Why should anyone take this hypothesis serious, and ontologize such an abstract cow, anyway...? — jorndoe

Presumably because it offers the best explanation as to why things can be seen as similar or different, which can also be seen as different and "more different".

There's all sorts of issues related to Platonic universals:

Like you said, how do these Forms interact with the stuff around us? This is somewhat similar to the problem Lady Elisabeth pointed out to Descartes regarding the interaction between his two hypothesized substances.

Is there really a Form for everything? Are there Forms for only the "simpler" things that have no necessary parts and seem to be simply adjectives, or should we also see objects and structures and whatnot as having Forms themselves? Here we start to have issues with composition.

Then there's the issue of how things in the world can change but still instantiate a the transcendental Platonic Form.

And of course there's Aristotle's critique of Plato's Forms and his subsequent theory of hylomorphism - the Matter-Form duality, that places universals squarely in the world itself. But then later on there were several Scholastics that denied universals of all stripes, and we call them nominalists. But nominalism has always struggled with a regress problem, and so has Aristotle's immanent universal theory.

Personally I've been reading more into Neo-Platonic metaphysics. It's "based" on Plato but effectively synthesizes a whole bunch of things, including Aristotle and Anaximander. Universals are important to the general theory.

By a semi-idealist reasoning, there's an "abstract cow" that somehow exists "objectively" and independently of all else, sort of in it's own ("timeless") realm of reified abstracts.
(I'm just using the term "semi-idealist" a bit broadly here; you get the gist.) — jorndoe

According to Plato, there's the eidos of a thing, which is its ideal form. I think to say that it exists 'objectively' is already mistaken, because that presumes a bifurcation of subject and object. Ideals don't exist in any objective sense, they're not 'out there somewhere'. They're implicit or inherent in the nature of reality itself, so that they are forms which actual material instances of things tend towards.

@jorndoe - you might find this review informative.

Not to hijack this thread; but, doesn't Godel's incompleteness theorem enhance or deny the existence of Platonic forms?

Godel had a generally Platonist view of mathematics:

Gödel was a mathematical realist, a Platonist. He believed that what makes mathematics true is that it's descriptive—not of empirical reality, of course, but of an abstract reality. Mathematical intuition is something analogous to a kind of sense perception. In his essay "What Is Cantor's Continuum Hypothesis?", Gödel wrote that we're not seeing things that just happen to be true, we're seeing things that must be true. The world of abstract entities is a necessary world—that's why we can deduce our descriptions of it through pure reason.

....Platonism was an unpopular position in his day. Most mathematicians, such as David Hilbert, the towering figure of the previous generation of mathematicians, and still alive when Gödel was a young man, were formalists. To say that something is mathematically true is to say that it's provable in a formal system. Hilbert's Program was to formalize all branches of mathematics. Hilbert himself had already formalized geometry, contingent on arithmetic's being formalized. And what Gödel's famous proof shows is that arithmetic can't be formalized. Any formal system of arithmetic is either going to be inconsistent or incomplete.

...Gödel made it harder not to be a Platonist. He proved that there are true but unprovable propositions of arithmetic. That sounds at least close to Platonism. That sounds close to the claim that arithmetical truths are independent of any human activity. Philosophers of mathematics can certainly avoid the Platonist conclusion but, so long as they don't just "bypass Gödel," they have to do fancy footwork. Even Wittgenstein, who said his task wasn't to address Gödel's theorems, couldn't help returning to them again and again. He argued about them in his class with Alan Turing. And of course Turing's own work, his demonstration that we can't solve the halting problem (roughly, knowing whether a given computer program will produce a result given an input or will grind away forever), itself entails Gödel's first incompleteness theorem.

Gödel and the nature of Mathematical Truth, Rebecca Goldstein.

Yup, that's Godel for you. I still struggle with the understanding of the implications of his theorems. As far as I know, it seems to me that his work has been ignored by the mainstream mathematicians excluding physicists like Tegmark.

The real problem with Godel's Incompleteness theorem is that Occam's razor can't be applied in such situations. So, in my understanding, it seems to be an insurmountable hard limit on the scope of our ability to make logical conclusions or create logical spaces/state spaces.

or

How exactly is this abstract cow supposedly related to the cows in the world?

Isn't the 'abstract cow' an epistemological or nominal concept describing what we know about cows; and that 'cow', that particular one sitting in the pasture is ontologically real. Epistemological universals seem to be necessary for the possibility of knowledge, their ontological status might be described an subjectively real, or as realities of thought, the objectivity of their existence as such being both
publicly known and agreed/disagreed on normatively or intersubjectively.

I'll take a swing at it. Not an argument I'd use, but you could say this: cows are cows because they have certain features. The sum of those features describes an "ideal cow." As to whether it exists "objectively..." *shrug*

By a semi-idealist reasoning, there's an "abstract cow" that somehow exists "objectively" and independently of all else, sort of in it's own ("timeless") realm of reified abstracts. — jorndoe

Can you provide the reason as to why that is? I think the reason is that if all particular cows in the world were to disappear today, there would still remain the abstract cow in our minds; and therefore the abstract cow is independent of the particular cows in the world. But this argument is refuted by Aristotle who states that although the idea remains in our mind, it was originally abstracted from the particular cows. In other words, if no particular cows existed in the first place, then we would never have conceived the idea of abstract cow, and therefore the abstract cow originated from the particulars. I think this is also what @Wayfarer was explaining in his first post above. Therefore the "realm of reified abstracts" is an unnecessary hypothesis.

In my adventures, I occasionally encounter a discussion going back to Plato (at least).
Let me just try a different angle.

8zqp0hvrke0ql5tq.jpg

Most can easily identify that as a cow.
Not a "real" cow, just a drawing, but there are many cows in the world, that just go about their business on their own.
By a semi-idealist reasoning, there's an "abstract cow" that somehow exists "objectively" and independently of all else, sort of in it's own ("timeless") realm of reified abstracts.
(I'm just using the term "semi-idealist" a bit broadly here; you get the gist.)

Of course this hypothesis spurs a few questions.
How exactly is this abstract cow supposedly related to the cows in the world?
Why should anyone take this hypothesis serious, and ontologize such an abstract cow, anyway...? — jorndoe

The objective existence is possessed by the actual computer screen with black and white dots on it that forms the shape of a 2-D cow. In this instance, the objective existence of the "abstract cow" has taken the physical form of a monitor emitting white light. This is why many different minds can now see the "abstract cow" in this shared forum.

If the "abstract cow" was drawn on a sheet of paper it would take on the objective existence of a physical piece of paper with ink on it in the shape of a 2-D cow.

I'd live to hear a "semi-idealist" (whatever that is) explain the relationship between a cow and this photograph of that cow,https://goo.gl/images/xDbG4C, and how that differs from the "abstract cow".

I'm surprised apo hasn't popped in. The word 'cow' and the cartoon are recognisably signs. For ontology-addicts signs have an ontology of their own, not necessarily that closely related to the mooing, farting creatures I can see sometimes from my window.

I like 'semi-idealist' I imagine they live in the English suburbs, are not quite philosophical enough to be 'detached' but don't mix with the riff-raff like the rest of the proles.

Thankye for the comments.

I wasn't going for Platonism in particular, though Plato is the first articulation of such thinking I know of.
There are a few angles, like Plato's forms versus instantiations (or ideals versus convergent instantiations), universals versus particulars, abstracts versus concretes, etc.

(Please don't get hung up on the words.)

The image wasn't intended to be our abstract cow, more like observing that cows in general doesn't seem to be just those creatures going about their business out on the grassy fields. :)

But, I'd say there is indeed such as thing as a reification fallacy.
An "external", wholly independent, abstract cow comes through as an example thereof, sort of.

How exactly is this abstract cow supposedly related to the cows in the world?
Why should anyone take this hypothesis serious, and ontologize such an abstract cow, anyway...? — jorndoe

Or is it that, what we (or some at least) consider an abstract cow, originates with our rough "maps" (recognition) of worldly "territories" (mentioned creatures), and so has attained a life of it's own...?

[...] Then there's the issue of how things in the world can change but still instantiate a the transcendental Platonic Form. — darthbarracuda

(Y) Those oddities with Platonism were among the objections that came to mind.

One of the areas where such thinking seems to resurface regularly is in logic and mathematics.

• Abstract Objects (Gideon Rosen, Stanford Encyclopedia of Philosophy)

Nice thread interesting one