Not exactly; when I say that I don't think that either idealism or materialism, per se are more conducive to spirituality I mean that to hold one or the other metaphysical view makes no difference.

Yes, likewise. Actually for me both metaphysical views dovetail nicely into one whole, absent the rhetoric in either which denies something in the other. In fact all this argument about metaphysics we see here is largely irrelevant to me because I have developed my own metaphysic a while ago, which neither comes close to.

What you say agrees, at least in part, with what I have been saying; that idealism and realism are the two sides of a counterfeit coin. I say counterfeit, because I think materialism reifies the object and idealism objectifies the subject, and I think both moves are illegitimate. I mean, both moves are fine for everyday thought and communication, but are not when it comes to making strong metaphysical claims or as establishing foundations for ethics. Actually I am distrustful of strong metaphysical claims altogether. I think metaphysical speculation is great for working out how the mind is capable of thinking about being, experience, thought and all the rest; but should never be taken too seriously.

Yes, metaphysics is always a means of limiting the mind, the imagination. There is an implication that we, humanity, have the capacity to both determine and understand the nature of existence, or something. I know that some folk would say that they build in an acknowledgement of our limitations. But this itself would lead to the realisation that we don't know anything, apart from what we find before us. So limiting again.

For me an understanding of the nature of existence is much more a living and intuitive experience, in which thought, thinking is nothing more than one of a number of tools in my tool kit.

Wouldn't any form, being extended and configured, have to be thought to inhabit some kind of a space, whether its a logical or purely conceptual space, or an actual or perceptual space? — John

No. that's the thing, you are not allowing the form to exist separately from the material object which it is the form of. We know that the form of the object is separable from the matter, because that's what we do in abstraction, when we come to know the object, the form exists in the mind, therefore it must be separable from the material object. The material object is what we know to have spatial existence, we cannot simply assume that the form also has spatial existence, especially since we need some principle whereby the material object itself is different from the form of the object, which can exist in the mind, separate from the object itself.

I don't know what you mean when you suggest that the form could inhabit a "purely conceptual space". We conceive of space as a necessary condition for the existence of material objects. The concept of "space" is the means by which we understand the object's existence, so we can conclude that space (real space) is necessary for the object's existence. Space is what all material objects have in common. We do the same thing with "time" and change. We produce the concept of time to understand changes to the object, so we can conclude that time (real time) is necessary for change. Time is what all changes have in common.

When we look at concepts, especially pure concepts, such as mathematical, we see unity and order as the fundamental principles which represent space and time respectively. Unity though, in its fundamental form, does not require spatial extension. We can conceive of a non-spatial point, as a single unit. That conceptual point does not require space for its existence in conceptual form. It is only when we utilize the point, to position the point within a spatial realm, that it becomes related to space. So the point, as a single, non-dimensional unit, is completely free from space, and this is why it is so versatile as a spatial implement. It also demonstrates that the concept need not inhabit a "conceptual space". The conceptual point is free from space, in an absolute sense. In fact, there are many ways to demonstrate that the non-dimensional, conceptual point, is fundamentally incompatible with space. These involve the problems with infinite divisibility, Zeno's paradoxes, the irrational nature of pi, and such issues. No amount of dividing space can give us the non-dimensional point, nor can any amount of non-dimensional points accumulate to produce a line. Each non-dimensional point adds absolutely zero in spatial extension.

Next, we have order, and order is a temporally based concept. We can have a succession of non-dimensional points, separated by time, and count them, one, two, three, and so on. Now we have the non-spatial unit, the point, with temporal extension, such that there is not a line, in the sense of a two dimensional, spatial line, but a succession of points, with time separating each point, such that the points may be numbered according to the order given to them by time. Now we have the fundamental mathematical concepts, the primary unity, and the ordering of numbers, and these require absolutely no spatial reference or spatial existence.

Ed Feser has a good blog post on this point http://edwardfeser.blogspot.com.au/2012/08/concretizing-abstract.html. — Wayfarer

As a physicalist, I actually agree with the vast majority of Feser's post. The primary aspects where I didn't agree with him were in his comments about brains, genes, etc. as (not being) "substances in their own right"--but primarily because I'm not sure just what he's claiming there, and in comments that seem to suggest that he believes that mentality is "whole body phenomena" rather than brain phenomena. I agree that brains can't be isolated and function anything like they normally function, but I don't agree that mental phenomena actually obtain in other parts of one's body. Being a necessary support and interactive system for x isn't identical to being x.

I can't make any sense of a form that is not a configuration, and a configuration cannot be coherently thought as being dimensionless, like a point may be able to be.

So an abstract form would have to be in an abstract space, just as a concrete form is in a concrete space. In other words form is unthinkable without space.

While searching for something else I stumbled across this, I think quite relevant, passage in the IEP:

In Zettel, Wittgenstein asks the reader to consider two philosophers, one an idealist, the other a realist, who are raising their children to share their philosophical beliefs. An idealist holds that physical objects only exist in so far as they are perceived; talk of unperceived physical objects is merely a means to making predictions about future observations. The realist holds that physical objects exist independently of our capacity to perceive them. Wittgenstein suggests that both philosophers will teach their children how to use vocabulary about physical objects in exactly the same way, except, perhaps, that one child will be taught to say, "Physical objects exist independently of our perceptions," and the other will be taught to deny this. If this is the only difference between the two children, says Wittgenstein, "Won't the difference be one only of battle-cry?" (Wittgenstein, 1967, 74). For Wittgenstein, to understand the use of a word, in the manner that is relevant to philosophy, it is necessary to understand the role that sentences involving that word play in our lives. His claim in this case is that those sentences which philosophers take to express substantive statements about realism and idealism play no role whatsoever in our lives. The metaphysical sentences have no use, and so there is nothing to be understood—they are strings of words without a meaning. Wittgenstein's hope is that once we see that, in a given metaphysical dispute, both sides are divided by nothing more than their different battle cries, both parties will realize that there is nothing to fight about and so give up fighting.

The primary aspects where I didn't agree with him were in his comments about brains, genes, etc. as (not being) "substances in their own right"--but primarily because I'm not sure just what he's claiming there, — Terrapin Station

That's because he's referring to the traditional, Aristotelean definition of 'substance'. This is not anything like the modern 'substance, stuff, or thing', but 'the subject in which attributes inhere'. So 'the soul' is a substance, due to its unity and simplicity; something similar to that is still represented in the problem now known as the 'subjective unity of experience'. In contemporary language, the body and mind are holistic, i.e. they function as a seamless and simple unity even though on the cellular level it is an enormously complex bio-mechanical-electrical system.

Refering to material though my position is such that I rarely ever see it mentioned on forums like this. That material as a philosophical concept is all forms of extension, division, differentiation — Punshhh

That's rather like the Aristotelean 'hyle', the 'prima materia' which is then imprinted with 'form'. Whereas, when I am talking about materialism, I am referring to the materialism that believes that only matter is real.

An idealist holds that physical objects only exist in so far as they are perceived — John

Berkeley is the only idealist whose explicit formulation was esse est percipe. But there are many forms of idealism which say something other than that. The idealism of the Greeks was born out of the discovery of laws or 'logos', the governing principles of both the cosmos and individual types. The discovery of types and forms, of form as distinct from matter, also gave rise to the idea of the 'form' as an 'ideal type', which is made explicit in Plato's dialogues. So the 'forms' in that context are almost like the potential or the perfect idea of some particular, which the particular form then 'realises' or 'instantiates'. Whereas nous is able to perceive mathematical and ideal forms directly (in the 'mind's eye'), perception of the physical forms is always mediated by the senses. So the 'ideal realm' is not something physically existent, it's like an 'idea in the mind of the One', which the physical specimens 'down here' can only try and emulate. That is the motivation behind the formality of classical art and architecture, which attempts to depict the perfection of the 'changeless realm of forms' that is behind or above the physical world.

For Wittgenstein, to understand the use of a word, in the manner that is relevant to philosophy, it is necessary to understand the role that sentences involving that word play in our lives. His claim in this case is that those sentences which philosophers take to express substantive statements about realism and idealism play no role whatsoever in our lives. The metaphysical sentences have no use, and so there is nothing to be understood—they are strings of words without a meaning. Wittgenstein's hope is that once we see that, in a given metaphysical dispute, both sides are divided by nothing more than their different battle cries, both parties will realize that there is nothing to fight about and so give up fighting. — John

I don't think Wittgenstein was right. First of all, I think ordinary language expresses naive realist views. Secondly, science has an awful lot to say about what goes on when we're not around, including the deep past and far off into space. That seems to be a bit more than just making useful predictions. As if science is an attempt to explain the world, not just provide useful predictions. And thirdly, people with an interest in philosophy, including professional philosophers have continued to have metaphysical debates, even while knowing what Wittgenstein had to say on the matter.

And finally, I believe even Witty himself was not entirely convinced that you could do away with philosophical issues by understanding how language works. That the puzzle of philosophy continued to bother him.

But then if an idealist says that objects exist independently of being perceived, then that idealist must be some form of realist, which is all fine and consistent unless you equate realism with materialism.

What other criteria could you come up with for distinguishing realists from idealists other than that of the perception-independent existence of objects that doesn't invoke the metaphysical mind vs matter discussion? If you invoke the latter then you are really talking about idealism vs materialism, and not idealism vs realism.

I think Wittgenstein's point is that when we talk about "perception independent" existence or non-existence of objects we don't really know what we are talking about.

I can't make any sense of a form that is not a configuration, and a configuration cannot be coherently thought as being dimensionless, like a point may be able to be. — John

We are talking about intelligible objects, ideas and concepts. A form in the way that you use "form" is an intelligible object. But it appears like you now want to restrict your definition of "form", such that a form is necessarily a spatial "configuration".

I suggest to you that this is a mistake. We create mathematical formulae which are by no means spatial configurations. Mathematical formulae are applied to spatial configurations. So for example we say that the circle has 360 degrees. This allows that the circle is divided into 360 distinct rays, or angles from the centre. Mathematics is applied to the circle, such that the convention is to have 360 degrees, but we could have made the circle with 320, 376, 400, or whatever number of distinctions we desired. The number of degrees in a circle is completely arbitrary. This indicates that the mathematical formula is completely distinct from the spatial representation.

So it is rather pointless, and a dead end argument, an untenable position, to insist that a form is necessarily a spatial configuration. Clearly mathematical formulae are not necessarily spatial configurations. Furthermore, you then deny yourself the means for dealing with the existence of these non-spatial things, numbers and non-dimensional points for example. You simply segregate these non-spatial things from their spatial application. Then what will you do with them, ignore them, or deny that they are real?

In other words form is unthinkable without space. — John

So the problem is, that there clearly is concepts such as numbers and points which are thinkable without space. To exclude mathematical formulae from your definition of "form", such that all forms are spatial, is just to close your eyes to the reality that not all forms are spatial. This is like saying that all human beings are men, but that closes your eyes to the reality that many human beings are women.

I would say that mathematical concepts inhabit a logical space. In any case algebraic formulae for specifying the configurations of abstract forms are intelligible only insofar as they can be converted into visualizable forms.

A form simply cannot be intelligibly grasped unless it is visualized, and to be visualized it must be as possessing spatial dimension

I agree with you that ordinary language's 'native land' is naive realism. The problem is that the naive part of naive realism is where we naively imagine objects as existing just as we see them, independently of our seeing of them. I believe we are in a way logically committed to that in relation to our everyday communications; but I don't think that, on analysis, it can be shown that we really understand how that could be possible, or how it makes sense; it's just something we take for granted in an unexamined way.

It is when we try to examine it that the antinomies and the aporias begin to proliferate.It doesn't seem that it could be non-paradoxical to say either that objects exist independently of our perceiving them, or that they don't. We are kind of stuck in the middle; but we are not satisfied with our inability to solve this paradox; and so the endless debate rages on.

But then if an idealist says that objects exist independently of being perceived, then that idealist must be some form of realist, which is all fine and consistent unless you equate realism with materialism. — John

Well, my view is that reality always includes an observer, and there is no 'mind-independent' reality in that sense. But that doesn't mean the past doesn't exist, or that train wheels dissappear when the passengers are inside the carriage, or that objects go in and out of existence depending on who is looking or not looking. All of that is simply a stage-play in the theatre of the imagination. The sense of the 'independent reality' of the phenomenal domain is bred into us as a consequence of the age we live in.

would say that mathematical concepts inhabit a logical space. In any case algebraic formulae for specifying the configurations of abstract forms are intelligible only insofar as they can be converted into visualizable forms. — John

As I said earlier, I really don't know what you mean by "logical space". Anyway, as I explained earlier, number is intelligible as order, and not necessarily as visualizable forms. Two comes after one, and three comes after two, and so on ad infinitum. That is how we learn numbers, we do not visualize one object then two objects, then three objects, etc., we learn the procession of numbers, one after the other. Numbers are an expression of order, not spatial forms.

And, as I said, you can insist that forms are spatial, all you want, but your only fooling yourself. What's the point in self-deception?

A form simply cannot be intelligibly grasped unless it is visualized, and to be visualized it must be as possessing spatial dimension — John

Are you telling me that you cannot grasp numbers strictly as order, without spatial dimension? If that is the case, perhaps you should go back to elementary math, and relearn these things.

Surely on that dualistic logic, reality also includes an observed; and why should we not think it is mind-independent outside the context of its actually being observed? After all, even when it is being observed, it is clear that what is observed does not exhaust its being.

And you say yourself that is doesn't mean "that objects go in and out of existence depending on who is looking or not looking." So, isn't that "not going out of existence" when not being observed a case of mind-independent existence?

I believe I can predict what you will say; you will say that that mind-independent existence is itself conceived by a mind. But that would just be to go around in circles within a state of conceptual self-confinement.

I will grant you, though,that we cannot get any clear idea of what a mind-independent existence (or non-existence) could look like. That's why I don't think it is an important issue; rather it's an insoluble issue. People come down on one side or the other of this argument, due to other preconceptions or preferences, or other ideas they favour, that they think are rightly associated one way or the other, with one side or the other.

We were not talking about numbers, per se, we were talking about forms.
We were talking about numbers only insofar as they be used to create formulas. Formulas can specify two dimensional and three dimensional configurations. They can even specify four dimensional configurations, but we cannot visualize those.

And, as I said, you can insist that forms are spatial, all you want, but your only fooling yourself. What's the point in self-deception? — Metaphysician Undercover

If you can explain to me a way to intuitively grasp forms which does not involve spatial thinking then I will reconsider.

Surely on that dualistic logic, reality also includes an observed; and why should we not think it is mind-independent outside the context of its actually being observed? After all, even when it is being observed, it is clear that what is observed does not exhaust its being.

And you say yourself that is doesn't mean "that objects go in and out of existence depending on who is looking or not looking." So, isn't that "not going out of existence" when not being observed a case of mind-independent existence?

I believe I can predict what you will say; you will say that that mind-independent existence is itself conceived by a mind. But that would just be to go around in circles within a state of conceptual self-confinement. — John

Right! Whatever we say, or science says, about 'what exists', there is always a subjective pole in any such statement. It's very clear to me how this is developed - in the Enlightenment, there was the gesture, 'sweep metaphysics off the table, let's get down to what is "really there"'. And what is "really there" is the domain of sensory phenomena and underlying laws. But notice - as soon as a thread comes up on 'what are laws'? there is vast confusion. Same with 'what are numbers'. So what appears obvious, presented, clear for all to see, is not actually obvious at all. And people take that as the yardstick for reality. That is why there is vast confusion.

Philosophy is penetrating that confusion, that illusion. Few do.

We were not talking about numbers, per se, we were talking about forms.
We were talking about numbers only insofar as they be used to create formulas. Formulas can specify two dimensional and three dimensional configurations. They can even specify four dimensional configurations, but we cannot visualize those. — John

Right, so this is contrary to your claim: "abstract forms are intelligible only insofar as they can be converted into visualizable forms". The fact is that some abstract forms are intelligible by a means other than visualizing them.

A mathematical formula is a type of form. A mathematical formula is grasped by a means other than visualization. Therefore not all forms are grasped by visualization.

If you can explain to me a way to intuitively grasp forms which does not involve spatial thinking then I will reconsider. — John

I already painstakingly described this, it's called "numbers". We grasp numbers through "order" which is non-spatial, it is temporal. Two comes after one, then three comes after two, then four, then five. We do not need a spatial number line to grasp the ordering of numbers.

Next, we have order, and order is a temporally based concept. We can have a succession of non-dimensional points, separated by time, and count them, one, two, three, and so on. Now we have the non-spatial unit, the point, with temporal extension, such that there is not a line, in the sense of a two dimensional, spatial line, but a succession of points, with time separating each point, such that the points may be numbered according to the order given to them by time. Now we have the fundamental mathematical concepts, the primary unity, and the ordering of numbers, and these require absolutely no spatial reference or spatial existence. — Metaphysician Undercover

If you still don't get it, try the concept of "God".

I think when it comes to the natural world what is there is "the domain of sensory phenomena". It is there for us as surely and reliably as we ourselves exist. I just tend to think the further question 'but what is REALLY there (in an objective sense) is misconceived, because we don't know, in any context independent of empirical experience, what we are asking. In a purely formal, everyday sense, in keeping with the logic of our linguistic usages, there is something there independent of us. But we can never analyze what that means.

But, I would say that what else is there is the domain of spiritual experience which is always personal, although obviously also conditioned by inter-subjective culture; the spiritual realities of ethical, aesthetic, interpersonal, religious and mystical experience. Those spiritual realities do not point to any further objective reality beyond themselves; to say they do would be to objectify the spirit; which I think is probably worse than denying it, because it causes people to think they are understanding something, when they are really confused. It's probably better to deny something on the basis of a commonsense understanding, rather than to misunderstand it. In practice, I don't believe anyone really denies the life of the spirit; it is not possible to deny it. They might say the words but then they go right ahead and live their lives as if the life of the spirit is true.

So, I just can't agree with you that there is confusion because people can't understand metaphysical idealism; I actually think metaphysical idealism (or materialism) as thought out positions which people cling to and defend is what causes all the confusion (but probably not amongst the majority who think such questions are "stupid" and a "waste of time" anyway). It is better for an unsophisticated materialist to believe in a materialist 'sky father' God, if that provides moral compass, than to turn away because an idealist has tried to correct him or because a materialist has managed to convince him it's all bullshit. But I don't think those not given to much thought often turn away under such influences; I think if they do turn away it is because they want to, not because they are influenced by idealist or materialist philosophy; unless of course in the context of materialism you are referring to the influence of consumerism; which is another story.

The fact is that some abstract forms are intelligible by a means other than visualizing them. — Metaphysician Undercover

But I have said I don't think they are intelligible as forms if they cannot be intuitively grasped as such. That's exactly why the warping of four-dimensional spacetime can be modeled mathematically, but I don't believe that makes it intelligible in the sense of it being able to be intuitively grasped. That is why relativity theorists and quantum theorists admit that they don't really understand what is going on and say that if you think you understand such things you don't really understand them. This is not to deny they can be understood mathematically.

I already painstakingly described this, it's called "numbers". We grasp numbers through "order" which is non-spatial, it is temporal. Two comes after one, then three comes after two,, then four, then five. We do not need a spatial number line to grasp the ordering of numbers.


If you still don't get it, try the concept of "God". — Metaphysician Undercover

Apart from the fact that number succession is understood by placing the numbers on a line, numbers, to say it again, are not the issue; forms are the issue.

God is not a form.

So what are you saying, that the ordering of numbers, and mathematical formulae in general, are intelligible, but because they are not spatial, they cannot be "intuitively grasped"? What does this mean? We understand mathematics, but we do not "intuitively" understand mathematics? Isn't this a sort of bias? You seem to be saying that because it isn't an "intuitive" understanding (whatever you mean by that), it is not a real understanding.

I actually think all understanding is intuitive. But, be that as it may, this conversation started off about the forms of objects, not about numbers or mathematics. Sure the forms of objects may be encoded in formulae in terms of numbers and other mathematical operations, but the form of an object can only be grasped visually or by touch, as least when it comes to most humans. When the form is intuitively grasped it is always grasped as a configured extension in space, however abstracted. It's quite simple, you can't have the form of the object without the spacial configuration of that form.

I actually think all understanding is intuitive. — John

I don't see how such a claim is tenable. We understand many things through the means of logic, and logic is not intuitive.

But, be that as it may, this conversation started off about the forms of objects, not about numbers or mathematics. — John

But the point was, the demonstration (which you didn't grasp because it was logical rather than visual) that the form of the object is necessarily prior to the material object. This implies that the actual form of the object, the form which determines what the object will be when it comes into existence, is completely different from the form that we grasp through perception, what we call the form of the material object.

As I explained, space is proper to the form of the material object, so the form which determines what the object will be must be non-spatial, therefore more like a mathematical formula. You cannot relate directly to the form which determines the existence of the object, through the material object itself, because the material object will be a medium, a separation between you and that form. So all you see is the form of the object, you do not see the form which determines the existence of the object. It's like looking at a screen with a projection on it. All you see is the projection, you do not see what's behind it, causing it. You can do all you want to analyze the forms on the screen, but this does not get you to the forms which are behind, causing the projection. And your intuitive understanding is really a big misunderstanding.

When the form is intuitively grasped it is always grasped as a configured extension in space, however abstracted. It's quite simple, you can't have the form of the object without the spacial configuration of that form. — John

But that's not true, the form of the object is not always grasped as a spatial extension. It may be grasped as a mathematical formula. That's what field theory gives us in quantum physics, a mathematical formula rather than a spatial extension. You would deny that the field mathematics represents the form of the object because it is not intuitive, it cannot produce a spatial configuration. Nevertheless, it is just as much the real form of the object as any spatial configuration which might be proposed. The point though, is that there is a separation between the two, the object itself which is the medium between the two forms is that separation. The spatial configuration is a representation, or form, of what the material object is, while the mathematical formula is the representation of what the object will be. So the material object exists as a separation between these two distinct types of forms, and this is why dualism is required in order to understand reality.

So, I just can't agree with you that there is confusion because people can't understand metaphysical idealism; — John

That is not the cause of the confusion; the confusion is that we can't distinguish truth from falsehoods, reality from illusion. We cite what we think is 'the scientific worldview' in a world which has severed facts from values. And look at what is happening, the most powerful nation has just elected a liar and charlatan as leader of the free world. Confusion reigns supreme.

I don't see how such a claim is tenable. We understand many things through the means of logic, and logic is not intuitive. — Metaphysician Undercover

If it is not intuited, then how do you know that one thing follows from another?

This implies that the actual form of the object, the form which determines what the object will be when it comes into existence, is completely different from the form that we grasp through perception, what we call the form of the material object. — Metaphysician Undercover

The form of maple leaves for example is a general form that can only be grasped as a visualization, it will be a description that will result in a visualization, an algebraic expression which specifies the coordinates on the x/y axis which will result in a visualization, or a direct pictorial representation. Now, let's take the example of the pictorial representation: it is probably never going to be the exact form of any particular maple leaf, because each particular maple leaf has its own form of the same general kind which can be abstracted to form a closer, but never perfect, visual representation. But there is no sense in which the present form of the maple leaf existed prior to the present moment. Prior to the present moment there were a succession of slightly different forms that evolved to the present form. Only the general form of maple leaves is prior to any particular maple leaf. But that general form too has evolved from a form that was once quite different.

The next paragraph reads to me like gibberish so I am not going to respond to that.

But that's not true, the form of the object is not always grasped as a spatial extension. It may be grasped as a mathematical formula. — Metaphysician Undercover

The visual form of an object cannot be grasped as a mathematical formula, well at least I can't grasp it as such, and I have spoken to mathematicians who say the same. The form can be modeled as a mathematical formula, the formula can of course be understood in purely mathematical terms, but it cannot be visualized directly, as mathematical formula; by definition it can only be visualized as a visual form. If you still disagree then there is no point continuing, because I am just going to say you are wrong; and you are probably just going to say I am wrong, and it will be a waste of time and energy.

I think the truth about Trump is not a scientific truth. That he is a reprehensible character or not cannot be empirically established, it is a judgement call, like the judgement as to whether an artwork is good or not. There is no objective fact of the matter in regard to such judgements, but there are truths of the spirit. Some people can see those truths and others can't, but they can never be demonstrated like empirical truths can.

Yeah, dumb argument on my part. It was only provided as 'symptom of general malaise'.

There is no objective fact of the matter in regard to such judgements, but there are truths of the spirit. — John

Which is what I try and arrive at, by philosophical means; that is what I regard as the overall aim of 'the idealist tradition' in Western philosophy.

If it is not intuited, then how do you know that one thing follows from another? — John

As I said, I really don't know what you mean by intuitive. My dictionary defines intuition as "immediate apprehension by the mind without reasoning". There is a second definition which is immediate apprehension by a sense, and a third definition which is immediate insight. Notice that all use the word "immediate". Logic is a tool which the mind uses, so there is a necessity to understand the premises, the principles of logic being employed, and how these are related, so that a conclusion is drawn. There is no immediacy here, the conclusion requires mental effort, so it is impossible that logical conclusions are "intuitive", instead, they are "rational".

The form of maple leaves for example is a general form that can only be grasped as a visualization, it will be a description that will result in a visualization, an algebraic expression which specifies the coordinates on the x/y axis which will result in a visualization, or a direct pictorial representation. — John

Again, I disagree with you. I think that it is impossible to grasp a general form through a visualization. That's the very essence of a "general" form. A visual image is always of a particular, and a general form is categorically different from this. There is an inherent incompatibility between the two. That is why the general is understood through definition, rather than through visualizing a particular. We can come to grasp the general through seeing particular instances, and abstracting certain properties, but we cannot immediately grasp the general from a particular instance. This would merely be grasping a particular, and clearly not a case of grasping the "general form", which requires understanding some general principles.

Now, let's take the example of the pictorial representation: it is probably never going to be the exact form of any particular maple leaf, because each particular maple leaf has its own form of the same general kind which can be abstracted to form a closer, but never perfect, visual representation. — John

Here is the difficulty with your presentation. Unless the representation is of a particular maple leaf, then it is not a visual, or "pictorial" representation at all. A pictorial representation, or imaginary image, is of a particular, even if that particular is only within your mind. The image consists of the particulars which your mind puts there. You can imagine the maple leaf as just a stem, with a vague shape on top, many particulars not filled in by your mind's imagining process, but this does not give you the general form. What it gives you is an incomplete particular.

So what you don't seem to be understanding is that when we abstract the form, from a particular, through sense and thought, it is always a particular form which is abstracted from that individual. The particular form abstracted will be incomplete, depending on which aspects of the form are apprehended as important. But this does not produce a general form. The general form is created by the mind adopting certain principles of recognition, and classification. This is what Aristotle described as distinguishing essentials from accidentals. By employing these principles, first to recognize the similarity between different leaves, and second, to hold that there is a classification called "maple leaf", the existence of a general form is demonstrated. Further, an individual human being is often mistaken in these principle, so the formal existence of a general form is by definition. The classification is named and the defining features are described, such that there is agreement amongst human beings, and the general form maintains its existence by means of this agreement, convention.

The point being made, is that the particular form is what is abstracted from the particular object. This is perception. The general form is something completely different, it is created by the mind. The general form exists as principles of recognition and classification, rules which the mind follows. There is a categorical difference between the two. The two cannot be conflated because there is a deep incompatibility between them, and this is why dualism is necessary.

But there is no sense in which the present form of the maple leaf existed prior to the present moment. Prior to the present moment there were a succession of slightly different forms that evolved to the present form. — John

Let me try once again, to explain this issue. As time passes, there is as you say, "a succession of slightly different forms". At each moment of the present, the maple leaf is this particular maple leaf, it is not that particular maple leaf which it was at the last moment, because it has changed. Therefore at each moment the maple leaf is a new, and different object. So at each moment a new object is created, we can call them MLt1, MLt2, MLt3, etc., each collection of symbols referring to a different object. Let's take MLt3 for example. When that object comes into existence, it necessarily comes into existence as the object which it is, MLt3, or else it is not MLt3. It does not come into existence as MLt2, Mlt4, or any random thing, it comes into existence as MLt3. Therefore we can assume that there is a cause of its existence as MLt3, a reason why it exists at that moment as MLt3, and not something else. This is the determining form of MLt3. Notice that in order for the object, MLt3, to exist at that present moment, as MLt3, it is necessary that the form of MLt3 existed prior to that. This prior form is not MLt2, it is not MLt4, because these are distinctly different. It is nothing other than the form of MLt3, which exists prior to the object MLt3, and ensures that object MLt3 will exist as that object, at that moment in time.

But we see material object MLt3. We abstract that particular form, and this constitutes our representation of object MLt3. Our representation is a representation of material object MLt3, it is not a representation of the determining form, which exists prior to material object Mlt3, ensuring that Mlt3 will exist as MLt3.

The visual form of an object cannot be grasped as a mathematical formula, well at least I can't grasp it as such, and I have spoken to mathematicians who say the same. The form can be modeled as a mathematical formula, the formula can of course be understood in purely mathematical terms, but it cannot be visualized directly, as mathematical formula; by definition it can only be visualized as a visual form. If you still disagree then there is no point continuing, because I am just going to say you are wrong; and you are probably just going to say I am wrong, and it will be a waste of time and energy. — John

The point I am making is that the visual form of the object is distinctly different from the form of the object which precedes the existence of that object in time, causing it to be that object which it is. The visual form of the object is created by human perception following the object's presence in time. It is a representation of the object's material existence at that time. The form which precedes the object's material existence, and determines what that object will be at any moment in time, as time passes, cannot be seen visually, because it is always prior in time to that object's material existence, which is what is seen. The only access we have to this prior form is the mathematical formula, which enables us to predict, and is inherently different from the visual form. The difference, I have argued, is that the visual form is spatial, and the mathematical is non-spatial. This, I believe, is due to the fact that there is no spatial existence prior to the present moment in time. Spatial existence is created at each moment of passing time.

So I am in agreement with you, that the visual form of the object cannot be grasped by the mathematical formula. The two are deeply incompatible, and that's why I advocate dualism. Here's an explanation of this incompatibility:

We see the object, thus creating a visual form. What we see is the object's material form, and this is necessarily post-present in time. The object is present to us, as a material object, at the present, so our representation of it is necessarily post-present, therefore this particular form is post-present. As human beings we proceed to create general forms, these are generalized rules, rules for naming, classifying, right up to the general laws of physics. Then, we turn back to the particular object, applying these general rules. So we have mathematical formulae, which we apply to the particular objects, attempting to determine the pre-present form of the object. This is prediction. But the essential nature of the pre-present form of the object is that it is particular. Each object has its own particular form, proper to it, which is prior to it in time, causing it to be the object which it is. Now we have general forms, mathematical, and physical laws etc., which are not specific to the particulars of the object. So we have an incompatibility between the general nature of mathematical formulae, and the particular nature of the pre-present forms of objects.

There is no immediacy here, the conclusion requires mental effort, so it is impossible that logical conclusions are "intuitive", instead, they are "rational". — Metaphysician Undercover

Understanding a complex logical argument results from the associating of its parts, The parts consist of immediately apprehended insights and the associations between them are also direct insights. What else could the associations be but further direct insights ? They cannot be composed of mechanically following rules without any insight, because then you would need further rules to tell you how to follow the rules, creating an infinitely regressive and complex proliferation of rules which would make any understanding or following of logical arguments impossible.

I think that it is impossible to grasp a general form through a visualization. — Metaphysician Undercover

Whether you draw the general form of the maple leaf or merely imagine it, it cannot be the exact form of any particular maple leaf. It is a kind of 'averaged' form.

So I am in agreement with you, that the visual form of the object cannot be grasped by the mathematical formula. The two are deeply incompatible, and that's why I advocate dualism. Here's an explanation of this incompatibility: — Metaphysician Undercover

Well, I'm glad we agree about something! :)

I think our understandings of the world are inevitably firstly in dualistic, but then more completely in triadistic terms. The subject, the object and the relation between them. Yes, no and undetermined. True false and irrelevant, Mind matter and symbol. Body, soul and spirit. Creation, preservation and destruction. Id, ego and superego. The three Gunas: rajas, sattvas and tamas. In Astrology the three qulaities: cardinal, fixed and mutable. And so on.

I am not going to attempt too address any of the rest of your long post. I think these are the salient points, anyway, and discussion will be much more manageable if we just deal with them.