Dragan

Interesting question!   We could not of course know because any question that is predicated on us not being there is unfathomable.  I would suggest that sets are a construction of human thinking in place in order to enable us to reason.

They are probably 'real' only in lingusitic terms in that if language is to work it must have structure, even an artificial structure.  

You should perhaps add lingusitics to the topic 'set'.

Dragan

Interesting question!   We could not of course know because any question that is predicated on us not being there is unfathomable.  I would suggest that sets are a construction of human thinking in place in order to enable us to reason.

They are probably 'real' only in lingusitic terms in that if language is to work it must have structure, even an artificial structure.  

You should perhaps add lingusitics to the topic 'set'.

Dragan,

'' Not as concepts but as the real, possible “description” of things about how the things really are?''

A concept is real possible ''description'' of thing.  A concept only exists for a person intending such a description of thing and sets is one such concept.  It is a great metaphor, a great communication tool, nothing more than this.  Sets exists as good communication tools. Especially important ones in mathematics. The day we find a much better communication tool for some of its current use,  we will drop it as a old rag.  It will certainly remain an important/usefull word/concept in the day to day language.  

So far all of us seems to agree on this.  A volunteer for advocating the platonistic opposite position : the real existence of  ''set'' in the world.  

Sets are abstractions that we create by putting together in a meaningful and non contradictory way to study behaviors of objects or find  solutions to problems of a particular kinds. We create sets to manage our works, they are not real objects as language is and we do not find them standing distinctly as real objects. For instance we consider the collection of non negative integers to find solutions for problems that seek non negative integers. We consider a part of the universe and search for natural phenomena in that part, the part we consider is taken as a set of objects of particular behaviors. We consider the set of points in the XY plane that satisfy particular algebraic properties and we may have a problem to find points in that set that satisfy conditions we want them to satisfy. Optimization problems are problems of seeking solutions to an objective function (maximizing or minimizing) over a set or domain that is bounded by conditions. 

Your question is so full of undefined terms that I find it impossible to understand. Do we behave as though sets existed independently of us? What behaviours would you point to that demonstrate this? And you jump from talking about the existence of the universe to the existence of sets, as though they were of the same order. The existence of the universe and the 'existence' of the set of positive integers are simply not comparable existences! 

But what puzzles me most is why this puzzles you! What difference would it make to you, your life or to life in general if some angel of the lord were to tell you the answer? What would you understand by the answer 'yes' or 'no'? What path would diverge at that point?

That's a lot of questions, but it seems to me that you have asked a Type IV question (one where, no matter what the answer, nothing actually is changed). 

interested question

Ronán

You are probably right. I did not explain enough.

Here below, and above after the question, I gave essential references. I hope this will make clearer what I asked.

Universals

http://www.iep.utm.edu/universa/

Nominalism in the Philosophy of Mathematics

https://plato.stanford.edu/entries/nominalism-mathematics/

Nominalism in Metaphysics

https://plato.stanford.edu/entries/nominalism-metaphysics/

Problem of universals

https://en.wikipedia.org/wiki/Problem_of_universals

Classification

http://www.iep.utm.edu/classifi/

Essential vs. Accidental Properties

https://plato.stanford.edu/entries/essential-accidental/

They are interested web links

Ronán

The concept of a Type IV question is fascinating, what is its origin?   Such questions posed here by Dragan are the basis of all philosophy and as such much is changed by the asking of them.

Questions are not simply information gathering tools or requests for instructions, it is by formulating what you call Type IV questions that we are educated rather than instructed.

I suspect that were in not in human nature to ask such questions that humanity would not have survived long past its ancient infancy.  Many millenia ago humans looked up at the stars and asked such questions.  It may very well have made no material difference to their lives or life in general to their peers but how impoverished would we be if they had never bothered to concern themselves with abstractions.

Barry

Ronán was probably frustrated because I did not put my question clearly enough. I hope I corrected this.

Whether a model is only an auxiliary means or is indeed intended to resemble the reality is important to know. How much our models correspond to the picture that we paint to ourselves about the “reality” (or what we believe that the reality is) is also important. There are plenty of examples in the history of science. Such were geocentric vs. heliocentric models, such were Pythagoras’s vs. modern mathematical concepts, such was Mendel’s vs. modern Crick and Watson inheritance concepts etc. (Those are not equivalent but only correlating examples.)

On the other hand even number of valid exacte science enquiries do not guaranty any immediate use of the findings.

Dragan,

I will comment the many claims in the question:

''We know that sets exist in books or in our minds, and that we behave as if they existed independently of us. We, most of us, believe that the universe, even if we were not there, would be as it is.''  

I agree. I see this a uncontroversial.

''And of course, the sets would be there too – in some way. We believe this, don’t we? ''

Some do, some don't.  I am among those that do not agree.

''They “would be there” may be not exactly as we see them and understand them.''

There is no set out there.  It is a word that allow to carve group of things out there but it is always a usefull human carving out of reality.  It help talking about usefull aspect of reality.

''Still, the universe would be coherent in a way that any “other” intelligence, that would be able to observe it, would have to admit - would have to see - that the universe would contain also sets. The sets would possibly be somehow different from "our" sets, but would be faithfully coherent sets - and they would be there.''

Alien intelligences most probably have a equivalent word but just because they are like us, they need to specify aspects of reality to each other.  Not because there are sets in the world.  

''But, are we sure? Would sets be still there? Not as some concepts but as the real, possible “descriptions” of the things that are inhabiting the world, objective descriptions of how the things that are there in the world really are?''

Sets are usefull for specifying aspects of the world , not aspects that really exist but that are really usefull.   The idea of the world as it is really is is what is called a God'eye view and this does not exist.  All knowledge is relative to a use, to a specific type of interaction.  THere is no knowledge of the world as it is.   

Louis

As you probably know from my comments on some other thematically related threads, I mostly (but not completely) agree with those positions, i.e. - "opinions". However, in an academic discussion we need more complete arguments and proves. I probably cited number of them in the discussions on other related threads that you may remember (and sometimes was attacked, not by you, for doing this).

Still, I insist here: when we introduce some arguments, please tell us which great thinkers “rose us up” so that we can have a complete pleasure from our armchair discussions.

https://www.youtube.com/watch?v=4RojlDwD07I

(Martin Hurkens: You Raise me Up)

Or more traditionally, as Danny Boy:

https://www.youtube.com/watch?v=rnLnwWjrIyk

https://www.youtube.com/watch?v=zc41L1-KcG0

An interesting example of a set that both exists and does not exist is a constellation.  From our location in the galaxy we see stellar images that our ancestors imagined were shapes of mythical beings and animals.  The constellation of Orion in the northern hemisphere is very pronounced as is the Southern Cross in the southern hemisphere.

In reality the formations of stars only exist from our perspective and in our imaginations. There is no real relationship between the individual starts in the constellations which would of course not appear at all to an extra terrestrial intelligence 50 light years away.

If there is an extra terrestrial intelligence 50 light years away however, with its own mythology it is without doubt that they too will experience stellar constellations of their own.  All intelligent life will recognise sets.