How can something be equal to itself unless it is seperate from itself? — eodnhoj7

Gee eodnnoj7, can't you read? The law of identity doesn't say that a thing is equal to itself, it says that a thing is the same as itself. So it's not expressing the equality of two distinct things, it is expressing the identity of one thing. That's why it's called the law of "identity". It implies that a thing has an identity, to itself, and that the thing cannot be other than its identity. Leibniz carries this further with the "identity of indiscernibles", stating the converse, if it has the same identity, it is necessarily the same thing, meaning that two distinct things cannot have the same identity.

There is no issue here of two things being equal, the issue is identity. I went through this already, "2+2" is not the same as "4". They are distinct, having a different identity, despite the fact that they are equal. One line is equal to an infinity of lines, but these two are distinct, having different identities, ergo not the same thing.

And what evidence is that? — eodnhoj7

Try the above for example.

We engage or approach the work in an organized fashion in addressing arguments raised by Wittgenstein. By which I mean we talk for example about the private language argument or language as a form of life or the beetle in a box or family resemblances.

Of course we would address each argument raised by Wittgenstein in some logical and coherent manner; but, I honestly doubt we could make it past a couple of pages reading each paragraph in logical order. — Posty McPostface

It is supposed to be a reading group, and context is important in reading. So I think it is important to start from the beginning and understand how Wittgenstein is using certain words, like "rule". However, the problem is as you say, we might have trouble getting beyond the first few pages, and the exercise could extend indefinitely in time. Some readers would insist some parts of the book are unimportant, wanting to skip ahead without grasping the nature of each problem as Wittgenstein exposes them one after the other.

But that is the theme of the Philosophical investigations, there is an endless supply of problems brought up, one after the other, with a thread of relationship connecting them. As the book proceeds, Wittgenstein offers direction toward a possible way of avoiding all these problems. But if one does not completely understand the nature of the problems, that person cannot adequately judge whether Wittgenstein's direction is correct. That is why it is important to address all the little problems, one after the other, as they are developed into one big problem. And then proceed toward the possible solution.

So it makes no sense to begin the reading group with a discussion of the beetle in the box, or some such thing, because we would have no context. The discussion would go in a multitude of different directions, following a multitude of opinions, and those who referred to the book, to put the analogy into perspective would most likely be scoffed at as offering a faulty interpretation of the book.

Basically what I'm hoping to do in talking about arguments is encourage discussion and dialogue. Not sure if it's the best way to do so or flawed. — Posty McPostface

There has already been many discussions here on those particular "arguments" which you mention, but many passages of the book have not been discussed here at all. The issue is that many parts of the book may be interpreted in many different ways (those produce interesting discussions), and other parts are less ambiguous (there is little to discuss). But the interpreters may refer to the ambiguous parts with interpretations of those parts which support their personal interpretations of the book as a whole, leaving behind some less ambiguous parts which do not support their personal interpretations. If these less ambiguous parts of the book which are incompatible with such an interpretation are brought up, the interpreter will be caught attempting to produce ambiguity in an unambiguous statement in order to support the personal interpretation. One might argue that a more ambiguous part is of greater importance than a less ambiguous part, but why would a more ambiguous part be of greater importance than a less ambiguous part? A true interpretation ought to offer consistency throughout the entirety of the book, because we ought to assume that Wittgenstein worked hard to present the piece in this way.

We're all blind, and Wittgenstein ensures that we proceed in this way, providing us with nothing in particular which we might see. So I'll follow, but I won't even pretend to lead because that would be the position of a fool.

I want to inform that I won't be able to handle the managerial aspect of the reading group. My role here is only that of an orchestrator for it.

Anyone up for the job? — Posty McPostface

Still looking for a guide? A few words of advice, don't ask of the blind for a volunteer to lead the blind.

The law of Identity is written as "P is P" or "P equals P" with "is" and "equal" having multiple interpretations. — eodnhoj7

The law of identity states that a thing is the same as itself. It gives each thing its own identity, so P, as a particular thing, is the same as P, itself, that particular thing. This is quite clear, unambiguous, and not open to equivocation. Your examples of multiple interpretations, ambiguity, and equivocation simply reflects your misunderstanding of the law of identity.

So in regards to your statement "Equal" does not mean "is", you are performing sophistry which does not match up with the evidence with the evidence being the common perspectives of the community, which in itself leads to further fallacies. Evidence itself falls under certain fallacies in these respects. — eodnhoj7

The evidence indicates that you either completely misunderstand the law of identity, or that you state it in an ambiguous way in order to deceive. I am beginning to think that perhaps your intent is deception.

So The law of Non-Contradiction is not defined by the Law of Identity, and the Law of Identity is not defined by the Law of Non-Contradiction? The Law of Non-Contradiction does not exist through the Law of Identity and defines it? Each law does not define the other? — eodnhoj7

That's right, each of these fundamental laws has its own definition, what it means. One does not define the other. if that were the case, then it would be only one law. But there are three.

Pi is a relationship. It is not a line. — BrianW

Here we go again, good luck convincing eodnhoj7 of that.

Here is a mathematical proof that one number is equal to an infinite series of numbers: — eodnhoj7

"Equal" does not mean "is". "Equal" means equivalent to, while "is" means the very same as. I very much agree that one line of any length is "equal" to an infinity of smaller lines, being potentially divided an infinity of times, but this does not mean that one line is an infinity of lines. The former is a mathematical equation, the latter is a logical contradiction.

Do you recognize the difference between "is" and "is equal to"? For instance, "4" is equal to "2+2". But this does not mean that 4 is 2+2, nor does it mean that 4 is composed of 2+2. It means that 4 is equivalent to 2+2. Do you see that "4" is completely different in meaning from "2+2", and therefore we cannot say "4 is 2+2", despite the fact that the two are equal? Do you see that "one line" is completely different in meaning from "an infinity of lines", and therefore we cannot say "one line is an infinity of lines" despite the fact that the two are equal?

2) A person can be composed of a multitude of persons in reference to one person being various persons given a length of time defining that person.

A person may be one person around another person and be a different person in presence of another, with one common person connecting these various identities. Your argument is fail two take into account two distinct phenomena can exist at the same time in different respects. — eodnhoj7

As I explained, you can only perform this sophistry through equivocation. One person is only various persons when you use multiple definitions of "person". That's equivocation.

A. P is defined by not P. — eodnhoj7

No, P is not defined by not P. That's not a definition, as a definition gives meaning to P, saying what P signifies. If this were a definition, it would leave P completely without meaning, and that's not what a definition does, it gives meaning. Therefore P is not defined by not P.

I do have ways that laws will play a part though - this will be part of diplomacy between factions/races (a whole other problem!) — I like sushi

The problem I see here though, is that laws are essentially applied within a society, they do not very well adapt to being inter-societal. In this way they act to close the society. The defining feature of "laws" is how they affect those within the society. But since they vary from one society to another, they may be the source of conflict.

We are born into a particular society and implicitly accept the laws, like the social contract of Hobbes. So the laws of a society play a large part in shaping that society, and to a lesser extend they play a part in shaping conflicts with other cultures.

I thought about the whole “social contract” thingy and “freedom,” but haven’t seen a means to incorporate the idea. — I like sushi

I would say that the form of laws is fundamental to the "shape" of the society, or what you would call "race" (btw, why use that term rather than differentiate by "culture" or something like that?). So the type of laws which are in force within the society are the defining features of that culture. You differentiate one culture from another by its formulation of laws. Then there are different means by which the type of laws can change within a particular culture. Slow and small changes occur through politics, while faster, larger changes occur through civil war, revolution, and invasion by others.

My problem is thinking up a intuitive measure of these items that is more abstract than material. — I like sushi

The "abstract" measure of a society might be found in one's laws. Like all abstract things, the real existence of laws and the exact formulations in historical societies is difficult to determine and gauge. However, laws may be seen as overarching and influencing all the aspects you named “diplomacy”, “economy”, “infrastructure”, “ritual”.

Here's a question to consider. Does an advanced culture have a more or less complex legal system than a less advanced one? Consider that the goal of an advanced society might be to provide maximum freedoms for its participants. So an advanced society would try to find ways to reduce the burden of unnecessary laws. For example, The Old Testament has ten commandments while The New Testament has one golden rule. And Plato, in The Republic, defines justice roughly as minding one's own business.

I have explained in detail why it is not an equivocation. Repeating your claims does not help. You need to show why the arguments I have made are unsound. — Dfpolis

You have made no such argument, only repeating your assertions that the form in the mind is in some way the same as the form in the object. I have produced multiple arguments showing why this is unreal. You have shown me no argument to defend your claims, but I have definitely shown your claims to be unsound.

Only to the extent that the work is poorly executed. To the extent that the work is well-done, it embodies the very form in the mind of its maker. — Dfpolis

So let's see your argument then. Prove that the form in the mind is the very same form as the one in the artist's work, rather than just a corresponding form. I think that all the incidents when the work is poorly executed is evidence that the two are not the same. And, when the work is acceptable, it is simply acceptable, and never perfect. Therefore never the very same form.

The context was that the matter is proportionate and suitable to the desired form. — Dfpolis

That the matter is proportionate, and suitable to the desired form, says that the matter must already have a suitable form. So it is clear that the artist is changing an existing form, not informing the matter with a form from one's mind. The artist uses the mind to determine how to change an existing form to produce a desired form. The artist does not take a form from one's mind and inform the matter. The matter is already formed and the artist simply changes that form.

Yes, but this does not advance you case that the form of the object is not also partially in the knowing subject. — Dfpolis

Well, the point is that "form" in the sense of what is in the knowing subject is "form' in the sense of essence, and "form" in the sense of what is in the material object is a different meaning, of "form", including accidentals. Therefore your claim that the form of the object is the form in the knowing subject is nothing but equivocation.

Consider a piece of abstract art. It's form occurred first in the mind of the artist, then in the work. — Dfpolis

But the form in the mind of the artist is not the same form as the form in the work. That's where you equivocate. The artist proceeds with a plan or a purpose, a form in mind, and creates a form in the work material. The two are not the same form. There is a medium in between which is the act of creating in the material. It is not the case that the artist takes the form out of the mind and puts it into the matter. A different form is created in the matter, from the one in the mind, and this is evident and obvious from the existence of accidentals.

The artist takes material and informs it according to the intended form. — Dfpolis

So this description is incorrect, wrong. The artist does not take the material and inform it with the form in the mind, the artist takes the material and changes the form which it has, to correspond with what's in the mind. The forms "correspond" rather than being one and the same. This is a very important difference, because the artist's act of creation is an act of taking an existing form and producing a new one, an act of change. Because it is an act of change, the artist's work is limited by the existing form. If it were a matter of the artist "informing" the material, there would be no way to account for these limitations, as the matter would not already have a form, being able to take any form. But this is not the case, the matter already has a form, and the artist must change that form, not inform the matter.

The artist can give the stone whatever form is desired. — Dfpolis

See here is evidence of that very mistake. The artist cannot give the stone whatever form is desired, being limited by the form which the stone already has. Once you deny the fact that what the artist is doing is changing the existing form, in favour of your principle, that the artist is informing the matter, you exclude the capacity to account for the restrictions placed on the artist due to the existing form.

Not the same form in the sense of having all the notes of intelligibility, but the same in the sense that they notes they do share are numerically one. — Dfpolis

The notes are not numerically one though, that's the point. Each note is different between the object and the mind, one having accidentals, the other not.

Every instance of a note of intelligibility is an instance of the identical note or it would not be an instance. The instances (tokens) are different, but what they are instances of (their type) is identical. For example, the abstraction <humanity> is one, even though many individuals have humanity. — Dfpolis

Each note of intelligibility in the mind is an abstraction, therefore not the same as the intelligibility of the thing abstracted from. So in relation to your example, the "humanity" in me is not the same as the "humanity" in you because of the differences in accidentals. And none of us are the same as the concept of humanity because we are particular instances, and that is a universal.

How? Further, I do not see that the law of identity ("What ever is, is") enters into differentiating individuals. — Dfpolis

Do you not know the law of identity? A thing is the same as itself. The purpose of the law of identity is to ensure that every individual has its own unique identity.

I can't agree with a word of this analysis. We can have two quite indistinguishable objects and still know that they are two, not one, in light of their relation to each other and to us. One is on the right, the other on the left. One is closer, the other further. — Dfpolis

That description is a formula, it is part of the form, not the matter.

Of course they would not be objects if they had no form. That is why they are countable, but the reason they aren't one is relational. — Dfpolis

"Relational" is formal.

There is no strictly axiom for the point. A line composed of infinite lines is still one line. It is similar not the same to a set containing infinite numbers, an aleph number, or Cantors work in multiple infinities. — eodnhoj7

One line cannot be a multitude of lines by way of contradiction. I explained this to you. If it is many lines it is not one line. if it is one line it is not many lines.

Show me your source considering this, according to you is a universal axiom, other wise you are pushing your own theory (which is fine) but does not hold according to its own logic.

Provide a source. — eodnhoj7

My reference is the law of non-contradiction. To say that one of some thing is at the same time a multitude of that very same thing, is contradictory. Is one person at the same time a multitude of persons? No, because this would be contradictory. Is one line, at the same time a multitude of lines? No, because this would be contradictory.

If we decide to put on a new roof to keep the rain out, we take certain precautions (safety straps) because we don't expect the ground to suddenly become mud and break our fall. — macrosoft

When working on the roof, one uses safety straps to prevent oneself from falling off the roof. No one considers the possibility that the ground might suddenly become soft. So you are just throwing in a red herring here, an unreal, irrelevant thought. The motivating factor in putting on the safety straps is that we believe we can prevent an unwanted occurrence. Therefore we clearly believe that we can have influence over what happens in the future.

The issue is not whether nature "is looking out for us". The issue is to what extent we have control over nature. So for example, if we had absolute control over nature, nature would be whatever we want it to be. This is similar to the theological position, but the theological way recognizes human deficiency, and places something human-like (God), instead of human beings themselves, as having absolute control over nature. The opposite way, is the determinist way, which would say that nature has complete control over us. The two opposing ways, nature is what we want it to be, and nature forces us to be what we are, are both wrong, so we need a medium, a compromise.

I'd say that it's this concrete worldly context that mostly informs notions of objectivity. If we imagine the table made of particles/waves, we still vaguely imagine a table-shape. If we 'know better' or think about it more, we can abstract away not only this shape but even our mathematics and waves and particles as indeed just another layer of human significance 'projected' on 'something' --albeit problematically as we abstract away everything intelligible. — macrosoft

The problem here, is that the "scientific way", becomes the way of "we have absolute control over nature", because it develops the attitude that we can conceive of the table in anyway that we want. So long as the mathematics is correct, and the behaviour of the table is well predicted, then we can describe the table in any way at all. There is no such object as "the table" anymore, there is just this or that description of what is going on, and we choose the one we want. Therefore we view nature as being whatever we want it to be.

It occurs to me that the thing-in-itself is a kind of direction. Remove the 'subject' as much as possible, etc., starting with the sensual and proceeding to the intellectual. Trying to go all the way leads to absurdities. Does isolating a pure subject in the same way lead to absurdity? — macrosoft

Clearly, there are two distinct directions, from two distinct starting points. Each one gets enveloped in problems sending one frustrated toward the other way. But the real problem is in those starting points themselves, the subject and the object, they do not produce sound premises, so they must be dismissed altogether for something different.

As Derrida might have put it, the desire for pure presence is the desire for death. — StreetlightX

Here you approach the true medium, presence, or the present. This is the only real grounding for the concept "medium", validating it as a true concept, signifying something real, the medium between future and past, the two fundamental aspects of reality. Presentism reduces all to the medium. Then, by making the medium all there is, without the reality of the separated things, future and past, the medium itself becomes meaningless.

So if I have infinite lines existing as one line, the line is not composed of infinite points? — eodnhoj7

Infinite lines being one line is contradictory, plain and simple. That a line is potentially divisible an infinite number of times, does not mean that the line exists as infinite lines. That would be contradiction, to say that at the same time, one line is many lines.

The points, which would distinguish the infinite number of shorter lines within the longer line, cannot function as a divisor of the longer line without annihilating the longer line through the act of division. It is impossible by way of contradiction, that the same thing is at the same time, one line and a multitude of lines. So either the points are functioning to divide the line, in which case there is no longer line only an infinity of short lines, or else the points are not "in" the line.

As I've explained to you, over and over, when we assume the existence of lines and points, we assume that the points are not "in" the line. You use an interpretation which is clearly contradictory, and produce a nonsense argument from that faulty interpretation.

The ice isn't going to politely melt before I unthinkingly skate on it and break my arm. If I am fixing a roof and tumble off, the ground will not soften as I descend. Or at least I do not live with such expectations, however merely logically possible such things may be. — macrosoft

The point is that you live acting in such a way as to prevent yourself from breaking your arm on the ice, and to prevent yourself from falling off the roof. Why did you want to go skating, or go on the roof in the first place? And how did you get onto that roof? Don't you know that you intentionally put yourself at risk by doing such things?

Here's Euclid's definitions from: http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

1. A point is that of which there is no part.
βʹ. Γραμμὴ δὲ μῆκος ἀπλατές. 2. And a line is a length without breadth.
γʹ. Γραμμῆς δὲ πέρατα σημεῖα. 3. And the extremities of a line are points.
δʹ. Εὐθεῖα γραμμή ἐστιν, ἥτις ἐξ ἴσου τοῖς ἐφ᾿ ἑαυτῆς 4. A straight-line is (any) one which lies evenly with
σημείοις κεῖται. points on itself.

Notice, #3. The extremities of a line are points. And, #4, a straight line has "points on itself".

Whatever makes you think that there is an axiom which states that a line is comprised of points? You are dreaming!

1. A line is an infinite number of points, hence is an infinite number of lines.

The line as infinite points is the axiomatic definition of a line:

http://www.bing.com/search?q=the+line+is+an+infinite+number+of+points&qs=n&form=QBLH&sp=-1&pq=the+line+is+an+infinite+number+of+points&sc=1-40&sk=&cvid=C8ED297B32114AA2A7406E89721E7552 — eodnhoj7

Your cited reference clearly states a line "contains", and a line "has" an infinite number of points. It does not say a line "is" an infinite number of points, as you claim. Do you not recognize a distinction between container and contents, a difference between what something is and what something has?

Change my mind and provide a source. — eodnhoj7

Learn how to interpret instead of changing words to suit your purpose, then read your own sources.

If pi is not a length, then neither is 1 units, 2 units, 3 units, etc. considering quantity is a unit. — eodnhoj7

Right, now you're catching on. 1 unit, 2 units, 3units, etc., are not lengths. There must be a specified unit of length, like "metre", "foot", etc..

So here is my insult, and you will never understand it:

"I hope you live a long life no different than who you are now." — eodnhoj7

If you like me to continue, attacking your faulty arguments, I will. Are you finally noticing the usefulness of my attacks?

Essences are the foundation in reality for essential definitions. In De ente et essentia Aquinas explains that form and essence are different. As it would be an error to leave out a body's materiality in defining it, the essence of a material thing includes both its form and matter. — Dfpolis

In Aristotle though, quiddity is a sense of "form". Aristotle doesn't make the clear distinction between form and essence which you refer to in Aquinas. In Aristotle this is just two senses of "form".

It is certainly true that we do not know all that a thing is. Still, the object as known is not what Aristotle means by "form." — Dfpolis

You ought to recognize that the word "essence" did not exist for Aristotle. And so, for Aristotle "form" (what a thing is), had multiple senses. One being what the thing truly is in itself, the other being what the thing is known to us as. It is wrong to take one of these senses, and say that the other is not what Aristotle means by "form", because we'd have to look at the context of each instance to decide. And clearly there are many instances when "form" is used to indicate formula, or essence.

Just as information is the reduction of possibility, so informing matter selects out of its possibilities the one it actually has. It does not mean that the form exists prior to matter being informed. — Dfpolis

I still don't understand how you can say that form informs matter without assuming separate forms. Are you saying that matter selects a form from possible forms? Wouldn't the possible forms which the matter chooses from, necessarily have separate existence? Otherwise that matter which is choosing, would already have all these different forms at once, and that's contradictory. So if the matter selects from possible forms, then these forms must have separate existence. Otherwise the matter would either have multiple forms at once (contradiction), or else these multiple forms would have no real existence at all, and there would be no forms for matter to select from.

If there were no moon, I would see no image of the moon. So, clearly the moon acts (via mediation) to form its image on my retina. — Dfpolis

Your logic is faulty here. You do not have the required premise to say that if you see something, that thing is necessarily acting. So you beg the question by assuming that if you see something, that thing is acting. However, according to accepted grammar, the seer is active in seeing, and the thing seen is passive. You might argue some sort of premise which states that to see requires that something act on your eyes. But this thing acting on your eyes might not be the object at all, as you note, it might be a medium. If the medium is acting then there is no need to assume that the object is acting. The moon might be completely passive, with an active medium, and then it would be wrong to say that the moon acts.

Notice that if light is such a medium, we do not even see light. So we do not even see the thing which is active in seeing (light), we just see the passive object. All the other sensations are similar. We sense "things", sounds, tastes, smells, density, etc.. And all these sensations are based in activities. But we do not sense the activities, we sense the things. I agree that there is activity involved in sensation, but the activity is proper to the medium, not the thing sensed. And the medium might just as well be within the human body as external to it.

You are confusing two kinds of potential here: the proximate potencies inherent in being the kind of thing a being is (which is its form), and the remote potential to stop being what it is, and become something else (which is its matter). The form of a thing is what it is now, defined by its present powers -- a living person, not a dead body; or an acorn, not an oak tree. What something is now is defined by all the things it can do now, even though it is not doing them. Thus, human beings are rational animals even when they are acting irrationally. — Dfpolis

It is you who is confusing things. We describe a thing as "what it is", it's form. If that thing has the potential to be something else, or has "potencies" (the ability to act), then we must refer to something other than the thing's form to validate this potential. So if you want to define a thing by "its present powers", then to account for its ability to act, which require a specific type of temporal relation, you need to refer to something other than "what it is". "What it is" refers to an existence now, but "ability to act" requires a relationship between past and future. So "form" as "what the thing is", cannot account for a thing's "present powers" and we must refer to "matter" for that.

Of course objects exist (or not) independently of how we think of them. My point about the sphere was that thinking of the moon only as that within the sphere does not mean that the moon is only within the sphere. It has a radiance of action that extends to everything it influences. The moon as an object with a tidy boundary is an abstraction. The real moon is that, and every effect it has. We can see this because if we remove the effects, say the tides, then we are no longer thinking of the moon as it is, but an abstraction that does not act like the real moon. Removing any effect diminishes the reality of the moon. — Dfpolis

You're begging the question again, with your assumption that objects act, when really they might only be passive, acted on. So you say that the tides are caused by an act of the moon. But we know that the tides are an effect of gravity. And gravity is not an activity of the moon nor is it caused by an activity of the moon.. If we assume that gravity is an activity, then it appears like the existence of the moon, as an object, is more likely the effect of this activity.

That is because your idea of the moon is a circumscribed abstraction, not the real being with its web of interactions. — Dfpolis

Right, my assumptions concerning activity are not the same as your assumptions, but I think mine are more realistic. You think an object like the moon is active, and interacting with other objects, like the sun and the earth. I think that these objects themselves are passive, and there is a medium between them which is active, and the activity of the medium is what accounts for "interactions". We do not sense the active medium.

This is a question about how to count. I count one form, you count two forms. Let me explain why there is one, not two forms. Clearly, there are two informed beings: the object and the subject. Does that mean that there are two forms? No! Why? Because the basis of the twoness is the different matter of the subject and the object. But, we are not talking about the informed matter of the object, or the informed matter in my brain, but about the form in abstraction from matter. — Dfpolis

This is contrary to the fundamental laws of logic. There are two beings, "the object and the subject". You are claiming that these two distinct beings have one and the same (numerically identical) form. That contravenes the law of identity. You are saying that two things, the subject and the object, which have different matter, can nonetheless have the exact same form, on account of them having different matter. But the very principle (the law of identity) which allows us to say that two distinct things have different matter, disallows us from saying that they have the same form. It is only by the fact that they have different forms, that we can say that they have different matter. Matter is only distinguishable as this or that particular matter by its form, so you cannot say that the subject and object have different matter without respecting that they have different forms. So the subject and object can in no way share have same form.

Still, as the notes of comprehension we do have are identical with notes in the object, they (the notes we have) are one with those of the object. — Dfpolis

This is where you do not appear to grasp reality. No single "note of comprehension" is the same within the mind as it is within the object. No note is a perfect, ideal, or absolute understanding. Each is in some way deficient. Each aspect of the form, in abstraction, is different from that aspect in the material object. You look at a horse for example, and see its eyes, nose, head, legs, hair, etc., and each one of these, as a property, is different within your mind from what it is within the horse itself. So there are absolutely no identical notes. There cannot be, or else our understanding of that particular aspect would be absolute, ideal and perfect. And no aspect of human understanding obtains such perfection.

In fact not only is it in mathematical axioms (line as infinite points), but these axioms are open to further expansion infinitely while each axiom is determined by the framework of proof which extends from it and not the axiom itself. — eodnhoj7

A line is not composed of infinite points. There are infinite points on a line. Your premise is a misrepresentation, not a mathematical axiom.

The line as "a injunctive of infinite points" observes the line as composed of infinite lines through these infinite points. The point is a continuum of further points through the line. The line and point alternate between eachother — eodnhoj7

I don't know what you mean by "a injunctive", but the grammar is terrible, so I would be dubious of wherever you got that quote from, as unreliable in educative value.

If the line is nor composed of points, but the line is composed of infinite further lines between points, the line is composed of points. — eodnhoj7

This is blatant contradiction. "If the line is not composed of points, but... [then] the line is composed of points." That's nothing but nonsense contradiction.

Pi = c/d where c is equal to Pi and D is equal to one. The circufermance containing a number of lines equal to Pi observes not the circumferance as a length equal to Pi (and the circumferance is a length...Do you want sources?) But the number of diameters as Pi as 1 line in itself. — eodnhoj7

More nonsense. That the numerical value of pi could be given to a length, in no way indicates that pi is a length. That pi is a length is not an accepted axiom. The numerical value of length must be qualified with a unit of measurement. Accepted mathematical axioms clearly indicate that pi is not a unit of measurement

We might also look at the gap between conceptualizations and a more ordinary sense of speeding trucks that might crush us, holes we might fall into, ice that we might slip on...I suspect that (to some degree) this is the dominant 'model'(?) by which other models are judged ultimately. — macrosoft

Look at your examples, they are all things which "might" happen. So we look at the world with a view to how we can prevent, or cause, identified future events. This does not jive with Sophisticat's "we all believe that much of the world is indifferent to our thoughts and desires".

It appears to me, like there is a deep inconsistency between how we actually live our lives, as if we can prevent or cause future events, and what you call the "dominant model", which produces a form of determinism. The problem being that we model "the world" as independent, "indifferent to our thoughts and desires", but this leaves us outside of the world, and renders the model incapable of representing how our thoughts and desires are actively changing the world. This is why our conceptualizations require that medium, "matter", as the indeterminate part of reality, bridging the gap of hypocrisy between our true perspective in which we act freely in the world influencing the future, and the dominant determinist model of the world.

You are not aware of what you are arguing:

https://math.stackexchange.com/questions/1293086/how-to-prove-that-a-straight-line-is-an-infinite-set-of-points — eodnhoj7

The cited proof demonstrates that there are infinitely many points on a line. It does not prove that a line is composed of points. My argument is that a line is not composed of points, because a line is what exists between points. And my argument holds, despite the fact that there are infinitely many points on a line. This just means that a line is divisible into an infinite number of segments.

Reread the argument I presented, you clear do not understand it, nor the axioms of geometry you are arguing. — eodnhoj7

You've already presented your argument over and over, so many times, and I've explained why it is unsound. You make fundamental errors such as assuming that pi is a line, and that "linear" means that the thing referred to as linear is a line. You argue not from mathematical axioms, but from a misrepresentation of mathematical axioms. So your argumenta are completely nonsensical.

That's what Plato's good for, pointing out flawed systems. It's a very useful talent, to be able to distinguish flawed systems. So Plato is a very worthwhile read, teaching one how to avoid wasting time on worthless philosophical systems.

1. The definition is subject to the framework which proves it. If memory serves in non Euclidean geometry a line is two points on a sphere. Axioms are determined by the frameworks which comes from them and the foundations of mathematics are not universally agreed upon. — eodnhoj7

In non Euclidean geometry, the parallel postulate is negated. This alters the understanding of a "plane" which is a two dimensional construct, from the Euclidean understanding of a plane. It does not change the definition of "line" (1d), it changes the way that one dimension is related to another dimension, as a plane. It is a different definition of "plane".

That one dimension may be related to another dimension through various means (different geometries), and the correct way has not been firmly established, supports my claim that there is a degree of unintelligibility to the relationship between one dimension and another.

2. So a line cannot change to a point relative to a much larger line? Geometric forms are determined by the framework of reference, which through the nature of the Monad (point, line and circle), is all forms as size through relation is determined by degree but most specifically quantum degrees (if one gives thought to the nature of fractal degrees). The degree, as one line relative to another, is the foundation of all size.

A line as infinite points can be observed as infinite lines. — eodnhoj7

No, as I explained earlier, an infinite number of 0d points cannot construct a 1d line. A segment of line is what lies between two points, the medium between points. There is a fundamental incompatibility between 0d and 1d which makes it impossible that a line is composed of points, it is composed of line segments which are marked by points. 0d provides absolutely no spatial extension, while 1d "line" implies spatial extension. Contrary to what you claim above, a line and a point are fundamentally incompatible and one cannot be reduced to the other.

3. If a line as infinite points is composed of infinite lines, the line is a continuum of relations...you habe not seem to understood this or much of the above argument for that matter. — eodnhoj7

It's not that I don't understand your argument, but that I reject it as invalid. A point marks a place on a line. A line is not made of points. That is your invalid assumption, and why I reject your argument.

4. A succession of units is a continuity of units, from which the word continuum is derived. Look it up in a thesaurus if you don't believe me. — eodnhoj7

A thesaurus? Continuous means unbroken, uninterrupted, connected. A unit is an individual thing, bounded and complete. Therefore an interruption is implied between one unit an another. When you say that a "succession of units" is continuous, "continuous" is predicated of "succession". But that such a succession (the activity of one succeeding the other) is continuous is just an assertion. There is nothing inherent within a multitude of units to validate your claim of continuity. Nor is there anything inherent within the concept of succession to validate your claim that a succession is continuous. Therefore you have simply predicated "continuous" of "succession", for absolutely no reason, other than to produce an argument from this axiom. That's begging the question.

1) There is not a strict definition to a line, or anything for that matter, except through the framework built around it. — eodnhoj7

Yes there is a strict definition of "line". It is a straight, one dimensional, geometrical figure. If mathematics did not have strict definitions which are adhered to, it would be useless due to equivocation.

2) A line can be both composed of angles (frequency) and exist as an angle within itself without contradiction considering all angles set the premise for size. — eodnhoj7

No, if there is an angle, then there are two distinct lines, because a line is one dimensional.

The line, as a unit of relation, is determined by its size relative to other phenomena. — eodnhoj7

As I explained, relations may be represented as a line, in the sense of "linear", but this does not mean that the relation itself is a line, it is merely represented by a line. You still do not seem to have understood this.

4. 1 exists as a unit, as a unit it must continue to exist through further units. It exist through 2 and 1/2, 3 and 1/3, 4 and 1/4, etc. One effectively inverts into one state, then into multiple states with each of these states being 1 number in itself. This progression of numbers manifests as a continuum as each number, composed from and as a unit of one, must follow that same nature and exist through further numbers. 1 along with all numbers composed of 1 as 1 in themselves must exist through a continuum where 1 and 1n exist through infinities as infinities. — eodnhoj7

No, the progression of numbers does not manifest as a continuum, it is a succession of discrete units. This fact is exemplified by your description referring to "states". If each number represents a different state, then there is a progression of different states, without an active "change" between the states. But that change is necessary to explain why one state is different from the next, and provide continuity between the states. Without the "change" between states, there is no continuity and no continuum. With the change between states, there is a separation and discontinuity between states. Either way, the states are not a continuity.

I think you're confused here. Forms are not material objects that can be different because they are in different places. They are what informs matter. That information can be entire, as it is with the the material object, or partial, as it is in the mind of the knowing subject. — Dfpolis

In Aristotle's philosophy "form" refers to "what a thing is". There are two distinct senses of "form". One is the essence of a thing, how we know a thing, and this is without the accidents which we do not observe. The other is the form of the thing in itself, the complete "what a thing is", including all aspect which are missed by us. In his physics, a thing consists of two aspects, the matter and the form. This form is complete with accidents. So we have two very distinct uses of "form", the what the thing is, proper to itself as described in his physics, the form that a thing has, and the what the thing is which is proper to the human knowledge of the thing, the form that we know. Since we are often mistaken in our knowledge of things, these two "forms" are distinct.

I don't know what you mean by forms are "what informs matter". This is not Aristotelian, but more like Neo-Platonist, perhaps. The Neo-Platonists assumed independent Forms which may act to inform matter in the act of creating objects. Aristotle assumed no such independent Forms. For him, the form was either within the mind as the essence of a thing (what the thing is to us), or else the form is united to the matter (as what the thing is, in itself). So for Aristotle form is strictly "what the thing is", and there is no such act of informing the matter.

Of course it is. It acts on my retina to form the image by which I see it. It acts on my eardrum so that I hear it, etc. These lines of action continue in the neural signals distributing the information to the brain's various processing centers which present the information of which I am aware. — Dfpolis

I do not believe that the moon is acting on your retina when you see the moon.

Why? When I mow the lawn, are all my capabilities revealed? Of course not. I am much more than a lawn mower. When things act, they reveal only part of the actuality, and forms are the actuality of a being. — Dfpolis

"Form" refers to actuality, what is actual, not "capabilities", what is potential. A thing's potential, or capabilities is not part of the thing's actuality (it's form). So it would be incorrect to say that a thing's potential, or "capabilities" is part of that thing's actuality.

This is the reason I said you were confused above. There is no "part" that leaves. There is a form that informs both within the sphere we draw around the moon and with in us. — Dfpolis

But the issue is the "form" that the moon has independently of the sphere we draw, and what exists within us. These two are really reducible to the same. The sphere we draw, is really within us. For Aristotle the object has a form which makes it the object which it is, independently of how we perceive it, and the sphere we draw.

Objects do change when we observe them. All observations are interactions, with action and reaction. We can usually ignore that fact because the changes to the object are negligible, but occasionally, as in quantum observations, they become pivotal. We could not see the moon were light not scattered off it. That light changes the moon, but in a small way we can ignore from a practical point of view. — Dfpolis

I think you are wrong here. Light scatters off the moon. The light changes the moon. But whether or not that light is received into the eye of an observer on earth, has no effect on the moon. So simple observation, in itself, does not affect the object.

Now, if we consider "reactions", then the object at a later time might be affected by an earlier observation, through a reaction, but the object as observed, is the earlier object, and the object affect by the reaction is the object at a latter time. So as much as there may be interaction in this way, we can still differentiate between the object observed (earlier time), and the object affected by the observation (later time).

P1 is ambiguous. "Very same" can mean numerical identity, which is present in experiential cognition, or it can mean having the identical set of properties, which is not the case when only some notes of intelligibility are apprehended.

P2 is true if you mean that we do not apprehend all the notes of the object's intelligibility, but false if you mean that we are not informed by the numerically identical form that informs the object. We could not possibly know anything if one form informed the object, and a numerically different form informed our mind -- for then we would know the second form, not the from of the object.

C is a non sequitur. — Dfpolis

The ambiguity of P1 is created by you, not me. I clearly mean numerical identity. You introduce ambiguity, suggesting a different meaning of "very same", in order to dismiss the argument by equivocation. The equivocation is yours, not mine, created with the intent to reject the argument.

Your objection to p2, I cannot even understand because you are talking about informing this and that, which as I explained above, I don't understand this usage. We are talking about the form of the object, what the object is, not "informing the object" whatever you mean by that.

Abstractions are not generalizations. For example, there are deep ocean species that have only been seen once. Still, if another individual were observed, we would recognize that it was the same kind of creature as the first. Thus, only one individual is needed to abstract a universal concept. — Dfpolis

Here is a good example of a non sequitur argument. Your conclusion here "only one individual is needed to abstract a universal concept", does not support your claim "abstractions are not generalizations". The universal concept is a generalization regardless of whether it is based on one individual or not. The problem is that the generalization based on only one instance of occurrence is much more likely to be faulty, though it still is a generalization. So if I only saw one instance of grass growing, I could still make the generalization that all grass is green, but it might not be correct.

What accounts for the universality of concepts is the objective capacity (intelligibility) of many individuals to elicit the same concept. — Dfpolis

Huh? What is "objective capacity' supposed to mean?

1. Something that is linear is a line, even the linear movement of a particle from point A to point B exists through a line from point A to point B. A line is a localization of directed movement in 1 direction. A curved line, as an approximation of a straight line, can be constituted as infinite straight lines composing and composed of infinite angles. — eodnhoj7

The problem here is that under a strict definition of "line", the line from point A to point B must be straight, one dimensional. If there are any angles in that course between A and B we are no longer talking about a line, we are talking about a multitude of different lines at angles to each other. If we try to resolve this issue by changing the angles into curves, and claim that we have one curved line instead of many lines at angles to each other, this is not a real resolution. What we would be doing is hiding the multitude of different lines behind the illusion of a curved line. But a curved line is really not a line at all, so that "hiding" is really a matter of deception.

Pi is transcendental and gives both proof and framework, as a number, that numbers exist through continuums. All lines exist as infinite continuums as well. A line can be both a quantity and quality. So can a circle and point. Numbers as spatial qualities have a trifold nature, due to there directed capacity where no number can exist unless directed to another number. — eodnhoj7

I can see how a line is a continuum but I cannot see how "numbers exist through continuums". Numbers appear to reveal the essence of discreteness by referring to individual units, and discreteness is the converse of continuity. So I really do not see how "numbers exist through continuums", as they are based in the concept of the discrete.

Is function the basis of teleology? Perhaps, as you say, teleology assumes a non-physical ingredient. I don't know. — TheMadFool

Function is not the basis of teleology, because it generally refers to an activity, while teleology is based in final cause, the end to the activity, the activity's purpose. The activity is the means to the end. So all these examples, brains thinking, lungs breathing, hearts pumping, and so on, are activities which are purposeful toward further ends. The activity is a means, and is not the final end, or purpose.

If we don't then we can still work with limited teleology restricted to the physical. Right?

There's too much uncertainty in spiritualism and the nothing-but physical is unpalatable. — TheMadFool

Do you think that there's no uncertainty in the physical?

I'm not saying that I do this, necessarily, but might not someone posit passive physical existents? — Terrapin Station

Yes, I think that what is developed in Aristotle's analysis, is that in each of the two classical categories, mind and body, there are both active and passive aspects. So both the physical and the non-physical would have active and passive aspects. This is where "accidentals" come into play. If we describe physical existence as essentially active, there are still passive aspects, and these would be accidental to the active nature of physical existence. And if we describe non-physical existence as essential passive, there are still active aspects which are accidental. It is by means of these accidentals that the two categories, mind and body, interact.

I still don't see anything life and mind have in common. — Andrew4Handel

Try this. All minds have life, but not all lifes have minds. What life and mind have in common therefore is life, but not mind.

Exactly. I too have been driven to Dualism. — SteveKlinko

Dualism appears to be the only resolution to many philosophical problems. This was demonstrated thousands of years ago by the ancient Greeks. At that time, there were two distinct forms of monism, the Pythagorean idealism displayed by Parmenides, stating that all reality consisted of "being", and the empirical (physicalist) approach of the Greeks, expressed as all reality consists of "becoming".

Plato investigated both avenues, and found them to be incompatible with each other, but each in itself, deficient in its capacity to account for the entirety of reality. So he turned toward an (at that time) ancient dualist perspective, and adapted it to fit the knowledge of his day. Aristotle then developed this dualism by defining and explaining terms of usage, and explaining the separation between the active and passive aspects of existence.

It is different in the sense that the part is different from the whole.is different from the part. It is not different in the sense of having a separate existence for in so far as it is the object acting within us, the form in our mind is part of the form of the object. — Dfpolis

That's nonsense. We have distinguished the form as it is in the object, as different from the form in the mind. You do not argue against this. But the form in the mind cannot not be a part of the form in the object, nor is the form in the object a part of the form in the mind, for the following reasons. In sensation, the object might act on us, being external to us, but it is not "acting within us". if it were acting within us then the whole form of the object, not just a part, would be within us. We already agreed that this is not the case. If a part of the object were within us, this implies that the whole of the object would not exist without the mind which apprehends it, it would be missing a part. The object would be incomplete without being apprehended by a mind. If a part leaves the object to act within the mind, then the simple act of seeing an object would change that object. How would seeing the moon change the moon?

You have not argued for a necessary conclusion. If you think you have, put it in the form of a syllogism. — Dfpolis

Oh, I thought I already made this very clear. P1: To take the form of the object means to have the very same form. P2: The form which exists in the mind is not the same as the form which is in the object. C:Therefore the mind does not take the form of the object.

Now, all you are doing is trying to validate this proven wrong position through some odd qualifications, saying that the mind takes a part of the form of the object, instead of taking the complete form of the object. But this qualification is subject to the problems described above. Why not accept the obvious, and simple solution, that the form in the mind is distinct from the form in the object, just like a representation is distinct from the thing represented?

I am not describing it hat way. "Perception" can mean either the sensory act, in which there is no separation or subtraction, or the mental act, in which we are not taking aspects away from the the form, but fixing on the object to the exclusion of its context. — Dfpolis

Are you claiming that in sense perception there is no separation, no medium, between the object perceived, and the perceiver? If so, how do you account for the fact that we see things, like the moon, which are far away?

Still, if we form our concept of <human> from Jane, the form of that concept is Jane's humanity informing us -- acting in us. So, in knowing Jane, she partially exists within us. That is what is meant by "intentional existence." — Dfpolis

But you cannot form the concept of "human" from one individual, Jane, because such a concept is a generalization of many humans. And so the concept "human" extends to all human beings. Therefore even if the human beings which one has met already "partially exist within us", this does not account for intentionality, which gives one the capacity to designate a person not yet met as human. So this explanation "partially exist within us" must be dismissed as inadequate to account for intentionality, and therefore necessarily wrong.

The definitions you argue are correct under standard axioms of mathematics. — eodnhoj7

I don't believe that there is a standard axiom of mathematics which states that pi is a line, or a length. If there is, maybe you can produce it.

2) A ratio, as how many times a phenomena can fit into another phenomena, with all phenomena as directional due to time, necessitates that ratio as existing as linear. How many times 3 lines can fit into one still necessitates the three lines as 1. The same applies for how many time 3 lines can fit into 6 lines as two lines. — eodnhoj7

That something is linear doesn't mean that it is a line, it means that it can be represented by a line. A thing, and its representation are two distinct things. If something is represented by a line this does not mean that it is a line. You argue by equivocation.

7. If the curved line of a circumferance is not as measurable as a straight line, then Pi is wrong because the measurement of the circumferance and diameter/straight line cannot form a ratio. — eodnhoj7

It does not necessitate that pi is wrong, it necessitates that pi is irrational. I could argue that being irrational is a case of being wrong, if I argued by equivocation like you. It cannot form an intelligible ratio, that's what "irrational" signifies, it's a ratio which has been determined as real, and existent, but which is unintelligible.

8. The curved line of a circle as irrational, neccessitates a continuum in that it is not finite. A line a 1 unit is equally irrational as a continuum. — eodnhoj7

I don't understand this, it appears as nonsense. Why do you assume a continuum? That assumption appears to be unwarranted.

10. The number of times a diameter goes into a circumferance necessites the circumferance as Pi. — eodnhoj7

This is nonsense. how do you think that "the circumferance [sic] as Pi" is necessitated?

I should have seen that comin, like a freight train. Oh baby! Don't stop me now!

When you learn to use a word, then you have also learned how to follow a rule. — Sam26

This is your premise. Now you must prove that it is true, justify it, or else you are just making an unsupported assumption which supports your conclusion (begging the question).

There is an implicit rule involved in using the word correctly, it goes hand-in-hand with language. — Sam26

Now you have made an unwarranted qualification, with the word "correctly". We learn how to use language, before we learn how to use language "correctly", (and if there even is such a thing as "using language correctly" is highly doubtful). It is evident that children use language, when learning, in a way which cannot be called "correct", but it can still be called "using language". So we must dismiss this qualification of "correctly", as unnecessary to "using language". Therefore "using words", or "using language" does not require that one do so "correctly".

So, to learn to use a word, as in my e.g., is to learn a rule about how to use the word. — Sam26

According to the above, this conclusion is invalid. To use a word "correctly" requires that one learn a rule, but to use a word, does not require that one learn any rules. Word use, and therefore language use itself, does not require that anyone learns any rules. Only "correct" word use, or language use, requires the learning of rules. But whether there is such a thing as "correct word use" is highly doubtful, because we have no set of rules to refer to, by which we could confirm whether a particular instance of usage is correct or not.

Premise (1): If all languages are rule-governed, then necessarily, learning to use a word is a rule-governed activity.
Premise (2): All languages are rule governed.
Conclusion: Therefore, necessarily, learning to use a word is a rule-governed activity. — Sam26

Premise (2) is obviously false, and manufactured to support the conclusion (begging the question).

Maybe you ought to read some other stories by Plato first, to get a feel for the writing style. They're shorter, somewhat entertaining, and easier to understand.

I am fully aware it is a ratio, but this does not negate it from being a line as well. All lines exists as x length relative to the lines the are composed of or compose. Each line however as composed of infinite lines or composing infinite lines is 1. — eodnhoj7

Each line is one line, as an identified thing, a line. But a line is not the number one. Nor is the number one a line, except as a numeral, you might make a line to signify the number one.

A ratio is the number of times one phenomena fits in another, in these respects we can use a line. — eodnhoj7

"Line" has no such definition, which would allow you to say that a ratio is a line.

The circumferance, as a length of 3.141, when unraveled, observes a line in itself that is equivalent to a diameter for one circle, with the diameter being a relative radius of another circle. — eodnhoj7

This assumption is itself problematic. You cannot "unravel" the circumference of a circle. If you took the circumference and made it into a straight line, it would no longer be the circumference of the circle, it would be a straight line. This is why PI has an issue, which makes it irrational, it assumes that a curved line (2d) can be measured as a straight line (1d), as if the circumference of a circle were like a string, which could be cut and laid out in a straight line.

In reality though, a curved line is necessarily two dimensional while a straight line is one dimensional. And, there is an incommensurability between two dimensions, expressed by the irrational ratio between two perpendicular side of a square, which indicates that a two dimensional line, the curved line of a circumference, is fundamentally not a measurable as a straight line. The curved "line" of a circle is fundamentally irrational, and not a "line" at all, because it requires (or assumes as a premise) that the irrational ratio between two dimensions has been resolved, and that a two dimensional line is measurable in the same manner as a one dimensional line. But this is clearly false, the nature of the relationship between two dimension has not between understood, and therefore not resolved.

In these respects the diameter of 1 results in a circumferance of Pi, hence a line equivalent to Pi where Pi becomes a length. — eodnhoj7

To say that a line may have a length which is equivalent to pi, is not to say that pi is a length. It is actually nonsense. It is nonsense because pi has no units of measurement, metres, or centimetres, it is just a value for the "number of times" the diameter goes into the circumference. So to say that a line has the length of pi is nonsense, because no unit of measurement has been specified. And, if a unit of measurement were indicated, we must respect the unresolved (irrational) nature of pi, which would indicate that the exact number of units, or exact length of the line is really undeterminable. This is due to the incommensurability of one dimension in relation to another. A curved line cannot be measured as a straight line.

Pi is a length, not just a ratio and alternates with 1 as the foundation of length.

All lines are equivalent to Pi just as all lines are equivalent to one in themselves. — eodnhoj7

Nonsense. "Pi" is unresolved, irrational, while "one" is resolved, rational. Therefore there is a fundamental difference between "one" and "pi". To say that there is one unit which has the length of pi, is nonsense because it would render your unit as undeterminable. That's fundamentally contradictory, to determine an undeterminable unit of measurement.

As the mutiplication/division of a length requires another length, Pi is a constant length of a line as regardless of the size of a line relative to another line, a line is always a line. — eodnhoj7

No. Pi is not itself a length. It is the number that a length is divided, or multiplied by. The length of the diameter is multiplied by 3.14... to give the length of of the circumference. But 3.14... is not itself a length, it represents a ratio, a relationship between the circumference and diameter which is constant for any circle. You can know that Pi is not a length because it's always the same number no matter what size the circle is.

Fixed that for you. — Terrapin Station

Come again?

We have the form partially, not exhaustively. I fail to see how admitting this is nonsense. — Dfpolis

The point I've been trying to make, is that the form in the mind is a different form from the one in the object. You have been insisting that they are the same form. They are not, and the differences you refer to indicate that you ought to respect this fact. We do not have "a part" of the form in our minds, because that would require taking a part away from the object, so we do not have the form "partially" within or minds. What's in our minds is a completely different form from the form which the object has.

Our experiences are complex and contextual. In fixing attention on the object, we remove notes of comprehension that are irrelevant. We do not add notes in the act of perception, but we may add them in a second movement of mind in which we use past experience to fill in gaps. In adding these supplemental notes we may create an enhanced form that is not fully justified by the current experience. — Dfpolis

You still continue to deny the necessary conclusion. Since the form in the mind is completely different from the form which is in the object, you cannot describe the act of perception as the mind taking the form of the object, and subtracting things from it. In reality, the mind is creating a form, which is a representation of the object. Since this act is an act of creating something to represent something else, there is no necessity that the two are at all similar, in reality. The form which is in the mind might be just a symbol of the object, and as in the case of words, a symbol doesn't have to have any similarity to the object represented, it just needs to represent.

Repeating the claim does not justify it. — Dfpolis

Well, I could quote a passage to justify that claim, but I know from my experience with you, that you will just turn around and say "that's not what the author meant". So what's the point? If what the author said is not what the author meant ( according to you), then how could I justify my claim of what the author said, by referring to what the author said?

2) Pi is a line between two points that exists from the center point of the circle to the circumference. All lines in turn exists as center points of a circle towards is circumference where all lines exist as the ratio of Pi as 3.14159... — eodnhoj7

Pi is not a line, it is the relation between two measurements. As it is an irrational ratio, we can conclude that the two measurements are actually incommensurable.

This is just not true. Think of how a child learns to use the word cup. The child has no idea what a rule is, but by learning to use the word in social settings they implicitly learn to follow rules. The two go hand-in-hand. — Sam26

No, you have just made an invalid inference. You claim that if the child has learned how to use the word "cup", this implies that the child has learned how to follow rules. That is begging the question. It's only true if using language requires following rules. But that's what you need to prove, not assume. You will never prove it though, because the converse is obviously what is true.

In reality, rules exist, and are dictated as words, and the person must know words in order to understand any rules. Therefore learning language is necessarily prior to learning rules, and it is impossible that learning how to use a word implies that one has learned a rule. One must learn words in order to understand rules. That is why we must look to something other than rule-following for the true nature of language. The existence of rules is something which requires language, and follows from language. Rules cannot exist without language. Therefore language itself is necessarily prior to rules, and must be based in something other than rule-following, because language produces rule-following.

Abstraction is a subtractive process. It adds nothing to sense data but awareness. So, the universal, abstracted form in the mind is just the individual form in the object of perception with the individuating notes of intelligibility left behind. — Dfpolis

That does not make sense. If the "individuating notes" are left behind, then the form in the mind is not the same as the form in the object. Necessarily, it is a different form. Whether the process subtracts or adds, or does some of both, is actually nonsensical, because the mind never has the proper form of the object within, it has something different. So it cannot use this as a base to add or subtract from. It must create the form, using whatever information it has, but the created form is clearly in no way the same form as that which is in the object, it is created separate from the object..

This is clearly an error. The concept of time is not prior to (not intuited as a condition for) our perceptions of the changing world, but one deriving from our experience of change. Babies have no <time> concept, but they do recognize change. — Dfpolis

If you read Kant's Critique of Pure reason, you will see that time and space are intuitions. Further, space is an external intuition while time is an internal intuition. These intuitions are not derived from our experience of change, but necessary conditions for the possibility of experiencing change.