Abstract objects don't "exist" in any particular mind. Pi is an abstract object. It's not a resident of my mind in the way my grocery list is. I can't be wrong about my grocery list. I can be wrong about pi. It's that sort of thing. — Tate

Abstract objects, last I checked, have been, at the very least, more closely associated with the mind than the physical world. So, taking this simple intuition to its logical conclusion, I ask, again, what object, if any, is purely mental?

Also, for the moment, ignore the notion of abstract(ion) and give me an example, if there is one, of an object that's exclusively mind, having no connection at all with the physical world.

Abstract objects, last I checked, have been, at the very least, more closely associated with the mind than the physical world. — Agent Smith

They aren't mental objects.

Also, for the moment, ignore the notion of abstract(ion) and give me an example, if there is one, of an object that's exclusively mind, having no connection at all with the physical world. — Agent Smith

I don't know. Did you know Pythagoras didn't invent the Pythagorean theorem? It was known for ages before him by the Babylonians and Egyptians.

Do as you like. But if you read the article your responses might improve.

You, too, .

Earl Grey?

They aren't mental objects. — Tate

Why? Explain with examples. Danke in advance.

I don't know. — Tate

:Ok:

Perhaps Art48 can clear up thd matter.

Please wait...

Earl Gray? — Banno

Best way to drink it (minutes brewed, cream, anything to eat with it, etc)? I'm not Aussie or British, so forgive the ignorance.

“Suppose you see a hurricane on TV. You directly experience the TV's light and sound; you indirectly experience the hurricane. Similarly, you indirectly experience the tree; you directly experience light, sound, touch, taste, odor. “

This example works if I can directly experience a hurricane. The lights and sounds from the TV are about something that we can experience directly. However, if all I directly experience is light, sound, touch, taste, or odor; the example is problematic because your are not seeing a “TV” or a “hurricane” because all they are is light, sound, touch, taste, or odor.

But a difficulty emerges as soon as we ask ourselves how we know that a thing is white or a triangle. If we wish to avoid the universals whiteness and triangularity, we shall choose some particular patch of white or some particular triangle, and say that anything is white or a triangle if it has the right sort of resemblance to our chosen particular. But then the resemblance required will have to be a universal. Since there are many white things, the resemblance must hold between many pairs of particular white things; and this is the characteristic of a universal. It will be useless to say that there is a different resemblance for each pair, for then we shall have to say that these resemblances resemble each other, and thus at last we shall be forced to admit resemblance as a universal. The relation of resemblance, therefore, must be a true universal. And having been forced to admit this universal, we find that it is no longer worth while to invent difficult and unplausible theories to avoid the admission of such universals as whiteness and triangularity. ... — Bertrand Russell, World of Universals

I don't think that this is a correct portrayal. We do not utilize "resemblance", when judging distinct things as having the same quality. I think this is what Banno refers to when he mentions the use of "grey". Two distinct grey things, are not both judged as grey because they have some resemblance to each other. Instead, I think that such judgements ought to be seen as a sort of categorization.

So each grey thing is placed into the category of having the colour, or quality, of being grey. This is not a resemblance, which is a type of similarity, but it is a sort of sameness. And "same" is a very distinct category from "similar" because "similar" implies necessarily a difference, whereas "same" is to deny difference.

However, by the law of identity, we cannot say that the two distinct things, which are said to have the same quality, are the same in any unqualified or absolute way. So to facilitate communication, and show that we recognize the difference between them, it is commonly said that the two things are similar. But this common way of speaking veils the reality of the mental process which is behind this use of the same word to describe two distinct things. It misleads us into thinking that the two different things have been judged as being similar, when in reality they have been judged as being in some way the same, i.e. having the same type of quality.

And, that this is a case of being misled is justified by the fact that "same" is logically distinct from "similar", such that two distinct things having been judged as having the same type of quality does not necessitate that the two things are similar, unless we define "similar" in this way. But then we see that what constitutes "a type" is simply a definition, and we are led toward nominalism instead of the realism which you prefer.

Or if you prefer, abstract objects do not exist. — Banno

You've talked before about unspoken propositions. How does that square with abstract objects not existing? Does it just mean that we can say things that haven't been said before?

Brief defense of universals, bolds added. — Wayfarer

Yes, thank you.

But universals do not exist in this sense; we shall say that they subsist — Russell, World of Universals

OK, if we require “exist” to apply to only things in space/time, then universals don’t exist but they subsist.
But if we make this requirement of "exist", then it seems “is” and “was” are fundamentally different.
In 1861, I could have said “Lincoln is president” and indeed Lincoln existed in space/time then.
But today, if I say “Lincoln was president” I speak of someone who does not exist today in space/time.
So "is" applies to things which exist, but "was" sometimes does not? Rather, "was" sometimes applies to things which subsist? I don't see any logical problem but if feels wrong to me to require "exist" to only refer to things in space/time.

Can you give me an example, one will do, of a pure abstract object and by that I mean an (abstract) object that has no links whatsoever with the physical world? It should exist only in the mind is what I'm saying. — Agent Smith

How about the following? "Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), something that waves should not be able to do."
The luminiferous aether is an abstract object that the universe fails to instantiate.

OK, if we require “exist” to apply to only things in space/time, then universals don’t exist but they subsist. But if we make this requirement of "exist", then it seems “is” and “was” are fundamentally different. — Art48

I wouldn't bring time into it. I think Russell is reaching for a word to describe something which is very difficult to articulate in common language. The literal meaning of 'subsist' is nothing like what he's trying to convey here. He wants to say that although universals are real, they're not existents, so he coins the term 'subsist' to try and convey the sense in which they are real.

Consider the meaning of 'to exist'. It is a compound of 'ex-' meaning outside (compare external, exile) and 'ist', to stand. So 'to exist' is to be differentiated, to have an identity, to be this as distinct from that.

But then, the question is in what sense universals exist. Russell says:

the relation 'north of' does not seem to exist in the same sense in which Edinburgh and London exist. If we ask 'Where and when does this relation exist?' the answer must be 'Nowhere and nowhen'. There is no place or time where we can find the relation 'north of'. It does not exist in Edinburgh any more than in London, for it relates the two and is neutral as between them. Nor can we say that it exists at any particular time. Now everything that can be apprehended by the senses or by introspection exists at some particular time. Hence the relation 'north of' is radically different from such things. It is neither in space nor in time, neither material nor mental; yet it is something.

But, just to add a bit more depth to that concept - what of real numbers? They too are real in the sense that they are the same for all who can count, but they too do not exist as phenomenal objects. They too are in that sense 'outside' time or space (although that can be a misleading metaphor if it connotes some real location, some ethereal realm.)

So on that account I think a distinction can be made between what is real, and what exists - whereas it is generally assumed, I think, in modern philosophy, that these are synonymous terms.

There's a passage I have often quoted on this forum (and the earlier forum) on Augustine on Intelligible Objects. It conveys very clearly, in my mind, the nature of intelligible objects, which include things like numbers, geometrical principles, and much else besides. It's a link to a Google Books passage, I trust it will display alright, click here (scroll up, the list starts on the previous page.)

The luminiferous aether is an abstract object that the universe fails to instantiate. — Art48

I don't see it like that. I think the aether is a failed hypothetical posit. It's not abstract in the sense that numbers or universals are.

Or if you prefer, abstract objects do not exist. — Banno

The relationship between a circle's diameter and circumference doesn't exist?

And RMS doesn't exist! Those crazy engineers, using non-existent items to do their jobs. :cool:

That's just not true, though; they each reflect light at wavelengths closer to each other than objects of other colours do compared to them, and consequently they look more similar to each other in terms of colour than objects of other colours do compared to them. The first is a material condition of the second and the second is the reason we refer to both as being grey, for our use of the word "grey". — Janus

So light with a wavelength of 650nm is the same colour as light with a wavelength of 651nm because they're very similar wavelengths?

Without the idea of two, we cannot apply the idea of two to a pair of apples. Example, I define “xyz” as the set of all xyz things. Not a very useful definition. — Art48

From where did we get the idea of two if not by first observing more than one thing? How can we observe more than one thing if we don't already posses the category "tree" of which many similarly looking things are are a member of? Without categories there would only be one of everything.

It seems to me that the fact that there are things that share a number of similarities and differences is what allows us to create categories in the first place. If everything was different in which there was no one thing that shared even one characteristic with another thing there would be no categories, or universals.

An analogy: Imagine indirect experience as watching a baseball game on TV, as opposed to being in the park. We don’t directly experience the tree; our senses play the role of TV. — Art48

Don't you mean our mind plays the role of the picture on TV and the cameras and microphones at the baseball game play the role of the senses? Do we directly experience our mind? What information are we missing when experiencing something indirectly vs. directly? For instance, what information are we missing by watching the game on TV vs being at the game? We know the score and can see and hear the announcer describing the plays whether we are at the game or watching it on TV, so what is missing? If you asked me about the game the next day and I was able to tell you the score, who won and about the great plays that were made, how could you tell if I was at the game or watched it on TV?

Apple is a universal. A particular apple is an instantiation of the universal called “apple”. — Art48

How did we come to understand, or possess, the idea of "particular" and its relation with the idea, "unversal"?

Without the idea of two, we cannot apply the idea of two to a pair of apples. Example, I define “xyz” as the set of all xyz things. Not a very useful definition. — Art48

What reason does one have for "applying the idea of two to a pair" of objects, if not for communication?

I think "applying" is not an apt term to describe this process. We perceive multiple objects that have a number of similarities and differences. We even notice a similar pattern among different objects - such that there can be two of every thing that is not unique. No language is necessary up to this point. It is only when you intend to communicate this latter pattern of two that you need to have an agree upon symbol to use to refer to this pattern of observations - the scribble "2".'

Moreover, the set of all existing two things is constantly changing. If I eat one of the two apples, then the “set of all existing two things” has changed. If two atoms are crushed out of existence in some neutron star in another galaxy, the “set of all existing two things” has changed. — Art48

Is the apple/atom left the only apple/atom in existence? If not, then there are still at least two apples/atoms that exist.

Ideas exist in the “mindscape.” Physical cats exist in the physical world. — Art48

How do ideas and physical objects interact? How did you come to know of the concept, "physical"? What are you referring to when you use this term?

Experience is concrete. I physically experience rough brown patches and smooth green patches, which lead me to mentally experience a universal, i.e., the idea of a tree. — Art48

How did you come to experience the universal by observing just one pattern (a particular) of rough brown patches and smooth green patches?

From where did we get the idea of two if not by first observing more than one thing? — Harry Hindu

My view is that ideas already exist in the mindscape, just as trees exist in the landscape. Seeing a pair of apples may awaken our mind to the idea of two, but the idea already exists. Any being which lacks the mental capacity will never perceive the idea "two." Imagine an earthworm, for instance, crawls over two pebbles. I doubt the idea of two ever enters what mind it has.

How did you come to experience the universal by observing just one pattern (a particular) of rough brown patches and smooth green patches? — Harry Hindu

See previous answer. All ideas exist in the mindscape. Some minds (like ours) access ideas to make sense of sensory input. We find an idea in the mindscape that fits what we observe.Newton found F=ma. Einstein found different ideas which better describe what we observe.

So, in my view, the idea 2+2=4 has existed for all eternity. We didn't invent it; we discovered it.Of course, the idea is independent of the symbolism. The Roman Numerals II + II = IV express the same idea.

My view is that ideas already exist in the mindscape, just as trees exist in the landscape. Seeing a pair of apples may awaken our mind to the idea of two, but the idea already exists. Any being which lacks the mental capacity will never perceive the idea "two." Imagine an earthworm, for instance, crawls over two pebbles. I doubt the idea of two ever enters what mind it has. — Art48

Probably because it would be useless to its survival. Would it be useful to know that there are two birds looking to eat it for lunch? Perceiving more than one bird but less than 3 birds would be useful to its survival.

What do the ideas in the mindscape consist of? What form do they take? Can you have an idea of "tree" without having first perceived more than one tree? What is the difference between the idea of the universal tree vs the particular tree? How can you tell the difference? What does the idea of two look like in the mind independent of the scribble, "2" or "two" and independent of the observation of two particulars? How do you know that you are holding the idea of 2 in your mind independent of these forms (the scribbles and a quantity of particulars that share several characteristics)?

Can you have an idea of "tree" without having first perceived more than one tree? — Harry Hindu

Sure, just as we can have the idea of a unicorn without ever having seen one.

What is the difference between the idea of the universal tree vs the particular tree? — Harry Hindu

A particular tree is a concrete object which we recognize as an instantiation of the idea of a tree. The idea of a particular tree is the idea, say, of the oak tree in my yard.

What does the idea of two look like in the mind independent of the scribble, "2" or "two" and independent of the observation of two particulars? — Harry Hindu

What does the idea of two look like? It has various properties: synonym for pair; the first natural number after one; the only even prime number, etc.

How do you know that you are holding the idea of 2 in your mind independent of these forms — Harry Hindu

Is the idea of "two" independent of observation of two particulars? Yes. I grant that empirical experience often leads the mind to ideas but I regard the ideas as pre-existing. Just as when I take a walk, I see a rock that was there before I saw it. Similarly, the idea "two" existed before anyone thought of it.

Of course, my perception of the rock may not be 100% accurate. Similarly, someone might believe 2 is not prime, or conversely prime but not the only even prime. In this case, they don't see the idea clearly and need to be educated.

But if "two" was my own personal creation, then who is to say I'm wrong if my "two" is not prime?

“My view is that ideas already exist in the mindscape, just as trees exist in the landscape. Seeing a pair of apples may awaken our mind to the idea of two, but the idea already exists. Any being which lacks the mental capacity will never perceive the idea "two." Imagine an earthworm, for instance, crawls over two pebbles. I doubt the idea of two ever enters what mind it has.”

Could we not imagine a world where inhabitants sense and emphasizes differences than commonalties that they view all objects as individuals to be named, and that they have memories so great that universals are not needed?Why would I need to hypothesize that inhabitants who use universals can perceive some Platonic realm, when I simply can appeal to our make up that favors detecting commonalities and creating language of universals vs detecting differences and name individuals?

they view all objects as individuals — Richard B

If all objects are viewed as individuals, it seems that some types of knowledge would be difficult or even impossible. Yes, I could gain knowledge about this particular object but I couldn't apply that knowledge if I encounter a similar object later because I wouldn't recognize the two objects as being instances of the same universal.

Example: "Fire burns" uses the universal "fire" to describe a general law of nature. If I walk up to a camp fire and recognized it as an instance of the universal "fire" then I know it will burn me. But if I view everything as an individual, then the camp fire is an new object and I won't know it burns until it's too late.

Why would I need to hypothesize that inhabitants who use universals can perceive some Platonic realm, when I simply can appeal to our make up that favors detecting commonalities and creating language of universals vs detecting differences and name individuals? — Richard B

I'm not sure I understand what you're saying. How do we create a language of universals without acknowledging the existence of universals?

You're becoming ever more lazy and arrogant. I'm here to discuss with others, not to be insulted or pompously advised to read papers that are not even the subject of the thread. If you can make an argument of your own or rehearse the part of Austin's thesis that you think might refute what I've said, then I'll respond, otherwise you're wasting my time.

So light with a wavelength of 650nm is the same colour as light with a wavelength of 651nm because they're very similar wavelengths? — Michael

I don't believe I've said that or that it is implied by anything I've said.

The literal meaning of 'subsist' is nothing like what he's trying to convey here. — Wayfarer

Russell's is a recognized usage:

subsist (səbˈsɪst)
vb (mainly intr)
1. (often foll by on) to be sustained; manage to live: to subsist on milk.
2. to continue in existence
3. (foll by in) to lie or reside by virtue (of); consist
4. (Philosophy) philosophy
a. to exist as a concept or relation rather than a fact
b. to be conceivable
5. (tr) obsolete to provide with support
[C16: from Latin subsistere to stand firm, from sub- up + sistere to make a stand]
subˈsistent adj
subˈsister n

From here

The Austin article concerns universals, the topic of the OP. I suggested it to , not to you. What you do with it is not my concern.

Evasive bullshit! You said that if I read the article "my responses might improve"; a veiled insult designed to divert attention from your apparent inability to address this:

That's just not true, though; they each reflect light at wavelengths closer to each other than objects of other colours do compared to them, and consequently they look more similar to each other in terms of colour than objects of other colours do compared to them. The first is a material condition of the second and the second is the reason we refer to both as being grey, for our use of the word "grey". — Janus

thanks, hadn't noticed that second usage. Careless on my part. Hope it doesn't detract from the main point.

“Object” should not be taken too literally; think “abstract entity.”) — Art48

There might be an error even here. Perhaps at least some of what you call "abstract objects" are things we do, not things we find.

Let's take a look at numbers. "1" has the superficial grammar of a noun, but this is misleading. Rather "1" might be understood through its role in the process of counting. We come to understand "one" by learning how to count.

We might be misled by an expectation that because "one" is a noun, there must be a thing to which it refers. But perhaps instead of a thing, what we are referring to is a certain way of talking, and of dealing with the things around us in the world

One cannot physically list the integers. Does that mean that they do not exist? In understanding the sense of "integer" we understand how to construct the list. We do not need to construct the whole list in order to say we know what an integer is. The process suffices.

The red of the sunset and the red of the sports car are not the same. Indeed, the red of each changes even as we watch. We use the same word for different colours. How can that be, if the meaning of the word is some entity? Again, we might be misled by the expectation that since "red" is a noun, there must be some entity that it is the name of.

Plato took this to the extreme, positing a world of forms and puzzling philosophers for generations.

Those with a background in philosophy may recognise what I am suggesting as deriving from philosophy of language. Instead of looking for the meaning of the terms we use, stand back and look at how they are used.

There are distinct types of types. For example, there are types of qualities, colours, tastes, etc., and there are also types of objects, houses, cars, cups etc.. As universals employed in logic, the qualities are named as predicates, and the things are named as subjects. There is a big difference in role, between a type of thing, and a type of quality.

In the case of numbers however, there is ambiguity. Some would say that a number is a type of thing, and others would say that a number is a type of quality. And of course, it depends on how you use numbers, as subjects or as predicates. Is there a thing called "three", or is "three" a specific quality of a group?

Just keep in mind that if you find that your analysis of abstract objects contains the very thing you're trying to analyze (such as 'things we do', which is a set, and therefore an abstract object), you may take that as a signal that what you're dealing with is more primal than you previously may have thought.

But at least at this point, you've recognized that they exist and all that's left is to join the ongoing debate about how to understand them.

How about the following? "Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), something that waves should not be able to do."
The luminiferous aether is an abstract object that the universe fails to instantiate. — Art48

The aether is a medium for waves, both these concepts have links to the physical (water waves/ripples).

Just keep in mind that if you find that your analysis of abstract objects contains the very thing you're trying to analyze (such as 'things we do', which is a set, and therefore an abstract object), you may take that as a signal that what you're dealing with is more primal than you previously may have thought.

But at least at this point, you've recognized that they exist and all that's left is to join the ongoing debate about how to understand them. — Tate

Just as "things we do" is abstract, like anything we say, and represents perceivable human actions, so, I would argue, are numbers abstract, and they represent the phenomenon of number, which is made possible by the recognition of perceptible similarity and pattern in the perceived environment. So, I can see one orange or I can see three oranges. Of course I don't see the number three in abstraction, but I see three similar objects, and I can see the different pattern that three objects show compared to one, two or seven objects. and then later abstract the notion of "threeness".

@Art48.

Taking hints/cues from math, we could say that abstractions are generalities aka patterns - there's a brief back and forth between two posters on the question of whether the mind is a sense that picks up patterns in here and out there à la the eyes, nose, ears, tongue, and skin.

Pattern-sensing/seeking seems to be the mind's forte if you catch my drift.

Then there are mathematical objects that have no physical counterpart - these objects, in a sense, exist only in our minds. I wish I was a mathematician - I could've given some examples to drive the point home. Suffice it to say that there's a controversy with regard to whether math is invented or discovered. A point worth making/noting is how physicists have tried to make sense of the physical world with mathematical models. You might be interested in The Unreasonable Effectiveness of Mathematics in the Natural Sciences (Eugene Wigner).