'Does reality contain universal features as well as particular entities?' — Wayfarer

The answer seems obvious; if reality "contains" "particular entities" then it must contain entities. In order to qualify as entities they must share common characteristics, i.e. "universal features".

Quod erat demonstrandum...case closed!

On the other hand is the question asking whether reality contains particular entities and universal features independently of us? Because it is obvious that at least for us, in terms of our experience and understanding,reality contains both of these; and this doesn't seem to be subject to argument. If the question is meant to address the nature of absolute reality, and the answer is "yes" then it is simply positing realism.

Quod erat demonstrandum...case closed! — Janus

That quote you attributed to me, was not my words or my expression. It is the way that the summary of the course put the issue of the question of ‘the reality of universals’. In my view the reality of numbers, principles, natural laws, and the like, is part of that question. And I maintain that number is real, but not physical. So the case is by no means closed.

The wording is irrelevant. You have focused on that instead of addressing any of the points or questions I raised. Oh well...

What’s your view on the debate between realism and nominalism in medieval philosophy? What effect do you think it’s had on subsequent philosophical thought?

I think that, for example, that the Pythagorean theorem describes something that is real whether or not perceived by humans. However it is is something that can only be grasped by a rational intelligence. So that is an example of an 'intelligible principle', i.e. something which is expressible in terms of a mathematical formulae; but that feature is not 'created by humans', only the notation is a human creation. — Wayfarer

The problem is that there aren't any right angle triangles except those created by human beings. So it doesn't really make any sense to say that The Pythagorean theorem describes something that is real whether or not perceived by humans, because the terms within the theorem refer to things only created by humans. So it is not correct to say that this feature is not created by humans.

The same is the case for pi, and circles. A cirtcle, as well as pi, are concepts created by humans. There are no naturally occurring circles, and that's why pi is an irrational ratio. All of these are concepts, are created by human beings, and are used to assist human beings in understanding the various natural features. They are tools, built by human beings. They are understood as absolutes, ideals, perfections, but without the human mind they have no existence because there is nothing natural that they refer to.

You claim that they describe something which is real, but there is nothing that they describe except themselves, and without the human mind, there is nothing there. The Pythagorean theorem, "the square of the hypotenuse is equal to the sum of the squares of the other two sides, of a right angled triangle" describes nothing but the Pythagorean theorem. Without that statement, which is produced by human beings, there is no Pythagorean theorem, and nothing which "the Pythagorean theorem" refers to.

This is a wide-ranging debate. I can only express my view on specifics. I really would much rather just discuss the ideas in our own words without reference to medieval debates.

Are you defining nominalism as the rejection of abstract objects or the rejection of universals, or of both?

The problem is that there aren't any right angle triangles except those created by human beings. — Metaphysician Undercover

Were any other species of beings - non human but sentient - to evolve on some other planet, then I'm sure they would discover the same thing.

Are you defining nominalism as the rejection of abstract objects or the rejection of universals, or of both? — Janus

Well, when you asked me to name 'two examples of philosophers for whom the reality of universals is important', I provided two sources: one, this Oxford external course I have mentioned, Being, Existence and Time, which has a whole section on the question. (Regrettably the way they have described the debate uses what I now consider to be an inadequate description of the topic. I am tossing up enrolling for January, but it is $500.00 and probably not even tax deductible :-d )

The other was Edward Feser, who as you may know has become quite a popular philosopher in the last few years on the strength of his various publications about Aquinas, Thomist philosophy, his refutations of the new atheists and his blog. It was a blog article of his on the concept of the triangle which started this debate. His summaries and presentations of these types of questions are very useful in my opinion.

But the topic of the nature of universals is by no means settled, in fact it was the inability to settle such debates which is one of the reasons that modern philosophy tended to reject the whole question - as if regarding it as settled, when it's not. Note, for instance, earlier on in this thread, I referred to a scientific paper which explicitly invokes the Aristotelean concept of potentia in relation to quantum physics.

The reason it's necessary to talk about it in historical terms, is because it's an underlying factor in our whole current world-view. We are all the children of nominalism - to all intents they won the debate, and 'history is written by the victors'. There are wholly different ways of understanding, which in turn give rise to a different way of seeing the world:

Thomists and other critics of Ockham [the major source of nominalism] have tended to present traditional realism, with its forms or natures, as the solution to the modern problem of knowledge. It seems to me that it does not quite get to the heart of the matter. A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.

WHAT’S WRONG WITH OCKHAM? Reassessing the Role of Nominalism in the Dissolution of the West, Hothschild, Anamnesis Journal.

Much of the anguished existentialist atheism of the 20th century, about the purportedly scientific understanding that the Universe is devoid of causality, can be traced back to that development:

Like Macbeth, Western man made an evil decision, which has become the efficient and final cause of other evil decisions. Have we forgotten our encounter with the witches on the heath? It occurred in the late fourteenth century, and what the witches said to the protagonist of this drama was that man could realize himself more fully if he would only abandon his belief in the existence of transcendentals. The powers of darkness were working subtly, as always, and they couched this proposition in the seemingly innocent form of an attack upon universals. The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence.

Richard Weaver, Ideas have Consequences

What lead me to this, was an analysis of how scientific materialism came to be the dominant worldview in the West. So the question of the immaterial nature of number and the reality of universals came out of that analysis. That's why I keep harking back to the historical development - it is a question which is simply not understandable in the frame of reference of the 'modern worldview'.

That is why, also, many of the proponents of such philosophies are reactionary. I don't consider myself reactionary, but I really do understand their rationale.

Were any other species of beings - non human but sentient - to evolve on some other planet, then I'm sure they would discover the same thing. — Wayfarer

That's highly doubtful. The other species might develop a system based on forty five degree angles instead of ninety. Or, the species might not even use the circle as the basis for geometry, it could start with the chiliagon for example, instead, and never develop any of the circle based geometry which we use. There are many different possibilities for conceptual structure, depending on what the species is exposed to, and what becomes important to it. Even here on the earth, there are differing world view.

Perhaps the species wouldn't even live on a planet which is spinning like ours. The observations of the stars, planets, and sun, from the perspective of the spinning earth, lead to the circle based geometry which we use. To say that another species, living in another part of the universe, would develop a geometry like ours, is like saying that ants, or bees should develop a geometry like ours. There's just no reason to believe this. We all like to think that our understanding of reality is "the" understanding of reality, but this is just vain conceit.

We all like to think that our understanding of reality is "the" understanding of reality, but this is just vain conceit. — Metaphysician Undercover

And if your diagnosis is correct, so is everything that used to be described under the heading of philosophy.

And I maintain that number is real, but not physical. — Wayfarer

You keep making statements that are confusing (and then don't have the stamina to back them up). What does it mean for something to be real but not "physical"? Why use that term, "physical", anyway? Numbers are real because they have an effect on other things, including on what many call "physical" and "mental". So it seems that numbers would either be both "physical" AND "mental", or we should just dispense with these two terms and talk about causation.

No, philosophy is to seek answers, to inquire, it is not to claim that we already have the answers. This is the problem with what you profess, and why it is a false representation of Platonism. If our concepts, what we supposedly "discover", are the way that they must be, because they are some type of independent form, then there is no room for error, it is impossible that our concepts are incorrect. This is the problem which Plato exposed in the Parmenidean, Eleatic, and Pythagorean principles, in general. This ontology of Idealism does not allow for the existence of error within human knowledge. "Knowing is being", what is known is what is. This is exactly what Socrates and Plato rallied against. So you have taken Plato's discussions, and demonstrations which expose the problems of such Idealism, and claim that this is what Plato actually promoted.

In Plato's dialogues, Socrates attacked this relentlessly, and over the course of many dialogues the weakness was exposed. It was exposed through reference to more subjective concepts, the various virtues. It was demonstrated that there is no consistency in these concepts, so it is impossible that the human being's concept is a participation in an independent Idea, because the human being's concept, with its individual idiosyncrasies, and variances, would necessarily be wrong in relation to the independent Idea, and therefore could not be a participation. Once this principle, concerning the nature of human concepts is established, the possibility that they are incorrect (or more precisely, that they are not the best, not perfect), can be extended right into the various mathematical principles, as Aristotle did. What is known, is not necessarily what "is", it is a possibility (one way of looking at things out of many possible ways). This forms the basis of skepticism. Then "the concept", "the idea", is a changing, evolving thing, created by human beings. It is not "discovered", and it can be doubted.

As an example, consider the evolution of the concept of "zero", its relevance to the modern day "equation", "algebra", "possible values", and "possible solutions". The zero, along with the negative integers allow for a possible existence. But the possible existence has no reality accept as posited by a human mind. Mathematics in general uses postulates, axioms, which the human mind must accept as real (like we must accept a premise as true), in order to proceed with the logical process, without regard for the fact that the postulate is itself just something created by human minds. Over time, the postulates change and evolve.

I hoist a flag that means "three-masted ship". You see the flag and write down "three-masted ship". Because i can convey the idea of a three-masted ship with a flag and you can write down the idea of a three-masted ship with ink, the idea of a three-masted ship is not physical. The flag and the marks in ink on paper are physical representations of something, an idea, that is not itself physical. This is the argument, yes?

If I draw a picture of my house, the picture is a physical representation of a physical object. If I draw another picture of my house, I have another physical representation of the same physical object. Having two distinct physical representations of something does not entail that what is represented is not itself physical, not even if those representations are dissimilar in some way, if, say, I use pencil for one drawing and charcoal for the other, of if one is a drawing and the other a photograph.

So, in your argument, it is not that there are multiple representations in different media that leads to the conclusion that what is represented is not physical; it is that what is represented is said to be an idea, not a particular three-masted ship, but a generic object, any member of the class "three-masted ships".

Thus in your scenario I am not conveying a single piece of information, but at least two: by hoisting a flag at all, any flag, I indicate that some object exists; by hoisting the particular flag I do, I indicate that the object is a member of a particular class. More particularly, flags indicate ships, and even more particularly, ships that I can see. I am not to raise a flag hypothetically.

Is the raising of a flag a physical representation of a ship the way a drawing I might make would be a physical representation of my house? Well, it's not a picture of the ship. If anything, it seems more natural to take it as a representation of my state of seeing-a-ship. Is it a picture of that? Hmm. It would seem not. Is it a representation at all? Well, it's certainly a symbol: my hoisting a flag indicates that I am in such a state. I don't think that's exactly what we usually mean by "representation", but I suppose we could make that work by defining our terms suitably.

What hoisting a flag has in common with hoisting a particular flag is that it too is generic: I do not have a flag for each particular ship I might see, and hoisting a flag does not indicate that I am seeing some particular ship, but that I am seeing some ship or other, again, a generic member of the class "ships". Similarly, I am in the state of seeing a particular ship, but what I indicate is that my state is a member of this class, seeing some member of the class "ships".

Thus my flag hoisting conveys two claims of class membership: one about my state, and one about the object that brought about that state. Agreed?

Abstracted things are artificial, and decided upon too. What else, other than a human mind would perform the act of abstraction, and whether the abstraction is correct or not, is decided upon by the human mind as well. — Metaphysician Undercover

I thought we agreed that the input cannot come from the same place as the output, and that we cannot conceive simple concepts we have not yet observed, as was the case for the blind person not conceiving colours, a deaf person not conceiving sound, and an emotionless person not conceiving sadness. I accept that the abstraction process is happening in the mind, but the input must come from outside. Or else, how would we test that what I conceive as green is the same as what you conceive as green, if not by both of us observing the same colour located outside of our minds?

I don't get this at all. We do not recognize a concept within things. The concept is within the mind, and when we apprehend a thing as meeting the conditions of the concept, we feel justified in calling the thing by the name which corresponds to that concept. — Metaphysician Undercover

I'm not sure I understand your distinction between "recognizing a concept within things" and "apprehending a thing as meeting the conditions of the concept". If we apprehend a particular object which has a flat surface with three straight sides, then we recognize a triangle in that object. And if our perceptions are true, then the object truly has triangle-ness as part of it.

Our concepts can be compared if we find their essential properties, based on our implicit knowledge of them. E.g. my concept of triangle-ness has the following essential properties: 'flat surface' and 'three straight sides'. If yours has the same essential properties, then this proves they are the same.

Finding the essence of concepts from our implicit knowledge of them is basically what Socrates did in Plato's dialogues, sometimes successfully; and this method presupposes that concepts are the same in everyone.

I thought we agreed that the input cannot come from the same place as the output, and that we cannot conceive simple concepts we have not yet observed, as was the case for the blind person not conceiving colours, a deaf person not conceiving sound, and an emotionless person not conceiving sadness. I accept that the abstraction process is happening in the mind, but the input must come from outside. Or else, how would we test that what I conceive as green is the same as what you conceive as green, if not by both of us observing the same colour located outside of our minds? — Samuel Lacrampe

I agreed that the input could come from outside the mind. I see no reason to believe that it necessarily does, nor do I see reason to believe that all of the input comes from outside the mind. As for your test, it's as I told you, a matter of whether or not we agree, and often we do not. As I told you, I often disagree with people as to the colour of something. So your test, and the fact that we often disagree about things, indicates that input must come from within the mind as well.

If we apprehend a particular object which has a flat surface with three straight sides, then we recognize a triangle in that object. And if our perceptions are true, then the object truly has triangle-ness as part of it. — Samuel Lacrampe

I still do not understand your use of English. I would not say that I recognize a triangle in the three sided object, I would say that I recognize the three sided object as a triangle. Do you see the difference? I recognize a certain object as a car, or another object as a house, meaning that for me these objects fulfil the conditions required for calling them by those names. I do not see the concept of a car, or the concept of a house within these objects. I think that you are using contrived English to support your position that the concept is within the physical thing, rather than within the mind of the observer.

You keep making statements that are confusing — Harry Hindu

The significance of something being 'real but not physical', is that if there are things which are real but not physical, then physicalism is false. As physicalism is the de facto philosophical attitude of today's secular intelligentsia, then this is significant.

And, numbers don’t cause anything. Not unless, say, you walked under a clock-tower at the precise time the numeral 7 fell off the clock-face and landed on your head. But, facetiousness aside, the ontological question concerning number is not whether numbers are materially efficient; I don't see how they can be. The question is about whether they're real and not simply the products of brains, as we are inclined to think.

***

If our concepts, what we supposedly "discover", are the way that they must be, because they are some type of independent form, then there is no room for error, it is impossible that our concepts are incorrect. — Metaphysician Undercover

My understanding is, there is plenty of room for error - we may fail to comprehend or see the Forms. 'The discerning of the forms by reason' is basic to Platonism, right?

What you're not seeing is the Platonic and Aristotelian notion of 'intelligibility'. I'm really not wanting to sound pedantic, as I'm well aware that I too am a rank amateur in this business. But it seems to me, you have only a partial grasp of the basics of Platonic epistemology. Have a look at the Wikipedia entry on the intelligible form. It starts with the assertion:

The concept of the form as being what makes knowledge possible dates back to the time of Socrates.

This is because, as you should know, Plato's Socrates questions the reliability of the senses; knowledge of sensory objects is pistis, or doxa; knowledge of mathematical and geometrical objects is dianoia; knowledge of the forms, noesis. The 'higher' you go, the more certain is knowledge - knowledge of math. is 'higher' than knowledge of material things, knowledge of the Forms is 'higher' than knowledge of math. This is in the Analogy of the Divided Line.

But nothing in Plato casts the 'knowledge of the forms' into doubt. What they are, and the manner of their existence, is, of course, a matter of huge debate.

***

This is the argument, yes? — Srap Tasmaner

Yes.

So, in your argument, it is not that there are multiple representations in different media that leads to the conclusion that what is represented is not physical; it is that what is represented is said to be an idea, not a particular three-masted ship, but a generic object, any member of the class "three-masted ships". — Srap Tasmaner

Yes, very good. That's getting close to what I think is the meaning of an idea or an abstract universal. Your use of 'generic' is significant, because the word itself actually evolved from the Platonist tradition in Western thought - 'genera' being a species or type, so one level of abstraction. I think it was the Platonic and especially Aristotelean tendency to 'classify by type' that gave rise to the whole idea of taxonomy which is basic to science itself. But, I digress.

If I draw a picture of my house, the picture is a physical representation of a physical object. — Srap Tasmaner

I wonder, again, how accurate it is to describe it as 'physical' . It's a representation, which you or I understand as 'a depiction of a house'. If I showed it to my dog here, the dog would sniff it to see if it's something to eat, otherwise would have no interest. Your mind is able to infer that the drawing represents a house and to impute meaning to the drawing - 'this particular house'. So the salient point, again, is that the drawing could be an architectural drawing, an impressionist oil-painting, or a sketch, but you will say 'it's a house' because you have the kind of intelligence that is able to impute that resemblance. That's the work of what Aristotle called 'the active intellect'.

Well, it's certainly a symbol: my hoisting a flag indicates that I am in such a state. I don't think that's exactly what we usually mean by "representation", but I suppose we could make that work by defining our terms suitably. — Srap Tasmaner

It is indeed a symbol or a sign. Hence the link with semiotics.

Overall, I'm in agreement with your analysis. What I'm trying to hone in on is, what faculty performs these transformations of meaning. On the one hand, it's obviously the role of intelligence, which seems simple enough - but, again, is intelligence something that is describable in physical terms, as Steve Pinker wishes to do in the quote I provided from his 'How the Mind Works'? (materialist philosopher that he is)

What I'm working towards, is the argument that the same principle applies on the neurological level as well as the representational; that meaning in a general sense, can't simply be equated with neurological activity, as 'neurological reductionism' assumes it must be.

****
Here's an encyclopedia entry on Platonic realism with some comments by me.

Platonic Realism is the view, articulated by Plato, that universals exist. ¹ A universal is a property of an object, which can exist in more than one place at the same time (e.g. the quality of "redness") ². As universals were considered by Plato to be ideal forms, this stance is also called Platonic Idealism, whereas in medieval philosophy, it was called 'realism'.

The problem of universals is an ancient problem (introduced by Pre-Socratic philosophers like Thales, Heraclitus and Parmenides) about what is signified by common nouns and adjectives, such as "man", "tree", "white", etc. What is the logical and existential status of the type that these words refer to? Is it in fact a thing, or a concept?³ Is it something existing in reality, external to the mind, or not? if so, then is it something physical or something abstract? Is it separate from material objects, or a part of them in some way? How can one thing in general be many things in particular?

Plato's solution is that universals do indeed exist, although not in the same way that ordinary physical objects exist, but in a sort of ghostly mode of existence, outside of space and time, but not at any spatial or temporal distance from people's bodies⁴. Thus, people cannot see or otherwise come into sensory contact with universals, and it is meaningless to apply the categories of space and time to them, but they can nevertheless be conceived of and exist.

1. 'Exists' is a misleading word in this context. Here is a passage from Russell's Problems of Philosophy that explains why:

Consider such a proposition as "Edinburgh is north of London." Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. When we come to know that Edinburgh is north of London, we come to know something which has to do only with Edinburgh and London: we do not cause the truth of the proposition by coming to know it, on the contrary we merely apprehend a fact which was there before we knew it. The part of the earth's surface where Edinburgh stands would be north of the part where London stands, even if there were no human being to know about north and south, and even if there were no minds at all in the universe. This is, of course, denied by many philosophers, either for Berkeley's reasons or for Kant's. But we have already considered these reasons, and decided that they are inadequate. We may therefore now assume it to be true that nothing mental is presupposed in the fact that Edinburgh is north of London. But this fact involves the relation "north of," which is a universal; and it would be impossible for the whole fact to involve nothing mental if the relation "north of," which is a constituent part of the fact, did involve anything mental. Hence we must admit that the relation, like the terms it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends but does not create.

Notice use of the word 'subsists' (underlined above). This is much more accurate for universals than 'exists'. Note that 'thought apprehends but does not create' - however it is the action of what Aristotle calls 'the active intellect' to 'apprehend'; that act 'creates' the 'meaning-world' which is to all intents 'the world' (c.f. Wittgenstein 'I am my world'.)

2. 'Exist in two places at once' - again, misleading - it's more that individual particulars instantiate these attributes. They're not spatially distributed.

3. It is not 'a thing' and it precedes 'concepts', because it is what concepts must assume if they are to be able to be formed (I think that's where Kant comes into the picture).

4. The 'existing in a ghostly or ethereal domain' is the entire problem and error of the understanding of forms, in a nutshell. This is what almost anyone thinks nowadays, and then rejects the idea on the basis of this poorly-formed understanding. Universals don't exist - that's why they're called 'transcendental', they're logically prior to 'what exists'. But, they're real, in a way that phenomenal objects are not. The 'ghostly domain' that is misleadingly named here, is sometimes referred to as the 'formal realm' - it's not actually 'a realm', but a domain, like 'the domain of natural numbers'. But it's the 'domain of form', namely, that of numbers, possibles, universals, and so on, that in some sense is logically prior to the 'phenomenal realm'.

The problem is, we've been acculturated to a form of naturalism whereby only things that exist in space and time are real to us.

Augustine on Intelligible Objects

Analogy of the Divided Line.

My understanding is, there is plenty of room for error - we may fail to comprehend or see the Forms. — Wayfarer

But this is not what you have claimed in reference to the Pythagorean theorem. You said that any mind would discover the same principle, or concept. This not only denies the possibility of error, it denies the possibility that there could be a better way of rendering what is expressed by the theorem, in a similar, but different principle.

My point is that we need to allow a separation between human concepts, and the Ideals, which are supposed to be independent from the human mind. That is the conclusion which Plato came to in "The Republic" There is the idea of a bed which the carpenter holds, and follows in producing a bed, but this is intended to be a representation of the divine Idea of a bed. So there is always a separation between human concepts, and the divine, independent Forms. The human concept can only obtain to the level of being a representation of the divine Idea, it is never the independent Form. What you need to respect, is that when we talk about mathematical principles, like the Pythagorean theorem, these are human concepts. As much as they may be intended as representations of divine Ideas, they are not divine Ideas, they are human concepts, and as such they are dependent on the flesh and bones of the human body. This is a point which Aquinas was very insistent on. The fact that human knowledge, ideas and concepts, are dependent on the material body of the human being, is what separates human knowledge from divine Forms.

This is because, as you should know, Plato's Socrates questions the reliability of the senses; knowledge of sensory objects is pistis, or doxa; knowledge of mathematical and geometrical objects is dianoia; knowledge of the forms, noesis. The 'higher' you go, the more certain is knowledge - knowledge of math. is 'higher' than knowledge of material things, knowledge of the Forms is 'higher' than knowledge of math. This is in the Analogy of the Divided Line. — Wayfarer

Yes, I fully understand this hierarchy of knowledge. Notice that knowledge obtained from mathematics is not the highest level of knowledge. That is because even mathematical principles are lacking in perfection. They are deficient because they are produced by human beings and are thus dependent on the material body of the human being. Mathematical principles are not true "Ideals" in the sense of independent Forms, they are human concepts and therefore do not obtain to the highest good, perfection.

Knowledge of the Forms is even higher than mathematical knowledge, because this is what gives us an understanding of the separation between human concepts and the divine Forms. Through this knowledge we come to understand the deficiencies of even mathematical knowledge. That is why it's a higher knowledge than mathematical knowledge, because only this knowledge can point to the errors in mathematical knowledge. The deficiencies, errors, are due to the nature of the human being, it is imperfect, dependent on a material body, but the deficiencies can only be discovered by allowing for a perfection which can only be found in independent Forms.

My point is that we need to allow a separation between human concepts, and the Ideals, which are supposed to be independent from the human mind. That is the conclusion which Plato came to in "The Republic" — Metaphysician Undercover

That is completely mistaken. The principle of intelligibility in ancient philosophy, was based on the exact opposite of what you’re saying.

They are deficient because they are produced by human beings and are thus dependent on the material body of the human being. — Metaphysician Undercover

This is not true at all. No Platonist would ever say that. You're instinctively modernist in your responses. The idea that mathematics could be 'the product of a brain' would never occur to Plato or Aristotle. Nor the idea that mathematics was something 'created by humans'.

Listen to this lecture from 38:40 up till 40:16 - pay special attention to the phrase ‘thinking is the Identity of the intellect with this intelligible'.



'Literally, you could not think if materialism was true.'

My argument exactly.

I agreed that the input could come from outside the mind. I see no reason to believe that it necessarily does, nor do I see reason to believe that all of the input comes from outside the mind. — Metaphysician Undercover

I think you are correct about not all concepts coming from outside the mind. Just because I have a concept of a unicorn, it does not follow that unicorns exist outside the mind (sadly). Only 'simple impressions' as Hume says, like colours, sounds, and basic shapes, must exist outside the mind.

As for your test, it's as I told you, a matter of whether or not we agree, and often we do not. As I told you, I often disagree with people as to the colour of something. So your test, and the fact that we often disagree about things, indicates that input must come from within the mind as well. — Metaphysician Undercover

Yes... We are back to that special case when perceptions of objects are false. But if we assume that the perceptions are true (I don't think this is a stretch), then the test would work, would it not? You and I observe a ball and both agree that it has roundness. Conversely, you and I observe a cube and both agree that it does not have roundness.

I still do not understand your use of English. I would not say that I recognize a triangle in the three sided object, I would say that I recognize the three sided object as a triangle. Do you see the difference? I recognize a certain object as a car, or another object as a house, meaning that for me these objects fulfil the conditions required for calling them by those names. I do not see the concept of a car, or the concept of a house within these objects. — Metaphysician Undercover

Honestly, I don't see a difference. The concept of X is by definition composed of all and only those properties essential to X. If you recognize a certain object as a car (again assuming no false perceptions), then some of the properties of that object must be essential to the concept of a car; or else, you would not recognize it as such. And if so, then the object has the concept of a car, by definition.

Saying the same thing with math:
Let concept X = A+B
Let observed object Y = A+B+C
Therefore Y = (A+B)+C = X+C

That is completely mistaken. The principle of intelligibility in ancient philosophy, was based on the exact opposite of what you’re saying. — Wayfarer

I guess I don't know what you mean by "the principle of intelligibility". It is not found in any ancient philosophy. There is much concern in ancient philosophy with intelligible objects, in contrast with visible objects, but I think that you mean something different than this when you say "the principle of intelligibility".

This is not true at all. No Platonist would ever say that. You're instinctively modernist in your responses. — Wayfarer

You ought to read some Thomas Aquinas, he is very insistent on this point. Human concepts are not independent Forms, because they are dependent on the human being which has a material body. Independent Forms are immaterial, and not dependent on a material body like human ideas are. This is a principle derived from Aristotle's cosmological argument.

The idea that mathematics could be 'the product of a brain' would never occur to Plato or Aristotle. — Wayfarer

Actually, this is the fundamental consequence of Aristotle's cosmological argument, where he firmly refutes Pythagorean Idealism in Bk. 9 of his Metaphysics. If ideas exist prior to being "discovered" by the human mind, they are eternal. But prior to being discovered, their existence could only be as "potential", because being discovered is what gives them "actual" existence. Being discovered actualizes them. However, according to the cosmological argument, it is impossible that any potential could be eternal. Therefore it is impossible that human concepts are "discovered". So they must be created by the human being. Aquinas expounds on this principle, explaining the difference between divine Forms, which are properly independent, separate, and immaterial, and human ideas which are not separate Forms, because the human soul is united with a material body, making it impossible for the human being to possess any immaterial Forms. Any ideas or concepts which the human being holds, are necessarily imperfect, i.e. not immaterial, because the human being is dependent on a material body, and so are the human being's concepts. This is stated very clearly in The Summa Theologica.

That is completely mistaken.
...
This is not true at all. — Wayfarer

I really don't care if you want to insist that what I say is mistaken, and not true. I've read the material, primary sources, and you obviously have not, relying on hearsay. However, you strike me as a person who is very interested in this subject, so I am bringing this to your attention in order that you might research and learn about these principles. This will open your eyes to a whole new way of seeing the Forms. It is what they call "seeing the light", from Plato's analogy between the good and the sun. The good is what makes intelligible objects intelligible, just like the sun is what makes visible objects visible. Perhaps this is what you mean by the principle of intelligibility.

4. The 'existing in a ghostly or ethereal domain' is the entire problem and error of the understanding of forms, in a nutshell. This is what almost anyone thinks nowadays, and then rejects the idea on the basis of this poorly-formed understanding. Universals don't exist - that's why they're called 'transcendental', they're logically prior to 'what exists'. But, they're real, in a way that phenomenal objects are not. The 'ghostly domain' that is misleadingly named here, is sometimes referred to as the 'formal realm' - it's not actually 'a realm', but a domain, like 'the domain of natural numbers'. But it's the 'domain of form', namely, that of numbers, possibles, universals, and so on, that in some sense is logically prior to the 'phenomenal realm'. — Wayfarer

Part of the "ghostly existence" problem is the issue of logical priority. I think Russell's example that Edinburgh is north of London shows that the particulars are prior to the universal (the relation in this case).

The "is north of" relation is simply the logical consequence of London and Edinburgh being located where they are in a physical world with poles. Without those particulars, no logical consequence follows and so there is no relation.

As Russell points out the relation obtains independent of language and thought, contra Nominalism. But, contra Platonism, the particulars are prior to that relation.

I guess I don't know what you mean by "the principle of intelligibility". — Metaphysician Undercover

Gerson refers to it in the video link I provided, specifically:

Aristotle, in De Anima, argued that thinking in general (which includes knowledge as one kind of thinking) cannot be a property of a body; it cannot, as he put it, 'be blended with a body'. This is because in thinking, the intelligible object or form is present in the intellect, and thinking itself is the identification of the intellect with this intelligible. Among other things, this means that you could not think if materialism is true… . Thinking is not something that is, in principle, like sensing or perceiving; this is because thinking is a universalising activity. This is what this means: when you think, you see - mentally see - a form which could not, in principle, be identical with a particular - including a particular neurological element, a circuit, or a state of a circuit, or a synapse, and so on. This is so because the object of thinking is universal, or the mind is operating universally.

….the fact that in thinking, your mind is identical with the form that it thinks, means (for Aristotle and for all Platonists) that since the form 'thought' is detached from matter, 'mind' is immaterial too.

Whereas you had said:

My point is that we need to allow a separation between human concepts, and the Ideals, which are supposed to be independent from the human mind. — Metaphysician Undercover

So - not independent or separate. That is the specific point at issue.

The "is north of" relation is simply the logical consequence of London and Edinburgh being located where they are in a physical world with poles. Without those particulars, no logical consequence follows and so there is no relation. — Andrew M

Nevertheless, the fact of there being 'north' is not dependent on whether there is a city called 'Edinburgh' or not.

Aristotle...firmly refutes Pythagorean Idealism in Bk. 9 of his Metaphysics. — Metaphysician Undercover

Book 9 of the metaphysics is online here. Kindly indicate where in it Aristotle 'refutes Pythagorean idealism'.

More references on the principle of 'intelligibility':

In philosophy, intelligibility is what can be comprehended by the human mind (in contrast to sense perception). ... Plato referred to the intelligible realm of mathematics, forms, first principles, logical deduction, and the dialectical method. The intelligible realm of thought thinking about thought does not necessarily require any visual images, sensual impressions, and material causes for the contents of mind.

Wikipedia entry 'intelligibility (philosophy)'

An intelligible form in philosophy refers to a form that can be apprehended by the intellect. According to Ancient and Medieval philosophers, the intelligible forms are the things by which we understand.

Wikipedia entry 'intelligible forms'

Nevertheless, the fact of there being 'north' is not dependent on whether there is a city called 'Edinburgh' or not. — Wayfarer

A relation depends on particulars whatever names they may have. For Aristotle, the empirical (or phenomenal) world just is the intelligible world. So you won't find universals prior to or separate from the particulars that they are predicated of.

This is what distinguishes Aristotle's solution to the problem of universals from Plato's.

Book 9 of the metaphysics is online here. Kindly indicate where in it Aristotle 'refutes Pythagorean idealism'. — Wayfarer

It is at Bk. 9, ch. 8 & 9, specifically 1050b, 1051a. It is first argued at 1050b, that actuality is prior to potency, and therefore nothing which exists potentially can be eternal. Imperishable things must be actual. That is the fundamental principle of the cosmological argument. Then at the end of 1050b, into 1051a, he directs his attention specifically toward the Idealists. In ch. 9 (1051a), he argues that the discovery of geometrical constructs is an activity of the geometer. Prior to this, they can only exist potentially. Therefore geometrical constructs cannot be eternal ideas.

Wikipedia entry 'intelligible forms' — Wayfarer

Notice that the "ible" of "intelligible forms", indicates that their nature is that of potential. The cosmological argument clearly indicates that actuality is necessarily prior to potential. That's the issue I continually point out to apokrisis who adheres to a first principle of infinite potential, from Peirce. The cosmological argument effectively refutes both materialism and idealism because both matter and ideas are reduced to having the same nature, that of potential. In modern metaphysics you cannot distinguish between materialism and idealism, because modern physics has reduced matter to ideas ("fields").

The Neo-Platonists, as idealists, get beyond the cosmological argument by assuming active, (actual) Forms. But this is why there develops a categorical separation between these Forms, which in Christianity are the active divine Forms, and human ideas which have the nature of potential. Neo-Platonists like Proclus give an outline for a structure of order within the divine Forms, but Aquinas develops this order much further, under the name of angels.

First, Aquinas expresses very clearly the separation between human ideas, and the divine Forms which are immaterial, as I explained already. Then according to the principles of Plato's Timaeus, in which immaterial Forms have creative power over the material world, Aquinas discusses a hierarchy of angels, which, being immaterial Forms, have providence over the various aspects of the material universe.

Further, notice that in Kant, the thing-in-itself, the noumenon, is said to be an intelligible object. But the human being, because it creates its knowledge through sense perception, phenomena, has no access to that intelligible object. This is another way of representing that separation between human ideas, which are tied to the human body, and the independent, immaterial, Forms,

So we are back at the very same discussion we had before, concerning the intelligibility of God, only approaching it from opposite sides. I said that God, being an intelligible object, is most highly intelligible, but you said that we cannot know God. Remember, I looked up the resolution to this, in Aquinas' "Summa", and he said that God, being an intelligible object, is in essence, most highly knowable. But God is an independent, immaterial Form, and the human intellect is united with, and therefore limited by a material body. So as much as God is most highly intelligible, the human intellect cannot know God while remaining in this state of being united with a body. That expresses the separation between human ideas, and independent Forms.

For Aristotle, the empirical (or phenomenal) world just is the intelligible world. So you won't find universals prior to or separate from the particulars that they are predicated of. — Andrew M

This is the point I brought up earlier. Each material object has a particular form which is unique and proper to that object alone. This comprises Aristotle's law of identity. This line of thought comes out of Plato's later work, "The Timaeus", in which material existence is "informed", through the process by which matter is given a form. In the Platonic, and Neo-Platonic rendition, the form is prior to the material object, and given to the material object by the divine mind, in the act of creation.

I think we have an important distinction here between ideas as universals, which is central to Pythagorean Idealism, as well as Plato's earlier writings, and forms as the forms of particulars, which comes out of Plato's later work. The difference between ideas as universals, and forms as particulars, manifests in an inversion in the way that one object is related to another, depending on whether that object is a universal or a particular.

So in Aristotelian logic, which deals with universals, the more general is said to be "within" the more specific. The concept of "animal" (the more general) is within the concept of "man" (the more specific), as it is within the definition of "man". The essential aspect, "animal", is the more general, and is within the more specific being defined by the more general. The broader is within the narrower. Conversely, in the case of physical objects, i.e. the forms of particulars, we observe that the more particular, the local, is within the less particular, the global. So for example, the form of the earth, as the form of a particular object, is conceived of as within the form of the solar system, as the form of a particular object. The narrower is within the broader.

These two ways in which forms are related to each other, the way that particular forms are related being inverse to the way that universal forms are related, gets very confused and ambiguous in interpretations of quantum mechanics where a clear distinction between the universal and the particular is not maintained. What is accepted as the particular, the particle, is really just a function of the universal, the field, so that the real particular is not at all defined, it has not been assigned an intelligible form.

The significance of something being 'real but not physical', is that if there are things which are real but not physical, then physicalism is false. As physicalism is the de facto philosophical attitude of today's secular intelligentsia, then this is significant. — Wayfarer

I didn't ask about the implications of your statement. I asked what it meant. I asked you why you used to the term, "physical", as it isn't necessary. All we need to do is talk about causation.

If there is some thing that is real, but not physical, that doesn't necessarily mean that there aren't also real things that are physical. The problem then becomes in explaining how these different real things interact. Maybe the problem lies in the making the distinction in the first place. If a physicalist says, "Everything in here is made of the same stuff as out there.", and an idealist says, "Everything out there is made of the same stuff as in here.", it seems to me that they are both saying the same thing. Again, it comes down to causation - the relationship between things "in here" and things "out there".

And, numbers don’t cause anything. Not unless, say, you walked under a clock-tower at the precise time the numeral 7 fell off the clock-face and landed on your head. But, facetiousness aside, the ontological question concerning number is not whether numbers are materially efficient; I don't see how they can be. The question is about whether they're real and not simply the products of brains, as we are inclined to think. — Wayfarer

Of course numbers have a causal effect on things. Take for instance the numbers in a recipe. If the recipe calls for 1 teaspoon of cayenne pepper and you put 10, the food will give the consumers a serious case of heart burn, not to mention mouth-burn. Numbers influence our behavior just as much as any word, law, or thunderstorm does.

It is at Bk. 9, ch. 8 & 9, specifically 1050b, 1051a. It is first argued at 1050b, that actuality is prior to potency, and therefore nothing which exists potentially can be eternal. Imperishable things must be actual. — Metaphysician Undercover

I really don't see any relevance to the topic, nor any ' firm refutation of Pythagorean idealism'. True, he argues that geometric constructs cannot be eternal ideas, but eternal ideas are nowhere denied in Aristotle.

in Aquinas' "Summa", and he said that God, being an intelligible object, is in essence, most highly knowable. — Metaphysician Undercover

It is forbidden in all Christian theology to talk of 'objective knowledge of God' in line with Ex 33:20 'And he said, Thou canst not see my face: for there shall no man see me, and live.'

Of course numbers have a causal effect on things. Take for instance the numbers in a recipe. If the recipe calls for 1 teaspoon of cayenne pepper and you put 10, the food will give the consumers a serious case of heart burn, not to mention mouth-burn. — Harry Hindu

In such cases, numbers are causally efficient only because human agents act on the basis of an instruction. The fact that numbers are able to influence human behaviour, is because humans are rational agents.

I really don't see any relevance to the topic, nor any ' firm refutation of Pythagorean idealism'. True, he argues that geometric constructs cannot be eternal ideas, but eternal ideas are nowhere denied in Aristotle. — Wayfarer

That's correct, eternal Forms are not denied by Aristotle. What is denied is that human ideas are eternal ideas. Now follow through with the simple deduction used by the Neo-Platonists.
P1. (from Aristotle). It is impossible that the mathematical and geometrical principles used by human beings are eternal ideas.
P2. (from Plato) We still apprehend the need to assume eternal Forms (forms outside of, or prior to temporal existence).
C. Therefore the eternal Forms are categorically different from the mathematical and geometrical ideas used by human beings.