Groot!
If you've seen the movie Guardians of the Galaxy you'll be familiar with the character Groot. He's a conscious, talking tree. The thing with Groot is his vocabulary is limited to one word viz. ''Groot''. Whatever the situation he only says ''Groot''. There are intonational variations, perhaps determined by emotion, but his speech entirely consists of the one word - ''Groot''. There is only one person who understands Groot's language - his companion, a fox(?). This fox comprehends Groot and converses with him as he would with a person who speaks normally.
What powers of imagination creative artists have. It's simply amazing to invent such stories.
What interests me is there's a real world twin to the imagined story described above:
To better make my point I'll be using only one field of human inquiry - science. It's the one which has had the biggest impact on our world. Scientific inquiry, if it is to be of any value, has to be quantitative i.e. it has to use mathematics and this requirement has always resulted in productive outcomes. It's as if mathematics is not really a constraint at all. In fact it appears that the universe itself is mathematical.
Now permit me to reduce this real world situation to a brief conversation between man and the universe. To whatever question man asks, the universe replies ''Mathematics''. Groot!
Your comments please.
What powers of imagination creative artists have. It's simply amazing to invent such stories.
What interests me is there's a real world twin to the imagined story described above:
To better make my point I'll be using only one field of human inquiry - science. It's the one which has had the biggest impact on our world. Scientific inquiry, if it is to be of any value, has to be quantitative i.e. it has to use mathematics and this requirement has always resulted in productive outcomes. It's as if mathematics is not really a constraint at all. In fact it appears that the universe itself is mathematical.
Now permit me to reduce this real world situation to a brief conversation between man and the universe. To whatever question man asks, the universe replies ''Mathematics''. Groot!
Your comments please.
Comments (57)
Not true. Also "I", "am", "we", and "are".
Raccoon.
There is certainly some reductionism going on here. There is something else in common between the two examples you have cited: in Guardians of the Galaxy the author has anthropomorphized a tree, while you have anthropomorphized the universe!
Could you expand on what you intended by the phrase "a real world twin"?
Following your lead, the language is only as good as the information it can convey. What I want to say is if the universe is not mathematical then our invented language would fail to describe it. This is not the case as mathematics has, up till now, seen amazing success in expressing the facts of our universe.
Perhaps my words were poorly chosen. I only wanted to say that there's a similarity between the two (the movie and real life).
Do you believe that the world is comprised of natural language, too?
What about paints?
No, I don't think your words were poorly chosen. I'm just trying to drill down to the specific nature of the similarity that you see or the analogy that you are making. On the surface I don't see a great deal of similarity between a science fiction tree-man and the cosmic reality of the universe. But there is obviously something behind your post that you wanted to express. I am trying to understand what that is.
What at first seems wrong could on analysis be true. Are we so dead sure that there's no hidden connection between words and their referents and all there is is simply convention?
Also, to answer your question, the laws of nature are mathematical. The laws are quantitative and so mathematics describes them accurately. We can't change the laws of nature by manipulating language, natural or mathematical.
If someone were to answer your every question with the same sentence/phrase/word e.g. ''I am Groot'', what would go through your mind?
I would probably think that their ability to speak english was impaired. I certainly wouldn't conclude that "I am Groot" is the only thing worth saying.
I'd think their statements could be infered from their very nature and the situation they are in.
I'd view it as a commitment to authenticity relying on mutual understanding for communication.
Your argument was that if the world itself is not x, then x could not describe the world.
Natural languages and paints on a canvas are two other things that can describe the world. Would you say that the world thus must be natural language and paints on a canvas?
It is quantifiable, though.
How about, if there was not something related to x that is also true of the world, then x could not describe the world.
In the case of paint, that would be visual light. In the case of math, it would be quantity. In the case of physics, it would be fundamental patterns that appear to be universal. And in the case of natural language, it would be similarities between particulars.
Or something along those lines.
Obviously the ways we talk about the world are going to have some relation to the world. The error is in assuming that they're identical to the world. That's a rudimentary conflation. More specifically a reification.
So take the nominalism/realism debate about universals. Reifying universals would be mistaking the universal abstractions in our language for universals in the world. But nominalism would be the opposite mistake in supposing our abstractions are arbitrary. That would mean conceptualism would be the proper alternative, I suppose. There's something about the world (or pariticulars) that's universalizable, leading us to form universal concepts.
Give me one word to describe:
1. life
2. your job
3. your best friend
4. your worldview
5. religion
6. music
7. the universe
etc.
Such requests force you to seek the heart of an issue, sifting through the superficial, the superfluous, the irrelevant and achieve a realization of the real truth. I'm not imagining this because there are many people who seek the truth in whatever field that draws their attention.
Natural language seems to be entirely arbitrary - words and their referents are a matter of convention. I question this view but that's another topic.
But math is not like that. It probably started off as a language but its uncanny ability to describe the laws of nature isn't accidental (as you suggest). While natural language is not expected to be universal - there are so many languages on earth itself - the general consensus among scientists is that math is. Many interstellar messages have been beamed to nearby stars and their content is, well, mathematical.
In my view nominalism and conceptualism aren't distinct. Nominalism isn't arbitrary. Under nominalism, universals are non-arbitrary abstractions that individuals make, where those abstractions are unique to each individual (in terms of whether they're particulars or somehow numerically identical among more than one individual). Under conceptualism, we can't have anything other than that.
Wait, "the cat is on the mat" doesn't describe any objective fact in your view?
What does this have to do with what I'm saying?
Do you think natural language and mathematics are completely identical?
I'll give you an analogy to describe the situation as it is.
We have two languages - natural language and mathematics. You travel to a distant galaxy and find an alien civilization. Which language do you think would be shared by you and aliens?
In fact I don't have to create such an elaborate scenario. Look at us. We have thousands of language which come under the term of natural language. They're not universal and people need translators if we're to understand each other . However, mathematics is universal e.g. Pythagora's theorem is exactly the same whether you're in China or USA. This is what I mean.
Your argument was that mathematics can't just be a language because it (non-arbitrarily) describes the world. Well, so does natural language, so does painting, and a number of other things.
You'd have to translate mathematics just as much as any natural language. You need to figure out their words and symbols and syntax etc. just the same way.
What you'd not have to translate is their representational visual art, whatever media they use.
I don't see how that's possible.
It's difficult for me to comment on "I don't see how that's possible" in the context of my comment, because I'm not sure just what you don't see as being possible.
Concept-formation is something that individuals do. It's a way that individuals think about things--they formulate abstractions, ignoring some details and generalizing others, so that the "same term" (again, it's not literally, numerically the same from instance to instance) can apply to many different particulars. Indviduals do this non-arbitrarily. It's in response to things experienced. And it can't be avoided as long as one is conscious and has anything like a normally functioning brain.
Concepts can not become something more than that, though. Different individuals do not literally share the same concept.
I see where you're misunderstanding me.
All languages are symbolic (including math). This is true. And symbols being arbitrary we have to translate if two culture are to understand each other.
However, there is something different between the message contained in natural language and math. The laws of nature are mathematical - the numbers that describe them are unalterable. For instance gravity will always be inversely proportional to the square of the distance between two objects. This element of necessity doesn't exist in natural language e.g. The sky may not be blue everywhere. To further clarify, the objective facts in the universe doesn't affect natural language but they do affect the mathematical formulae describing them.
I don't understand how humans generalize details in a non-arbitrary way if nominalism is the case. There must be something about certain details that makes them generalizable. That's the problem nominalism has always faced. Similarity between particulars needs to be accounted for somehow.
Right--that's your view, but that's what I'm explciitly disagreeing with, and I'm showing you why your arguments for it so far do not work.
In my opinion it's as absurd as saying that the laws of nature are literally paintings.
I'm not even a realist on laws of nature, by the way. That's not to say that I believe that everything is arbitrary.
"For instance gravity will always be inversely proportional to the square of the distance between two objects. This element of necessity doesn't exist in natural language"
Yet you just wrote that in natural language. We could create a painting representing that idea, too. When we do, does that imply that nature is literally comprised of paintings?
What we're doing there is reporting something about our interaction with the world, about the way that we think about the world, in a language that we created, in an invention to represent or describe our interaction with and thoughts about the world. That's the case whether we're talking about paintings, natural language or mathematics.
Before we go further with this, we should probably cement just how you're using "arbitrary." Are you using it with a connotation of "random"?
No, I mean like the rules of a game. There is nothing in nature that makes chess have the rules it has. Humans arbitrarily decided how the pieces would move, what the board would look like, that there would be two players, etc.
That doesn't work when it comes to biology. We can't just make up any categories we want and have it map onto living organisms. But we are able to create categories somehow, which would suggest there is something about living things that lends itself to categorization. We don't have to go full hog and call that something universals. But that something has to do with similarities between organisms. The details about them aren't utterly particular.
Okay, but I explained this above: "Indviduals do this non-arbitrarily. It's in response to things experienced."
You're not thinking that either either it's true that there are types that are (numerically) identically instantiated in multiple things or otherwise it's true that there are no degrees of similarity and everything is effectively a completely uniform soup, are you?
And if you are, why would you be thinking that?
No, there are similarities and differences among particulars in the world. That much we clearly experience. Maybe I misunderstand nominalism as failing to properly account for how particulars also have similarity.
Nominalism doesn't deny similarities. It denies numerical identities (that are multiply instantiated, which is what types are).
|..|
is more simliar to
|....|
in some respects than
*(^!*(&$%
is
But
|..|
is not identical to
|....|
That's the basic idea. Nominalism isn't at all denying this. It's just saying that no two things are numerically identical in any respect. (So |..| isn't identical to |..|--they're just similar in some respects, and more similar than |....| is in some respects to either)
So laws of nature would be ruled out. A lot of physics would be approximation. Every electron in the universe couldn't actually have the exact same charge and mass, right? It's just we can't measure the difference?
But then you're positing differences beyond observation to account for similarities that are observed to be numerically identical.
The idea of type realism is that there is one thing that's somehow shared between multiple things.
The following isn't a direct analogy, but it helps convey the idea: think of one slice of pizza that is shared somehow among more than one person. It's not that they each have a slice of pizza, a different slice. It's that they all have literally the same, single slice somehow.
That's not a direct analogy because type realists aren't saying that types are something physical like a slice of pizza. Although not being a type realist and being a physicalist because the idea of nonphysical existents strikes me as completely incoherent, just what they're saying isn't very clear to me. But charitably, it's something different than a slice of pizza.
So that is what nominalists are denying.
Right, so when physicists say that every single electron in the universe has the exact same charge, isn't that like saying every single person shares exactly the same slice of pizza?
And if the physicists are wrong, then why do they measure electrons to have the same charge?
Well, so the issue is if, among two electrons, there's just one charge that they happen to both share somehow (how?--how does the charge get completely parceled out from wherever it's located so that both electrons share a single thing completely?) Or whether each electron has its own charge, and the charges are both ?1.602×10^?19 coulomb.
I accept that the electrons each have their own charge, but that raises the question of how it is that electrons would have the exact same property.
So we have to be careful when we say "they have the exact same property." If you agree that they each have their own charge, you're not saying that literally they're sharing just one ("and the same") property somehow.
How exactly it obtains is a different issue than saying that they each have their own charge versus saying that they literally share just one charge, which is the nominalism vs. realism (on types/universals) debate.
That's a good way of explaining it. But that still leaves a question. How is it that separate properties have the same value? In virtue of what are they the same? You might respond that humans measured them to be the same, and that's the end of it.
But it's not really. The problem is how we recognize sameness. So then we ask what is it about the two properties that make them the same regarding electrons. And that will be numerical. And if anything in the world is identical, it would be numbers. So how is it that electrons have the same numbers while remaining distinct?
Or something along those lines. If the problem of universals were so easy to dismiss with, I'm guessing it wouldn't keep coming up.
That's an interesting question in itself though not the one you're initially posing. To my mind our likely shared language would be gesture. On this reading, language is the making and attempted communication of signs. Enter apo.
That's a different issue from what the core explanations of different civilizations might be built from. I can imagine a Pythagorean civilisation, for instance, where music is the core explanation. But I've been doing a lot of singing and harmonising lately so maybe my mind is leaning that way. :)
What I don't understand is how you seem to see no difference at all between math and natural language.
I agree that natural language has a longer history than math (some may disagree). I also agree that math is a language - to be truthful it's an extension of natural language invented to simplify and refine quantitave thought. That is why you may see stuff like ''gravity is inversely proportional to the square of the distance between two objects''. It's easier to write and read it in math but natural language captures the meaning too.
What I want to say is that math and natural language differ from each other in a significant way:
Imagine you're an explorer who knows math and English. Your expedition in a foreign land has discovered a couple of books written in a different language. One is on science and the other is on history. Lukily you find a translator and begin work on deciphering these books. What you'll find is that the science book, being mathematically based, matches number to number with what scientists in your world know of the universe. However this will not be the case with the history book. In essence, the laws of the universe are mathematical and, well, universal. Therefore the concordance between people, cultures, civilizations, and even galaxies.
So realizing that the properties aren't numerically the same (which of course isn't saying something about a number we might be assigning to anything; it just denotes whether we're talking about one "thing" or more than one "thing"), it doesn't seem mysterious to me that two different particulars would have or be non-numerically the same property. What would seem more mysterious to me would be a claim that they shouldn't be the same if they're unique particulars. Why shouldn't they be the same? Is there something about the world that's supposed to preclude two particulars from both having some property?
I kind of have to translate what you're saying there. First, concepts are occurences in individuals' minds on my view. What it means to say that a concept is a "universal concept" is that it's a concept that individual has about universals or types. (It wouldn't be that the concept is of a type or universal, because all concepts are. That's what it is to be a concept.) I'm an anti-realist on mathematical objects, and on abstract objects period. On my view, mathematics is a way that we think about relations on a very abstract level.
Nominalism doesn't have to explain anything while avoiding concepts/universals/types--and after all, language isn't possible without those things. It's just we're denying type realism.
I get that, but if nominalism can't explain why we find it necessary to utilize universal types to make sense of particulars, then it hasn't resolved the universals issue.
I don't agree with that claim, however.
We have to think in terms of universals in order to survive. There's too much information to deal with otherwise. We need abbreviations, generalizations so we have a good idea, that we can reach quickly, whether some animal, some plant, etc. is likely to try to kill us or provide nourishment for example.
But why?
Because it's just an example of fiction writing.
Well, the mathematical description of gravity is true everywhere and for everyone. What I said may've been hypothetical but the laws of nature are still real as ever.
Assuming that's the case, it doesn't at all follow that the way of expressing it in something akin to mathematics would be any more or less universal than the way of expressing "The cat is on the mat" in natural language or painting a landscape on a canvas.
The ''cat is on the mat'' is not true always and everywhere e.g. well, when the cat is not on the mat. However, the laws of nature are always true, everywhere.
A painting can capture the moment but that's it. Time and change will make the painting, to say the least, outmoded. But, again, the laws of nature are universal, both temporally and spatially.
But, perhaps it is also true that the people who understand best what the universe is saying, are those who are closest to it (whatever that means).
All I want to say is math seems to be the language of the universe. Do you think this isn't so? Why?
Hmm. Could be.. Have you read Paul Davies' The Mind of God?