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

I'm not sure whether it detracts from the point. I guess if subsist means

a. to exist as a concept or relation rather than a fact
b. to be conceivable — Janus

then we could say that particular numbers subsist in collections of objects that instantiate the appropriate numbers. As I say in my response to @Tate we cannot see the number three but we can see the pattern that three objects make.

I would argue, are numbers abstract — Janus

That is the prevailing view in philosophy of math.

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. — Banno

Processes are not a problem. Swimming, runnning, etc. are universals.

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. — Banno

True, the language we develop has indications of what exists but if our interest is ontology, language is subordinate to reality. In the middle ages, language included much talk of "witches" but that didn't mean witches really exist.

'things we do', which is a set, and therefore an abstract object — Tate

I see problems with defining abstract objects in terms of sets because it seems you need a definition of the universal before you can decide what is or is not in the set. For instance, "American" is used to refer to people in the U.S. and also to anyone living in Canada, Chile, Cuba, etc. (i.e., North and South America taken as continents, not a particular country.) We need to understand the meaning of "American" before we can define the set.

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

You originally asked: " 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?"
"no links" is vague. The aether doesn't exist; but you believe something which doesn't exist has links to the physical world? OK. How about the green pixies who built my home? They don't exist, either, but do they have links to the physical world because "built my home" is part of their description? And what about "the green pixies who did not build my home"? Do they have links to the physical world? If so, I don't understand what you mean by "have links".

there's a controversy with regard to whether math is invented or discovered. — Agent Smith

True and most working mathematicians say discovered; i.e., they accept Mathematical Platonism, which says mathematical objects exists "out there." True, our minds apprehend them but "triangles exist only in our mind" seems wrong. A geometry teacher is not trying to teach about what exists in his/her mind but the triangle "out there." Question: suppose I say triangles exist in my mind and they have four sides. How could anyone dispute what I say? Sure, triangles in another person's mind might have three sides but so what? Triangles in someone else's mind might have five sides. Clearly a definition of triangle is needed. Would you agree that definitions exist in the external world not only in our minds?

I see problems with defining abstract objects in terms of sets — Art48

A set is an abstract object.

I would argue, are numbers abstract — Janus


That is the prevailing view in philosophy of math. — Tate

The opponent of the view that numbers are abstract in the sense of being thought to be merely epiphenomenally parasitic upon the physical will argue that it doesn't answer the question as to the reality of numbers. 'What kind of reality does abstraction enjoy?' they might say, and if abstraction is real doesn't that tell against physicalism?

And then they might continue by asking what kind of reality does physicality have. And can we say more than that it is real only insofar as it is measurable, tangible, available to the senses? So, then analogously we could ask is not abstraction similarly real insofar as it is conceivable, available to thought, and then even seek to extend that condition to physicality itself.

So, then the question that seems to follow is as to whether the physical is derivative of the abstract or the abstract is derivative of the physical, or whether they are codependent. Since this question seems to be undecidable, those who support one or the other contention show their preconceptions and partiality, and the more vehemently they support one view or the other they show their ingrained prejudice and its extent.

But 'NO!' the physicalist will cry 'the view that the physical is primary is the more plausible'. Yet plausibility is not a precise measure and a sense of it is gained only by comparing many cases, and in this connection we have only the one case to consider. So, it seems that our sense of plausibility here is merely a reflection of conditioned habit and the dominant paradigms of our social milieu.

All that said, the view that the physical is primary does seem the more plausible to the majority of modern thinking minds. Could this consensual majority carry any rational weight or it is merely a prejudicial normativity. That is the million dollar question!

I agree. We just encounter this and that, categorize it to fit our needs, and we proceed without filling in the blanks.

You don't wait until physics is finished before you dig a hole for a pond. You just dig it.

:up: I was adding to the post as you were responding. But I agree it is pragmatism that rules.

But 'NO!' the physicalist will cry 'the view that the physical is primary is the more plausible'. Yet plausibility is not a precise measure and a sense of it is gained only by comparing many cases, and in this connection we have only the one case to consider. So, it seems that our sense of plausibility here is merely a reflection of conditioned habit and the dominant paradigms of our social milieu. — Janus

If you're a physicalist, you probably accept that in some sense the universe is aware of itself, so I don't know if it's more plausible. It's just the starting point our culture embraces.

If you're a physicalist, you probably accept that in some sense the universe is aware of itself, so I don't know if it's more plausible. It's just the starting point our culture embraces. — Tate

I know there is a movement towards pan-psychism among some physicalists; Galen Strawson and (not sure) David Chalmers spring to mind. Does this idea of the universe being aware of itself mean that the whole universe is aware of it wholeness, or just that some parts are aware of parts? Of course the latter is uncontroversial, as animals and humans seem to show various degrees of self-awareness.

That it is the starting point our culture embraces reflects the ascension of the methodology of science to be thought as the gold standard of investigative approaches.

Does this idea of the universe being aware of itself mean that the whole universe is aware of it wholeness, or just that some parts are aware of parts? Of course the latter is uncontroversial, as animals and humans seem to show various degrees of self-awareness. — Janus

I think of awareness as usually being like a flashlight in a dark room. I just meant that physicalism, to the extent that it's monistic, has to accept that the universe has awakened to itself. That's what we are.

I think of awareness as usually being like a flashlight in a dark room. I just meant that physicalism, to the extent that it's monistic, has to accept that the universe has awakened to itself. That's what we are. — Tate

I think that it is undeniable that without awareness the universe would be as good as nothing. It might be said to exist in some sense, but it would be an entirely blind, deaf, dumb and senseless existence, whatever we might dimly be able to imagine that could be.

Processes are not a problem. Swimming, runnning, etc. are universals. — Art48

True, the language we develop has indications of what exists but if our interest is ontology, language is subordinate to reality. In the middle ages, language included much talk of "witches" but that didn't mean witches really exist. — Art48

That's what I am inviting you to consider. Are universals things we find in the world around us, in the way we find this tree or this post? or are they a way of talking about the things we find around us, a way for us to group several things together? If the latter, then they are not part of the world around us, but a way of talking about the world around us.

Hence universals are not "objects", nor "entities", as you point out. This would explain why universals are neither spacial nor temporal - they are grammatical, in the broad Wittgensteinian sense.

I think that it is undeniable that without awareness the universe would be as good as nothing. It might be said to exist in some sense, but it would be an entirely blind, deaf, dumb and senseless existence, whatever we might dimly be able to imagine that could be. — Janus

I'm familiar with that weirdness. :grin:

Have you noticed that the way you "experience" a tree is not the same as the way you "experience" 1?

That seems to be at odds with your conclusion.

an abstract object does not exist in space and time. — Art48

It exists in the human mind, and the human mind is fundamentally temporal — in that things are constantly changing. So while numbers and classes and meanings don’t change the way material objects do — in the case of entropy, say— they still rise and pass in the mind/awareness of the thinker and perceiver.

Abstractions are a kind of being — “entity” as you said. Beings are individuated in the human being.

If you mean an object does not exist in space and time as traditionally understood in physics, then yes I understand your categorization. It’s just good to keep in mind that time (and even space) aren’t always understood in that way. Here again I use Heidegger as a starting point.

A geometry teacher is not trying to teach about what exists in his/her mind but the triangle "out there." Question: suppose I say triangles exist in my mind and they have four sides. How could anyone dispute what I say? Sure, triangles in another person's mind might have three sides but so what? Triangles in someone else's mind might have five sides. Clearly a definition of triangle is needed. Would you agree that definitions exist in the external world not only in our minds? — Art48

Here you're forced to accept the model of the world divided into the two domains - the mind 'in here', private and subjective, the world 'out there', public and objective. They're your only options.

But intelligible objects such as triangles do not exist in either sense. They're not the property of individual minds, but they're also not denizens of a purported external world. This is often regarded as baffling to modern thinking. While on the one hand Galileo claimed (and it is widely accepted) that 'the book of nature is written in mathematics', Einstein also said that 'the most incomprehensible thing about the world was that it was comprehensible.' His younger contemporary Eugene Wigner wondered about the 'unreasonable effectiveness of mathematics in the natural sciences' which seems to defy explanation (the word 'miracle' occurs 12 times in his famous essay of that name.)

So what's going on here? I think the problem has to do with the conception of mind and nature that characterises modern Western culture, and the way it divides the world into subject and object. These are imagined as separate domains - but they're ultimately not that. So in that picture, you have ideas 'in here' that somehow represent objects 'out there'.

That is the Gordian knot that needs to be untied. Frege understood it in terms of a 'third realm', neither objective nor subjective, comprising the objects of mathematics and geometry, which are grasped by rational thought:

Frege held that both the thought contents that constitute the proof-structure of mathematics and the subject matter of these thought contents (extensions, functions) exist. He also thought that these entities are non-spatial, non-temporal, causally inert, and independent for their existence and natures from any person's thinking them or thinking about them. Frege proposed a picturesque metaphor of thought contents as existing in a "third realm". This "realm" counted as "third" because it was comparable to but different from the realm of physical objects and the realm of mental entities. I think that Frege held, in the main body of his career, that not only thought contents, but numbers and functions were members of this third realm. Entities in the other realms depended for determinate identities on functions (concepts) in the third realm. Since logic was committed to this realm, and since all sciences contained logic, all sciences were committed to and were partly about elements of this realm. Broadly speaking, Frege was a Platonist about logical objects (like numbers and truth values), functions, and thought contents. — Tyler Burge, Frege on Knowing the Third Realm

So in this view, universals and numbers are real, but they're not existent in the sense that phenomenal objects are. And that's a no-go for today's empiricism. There is simply no conceptual space for the notion of reals that exist in any way other than as (external) things or (internal) ideas. And all of that ultimately goes back to the medieval debates about (platonic) realism vs nominalism. Nominalism - the forerunners of the later empiricist philosophers - won the day, and history, as it is said, is written by the victors. As a consequence, nominalism and empiricism is so deeply embedded in our cultural discourse that we can mostly only look through it, not at it. And that's what you're seeing here.

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

A lot of Cartesian dualism here— mind/body, subject/object, mental/physical, inside/outside.

Perhaps these categories too are simply part of human thought and perception and do change in time. Differing ways of interpreting the world.

When we’re even contemplating these questions, we’re “in” a type of experiencing (or a “mode of being”) that is quite different from our more common modes of experiencing — the abstract, theoretical, symbolic mode.

If we step back from this symbolic mode — what’s often called “thinking” — and notice thinking as a phenomenon, or “being” in its own right, then the question becomes: who or what is thinking? Who or what is asking these questions about thoughts/abstractions/dreams/words/numbers in the first place, and why?

I think this is very important to do, because we may be questioning on an infinite loop.

A lot of Cartesian dualism here— mind/body, subject/object, mental/physical, inside/outside. — Xtrix

Cartesian anxiety refers to the notion that, since René Descartes posited his influential form of body-mind dualism, Western civilization has suffered from a longing for ontological certainty, or feeling that scientific methods, and especially the study of the world as a thing separate from ourselves, should be able to lead us to a firm and unchanging knowledge of ourselves and the world around us. The term is named after Descartes because of his well-known emphasis on "mind" as different from "body", "self" as different from "other".

Richard J. Bernstein coined the term in his 1983 book Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis.

I think some of us are offering explanations prior to understanding what abstract objects actually are.

An abstract object is like a tree in that I can be wrong about it. Note the direction of fit. I learn about them. I don't make them up.

Let's get that straight first, then try to figure out what their basis is. Perhaps their roots are in my psychological make-up at a fundamental level. Maybe they're patterns in the universe that show up in the structure of my mind, for no other reason than that my mind is a natural thing.

Don't paint yourself into a corner before looking around the room.

They're both discrete ideas, or at least discrete enough ideas that we can give shorthand names to them. I can use the words "dog," "color," "hollow," "key," etc. to represent ideas specific enough that the vast majority of things I could be referring to are eliminated as potential references.

When the first key cards were rolled out at hotels it wasn't a huge conceptual leap to explain them to people because "key" was already a discrete idea they had a lock on, even though they look and function very differently. Similarly, it I tell someone who wants to help me that I'm looking for "my car keys," they eliminate the vast majority of potential things they could see from consideration and have a decent idea of what we're looking for.

That's my take anyhow.



lol, great term

I think there’s something to that, yes. I don’t know who Bernstein is, but I bet he read Heidegger.

I think there’s something to that, yes. I don’t know who Bernstein is, but I bet he read Heidegger. — Xtrix

Just now I was listening to the audio version of the well-known book The Embodied Mind. Chapter 7 is called The Cartesian Anxiety, and then they present Heidegger and Gadamer's philosophy as one of the antidotes to it. They note that this kind of perspective is more typical of Continental as distinct from analytic philosophy, which tends to cling to the kind of realist picture descended from Cartesian dualism. (When I read about that term I borrowed Bernstein's book from the library, but it's a pretty tedious academic text. However that phrase has become something of a meme.)

I was just reading about him on Wikipedia. Oddly, recently died on the 4th (perhaps that’s why you mentioned him?).

Anyway — I like some of what the article is citing him as saying:

Bernstein diagnosed a serious issue that affects much of modern philosophy as it oscillates unendingly between two untenable positions; on the one hand, the dogmatic search for absolute truths, and on the other, the conviction that “anything goes” when it comes to the justification of our most cherished beliefs and ideas. According to Bernstein, what underlies this predicament is a deep longing for certainty, the urge “to find some fixed point, some stable rock upon which we can secure our lives against the vicissitudes that constantly threaten us.”[10]

This is what he calls the Cartesian anxiety, a mostly unacknowledged existential fear that seems to lead us ineluctably to a grand Either/Or: “Either there is some support for our being, a fixed foundation for our knowledge, or we cannot escape the forces of darkness that envelop us with madness, with intellectual and moral chaos”.

Although in philosophy this Cartesian anxiety mostly shows up in the discussion of epistemological issues, Bernstein is pointing to something much deeper and universal with this notion, something that permeates almost every aspect of life and has serious ethical and political consequences.

This strikes me as important. It does seem that Descartes has caught us in these endless debates about minds and bodies, subjects and objects, and a search for “truth” in the form of certainty: some permanent, undeniable foundation upon which our lives make sense.

Nietzsche and Heidegger definitely start chipping away at this. Pragmatism does too, to a degree. Freud and Marx have interesting things to say about the world as well, but from very different perspectives altogether. I still say Heidegger is the source, though, even of Bernstein.

:100: This is also the exact topic of the chapter I mentioned in the Embodied Mind.

It's a coincidence that Bernstien has just passed away. It seems like the end of a long and very intellectually rich life. From that article, I'm very drawn to a lot of what he says - a consciously non-dogmatic attitude, very Socratic in his approach, it seems to me.

I attribute this sense of the division of the world into these contradictory opposites to be deeply embedded in Western cultural discourse and specifically with the emergence of liberal individualism.

Embodied Mind, at this point in the discussion, brings in the Buddhist philosophy of the 'middle way' - the Madhyamika of Nāgārjuna. They make the point that this has been influential in Asian cultures for millenia and that the West is only now catching on. Buddhism diagnoses the vacillation between what it calls 'eternalism and nihilism' from the early texts:

By and large, Kaccayana, this world is supported by a polarity, that of existence and non-existence. But when one sees the origination of the world as it actually is with right discernment, "non-existence" with reference to the world does not occur to one. When one sees the cessation of the world as it actually is with right discernment, "existence" with reference to the world does not occur to one. — Kaccayanagotta Sutta

There's a lot of convergence going on in that 'enactivist' domain between phenomenology and Buddhist philosophy, although it's actually quite tangential to the subject of this particular thread. (I'm one of the few on this forum who'll go into bat for the reality of universals, which is about as far from Buddhist philosophy as you can get.)

All I can say is this: The perfect-imperfect distinction feels relevant. Even if it's the case that no abstract object exists that has no association whatsoever with the physical world, it has to be highlighted that abstract objects tend to be/are perfect while their physical counterparts are imperfect. The perfect man/woman/deer/shoe/whathaveyou is a (pure) thought - we won't find these entities in the world.