Metaphysics: The Abstract-Concrete Distinction and Platonism vs Nominalism

[drug_mentor]

Abstract objects include numbers, sets, fictions and games. Concrete objects include cars, rocks, stars and fish. In order to make the distinction between abstract and concrete objects a little clearer let’s consider Dostoevsky’s Crime and Punishment. The fictional story is an abstract object, my particular copy of Crime and Punishment is a concrete object.

This way of describing the abstract-concrete distinction is known as the way of example. It should be clear that this is not a particularly satisfactory way of describing abstract objects. Whilst it does give you a pretty good idea what abstract objects are, it doesn’t describe any essential features of them.

Another way of elucidating the abstract-concrete distinction is referred to as the way of negation, this essentially involves picking out certain features which concrete objects possess and abstract objects lack.

One criterion which has been suggested by way of negation is that an object is abstract if and only if it does not occupy a determinate region of space-time. There are some problems with this definition. Let’s consider Crime and Punishment again. Dostoevsky wrote it in 1866, so it has a temporal beginning. It seems ludicrous to suggest that it existed before it was written, this suggests that in some sense the story does occupy a particular time. Moreover, whilst there is no one space in which this story is instantiated, it certainly seems like it exists on Earth to a greater extent than say, Kepler-16b. You might think that similar objections to this definition could be raised when thinking about games (e.g. soccer).

If we regard sets as abstract objects, then let’s consider the set of two people, e.g. my brother and I. It seems like the set comprised of my brother and myself occupies space-time, although which space will vary depending on the time. A potential response to this objection is that it is only the members of the set which occupy space and time. Similar to Crime and Punishment, it seems plausible to think that the set of my brother and I exists on Earth to a greater extent than some far away planet. It would also seem odd to suggest the set of my brother and I existed before we did, or that it will exist after we are dead. This seems to indicate that the set is limited to a particular stretch of time.

These considerations are intended to motivate the thought that defining abstract objects as those objects which don’t occupy a determinate region of space-time is inadequate.

Another definition which has been suggested by the way of negation is the causal inefficacy criterion, an object is abstract if and only if it is causally inert. Again, there are some problems with this view.

There are works of fiction which have sad storylines. Someone might read The Fault in our Stars and be moved to tears. In such a case is seems entirely plausible to suggest that this fiction caused that person to cry. A potential response to this objection is that it was the concrete instantiation of the fiction which caused the person to cry. I think this response is inadequate because I don't think it would matter which concrete instantiation of The Fault in our Stars this person read, they would still be move to tears. This suggests that it is a feature of the fiction itself which causes them to cry.

Another problem with this definition is called the epistemological problem. If abstract objects are causally inert, then how do we come to know about them? If they can’t cause anything to happen in our minds then it seems strange that we could come to know about them. This is not such a problem for things like games and fictions, but when you consider numbers it does raise some issues.

Again, these considerations are intended to motivate the view that this definition is inadequate.

I am not going to go further and list them here, but other attempts at making the abstract-concrete distinction have been suggested. To date there is no view which does not have distinct problems associated with it. I created this thread in the hopes of generating some discussion about a more satisfactory way of drawing this distinction, or perhaps some thoughts as to why the objections raised against the views I have mentioned fail.

There is another interesting debate to be had on the topic of abstract objects: whether they exist or not. Platonism is the view that abstract objects exist. Nominalism is the view that abstract objects don't exist. Both views face reasonably large explanatory problems.

Do abstract objects exist? What sorts of considerations motivate your answer to this question?

 

[neurotic]

I think that things get tricky when dealing with (particular) concrete objects as well. For instance, what is a book? Can one give a formal definition of a book? Pages arranged in that familiar way, containing words within it? Then, what about magazines? Why is this a magazine and not a book? Is it the content? If I make a book with one page on it, is it still a book? What about a book with zero pages? On what number of pages does something begin to be a book, when is the cutoff point? What about one hundred pages, but no cover? Or no pages and no cover? What about food? What is food and what isn't? Animals eat something we humans cannot. And what about a peach? If we modify genetically a peach tree, is it still a peach tree? But aren't there already slight genetically differences between peach trees found in nature? And when one makes different strains of marijuana, are they all marijuana? When do they stop being marijuana plants? By this reasoning, all of those things, books, rocks, peaches, lemons, libraries, planes... are just concepts, ideas through which we organise the world. Beyond the names, things just are. It is all a bunch of 'stuff', with no defined distinction between this or that.

To deal with abstract objects, I think one would have to formalise/elaborate the definition of 'existence', and then the existence of abstract objects would depend on the definition, but I imagine no definition would truly satisfy us. I think numbers aren't entities, but rather descriptions, relationships. The atomic pieces of our understanding. If we use the frequency to describe a sound wave, then the ratio between the dominant and the tonic - probably the most common chord transition in Western music, used to end a song - can be described by the number "1.5". In that sense, numbers are just like words - empty descriptions.

 

[drug_mentor]

Thanks for the response neurotic!

I think that things get tricky when dealing with (particular) concrete objects as well. For instance, what is a book? Can one give a formal definition of a book? Pages arranged in that familiar way, containing words within it? Then, what about magazines? Why is this a magazine and not a book? Is it the content? If I make a book with one page on it, is it still a book? What about a book with zero pages? On what number of pages does something begin to be a book, when is the cutoff point? What about one hundred pages, but no cover? Or no pages and no cover? What about food? What is food and what isn't? Animals eat something we humans cannot. And what about a peach? If we modify genetically a peach tree, is it still a peach tree? But aren't there already slight genetically differences between peach trees found in nature? And when one makes different strains of marijuana, are they all marijuana? When do they stop being marijuana plants? By this reasoning, all of those things, books, rocks, peaches, lemons, libraries, planes... are just concepts, ideas through which we organise the world. Beyond the names, things just are. It is all a bunch of 'stuff', with no defined distinction between this or that.

The problems you have raised here (particularly books and magazines) are interesting. However, they don't seem like problems surrounding the definition of concrete objects, they are problems with classifying certain kinds of concrete objects. Some of your questions surrounding books seem like an interesting variation of Sorites paradox.

I think some of the issues you have mentioned could be resolved. I might say food is something an organism is capable of digesting and/or deriving nutrients from which it consumes for sustenance or pleasure. It seems logical to me that there would be some level of species relativism, its natural when a person refers to food they mean food a human will consume, unless they qualify it by saying dog food, plant food, etc. I suspect there would be some problems with this brief account but we are getting a touch off topic.

I feel the issue with peaches, marijuana, etc. could likely be resolved by saying peaches (etc.) are a class of plants, there doesn't have to be just one kind of peach. The genetic modification aspect might raise some more issues though, but again, that is a little off the thread topic. (Not trying to be rude, I just don't want to derail it before it gets started)

To deal with abstract objects, I think one would have to formalise/elaborate the definition of 'existence', and then the existence of abstract objects would depend on the definition, but I imagine no definition would truly satisfy us. I think numbers aren't entities, but rather descriptions, relationships. The atomic pieces of our understanding. If we use the frequency to describe a sound wave, then the ratio between the dominant and the tonic - probably the most common chord transition in Western music, used to end a song - can be described by the number "1.5". In that sense, numbers are just like words - empty descriptions.

I think you are right that a precise account of existence would have to be provided in order to resolve the platonism vs nominalism debate. I don't think it is necessary to formulate the abstract-concrete distinction though, unless perhaps you wanted to take a nominalist position and say that abstract objects differ from concrete objects because concrete objects exist and abstract objects don't. Even on this account I think you would run into problems, surely you would still want to distinguish between abstract objects and other sorts of things which don't exist.

 

[polymath]

Is a conscious perception of an object (such as seeing and feeling a copy of a Dostoevsky book in your hands) a concrete or abstract thing? The sensory information about a material object has to first travel to your brain, and once it is there it goes through a lot of subconscious processing before it becomes a conscious experience. The experience per se is some kind of a pattern in the firing of your neurons and it's not a very concrete "object", at least it doesn't seem like that to me.

 

[Nixiam]

Do abstract objects exist?

No, not tangibly anyway. You can write the number one but all that is in actuality is just a graphite mark.

But numbers, though an abstract object, has helped humanity create awe inspiring things without being tangible. It's a constrution, a rule of thumb we made. A value system we have seen in nature.

A number isn't like a thought. It isn't an electrical impulse, nor is it a physical something we dug out of the ground.

They don't exist yet they're very real, abstract objects. Do the only exist in the mind? No, but they aren't described in nature except by people.

The only things that exist in a physical sense are the elements that construct the nonphysical ones. How can a number exist if you don't think about it? The same way it has always existed without people describing it. In nature.

A number isn't a number until given thought, yet it is always a number. The number one will just be a log in a pile of logs after I die, but right now it is the first log I count. Astract objets assigned physical things is what makes a number feel real. The same way fiction in a story is assigned to something we can imagine to make it seem real, yet the only reality is the paper and ink.
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Abstract objects are real when they exist from tangible objects, like a dependent claus.

A solved equation is only a work of fiction until it does something, right?

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Starting over, what is a number? It is something we have made, but exists in nature, so we have made it's language, and nature has made it's concept.

A story is made in the mind. The mind is real, the events are not. The events are read in firing neurons, but the events never happened. Fiction is fiction, the reality is the book.

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I have never thought about this before and my opinion will likely change when I'm less high and less sleep deprived.

 

[drug_mentor]

Is a conscious perception of an object (such as seeing and feeling a copy of a Dostoevsky book in your hands) a concrete or abstract thing? The sensory information about a material object has to first travel to your brain, and once it is there it goes through a lot of subconscious processing before it becomes a conscious experience. The experience per se is some kind of a pattern in the firing of your neurons and it's not a very concrete "object", at least it doesn't seem like that to me.

I think mental states are abstract objects, but there are problems with classifying all abstract objects as mental states (I realise you never explicitly suggested this as a solution to the abstract-concrete distinction). In particular there are issues with regarding numbers as mental states, I am a little short on time right now but can go into detail on this later if you would like.

Do abstract objects exist?

No, not tangibly anyway.

I am fairly certain that even the most ardent platonist would concede that abstract objects are intangible.

A solved equation is only a work of fiction until it does something, right?

I don't know if this definition makes sense. We wouldn't ordinarily regard a fiction as being true. It seems to me that 2+2=4 (or any other correct equation) is objectively true, whether anybody applies it to everyday life or not.

 

[Nixiam]

I meant fiction as in not real, not untrue.

I suppose I can better put it this way:

2+2=4 is intangible, abstract, and true. Therefore it exists, yet it being intangible, it doesn't exist. However, when assigned to something tangible, all numerical systems or arithmetic become less abstract and more concrete, the only thing being abstract is the concept behind numbers.

Where exactly does 2+2 exist?

 

[drug_mentor]

I suppose I can better put it this way:

2+2=4 is intangible, abstract, and true. Therefore it exists, yet it being intangible, it doesn't exist.

Taken at face value this is a contradiction, which can't be true. I am sure this is not what you meant, and on a more charitable reading I am sure you are trying to say "they (numbers, equations, etc.) exist, yet because they are intangible, they are not concrete objects." Numbers are definitely not concrete objects, what I find interesting is trying to define what kind of objects they (and other abstract objects) are.

It seems you lean towards platonism (at least some abstract objects exist), so do I, but it is maddeningly difficult to come up with a coherent account of the sense in which they exist.

Where exactly does 2+2 exist?

That is a very good question, one which this thread was created in part to try and answer. Unfortunately I don't have a satisfactory answer to that question at present.

 

[Nixiam]

Gah. My words do this conversation no justice, I'll need time to think of the best way to present what I've got in my head, but I think you've already got a good picture.

If something is non physical then it does not exist, unless we can still percieve it, which validates the existence of abstract objects.

Reason why it seems so contradictory is because of the nature in which we percieve existence. Something like bread, we can feel, smell, taste. It is tangible, it exists in our physical universe.

Abstract objects can be percieved without necessarily being touchable. We cannot hold mathematics, but we can percieve it, in the same sense we don't hold a story. We hold a book which is built from other elements, yet we percieve the story inside.

I think that quite justifies abstract objects in some sense.
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I'm not saying that the fictional writing in the book actually happened, but that the percieved abstract object which is the story exists as a seperate entity than the tangible book with pages and ink.

Although, when we read a book it is probably just a bunch of thoughts and when we solve a problem it is the same. Maybe the described numerical system disappears when not thought about.

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As much as I love conversation, I have not slept in 48 hours, I am going to go to sleep for about 5 hours, wake up, take some Norco anb j not d lok likef

It hard to see the keuboard. My vision is leaving me forf a bit,

Good topi

 

[drug_mentor]

So, I thought I would bump this. I think it's an interesting topic and I am hoping that it will generate more discussion this time around.

So it is not just a shameless bump. Michael Dummett had a rather interesting view that metaphysical disputes can be understood as a disagreement over what the correct logical laws are. Realists (in this context platonists) believe that the Law of Excluded Middle (pv~p) always holds, which is to say that every proposition is either true or false, whereas antirealists (in this context nominalists) reject the Law of Excluded Middle.