out of the ill-defined nature of borders and nations. Are there other things we can apply it to? It might be helpful in rigorously defining concepts.

Comments (56)

Terrapin Station September 05, 2019 at 14:29 #324637
First, even if everyone agrees on it, borders aren't objective things, so they're not "real" in that sense. (Even if there's something like a wall or fence, or we're talking about border stations/border guards, etc.--that doesn't make the border itself objective/real; the wall/fence, etc. aren't identical to the border).

A border is a concept that people have and can agree on.

So nearly everyone can agree that there's a border between two countries (where they have to agree there are two countries), with no other territory between them, while disagreeing on just where the border should be considered to be.

What it is for there to be a border is for people to have a particular sort of geopolitical concept in mind. Pointing to it is pointing to that concept, and pointing to its expression, such as statements in almanacs, etc.
T Clark September 05, 2019 at 14:37 #324639
Quoting Paralogism
This paradox arises out of the ill-defined nature of borders and nations. Are there other things we can apply it to? It might be helpful in rigorously defining concepts.


It applies to much of what we know or perceive. Some examples - colors, races, languages, motorcycles, species, forests, science, art, mental illness.

Rule of thumb - anything an elephant wouldn't recognize as a thing.
Deleted User September 05, 2019 at 20:45 #324818
Reply to Paralogism makes me think of relationship. Two people are in a relationship, I mean this in the romantic sense of relationship. But each of them are certainly going to have differences in their conception of that relationship. There will likely be overlap, at least in the language used to describe the R, but also differences. In some relationships a lot of differences. The description of the contested border will have some overlap - between mountain chain X and river Y. Like which portions of the countries touch - the NW corner, etc. Differences and overlap. A border between countries is a facet of their relationship with each other and to the area of the border and less so to other countries.
fishfry September 05, 2019 at 23:03 #324871
Quoting Paralogism
This paradox arises out of the ill-defined nature of borders and nations. Are there other things we can apply it to? It might be helpful in rigorously defining concepts.


National borders are historically contingent. Surely this is a trivial point, not a profound one. The US was the US before and after the Louisiana purchase. It just had more land. Just as you are still you if you buy your neighbor's property and adjoin it to yours.
Wayfarer September 05, 2019 at 23:38 #324877
Quoting Terrapin Station
First, even if everyone agrees on it, borders aren't objective things, so they're not "real" in that sense.


Is anything?
Janus September 06, 2019 at 01:25 #324917
Reply to Terrapin Station Are the boundaries (borders) of objects real, according to you? I've heard you say that there are no real, as opposed to merely conceptual, universals. If you say there are no real, as opposed to merely conceptual, boundaries to objects, then it would seem there are no real particulars either, and it would all begin to look like being mental phenomena "all the way down", a conclusion which, if you were to be consistent, should make you an idealist.
Janus September 06, 2019 at 01:27 #324918
Reply to Wayfarer Jesus, what's going on? We seem to be making the same point! :yikes:
ssu September 06, 2019 at 06:39 #325014
Quoting Paralogism
However, when we make the claim that something exists, it seems evident that we ought to be able to point to that entity, to define it.

Not really,

We might start with saying that a) Beijing is in China, b) Mumbai is in India and c) if there is a route from Beijing to Mumbai where there isn't third country or a sea between the two, there has to be a border between the two countries. That two countries don't agree where exactly this border goes is actually not uncommon in history, yet that doesn't at all refute the existence of the border. We simply will define an area to be disputed, hence there is no paradox. India isn't arguing that Beijing belongs to India and China doesn't hold that Mumbai is in China, hence there has to be a border.

Do notice that my counterargument can be found in mathematical logic too and these kind of problems have left mathematicians scratching their head also.
Terrapin Station September 06, 2019 at 09:28 #325074
Quoting Janus
Are the boundaries (borders) of objects real, according to you?


Yes, real, but (a) they can be more or less fuzzy depending on the point of reference, and (b) there's nothing about them in terms of concepts that's real(/objective).
Terrapin Station September 06, 2019 at 09:36 #325076
Quoting Janus
If you say there are no real, as opposed to merely conceptual, boundaries to objects, then it would seem there are no real particulars either,


Re that, by the way, if someone thought that there was no clear/discernible real border for "objects"--for example, maybe they think that everything is really a more or less lumpy continuum (and somehow they thought that there was no intelligible way to parse "borders" for the lumps), they could simply say that there's one real particular--the more or less lumpy continuum.

That's not my view, by the way. It's just a possible view.
Terrapin Station September 06, 2019 at 09:38 #325077
Quoting Wayfarer
Is anything?


Of course. Most things are real in that sense.
TheMadFool September 06, 2019 at 09:40 #325079
Quoting Paralogism
Without some criteria for favoring one over the other, we are unable to say that any real border exists at all.


An inability to determine the truth of a proposition x doesn't imply that x doesn't have a truth value. We just don't know the truth value. The border exists but we just don't know where it is. If only we could make war, racism, and everything bad disappear by disagreeing.
Terrapin Station September 06, 2019 at 10:09 #325094
Quoting TheMadFool
An inability to determine the truth of a proposition x doesn't imply that x doesn't have a truth value. We just don't know the truth value. The border exists but we just don't know where it is.


How would you suppose the geopolitical border exists where we just don't know where it is? What, exactly, do you think the geopolitical border is?

Quoting TheMadFool
If only we could make war, racism, and everything bad disappear by disagreeing.


Racism is a way of thinking about people. So if racist folks thought differently, racism would disappear.

Likewise, war only obtains via people deciding to engage in particular actions. If people made different decisions, war would cease.
TheMadFool September 06, 2019 at 12:32 #325143
Quoting Terrapin Station
Racism is a way of thinking about people. So if racist folks thought differently, racism would disappear.


The OP made things disappear simply on the basis of disagreeing. This isn't possible I believe. If we disagreed on matters of taste, which I presume is subjective, that would be different. Borders I hope are objective and disagreeing on it wouldn't make it magically vanish.
ssu September 06, 2019 at 12:45 #325147
Quoting TheMadFool
Borders I hope are objective and disagreeing on it wouldn't make it magically vanish.

When enough people agree on there existing a state, that state and it's borders do exist. Sometimes people have problems in understanding the existence of human institutions and think they wouldn't exist because they are just 'made up', 'invented' or 'agreed upon'.
Terrapin Station September 06, 2019 at 13:30 #325167
Quoting TheMadFool
The OP made things disappear simply on the basis of disagreeing. This isn't possible I believe. If we disagreed on matters of taste, which I presume is subjective, that would be different. Borders I hope are objective and disagreeing on it wouldn't make it magically vanish.


Are you using "objective" to denote agreement basically?
TheMadFool September 06, 2019 at 13:42 #325172
Quoting Terrapin Station
Are you using "objective" to denote agreement basically?


As I understand it borders are physical. It would simply exist whether we agree or not.
Terrapin Station September 06, 2019 at 13:53 #325179
Reply to TheMadFool

It's not easy to find a picture of what I'm looking for (though it's easy to find in person), so for the pic below, you have to imagine the sign isn't in the frame.

User image

What would you say is the physical border there?
ssu September 06, 2019 at 15:21 #325207
Quoting TheMadFool
As I understand it borders are physical. It would simply exist whether we agree or not.

?

Even in my lifetime a lot of borders have been redrawn, one important border that I personally crossed over has vanished after the unification of two states. And where I live there are historical borders in my neighborhood where earlier was the border. A border is a perfect example of an institution, just like the picture above from Terrapin Station shows.
Pattern-chaser September 06, 2019 at 15:55 #325226
Quoting Terrapin Station
What would you say is the physical border there?


Well, you see that piece of grass, immediately to the right of the sign...? :wink:
Pattern-chaser September 06, 2019 at 15:58 #325229
Reply to ssu There are borders that exist only because we recognise them. But surely there are also borders that exist because they lie between different things, like the sea-shore, which bounds the sea (or the land, depending which way you're oriented)?
Janus September 06, 2019 at 21:40 #325336
Reply to Terrapin Station What is it about the boundaries of objects that is real according to you? I mean you say that what is real about the boundaries of objects is not at all conceptual, which I take you to mean is not mental.

Granting that a boundary is not something we merely think, it must be something we see or feel. Yet seeing and feeling are neural processes which means that they are also at least in part mental processes (if the brain is as you say identical with the mind). This leaves me wondering what it is that you think is real and yet wholly non-conceptual about the boundaries of objects.
Terrapin Station September 06, 2019 at 22:09 #325349
Quoting Janus
What is it about the boundaries of objects that is real according to you? I mean you say that what is real about the boundaries of objects is not at all conceptual, which I take you to mean is not mental.


So for example, material particles have spatial extension, but the spatial extension isn't infinite. The limits of that spatial extension is a boundary.

The same is true of particles in bonds with other particles. There's a spatial extension that isn't infinite.

And the same is true of particles in dynamic motions relative to other particles--for example, where those dynamic motions are dictated primarily by electromagnetic forces. The motions aren't just random and infinite in terms of spatial extension. They only spatially extend over a particular area. The limit of that is the boundary.

Quoting Janus
Granting that a boundary is not something we merely think, it must be something we see or feel.


That's talking about perceiving boundaries, which is different than the boundaries themselves. The boundary of a particle is in no way dependent on us perceiving it.
Possibility September 07, 2019 at 04:36 #325415
What you’re talking about is a shared subjective 5D experience of a 4D event, and how it relates to 3D objects in a 2D space.

A ‘border’ aims to signify the moment of four-dimensional change in spacetime from one ‘country’ (as a 3D object) to another. It can be defined only in relation to the experience of others. An exact position of the border in 3D or 2D space remains ‘fuzzy’ until a shared experience can be observed (in relation to another observer), and then measured (in relation to other objects) and marked (on a 2D plane) - in mutual agreement.

At this point in the negotiation, one may wonder why a border needs to be defined in the first place...

So the border signifies a relationship between subjective experiences of a particular four dimensional event.
Janus September 07, 2019 at 05:11 #325427
Quoting Terrapin Station
The boundary of a particle is in no way dependent on us perceiving it.


How do you know that is the case, or even what it would mean? Does it even make sense to speak of fundamental particles having spatial extension?

See for example this: https://www.google.com.au/url?sa=t&source=web&rct=j&url=https://thedutchparadigm.org/13-2/the-standard-model-of-fundamental-particles-and-interactions/point-particles/&ved=2ahUKEwiPm_Du973kAhUIfysKHdklAm4QFjANegQIChAB&usg=AOvVaw28lIcgNBmjbkmQTBoZmarh&cshid=1567833017704
Terrapin Station September 07, 2019 at 11:03 #325478
Reply to Janus

So first, let's clarify that "Are the boundaries (borders) of objects real" and "What is it about the boundaries of objects that is real" are ontological questions.

"How do you know that is the case" is an epistemological question. And "What would it mean" is a question of semiotics or semantics.

Ontological questions don't require epistemology, because, for example, ontology can simply present a possibility, and that possibility can be chosen while discarding other possibilities for a number of reasons including coherence, pragmatism, and so on, where we don't have to be making a knowledge claim to not only present but to also choose an ontological stance. So making sense of an ontological stance, understanding the ontological stance, and choosing an ontological stance do not require epistemology.

When we start addressing the epistemological question as well as the semiotics question, we're doing something different than we were doing in addressing the ontological question.

We can move on to the epistemological question, but before we do, I want to clarify that the ontological stance was understood as a possibility. (And this includes the stance I presented as not my own, but a possible stance where one asserts there are no clear boundaries, yet there's a particular.)
Janus September 07, 2019 at 22:43 #325770
Quoting Terrapin Station
Ontological questions don't require epistemology, because, for example, ontology can simply present a possibility, and that possibility can be chosen while discarding other possibilities for a number of reasons including coherence, pragmatism, and so on, where we don't have to be making a knowledge claim to not only present but to also choose an ontological stance. So making sense of an ontological stance, understanding the ontological stance, and choosing an ontological stance do not require epistemology.


This seems quite wrong-headed to me.

The claim that objects have real boundaries completely independently of our perceptions of them is either an empirical claim or it is not. If it is an empirical claim it must be testable, and if it is testable then it belongs in the realm of epistemology and is thus an epistemic claim. Now it is trivially true that objects are perceived as having boundaries, and thus it is epistemically true that objects have boundaries since that is how we know them. By the same token it is also obviously phenomenologically and semantically true that objects have boundaries.

If you want to make a claim beyond that you are entering the arena of metaphysics, of ontology, but the problem is that it doesn't really make sense to say that we can make metaphysical claims, because in order to qualify as a claim a speculation should be testable, or else merely be a claim in the form of a description of the way we speak coherently about things, but again such claims are just epistemic or semantic.

Of course there is no problem with ontological speculation per se, but such speculations should not be interpreted as stances that can be defended, simply because they are untestable.
Terrapin Station September 07, 2019 at 23:34 #325777
Quoting Janus
If it is an empirical claim it must be testable


Are you (partially) defining empirical claims that way?
Janus September 07, 2019 at 23:43 #325783
Reply to Terrapin Station What do you mean "partially"? If a claim is not testable (at least in principle) it cannot count as an empirical claim. Of any theory that claims to be empirical it should be possible to ask what imaginable observation would refute it. This is so basic I can't understand why you would ask the question.
Terrapin Station September 07, 2019 at 23:51 #325784
Quoting Janus
What do you mean "partially"?


Not wholly. (Shouldn't that be obvious?) In other words, I don't want to assume that's your complete definition of "empirical." Maybe it is, but I'm asking if it's at least part of how you'd define "empirical."

Okay, so presumably you'd say that some ontological claims are not empirical claims, right?
Terrapin Station September 07, 2019 at 23:56 #325786
Reply to Janus

I don't know if you realize it or care, by the way, but every post you type to me comes across like you're a complete asshole who is only interested in arguing.
Janus September 08, 2019 at 00:27 #325789
Reply to Terrapin Station I'm saying it is the central characteristic of empirical claims that they should be testable.

Quoting Terrapin Station
Okay, so presumably you'd say that some ontological claims are not empirical claims, right?


It depends on what you mean by "ontological". Of course ontic claims can be interpreted to be within the epistemological domain in which case they are either testable or semantic (true or false by convention or definition; for example "Sydney is the capital of New South Wales").

Quoting Terrapin Station
I don't know if you realize it or care, by the way, but every post you type to me comes across like you're a complete asshole who is only interested in arguing.


Why would say that? I have been nothing but polite and am merely telling where and why I disagree with what you have said. Are you saying that I should not disagree with you or that you should be exempt form supporting claims that you make or that your arguments should not be subjected to fair criticism?

I am open to different ideas, but only if they are supported by convincing arguments.

Terrapin Station September 08, 2019 at 00:30 #325790
Quoting Janus
It depends on what you mean by "ontological".


The standard definition. Ontology is theory/philosophy of existence or being.

So you'd say that all ontological claims are either testable or semantic (i,e, true or false by convention or definition)?

Quoting Janus
Why would say that?


Because it's the way you come across. It's an attitude that's projected.
Janus September 08, 2019 at 00:34 #325791
Quoting Terrapin Station
The standard definition. Ontology is theory/philosophy of existence or being.

So you'd say that all ontological claims are either testable or semantic (i,e, true or false by convention or definition)?


I didn't sat that. Here it is again: Quoting Janus
Of course ontic claims can be interpreted to be within the epistemological domain in which case they are either testable or semantic (true or false by convention or definition; for example "Sydney is the capital of New South Wales").


Whenever you say what something is that can be interpreted as being an ontic claim. For example: 'water is H2O'.

Heidegger makes a distinction between 'ontic' and 'ontological' on just this kind of basis.

Quoting Terrapin Station
Because it's the way you come across. It's an attitude that's projected.


So, just a subjective impression then; perhaps driven by your dislike of having your ideas challenged?
Terrapin Station September 08, 2019 at 00:36 #325792
Quoting Janus
I didn't sat that.


Sure. So then you'd agree that some ontological statements aren't either testable or semantic?
Janus September 08, 2019 at 00:39 #325793
Reply to Terrapin Station

Of course, I said as much above:

Quoting Janus
Of course there is no problem with ontological speculation per se, but such speculations should not be interpreted as stances that can be defended, simply because they are untestable.
Terrapin Station September 08, 2019 at 00:41 #325794
Reply to Janus

Okay, so why when I'm talking about ontological claims are you reading it as if I'm saying something about them being testable?
Janus September 08, 2019 at 00:59 #325798
Reply to Terrapin Station Not necessarily; I wasn't sure whether you thought they were testable or not. I'm saying that in order to count as a claim a proposition should be either testable or logically true. Otherwise it is just a imaginative speculation, which as I've said is no problem as long as it is not mistakenly thought to be asserting something determinable
Terrapin Station September 08, 2019 at 01:00 #325799
Quoting Janus
I'm saying that in order to count as a claim a proposition should be either testable or logically true.


Why would you say that?

Is it just an idiosyncratic way you use the word "c!aim"?

(Also, so we're saying that conflating ontology and epistemology is the result of some sort of quibble over the word "claim"?)
Janus September 08, 2019 at 01:03 #325802
Reply to Terrapin Station Why would a proposition count as a claim, as opposed to merely an idea that one likes, if its truth is not determinable? Claims must be supported, no? If they are neither testable nor logically true, then I can't see how they could be thought to be supportable. Are you appealing to consensus or commonsense or something like that instead?
Terrapin Station September 08, 2019 at 01:05 #325804
Quoting Janus
Why would a proposition count as a claim, as opposed to merely an idea that one likes, if its truth is not determinable? Claims must be supported, no? If they are neither testable nor logically true, then I can't see how they could be thought to be supportable. Are you appealing to consensus or commonsense or something like that instead?


So here's one common definition of the word "claim": "state or assert that something is the case, typically without providing evidence or proof."

Can you find a definition of "claim" that says claims must be testable or semantic?
Janus September 08, 2019 at 01:06 #325806
Quoting Terrapin Station
So here's one common definition of the word "claim": "state or assert that something is the case, typically without providing evidence or proof."


Where does that definition come from?
Terrapin Station September 08, 2019 at 01:07 #325807
Reply to Janus

Oxford dictionary via Google.
Janus September 08, 2019 at 01:16 #325809
Reply to Terrapin Station OK, sure you can claim that something is the case without providing evidence or proof. You can claim that God is purple with pink polka dots if you want. But this is in the context of philosophical, not idiomatic, usage of the word. What about argument? Would you say that a claim counts as philosophical if you make it without providing either evidence, proof or argument?

Let's return to your original claim that objects have boundaries independently of all human thought and experience. How would you argue for that?
Terrapin Station September 08, 2019 at 01:19 #325813
Quoting Janus
OK, sure you can claim that something is the case without providing evidence or proof. But this is in the context of philosophical, not idiomatic, usage of the word. What about argument? Would you say that a claim counts as philosophical if you make it without providing either evidence, proof or argument?


First, you didn't answer what I asked you: can you find a definition of "claim," in a philosophical context, that suggests that claims must be testable or semantic?
Janus September 08, 2019 at 01:25 #325819
Reply to Terrapin Station I haven't said that philosophical speculations must be testable or semantic.I am saying that to be counted as claims they must be at least able to be argued for. On what basis would you argue for any philosophical speculation if not in either a posteriori or a priori terms, or by an appeal to common intuitions?
Terrapin Station September 08, 2019 at 01:29 #325821
Quoting Janus
I haven't said that philosophical speculations must be testable or semantic


The question was about the word "claim."
Janus September 08, 2019 at 01:40 #325823
Reply to Terrapin Station I used the word "speculation" because I don't think untestable, non-tautologous or non-a priori or unargued speculations or propositions really count as claims. In any case I'm not interested in arguing about definitions of the word "claim". That is a diversion from the original point of the discussion which was your statement that

Quoting Terrapin Station
The boundary of a particle is in no way dependent on us perceiving it.


You introduced the "particle"; originally the argument was about whether objects in general have boundaries independently of our perceptions of them. I want to know how you would argue for that.

(If you won't let this minor quibble over the word 'claim' go, then can you find a definition of "claim," in a philosophical context, that suggests that claims do not need to be testable, semantically true or argued for)?

BC September 08, 2019 at 01:56 #325827
And even when everybody agrees that there is a boundary, and the boundary is extremely visible (river, big fence) people can't / won't agree on what it means. Does it mean, "Stay on your side until a guard or customs agent says, "Welcome to the -----"? Does it mean that the boundary is irrelevant? "Borders? We don't need no stinking borders!" Does it mean that people who insist on the border not being crossed willy nilly are racist sexist xenophobic white supremacist nazi scum? (to some...)

These borders are well marked but it doesn't make all that much difference:

User image

And thanks for going back to wherever you came from.
Terrapin Station September 08, 2019 at 16:10 #326005
Reply to Janus

lol re adding "support" to your definition of claim now. Anyway, the only reason I was pressing this is because you were stressing it, but the definition you were proposing is idiosyncratic.

The reason you were stressing it was as a diversion from the point I was making.

You had asked:

"Are the boundaries (borders) of objects real, according to you?"

And then you asked:

"What is it about the boundaries of objects that is real according to you?"

I answered both of those questions, which are ontological questions, in some detail.

Then you wanted to switch to talking about epistemology. The epistemological question is a different issue than the ontological questions.
Pattern-chaser September 08, 2019 at 16:26 #326029
Quoting Terrapin Station
"Are the boundaries (borders) of objects real, according to you?"
[Sorry, the actual quote came from @Janus.]

Now that's an interesting question. I know of no reason to subdivide Life, the Universe and Everything, except that it's too much for a human mind to swallow in one bite, so we split it up. This, if accurate and useful, is a good reason to classify borders as an illusion; a human invention. :chin:
Terrapin Station September 08, 2019 at 18:16 #326099
Reply to Pattern-chaser

So would you say that there's no real edge of a cliff, say? We just invent that, so if we decided to think about it differently/invent it otherwise, we could walk 15 feet further out without falling to our deaths?
ssu September 08, 2019 at 19:06 #326126
Quoting Pattern-chaser
But surely there are also borders that exist because they lie between different things, like the sea-shore, which bounds the sea (or the land, depending which way you're oriented)?

The sea shore, a river or a sea does exist physically just like a mountain range. That they are a border between two states is something totally else.
Pattern-chaser September 08, 2019 at 19:12 #326128
Reply to ssu Yes ... which is also the answer to @Terrapin Station's post. :smile:
Terrapin Station September 08, 2019 at 20:36 #326163
Reply to Pattern-chaser

I thought maybe you were talking about borders more broadly, since for whatever reason that's the direction Janus started pursuing.
Pattern-chaser September 09, 2019 at 11:43 #326383
Quoting Terrapin Station
So would you say that there's no real edge of a cliff, say? We just invent that, so if we decided to think about it differently/invent it otherwise, we could walk 15 feet further out without falling to our deaths?


I don't understand why people sometimes respond like this. If you suggest the possibility that the world our senses show us pictures of ... might not be Objective Reality. That it might not exist in the way we think it does. Then people respond by saying "stand in front of a large lorry, then".

Such responses miss the point and ridicule the point, at the same time. I can only conclude such responders are scared of the idea(s) raised, and just want to run away. :chin:

Anyone care to offer clarification?