The debate between the three views is ancient, and extremely complicated. It can also seem at first glance to be very dry, esoteric, and irrelevant to practical life. But nothing could be further from the truth. Indeed, it is not too much of an exaggeration to say that virtually every major religious, moral, and political controversy of the last decades — of the last several centuries, in fact — in some ways rests on a disagreement, even if implicit and unnoticed, over the “problem of universals” (as it is known). That includes the dispute between the “New Atheists” and their critics, ignorant though the former (though also often the latter) are of the true roots of this dispute. When Richard Weaver famously made the observation that “Ideas Have Consequences”, he was not making the banal point that what we believe affects the way we act; he was referring to the radical social and moral implications that the abandonment of realism and the adoption of nominalism has had within modern Western
civilization.— E. Feser, The Last Superstition
The three views Feser refers to in the quote are realism, conceptualism and nominalism. In this last post I will illustrate how the “implicit and unnoticed” disagreement over the problem of universals gets tangled up in a typically modern debate.
But first, it is useful to summarize the long trek that lead us up to where we are, and get a high-level view of the structure of the argument for realism. One way of framing the problem is to ask what does it mean to say that
- Fido is green.
- Rover is green.
- Socrates is green.
Enjoining these phenomena to justify the need to posit universals serves two different functions. First, as a springboard for direct arguments in favor of realism. So I have, from explicit enunciation to only brief adumbration, and spread across all posts, made several arguments for realism: the necessary modal status of logical and mathematical truths, the argument from the objectivity of our concepts, the argument from science, etc. Second, if the anti-realist is to make his case, then at the very least he will have to meet the realist challenge.
As I tried to argue in the third post, all the anti-realist responses suffer from fatal flaws. The flaws were illustrated by the phenomena that I took as basic: predication, unity within plurality and abstract reference. But these difficulties trickle down and will plague anti-realist accounts of the laws of logic, mathematical principles, laws of science, etc. Finally, in the fourth post I responded to some of the objections against realism. This is a cumulative case for realism; whether the reader is convinced or not, at least my hope is that the issues at stake are clearer.
In some of the arguments for realism, we already see the central importance of the debate over universals, one of the oldest, still running debates in the history of philosophy. But what about Feser’s contention about its importance for religious, moral and political questions?
I could, as Feser does, and I will, direct you to Richard Weaver’s Ideas Have Consequences. But as a typical illustration, consider the debate about same-sex marriage (SSM for short). How do SSM advocates tend to argue? First note that this is a typically modern debate, with only a few decades long. Since biology, history and anthropology are not on his side, the SSM advocate will tend to emphasize the social, conventional aspects of marriage. By the nature of the case, he must deny the essentialist picture of human nature or that marriage has an objective, essential basis on reality.
If facing a stern Dominican, steeped in the tradition of natural law, when not offering caricature straw man arguments against it, he is forced to reject the essentialist metaphysical picture of human nature on pain of conceding the point to the Dominican. In short, they have to deny that the concept of marriage has any objective basis on reality, and is “just a piece of paper”, a conventional contract between two sovereign wills, and along the way add their own prejudices and insist that marriage, while a convention, can only be between two adult persons and other such ad-hoc strictures.
This prejudice is little more than the Humpty Dumpty position: words mean what we (where “we” is the community of enlightened liberals) say they mean. And what is this but a distant echo of the nominalist position? There are no universals, there are no fixed natures. They are mere “convenient fictions” to borrow an apt expression of a combox poster. And if they are “convenient fictions”, we might as well choose one that accords to our tastes and emotional hang-ups.
I do not intend to argue the merits and demerits of the pro-SSM arguments. Although my position should be clear (they are worthless), that is a discussion for another day. What I am trying to do is point to what the SSM advocate must say to rationally make his case, and what he must say will almost inevitably be anchored in some form of anti-realism, whether he realizes it or not.
Whatever the path that Western civilization follows, and quite apart from all the myriad factors that enter into the SSM debate (political, cultural, social, etc.) that struggle alongside a more philosophical approach, it seems to me that knowing something of the root metaphysical disagreements would have the benefit of clarifying the issues involved. We may not be able to convert each other through rational dialogue as there is more to the pragmatics of belief than just the philosophical dialectic of argument and counter-argument. But as human beings, rational animals as Aristotle put it, rational dialogue can at least clarify the bones of contention. That may not be enough, but is no small thing either; it is one of the things that separates civilized society from barbarity.
I love the contrast between the well educated and polite Rodrigues in the posts and the rude, bitter handwaving Rodrigues in the comment chatter box. Which is a disappointment. We could have all learned a lot more if the tone of the conversation wasn’t so bitter.
Or perhaps it’s just me whining. I do have to congratulate some posters’ patience to deal with all this, and hope that someone has learned anything.
“What I am trying to do is point to what the SSM advocate must say to rationally make his case, and what he must say will almost inevitably be anchored in some form of anti-realism, whether he realizes it or not.”
And why is this a problem? If the SSM advocate’s support for SSM will result in the optimal situation, then he is rational according to Rational Agent Theory.
Human beings transcend human nature would you not say? I am not just a man, a woman is not just a woman. This is how I would argue against natural law.Not by downplaying the realist view, but pointing to it’s culmination. Should we say to two individuals who have clear understanding of why they want to marry that they should not because of their respective natures?
@ Rembie
First question, no. How does man transcend his nature? It seems he simply fulfills it.
Second question, yes. But it’s not that they ‘should not’, but that they in fact cannot. The point is that the concept of marriage is in accordance with reality, and an ‘understanding of why’ they desire it has no bearing on what it is. It’s not that I ‘should not’ insist that a square is round, but I cannot (and remain rational).
——–
Good posts, G. Rodrigues.
@JTC
Except marriage doesn’t fall into any catagory for which you can construct such a cannot argument.
Marriage is not a universal, it is a social / religious construct, and it differs significantly from one society / religion to another.
Marriage as strictly one man, one woman is a relatively recent idea, dating back only to about the 1st century AD. Many ancient cultures practiced (and a few modern ones still practice) polygamy (mariage of one many to many women). In fact, US law did not prohibit polygamy until 1862.
@JTC
I see what you mean. To me however there is a difference with regard to man relative to all other creatures. He refers to himself by saying I and he can strive to overcome himself. If all that is fulfillment of nature to you, so be it. The term strikes me as inadequate though. If that were to be true, we would have as many natures as there are I’s in this world. As a man or a woman I have a nature, not as an I, me thinks. I do not share it with anyone. I would not accept it from anyone if I was told I could not do something because of my nature. Therefore gay marriages seem to me a necessary phenomenon, even if it does not make much sense given the idea of marriage in natural law.
Luis Dias
.
Or perhaps it’s just me whining. I do have to congratulate some posters’ patience to deal with all this, and hope that someone has learned anything.
I do not think so. This kind of discourse has merely missed one century of science and brings us back to the age old misconceptions about the Nature.
As I said in the comment to the previous post, in the meantime quantum mechanics happened.
Many questions that puzzled people 1 century ago, Ã fortiori much earlier, are answered today. But more than answered, measured and decided by experiment.
.
Realistic theories/models of the Nature have been falsified by QM 80 years ago and by experiment 30 years ago.
There are no identity conditions for bosons and it doesn’t make sense to speak about sharply defined unambigous properties of quantum objects before measure.
Any discourse about the Nature prior to the measure can only be probabilistic and this has been decided by experiment too.
These are just a few examples of insights that we have discovered during the last century.
The fact that there are some philosophers in the 21st century who want to make believe that these questions are still open, doesn’t change much their irrelevance.
While there could be some virtue to correctly formalise and make logically consistent soft, subjective disciplines like ethics or religion, it is better to look at actual experimental and theoretical scientific results when one wants to talk about the Universe.
@rembie:
No. Even God’s grace does not violate human nature, but rather perfects it and completes it. There is no idea of “transcendence” because that would mean that we would become something other than human.
Unless you mean by “transcendence” something else.
@TomVonk:
No it has not.
And if you are going to quote to me the Bell inequalities or the Aspect experiments, think twice. On my first post, I said my background was in mathematics and physics; I know what I am talking about.
No, it has not.
But even if your claims about QM were correct, this would have little bearing on the Thomistic realist understanding (I say Thomistic, because that is the one I know best and the one I favor).
@TomVonk:
I forgot to add the most important: realism about nature, as the problem is formulated when pondering over QM, is not the same thing as realism about universals. So as far as the subject of the series, your complaints are simply misdirected.
@Rodrigues
Indeed it depends. If your endgoal (Gods plan if you will) includes what human beings make of themselves, then there is no transcendence. It is in the nature of plants to bear fruit, but the human being being does not bear fruit so to speak without making himself an effort. In that way he is different from all other natural beings. So if you say: self creation is human nature, then there is no transcendence. Yet the human animal is transcended I would say. Not completely, but in part. I would argue that this includes our sex.
@TomVonk
The Book “Der Glanz von Kopenhagen” (available from amazon) is very nice. In it you will find a thorough Aristotelian interpretation of quantum mechanics Copenhagen style.
Rodriguez
And if you are going to quote to me the Bell inequalities or the Aspect experiments, think twice. On my first post, I said my background was in mathematics and physics; I know what I am talking about.
Whatever your background is, it is not quantum mechanics because what you have been saying is in contradiction with it and has been shown wrong for more than 50 years. At least if you ambition some generality in your statements.
The experiments of Haroche (Nobel 2012), Aspect and Delayed choice eraser have falsified realistic theories with no ambiguity.
Every beginning student of QM knows that.
I just reformulate :
1.Photon Fido is spinup.
2.Photon Rover is spinup.
3.Socrates is spinup
This makes (with some reservations) sense after a measure of the spin. It of course doesn’t make sense for Socrates because as a macroscopical system, his spin can’t be measured.
And what about before measure?
The realistic theory postulates that the 2 photons can be individually defined and have some sharply defined spin.
QM says that the 2 photon system is described by a single wave function so that it doesn’t make sense to talk about individual photons Fido and Rover. It also says that the spin of the photon system is described as a combination of the 4 spin couples so that it doesn’t make sense to talk about a sharply defined spin state of the system before measure. It is the decoherence during the interaction with the measure instrument that will choose an Eigenvalue of the system as a result. Before measure the system can only be described in a probabilistic way determined by the wave function.
And this is no philosophy because the realistic and the quantum hypothesis predict different outcomes of the experience with a 2 photon (or 2 fermion if one wants) system. These experiments have been done long ago and the result falsifies the realistic hypothesis. The photons are not distinguishable, the system is in no defined spin state before the measure and the decoherence works. Only probabilities can be known before measure and QM is right. The 3 statements above make no sense and lead to wrong conclusions.
Now I find this kind of philosophical dissertations amusing as long as they don’t pretend to contribute anything relevant to the understanding of the Universe. Of course if one adds that the considerations about Fidos and greenesses explicitly exclude anything related to the reality like atoms, photons, energies, spins, momentums, measures etc, then anything is authorized as long as it is at least logically consistent.
My comment simply meant that the realistic expectations (individuality, universals etc) are simply wrong when applied to the real world that we observe, measure and explain with QM. This is actually trivially obvious because the people you quoted didn’t even suspect that QM (or relativity) would exist one day – their opinions have been shaped by the classical view of the world which we know to be wrong today.
This case has been closed for 50 years already.
Rembie
I already told you in the other thread that this has nothing to do with Copenhagen. The realistic theories with hidden local variables have been falsified for every quantum physicist whatever interpretation he chooses – either Copenhagen (99%) or some more exotic ones (1%).
These exotic interpretations may actually only exist because they can’t be experimentally distinguished from Copenhagen. So this is a red herring.
More about QMs and “realism”, via Lubos Motl, this time regarding Hardy’s paradox:
http://motls.blogspot.pt/2011/01/hardys-paradox-kills-all-realistic.html
@TomVonk:
First things first; realism has many senses and the way you are using the word has nothing to do with the subject of the OP which is realism about universals.
Now, on to your claims. I will make this short, as I already have had my share of protracted discussions about QM and am not inclined to pursue another.
1. No-go theorems like the Bell inequalities or Kocken-Specker have loopholes that can be exploited to regain local realism. One is counterfactual determinism, but only someone completely mad would choose (nice irony this one) this option. Another is the use of Boolean logic. This is important for the program initiated by C. Isham, one of the foremost leading experts on quantum gravity, and colaborators such as Doering, Spitters, etc. And this is just one example: contrary to your ignorant claims, the problem is not closed.
2. You said to Rembie, and I quote:
But who said we had to choose *local* realism? In fact, if there is one thing that QM seems to point to is intrinsic non-locality. In the standard Copenhagen interpretation, non-locality is hidden in the state vectors but then re-appears in the form of spooky action at a distance, entanglement and all sorts of wonderfully weird bizarreries.
The most that invoking Bell inequalities or other no-go theorems can give you is that *physical theories*, whose job is to explain and predict the outcomes of *experiments*, cannot have local hidden variables. Making the leap to metaphysical statements about the very nature of reality is unwarranted without further argumentation. This is an elementary point, but that seems lost on you. But you yourself shun such an argumentation — or as you said:
You find philosophy amusing and irrelevant to understanding the universe, and yet you have no qualms making metaphysical claims about the nature of reality based on naive reading offs of the *physical theories*. The debate, while certainly informed by the discoveries of physicists is eminently a philosophical debate. That you are not even aware of this is very telling.
The fact is is that the formalism of quantum mechanics, like any other physical theory, is a map of reality. It is constrained by the specific methodology of physics that entail a reductionist view of physical reality to the aspects that are amenable to a mathematical treatment. Currently, we do not have a scalpel fine enough to cut through reality at the subatomic level; it may even be the case we will never have such a scalpel. Either way, QM is still a map not the territory. It is an illegitimate move to go from an *epistemic* *operationally-descriptive* vision of reality to the imposition of an ontological status on said reality.
3. There are several ways to rationalize no-go theorems like the Bell inequalities.
a) Deny that events have any cause in nature as per the anti-causality peddlers. This is the way of anti-rationalism and the anti-science crowd.
b) Non-local causes. This keeps the possibility of science and rationality intact and in fact I have a lot of sympathy for it for the reasons I have state above. The problem with non-local variables is that it opens a *really nasty* can of worms; it does not bode very well for the intelligibility of the universe.
There are more solutions from the purely physics theory side. But either they are completely mad (many-worlds interpretation), I do not understand them (transactional interpretation) or are still waiting trial.
c) Following the paragraph just preceding 3, posit a cause that cannot be described in mathematical terms. The cause in question could still be local, natural and real, but just not describable by mathematical formalisms, and concomitantly by the empirical sciences.
I never read anything by Tom stating that he finds philosophy in general to be “irrelevant” to understanding the universe.
@Luis Dias:
From the post I responded to:
I do not know what you take “Now I find this kind of philosophical dissertations amusing as long as they don’t pretend to contribute anything relevant to the understanding of the Universe” to mean, but to me it sounds like “irrelevant”.
MiÅ‚o siÄ™ czyta. Blog dodany do mojej listy interesujÄ…cych stron 🙂
The arguments against Realism and the existence of Universals have not been invented because Fido is green, and Socrates is not green. Universals are also being used to try to prove that some very specific non-observables really exist. Plato for instance invented some of those universals. And the idea that universals are not in the physical world. Not discussing those kinds of universals and the exact nature of the world the universals are in, in a discussion about Realism versus Anti-Realism is not really discussing Realism and why it is better than the Anti-Realisms.
Rodrigues, the usage of the expression “this kind” is extremely precise in that context.
@Sander
I sympathize with your remarks here since it might prove very difficult to express what the content of a certain universal is. If you go by the route of abstraction, you do not find it, like we have seen in the example of the house. If we abstract from triangles drawn on paper (disregard their differences and distill what is common to all) we will not arrive at the definition of a triangle and hence, if you ask me, the universal associated with it. It is only by constructing the triangle from intuitive notions that we may hope to experience the universal element within the triangle that appears to us on paper or otherwise.
However, I expect there to be a universal for green too, despite all the difficulties with color we have been discussing. One such difficulty would be that a certain shade of green is perceived relative to adjacent colors. It appears in a certain way depending on something else, thus it’s identity as a particular shade of green is in question. It happens in geometry too. There are many examples of lines and shapes appearing next to others in a way they do not when viewed by themselves. If I think about these examples I cannot help but drawing the opposite conclusion. If it is indeed so that the world we perceive is like a kaleidoscope and every appearance is dependent on a context, the sense of identity we have with respect to the things and beings that surround us, must have another source.
If the sense of identity we have with respect to what is around us is a subjective notion or a necessary intuition with regard to what is given to us in perception, is what the debate revolves around. It is important to separate this kind of realism of physicalism. Physicalism is a kind of realism that seeks a foundation for the world not by means of ideas or forms, but by positing a special kind of semi-sensible objects that are constitutive of all others. This kind of realism seems indeed refuted by QM, but that’s just my impression as a layman.
@Luis Dias:
Point taken. Then amend my response statements by inserting “of this kind” that the claim still goes through all the same.
This is important for the program initiated by C. Isham, one of the foremost leading experts on quantum gravity, and colaborators such as Doering, Spitters, etc. And this is just one example: contrary to your ignorant claims, the problem is not closed.
Isham is no “leading†expert on quantum gravity. He defends a marginal theory called “Loop Quantum Gravityâ€. Variations of this theory lead to pathological Lorentz invariance breaking. For leading experts on quantum gravity look for Witten, Maldacena or Hawking. And these are just few examples contrary to your ignorant claims.
You really don’t have a clue, have you?
But who said we had to choose *local* realism? In fact, if there is one thing that QM seems to point to is intrinsic non-locality. In the standard Copenhagen interpretation, non-locality is hidden in the state vectors but then re-appears in the form of spooky action at a distance, entanglement and all sorts of wonderfully weird bizarreries.
Non locality is “hidden†nowhere in QM. It is trivially apparent already in the introduction (linearity of the Hilbert space). So you would like to choose “non local†realism? Care to define what it means and if you can, how it is relevant to Fidos be they lizards or photons?
Of course there is nothing spooky or weird about QM. There are just ignorant people who won’t learn and find spooky what they don’t understand.. After a certain time one has to conclude that they can’t be helped.
The most that invoking Bell inequalities or other no-go theorems can give you is that *physical theories*, whose job is to explain and predict the outcomes of *experiments*, cannot have local hidden variables. Making the leap to metaphysical statements about the very nature of reality is unwarranted without further argumentation. This is an elementary point
This is indeed an elementary point. You achieve a feat to be amusing and thick at the same time. The only way to know something about the reality is to make a measure. In the second stage one makes a model, preferably mathematical. There are only 2 constraints – it must be logically consistent what the correct use of mathematics normally guarantees and it must not contradict measures. You didn’t understand my point – I make no “leaps†to some very “natures†of the reality – this is something that you did. I make statements about models which contradict measures. And I have shown that your model is trivially falsified when one replaces lizards by photons and greenness by spinupness. But if your model is wrong for photons, electrons, atoms etc which are demonstrably elements of the measured reality, why should it make sense for anything? Indeed there is no reason and this is an elementary point.
You find philosophy amusing and irrelevant to understanding the universe, and yet you have no qualms making metaphysical claims about the nature of reality based on naive reading offs of the *physical theories*. The debate, while certainly informed by the discoveries of physicists is eminently a philosophical debate. That you are not even aware of this is very telling.
Also handicapped by reading difficulties?. I wrote : “Now I find this kind of philosophical dissertations amusing as long as they don’t pretend to contribute anything relevantâ€.
To spell it out for you – it is your kind of musing that I find irrelevant. The rest of your comment is a red herring and you just waste our time.
. It is an illegitimate move to go from an *epistemic* *operationally-descriptive* vision of reality to the imposition of an ontological status on said reality.
Another red herring – it seems to be your specialty. It is you who clumsily tried to impose an ontological status on the reality. I merely commented that this particular attempt contradicts both the QM theory (model) and the measure. Some of the lesser philosophers try to evade their errors by denying the relevance of measures and for some even of science as a way to construct operating and predictive models. If any ontological model contradicts an experiment then it is garbage regardless of how often one yells that it is “ontologicalâ€.
3. There are several ways to rationalize no-go theorems like the Bell inequalities.
b) Non-local causes.
As the quantum entanglement is non local anyway, I guess that this means Bohm’s theory. This belongs to the same category as Everett e.g undecidable. See http://arxiv.org/pdf/quant-ph/9812059v2.pdf
There are more solutions from the purely physics theory side. But either they are completely mad (many-worlds interpretation)
The MWT has nothing “madâ€. It is perfectly consistent and obtains the same results as QM. If I inclined to using jargon (what I don’t) I could follow by an overblown phrase about the ontological status of MWT. But like Bohm’s theory it is undecidable by definition.
I do not understand them (transactional interpretation)
TIQM is sponsored only by one person and as its name suggests, it is not a theory but an interpretation. So it belongs to the same category as MWT. I have not read more than the Cramer’s paper about TIQM (it is based on the idea that the wave function is a sum of an advanced and retarded wave) . It can apparently deal only with 1 particle and could probably be shown wrong but nobody bothers to spend time with it.
c) Following the paragraph just preceding 3, posit a cause that cannot be described in mathematical terms. The cause in question could still be local, natural and real, but just not describable by mathematical formalisms, and concomitantly by the empirical sciences.
Sure ïŠ If you were able to express simple ideas simply, you could have said that much shorter : “Voodoo is also an interpretation that I find acceptable.†After all why not? That’s about the level of your post.
There is an infinity of logically consistent interpretations of QM and anybody can invent his own. They either are undecidable (like MWT) or wrong.
So while we are waiting on something more convincing than Bohm on non local variables and nobody thinks seriously that it will ever come, it stays that the only correctly formulated realism is the one which has already been falsified.
Clearly “Photon Fido is spinup†is a statement that doesn’t make sense before measure regardless the model used, be it ontological. And the same extends to your pedantic and wordy beating of this dead horse.
@TomVonk:
You persist in making the mistake that realism as concerning the interpretation of QM has anything to do with realism as discussed in the OP. It has not.
There is a thing as quantum gravity apart from the specific models that implement it, be they loop quantum gravity, string theory, causal sets, non-commutative geometry or what have you. It is in the former sense I was using the word “expert” and I stick by my qualifications. Isham has not written about LQG in a while; if his more recent work will pan out or not, I cannot say. If I invoked him was simply to point out that the issue of realism is not closed.
As far as Lorentz invariance, you may be referring to distinct phenomena so I will make a guess. In general, there is no global Lorentz invariance in general relativity and therefore, no such global Lorentz invariance in LQG. However, there is a local Lorentz invariance in classical general relativity and likewise in covariant LQG, where it is possible to show that the transition amplitudes are Lorentz invariant under local Lorentz transformations. Either way this is a technical debate that I am not competent to judge, so if you tell me that the deal has been sealed, I can believe you; it is irrelevant to what I said.
While I do not doubt the expertise of the names you mention (Witten is a big name in mathematics), it is something of a moot point. The fact is that there is no complete, consistent quantum theory of gravity, all the candidate models need to overcome major technical and conceptual problems, and while phenomenological considerations (usually coming from astrophysical data) do impose bounds on the possible range of theories the fact is that they are not sufficient to rule the models wholesale.
You mean relevant to the subject of the OP? As I have said several times already, it is not, but it was you who dragged QM into the thread. While I disagree with non-realist interpretations of QM (even more specifically, with alleged violations of the principle of causality), the issue is orthogonal to the problem of universals.
It is indeed an elementary point. For if you were correct, then to know that the claim “The only way to know something about the reality is to make a measure” is true, you have to give some sport of evidence. By the nature of the claim, that evidence must consist in a measurement. So do you have any measurement to back your claim? If you say you do not need a measurement, then you recognize that not all claims about reality can be decided by empirical means and that your claim in particular is false.
My “model”? For the umpteenth time, realism about universals is orthogonal to the realism controversy, to call it that, about QM. As far as realism, as the word is understood when talking about the controversies surrounding QM, no you have not “falsified” anything — the very word “falsified” is the wrong approach to the problem anyway. Not that considerations from physics are not important, but that of and by themselves, they cannot settle the issue because the issue is at bottom a philosophical one.
In order for my realist “attempt” (which to repeat, has nothing to do with realism about universals and is only concerned with claims concerning alleged QM violations of the principle of causality and anti-realist interpretations of it), which I have barely spelled out, to be judged in direct contradiction of QM you would have to do a few things like define what is causality writ large, that the physical theory of QM does entail such a non-realist take on the nature of reality (which is the point I made, not a red herring), etc. You have not done that. In fact, I suspect you have not got the faintest idea of what I am talking about — and at this point you probably say that I am saying nothing worth listening to. That may be true, in which case I am sure I will hear no response from you.
No it is not voodoo, but philosophy. But methinks you do not know the difference.
@Rembie
Let me give an example. It has been claimed that Universals are in the mind of God (according to wikipedia, it was Proclus who said that). People who do not want a God, any kind of God, are bound dismiss the Universals because of such a statement. Already Plato’s claims of a separate world are hard to stomach.
Besides, such a world is not necessary. We get all the attributes of the universals if they are a construct of our minds. Things do not get more greenness if greenness is also outside our minds. Universals are not a better explanation if they are also outside our minds. Being in our minds is all that is necessary to be a universal.