Plato's concept of participation (metoche) is particularly enlightening. Sensible objects exist by participation in a Form's property. On this subject, Proclus distinguishes between (1) that which participates, (2) that which is participated in, and (3) that which is unparticipated.

The Form's being a Form is its being a paradeigma whose property or properties are participated in by sensible objects. In other words, a Form is the eternal paradigmatic cause of the things that are eternally constituted according to nature: — Apollodorus

This is where Neo-Platonism can become inconsistent with Aristotle. Aristotle's description necessitates that forms, and therefore Forms. are actual. And actual as active is distinct from potential, which is passive. In the theory of participation, material objects (actively) participate in the Forms, which (passively) are participated in. This problem is evident in Plotinus' description of the One. He describes the One as pure, or absolute potential, but he also says that everything else follows from the One as the cause of everything. But in Aristotle's metaphysics, pure absolute potential cannot have any actuality, and therefore cannot be the first cause (cosmological argument), a cause necessarily being active..

This is the problem with the theory of participation, as addressed in the Timaeus. Forms, as prior to the material things which follow from them in creation, must be actively involved in the act of creation, as causes. Therefore we cannot accurately describe the Forms as passively being participated in, they must be described as actively creating the material things.

As the Timaeus shows, the Form is perfect, the sensible objects fashioned after it are not so. The Form itself is the perfect paradigmatic original which is "unparticipated" and therefore transcendent. Its image, on the other hand, is an imperfect version of the perfect paradeigma or model, is "participated" and therefore immanent. — Apollodorus

This is why Christian theology has adopted a distinction, based on Aristotelian principles, between perfect independent Forms, and the forms, or ideas, created by the human mind. The latter are imperfect, being derived from, and therefore dependent on, the material existence of the human being.

I do not understand the Stranger to be saying that "proceeding by the method of division, we would take the kind, "beautiful things", and divide it into further types, bodies, souls, institutions, etc."
I realize just now that I failed to type in the full quote from the Stranger. My apologies. Let me try again: — Valentinus

As I said already, I find that passage in The Sophist to be very ambiguous and confusing, subject to many different translations. I don't think it's a good indication of what Plato says about ideas, that's why i gave what I thought was a better one, from The Symposium. I think that passage in The Sophist represents what the stranger (who is a sophistic philosopher) is saying about forms, intentionally creating ambiguity to make it look like Forms are the same thing as kinds.

So there is a limit to proper division and designating what combines into wholes. That relates to the Hippias passage of how a whole relates to the parts it unifies. Socrates distinguishes a difference between the whole and its parts. Hippias says Socrates is needlessly dividing things to say that. — Valentinus

But Socrates' point here is valid and very important. There is a fundamental difference between a part and a whole, involving dependence and independence, such that parts cannot be treated as wholes, and wholes cannot be treated as parts. This important difference is almost completely ignored in modern scientific enquiry, as atoms, electrons, protons, etc., which are fundamentally parts, get treated as wholes. But a part, by the definition of "part" is necessarily dependent on the whole which it is a part of, while a whole, by the definition of "whole", is in itself complete and independent, and cannot be a part of something else.

So in Socrates' example, if each person is "one", then they are described as independent individuals which are not part of any further whole, but are themselves, in themselves, whole.. But if two people are described as "two", then each of the two are necessarily parts of a whole. Then each , therefore, is not an independent whole, but a part. And, we cannot call each of them "one", because we'd have to call each of them "half" or something like that.

The Forms are said to be eternal and at rest. The category things that are eternal and at rest consists of Forms. — Fooloso4

This is the problem I address above, in this post. Forms are described by Plato in the Timaeus as causally active in creation. Therefore to say that Forms as conceived of By Plato, are eternal and at rest is a mistaken proposition. We must account for the reason why a thing comes into being as the very thing which it is, and not something else. The Form must be prior to the material thing and play an active, causal, role in making the thing be what it is. Therefore Forms cannot be in the category of "at rest". Forms are active causes.

Further, eternal things must be actual and therefore cannot be passive . This is what is exposed by Aristotle's cosmological argument, anything eternal must be actual (Bk9,Ch8, 1050b). So Aristotle straightens out all this confusion caused by the deficiencies of the theory of participation, by placing forms in the category of active, or actual. This inclines the Christian Theologians to posit active independent Forms, like God and the angels.

First, according to your argument no two things are the same. No two dogs are the same dog, but all dogs are the same in so far as they are dogs. It is this sameness that is fundamental to Forms. To be the same does not mean to be identical. — Fooloso4

By the law of identity, "same" refers to the very same, particular thing. A thing is the same as itself. That's what "same" means by the law of identity, one and the same, no two distinct things are the same.

No two dogs are the same dog, but all dogs are the same in so far as they are dogs. It is this sameness that is fundamental to Forms. — Fooloso4

Again, I really think that this is a mistaken proposition. Any particular thing has a form unique to itself. This is what Aristotle describes with the law of identity, This form which a particular material thing has, is complete with accidentals (what the human description, using kinds, or "forms" in that sense does not include". This means there are two distinct meanings of "form", the form which a particular has, and the form which a human being attributes to the thing in description. The latter being a description of kinds. What the latter does not include is what we call accidentals. So the latter sense of "form" does not involve "sameness", it involves similarity. And "similar" indicates a type of difference, not sameness, which by the law of identity is a things relation to itself.. So "sameness" in the philosophically disciplined sense, is reserved for the former sense of "form", what an individual has unique to oneself.

You are confusing the Forms 'Rest' and 'Change' with things that are at rest or change. — Fooloso4

This is a typical example of Parmenidean sophistry. Next you will say that 'Change" is at rest, because change is some eternal unchanging form, and argue some absurdity from this contradiction.

One more try, because I'm tired of your inability to grasp the type/token distinction. — Luke

You don't seem to understand the fact that the type/token distinction cannot be applied in the context of the private language.

However, there is no such Form, there is only the word/concept/type "pain" that we use to refer to actual instances/tokens of pain. — Luke

As I said, I do not believe there is any such a thing as an actual instance of pain. You'll have to show me one before I believe you. That's how you're using "instance", to signify an example of something, a "token". A token is an example of a type. So you'll have to show me your example. To talk about the existence of a token is insufficient, because you are telling me about a type, "pain" and insisting that there is such a thing as examples of this type, "tokens" without showing me these tokens.

I can have a toothache and you can have a toothache and so can everyone else, and we can all refer to it as "a toothache". — Luke

You are insisting that you have something in your box, a token of the type "beetle" (in this case, a token of pain), But to be tokens of a particular type, they must serve to exemplify that type. Since you cannot use what's in your box, as an example of the type you are talking about, "pain", to demonstrate that type to me, we cannot truthfully say that what is in your box is a token of pain.

Do you understand the reality of the type/token distinction? A token is an example of a type, by definition. If there is something which cannot serve to exemplify a type, such as an inner, private sensation, it cannot be called a token. Otherwise, you could make up all sorts of fictitious types, and claim that there are real existing tokens of those types, like unicorns and flying spaghetti monsters, but all the tokens are in your mind.

Lying about what? That you've had pain before? You could be lying, but you could also be telling the truth. What then? — Luke

You really do not understand what a token is. Suppose you name a type, "beetle", and I say, yes, I have one of those at home. The thing I have at home does not serve as an example of a type, and therefore cannot be called a "token", until it is displayed as such.. Since a token, by definition, is an example, used to demonstrate a type, anything which does not serve that purpose cannot be called a token.

This means that we can have real existing things which are not tokens. You seem to be bogged down by some type of dichotomous thinking within which everything must be either a type or a token of a type. So you do not recognize the fact that I can claim to have something, and even call it by the name of a type, "a pain", yet it is not a token of that type because I cannot use it to exemplify that type, as required by the name "token". Therefore it is not a token of that type, as required by the definition of "token".

You seem to misunderstand. An expression, such as "I have a headache", is not a token of the type "pain". It is an expression, which you (mistakenly) take to represent a token. It does not represent a token, it explicitly states I have a sensation which is of the type, "headache". This is what Banno attempted to do earlier, remove the separation between the expression, and what the expression indicates, to say that the expression is the pain. But this proved to be nonsensical.

You invalidly concluded that I must be in possession of a token of that type (beetle in the box), from the fact that I assert that I have something of that type. That your conclusion is invalid is evident from the fact that I could be lying. .

I think this issue demonstrates the area where language does not serve us well, at the fringes of our knowledge. The reason for this is obvious, what we do not know, we cannot talk about. However, philosophy is the desire to know, and this desire inspires us to expand what is known, beyond the currently existing boundaries, thus expanding the evolving body knowledge.

Our knowledge of Forms is such a thing. Some participants in this thread seem to think that a Form is a kind, and I have been saying that "kinds" are the way that we divide things, and I put Forms into a different category, as something other than a group of things. Now there is a clear need to distinguish between a group of things, divided by kind, and the principle itself, which supports the division of groups of things. Without this distinction here is much ambiguity and confusion in philosophical discussions.

The issue is well exemplified, and exposed in discussions of set theory in the philosophy of mathematics, particularly in reference to "the empty set". If there is such a thing as an empty set, then "set" cannot refer to a group of things, because it's incoherent to say that there's a group of things which consists of no things. This means that in the case of the empty set, "set" must refer to the defining principle, which allows that we might define a 'type", a "kind", and talk about that that "kind", as if it is itself, some sort of "thing", independently from any members which are supposed to be of that kind. This is the only way that we can have an empty set, if the thing referred to as "the set" is something completely independent from the members which compose the set. However, we find in the philosophy of mathematics, some people will assert that "set" refers to the group of things itself, but also assert that there is such a thing as an empty set. This is incoherent.

In relation to understanding "Forms" now, if "Form" refers to the defining principle of a group of things, then we must allow that the Form is independent from the group of things, as evidenced by "the empty set". Someone might propose "a kind" which has no members of the group This makes the Form itself something which needs to be understood as something independent from the group of things which serve to exemplify it. Therefore no degree of analysis of different groups of things can give us an adequate understanding of Forms themselves. To understand Forms, we need to separate the Form from the group of things, and grasp its independent existence. If we deny that a Form is something independent from the group of things, we will never understand how it is that there could be an empty set.

No, because a token is an object which serves as an instantiation of a type. Pain is not an object, so if we use the type/token distinction it can never be other than a type. Think about it, all descriptions of pain are descriptions of a type, tooth-ache, sore toe, etc.. Even if I think about the pain I have right now in my..., it's always a type.

The very same is also true of physical objects, we describe them in words which typify them. The only reason why a physical object can be a token is because we can point to it, without describing it in words in which case the words describe a type. Then, when it's pointed to, we can see it as an example of a type. The internal sensation we cannot see, nor point to, so it cannot serve as a token of a type. Therefore if we class it by type/token distinction, it must be a type.

It is not difference that makes things similar. Things that are similar are in some way or ways the same and in others different. — Fooloso4

Each thing is different. The "way" that it is similar can be said to be "the same way", but there is no need for "same" here, there is simply a way in which they are similar. And the "way" is artificial, as what is said about the things. Therefore sameness is not part of the things themselves, but only what is said about the things which are said to be similar, in a way. However, to say that they are similar, is to say that they are different, and this is to say that they are not the same, so this is a false form of sameness, which you propose, as property of the judgement rather than property of the things, which are said to be in some way, similar. Aristotle's law of identity, on the other hand attributes true sameness to the thing itself, by saying that a thing is the same as itself. But this means that no two things are "the same", and "the same way" is a completely different meaning of "same", because a way is not a thing. It's a superfluous use of "same", which serves no meaning.,

Rather than show it is mistake to assume sameness and difference as both necessary for intelligibility, your example shows why they are necessary. — Fooloso4

No, it just demonstrates that by some corrupt and undisciplined meaning of "same" , which allows that any two things are "the same" in some way (even if just by the fact of being things), and they are therefore similar, then any two things can be said to be the same kind. This sort of ambiguity is a feature of unintelligibility rather than intelligibility.

Things can be classified according to those that are at rest and those that change. — Fooloso4

This is very obviously another feature of the unintelligible metaphysics you are promoting. Any thing can change from being at rest to being in motion at any moment. So any thing which might be classified as a thing at rest will also be classified as a thing which can change, unless that rest is eternal. Since "rest", to be distinguished from "change" requires that change is impossible, your classifications would be better stated as "eternal" and "temproal". But the classification of the eternal cannot be said to consist of "things" because no things are eternal. Therefore the category of "eternal", or "rest" cannot consist of things at rest, and the eternal cannot be a "kind", as "kinds are how we classify things. Nor can "at rest" be a kind of thing. Of course you just need to look at relativity theory to see that there is no kind of thing which is at rest.

I will have to think more about your charge of a 'category mistake' in this context. The method of division is used throughout the dialogues. Socrates has been charged numerous times for being sophistical on account of it. See the Greater Hippias at 301 for a particularly exquisite example of the style. — Valentinus

The mentioned argument in Greater Hippias is not that type of argument at all. Hippias had said that if the same thing is true of each of us, then it is true of the both of us. But Socrates demonstrates that this is not the case, because it is true that each of us is one, but also true that both of us is two.

The category error I referred to, can be understood better through the premise of The Symposium. Remember when Socrates tells about his teacher, in love, Diotima? Diotima teaches him to see beauty in all sorts of different things. First, the beauty in bodies, then the beauty in souls, then in activities, customs, laws and institutions, and finally the beauty in knowledge and wisdom.

Now, if we were proceeding by the method of division, we would take the kind, "beautiful things", and divide it into further types, bodies, souls, institutions, etc.. And of course, each of these could be divided again. The problem is that with this method we are always dealing with things, dividing them into kinds, and we do not ever approach, or apprehend the idea of beauty, or form of Beauty itself.

So the method of Diotima differs because it goes in the opposite direction from dividing, Diotima proceeds in what is called the upward direction. Instead of dividing, Socrates is taught to see that in all these different classes of things, there is one thing in common, which unites them all. This is Beauty itself. Then the "Idea", or "Form" of beauty is apprehended as what all beautiful things partake of.

This is what it is to go aright, or be led by another, into the mystery of Love: one goes always upwards for the sake of this Beauty, starting out from beautiful things and using them like rising stairs: from one body to two and from two to all beautiful bodies, then from beautiful bodies to beautiful customs, and from customs to leraning beautiful things, and from these lessons he arrives in the end at this lesson, which is learning of this very Beauty, so that in the end he comes to know just what it is to be beautiful — Symposium 211c

That, in itself, is a beautiful description of the method of Platonic dialectics. Dialectics, in the Platonic sense, is not a matter of dividing things into types, in a downward direction, as if we might find the Forms in that way. It is a matter of starting with particular individuals, following what they have in common, in an upward direction, until one grasps the reality of the Form itself, which accounts for the reason why they have such in common.

Understanding of the Idea itself is derived from observations of the things which partake in that Idea, but the Idea is not a thing which can be divided, like a class, or a kind is said to be divided. Socrates explains this in The Parmenides, but I don't have the reference off hand. The Idea is like the day. No matter how many different places are taking part in the day, it is never more or less than what it is, i..e. the day. Likewise, the divisions which we make of kinds, are not divisions of the Idea itself, they are divisions of the things which partake in the Idea. To say that the Idea itself is what is divided is a category mistake, the groups of things are divided.

Well, the way the world is going today, it won't be long before there's a wiki for vilified sources, (if it's not already out there). The alternative wiki, for those who don't accept the mainstream "facts".

You proposed that the Sophist was written specifically as a refutation of Parmenides. — Valentinus

No, I said that the arguments purportedly made by Parmenides, as expressed in Plato's "Parmenides", are deficient, i.e., contain category mistakes. This is consistent with what you say here:

Plato is not content with Parmenides' position either. — Valentinus

Both sameness and difference are necessary for intelligibility. — Fooloso4

It is a mistake to put sameness and difference in the same category. "Similar" is a type of difference, but "same" is fundamentally different from similar. So it is a mistake to assume sameness and difference as both necessary for intelligibility. Sameness, when analyzed, is not a part of intelligibility. Just ask yourself what does "not different " mean, and you'll see that "same" is unintelligible. "Difference" is defined by change, and so is intelligible as such. "Same" is defined by lack of change, so same defines the category of "eternal", which we cannot relate to because we have no experience of it. So "same" is some mystical unintelligible category of "eternal", which people claim to have knowledge of, when this is not really knowledge at all. It's like "God", purported to be the most highly intelligible, but also completely unknowable.

Is the coupon cutter a hunter? Is a fisherman a hunter? Treating them as if they are the same or similar leads to some comical images. Fish and game requires separate fishing and hunting licenses, but no shopping licence for bargain hunters. — Fooloso4

They all have things in common, and there is nothing comical here. It only becomes comical if we try to say that they are "the same". But that's because "the same" is unintelligible.

The text refers to the use of Kind and Form in the following way: — Valentinus

Yes, this is the stranger's way of talking, to equate forms with types. Now proceed to his examples "rest" and "change". In no way does "rest" or "change" refer to a kind. A "kind" is a class of things, as Appollodorus has been pointing out, and neither "rest" nor "change" refers to a class of things. We can still say that "rest" and "change" signify forms though, as intelligible ideas, but neither signifies a class of things (a kind). Therefore there is a difference between "kinds" and "forms".

Now the stranger starts the discussion by referring to kinds of things, and dividing them, hunters, fishers, etc.. Then he (falsely) proposes an equality between "kind" and "form", as you've quoted, and proceeds to talk about some forms, "rest", "change", "being", "different", "same", as if they are kinds. But these words do not refer to kinds, the stranger has made a category mistake, and so the argument is faulty.

By the way, Valentinus, you seem to be very adept at pulling up the most highly relevant and significant passages from Plato. How do you do this? What supports that skill?

The passage you quoted above is completely different in my translation, Nicholas White, and there is a footnote proposing an alternative translation, which is completely different from yours as well. In any case, we do not need that passage, where the stranger explicitly attempts to equate "forms" with "kinds", (but is so highly ambiguous that translation consensus cannot be obtained) to see that he makes a category mistake when he proceeds to talk about the forms which follow from this point onward, as if they are kinds,

As I said, change occurs between time 1 and time 2. If change occurs then there is difference. That's what sensation is, the perception of change.

And what constitutes a single instance/token of the sensation? — Luke

There is no such thing as a "token of sensation". That's why I objected to your application of the type/token distinction here. And it's the point Banno was making weeks ago. We ought not talk about inner experiences as if they consist of things. That way of speaking is the illness which Wittgenstein referred to, requiring philosophical treatment (254-255). The reply I made to Banno though, was that we can equally apply the same principles to external "things", as process philosophy does, and Heraclitus, did; there are no things, internal nor external, all is flux.

You refuse to consider metaphysics as relevant though..

If you know this stuff, have a go. — Banno

If I wrote anything it wouldn't even last an hour.

Why would the diarist mark "S" if they thought it was incorrect to do so? — Luke

I think that the diarist would do that, because I see that people do that all the time. The sensation isn't exactly like the other one, but it's close enough, so I'll mark it as S. The person knows it is not the same, but marks it as the same anyway. I think that this type of behaviour is very common.

What criterion is there by which the sensation could be different? — Luke

Change is the criterion of difference. A person senses change and concludes difference. Change is sensible.

There’s is mystical union, theosis, which is said to be non inferential. — Wayfarer

This "cause" which I spoke of, is a part of the person, so the union is there, clearly it is logically as necessary.

That's natural and happens to everybody. — TheMadFool

Every self-respecting Christian has a personal relationship with God. — baker

The question is how is this, what I described as a "cause", and "the fundamental capacity to anticipate the future", known to us. As explained, it cannot be observed in any way. We can call it a "mystical union" like Wayfarer did, but that does not validate it as a form of knowledge. All it is is a statement of fact, what is common to us all.

This is probably the same issue which Wittgenstein grapples with in the private language argument. What is known directly to a person, through the inner source, might actually be the highest form of knowledge; Aristotle classed intuition as the highest form of knowledge; but when it comes to validating this form of knowledge to others, through public language (justification), it does not even class as "knowledge".

Again, no, not in the case of God and people who believe in God (and whose knowledge of themselves proceeds from their knowledge of God).
Because these people's knowledge is not derived from the observational, empirical knowledge, but is a (directly) received revelation from God. — baker

The problem is, that even this sort of "knowledge" (I'll call it that, though it does not qualify as knowledge by epistemological standards) which one obtains from within, "intuition", or "mystical union", must be expressed in some sort of words, if one is to proceed in a logical manner from principles derived here. So. if this "knowledge" is to form the basis for premises by which one might proceed toward understanding one's inner self, it must be expressed in language which is suited to, or conformed around observational knowledge. That is the reality of our language. So there is an inherent problem in describing inner experience with language shaped toward describing external observations.

Therefore, a person can proceed toward a "knowledge of themselves" which is completely based in their "knowledge of God", as you say, but they cannot get anywhere in this procedure. It's a dead end right off the bat because that sort of "knowledge" is not at all consistent with the language that we use to make premises for a logical proceeding. So the very first step, must be to justify , through the use of words, that inner experience. Otherwise, any sense that the person has, and is claiming, that their "knowledge of themselves proceeds from their knowledge of God", is just imaginary, an illusion. It's not real knowledge because the person is incapable of making any statements concerning what is pretended to be known. It's simply pretense.

It's immaterial whether you agree with this epistemic method. The point is that it avoids all the usual problems related to knowledge that is derived from observation, empiry. — baker

Sure, it avoids all the epistemological problems, but that's just because it isn't real knowledge, it's pretense. The epistemological problems are involved with real knowledge, not pretend knowledge.

Are you going to address the point or not? Clearly Wittgenstein is not talking about what seems to be wrong, rather, what seems to be right. And "right" cannot simply be exchanged with "wrong", because the two are completely different, so you have made no point.

I see from another of your responses that you reject 'kinds'. You seem unaware that Forms are Kinds. — Fooloso4

I think that to say that a Form is a kind, is a misunderstanding of Forms.

We have not identified the philosopher. In your opinion the philosopher would not divide things into kinds. In your opinion then Socrates was not a philosopher, for he asks "What is the just?" and rejects all examples of justice as an adequate answer. He is asking about the kind of thing it is that makes all those examples examples of the just. He is asking in what way they are all the same and come under the same name. — Fooloso4

I am not saying that a philosopher would not divide things into kinds. I am saying that an argument which proceeds in this way could be deceptive. Because of this we have to be very careful to analyze, and carefully understand the proposed divisions, and boundaries, to ensure that they are appropriately created.

To ask in what way are all the things which are called by the same name similar, is a completely different process than to divide things into kinds. Do you see this difference? Take the strangers example of "the hunter". The stranger says, lets divide "hunters" in to type A and type B. Then we can take type B and divide that into B1 and B2, and further we can divide B2, etc.. The Socratic method is to look at all the different examples of people who are called "hunters", to see what they all have in common, so that we can glean an idea of what it means to be a hunter.

The usual modern view is that the forms of inference we rely on, or should rely on, are merely truth-preserving, so an argument yields truth only by being founded upon truth. If you make a proper inference from what purports to be truth but is not, or if, in an informal argument, you rely on true premises that you have stated and untrue premises that you have not, you are abusing or misusing inference. — Srap Tasmaner

The type of argument I am talking about here is the type which attempts to prove the truth or falsity of a premise. This is the issue, how do we determine whether premises are true or false. So, for example, in the dialogue The Sophist, there is a premise that the sophist, the philosopher, and the statesman, are three distinct types. But then in the course of the dialogue, it is demonstrated that this premise is not true. Therefore the stranger, who was introduced as a true philosopher, might also be a sophist, because the premise that the philosopher is a distinct type from the sophist has been shown to be false.

In the Theaetetus, Socrates rips the Heraclitean thesis that "all things change" to shreds — Valentinus

That Heraclitus is wrong does not mean that Parmenides is right. That would make a terrible argument. You are wrong, therefore anyone who says something different from you, must be right.

Here we can’t talk about ‘wrong’, either. — Luke

Yes we can, that's the point. In fact, "wrong" is necessary, and that's why we cannot talk about "right". The only reason we cannot talk about "right" here, is because the person knows oneself to be wrong. If we so much as allow the possibility of being right, then we can talk about "right". And one can only exclude the possibility of being right if the person knows oneself to be wrong. Therefore the only reason we cannot talk about "right" , is because "wrong" is necessary.

So, we can apply this to Wittgenstein's example, the sensation of pain. Every moment that I have pain, I know that it is different, and not the same as the moment before. So every time I mark "S" to name the pain as the same pain as before, I know that I am wrong, it is not really the same pain. Since this knowing that it is not the same (because there is no criterion by which it could be the same), necessitates that I am wrong in naming it as the same, therefore there is no possibility of me being right, we cannot talk about being "right" in this context.

The passage connects to both the distinguishing between kinds and the use of 'same and different' being discussed in the dialogue. — Valentinus

The visitor's use of "kinds" is the chief indicator that he practices sophistry. We might call this the theme of The Sophist. That mode of argumentation, which is to divide things into kinds, is extremely defective, and is actually just sophistry. This is because the division of a kind into further kinds may be extremely subjective, arbitrary, or done solely for the purpose of bringing about a particular desired conclusion.

The evidence that this is sophistry is thus. Socrates asks the stranger if he recognizes philosophers, sophists, and statesmen, as three distinct kinds. The stranger says yes, these are three distinct kinds. However, throughout the stranger's discourse, we see that each of the three shares characteristics of each of the other. So such a division of kinds is really just random, or proposed for a purpose, of producing a desired conclusion.

This fact is further demonstrated by our discussion here, some of us say that the visitor is a sophist, and some of us say that the stranger is a philosopher, and neither of us is truly correct, because such a division of kind is not a true division. We say he is a sophist (he is of that kind) for the sake of discrediting his argumentation. Fooloso4 says he is a philosopher, for the sake of claiming that Plato is supporting the metaphysics he professes. In reality though, Plato is demonstrating that this form of argumentation, to divide things into "kinds", the various kinds being created solely for the purpose of the argument, is a very defective form of argumentation.

Any close examination of the proposed "kinds" will show that the divisions are defective. As demonstrated by the dialogue, the division between sophist, philosopher, and statesman, is an untenable division. And if we look at some of the other divisions which the stranger proposes, hunting, angling, trading, etc., we'll see the very same problem. Many instances cross the proposed boundaries, and the divisions are just created for the sake of producing the desired conclusion. Close examination, and understanding of the proposed kinds, and boundaries is required to expose the deficiencies. those deficiencies are what we've come to know through the existence of category mistakes.

This form of argumentation is what supports the stranger's metaphysics. The deficiencies of it are exposed more clearly in The Parmenides. But the proposed kinds, boundaries, and consequent category mistakes, expressed by Parmenides are extremely difficult to following, requiring great attention to detail. It is evident therefore, that Plato is rejecting this metaphysics, as based in faulty arguments, rather than supporting it.

I can reflect on myself, I can think about what I think, but this problem of reflexivity remains, because, as I said, the subject who thinks is not an object, except for by inference. — Wayfarer

I think that this is a temporal issue. To reflect on yourself is always to look backward in time at what has occurred, the past. This is an observational act, and it is the issue with the empirical sciences in general, what is observed is always what has happened, and is therefore in the past.

There is another aspect of human existence, and living being in general, and this is the way that we relate to, and anticipate the future. We can access this to a small extend, through introspection (which is somewhat different from reflection) , but the problem is that introspection is still an observational position. Because of this, the knowledge that we get through introspection, concerning the way that we anticipate the future, is always through the lens of how this fundamental capacity to anticipate the future, affects us (alluding to human affections), as living physical bodies, rather than being able to see this capacity as a cause

So even in introspection we are always looking at the effects of that fundamental capacity to anticipate the future, and we cannot see its true nature as a cause. This is the very same issue we have with God. We know God through His effects, the reality of physical existence, but we cannot see Him directly as the cause, His existence is inferred. Therefore when we proceed toward understanding this form of causation, it is through logic alone, and the logic is only as reliable as the premises employed. Since our premises are derived from the observational, empirical knowledge, they are in a sense tainted, as backward looking, toward the past, so that they need to be inverted to be fully logical. This is why the physicalist who sees everything from the perspective of empirical knowledge, without inverting that knowledge to make it fully logical, i.e. consistent with the rational mind, will think that the idealist, or dualist has everything backward.

Then we are all, including the philosopher, sophists. Five apples are five whether they are red or green or yellow. Unless we want a particular color apple we treat that difference as the same. — Fooloso4

No we don't necessarily treat them as the same. "Five" to me, implies five distinct and different objects. They cannot all be the same or else there would not be five but only one. It's only if you think of "five" as implying five of the same, "ones", that you treat the different as the same. But that way involves contradiction, because there cannot be five of the same thing.

Which of the pre-Socratic philosophers make the good the focus of their philosophy? — Fooloso4

Many of the ancient myths which Plato refers to are concerned with the good. The difference between good and evil has been an issue for thousands of years.

It is the context in which it is being used in the dialogue that is at issue. The way the Stranger uses it. — Fooloso4

I know, that's the point, the stranger switches meaning, equivocates, because the stranger is a sophist.

In this context, the role of the Sophist as a whole dialogue can be sought after. In what way does it impart the art of the philosopher? — Valentinus

I don't think The Sophist as a Platonic dialogue was intended by Plato to "impart the art of the philosopher", I think it was meant to expose the Eleatics as sophists rather than honest philosophers. That's what I've been arguing. The stranger is an anonymous person from that school, who is portrayed as behaving in a way which is consistent with his description of how a sophist would behave. So what is imparted is a lesson, by way of example. Imagine if there was a dialogue where a person described what it was to be racist, and in the process of that description demonstrated themself to be just like the description.

The "art of the philosopher" would be to see through the stranger's disguise, and see him as the sophist which he is. So the lesson to be learned from Plato here, is that the sophist is well disguised, and the logical arguments of sophistry may appear infallible, but the sophist is best revealed as a hypocrite, behaving in a way which he would say is not a good way to behave.

I'd say the reason for this difference is that cars typically last for about 10 or 15 years, while feelings typically don't last as long. However, feelings can last for more than a day, as I noted earlier. You might tell the doctor that you've had the same pain for weeks, months or years. — Luke

What Wittgenstein is saying at 258 is that the person has no criterion by which to judge the pain as the same from one moment of occurrence to the next, therefore there is no such thing as correctness in this situation.

However, I believe we ought to consider this principle much more closely. This is derived from Wittgenstein's definition of what it means to follow a rule, and the assertion that to think that I am following a rule does not necessarily mean I am following a rule. This results in the problem above, that the person has no criterion by which to assign the symbol "S", and there is no correctness.

But there's a principle pointed out by Plato, which is that a person can knowingly act contrarily to a rule. This is to knowingly break a rule. And this is a strong argument which Socrates used against the sophists who claimed that virtue is knowledge. Knowing what is good and correct, virtuous, does not ensure that one will act in this way. A person can knowingly break a rule. So if there is some truth to "I know that I am acting in a way which is contrary to the rule, therefore I am breaking the rule, there must also be some truth to "I know the rule, and I am obeying it, therefore I am following the rule".

Applied in this case, we can see that a person might continuously have a tooth-ache, and refer to it as one thing, the same thing. This might be for the sake of convenience in the public communication. But in the privacy of one's own mind, the person would see that it is not the same pain from one moment to the next, it goes through many different phases of intensity, etc.. So the person would know that it is incorrect to call it by the same name, "S". Yet in Wittgenstein's example, the person proceeds to do what is known to be incorrect.

This demonstrates a peculiar use of words by Wittgenstein. He says "whatever is going to seem right
to me is right. And that only means that here we can't talk about 'right'." What is really the case, is that there is no such thing as "right" here, and we cannot talk about 'right', because the person always knows oneself to be wrong. So the only reason why we cannot talk about "right" here, is because the person has excluded the possibility of being right, by knowing oneself to be wrong.

This implies that a person can know oneself to be wrong, without reference to any rules.

The philosopher appears to be what he is not. If the Stranger is a philosopher then he may appear to be what he is not. It is only by successfully identifying the philosopher that we can identify the imitator. — Fooloso4

But the stranger appears to be a philosopher, he doesn't appear as a sophist. The question is whether he really is a philosopher, or a sophist.

The Stranger's method abstracts from value, it treats such differences as the same. — Fooloso4

To treat differences as the same is sophistry to me. It is contradiction.

His concern is not Socrates' concern for the good. But this does not mean he should simply be dismissed as a sophist. If the search for the good is the mark of philosophy then Socrates would be the first philosopher. He was not. — Fooloso4

It is very clear from Plato, that he believes that the search for the good is the mark of philosophy. Also, it is clear that Plato did not believe that Socrates was the first person ever to have concern for the good.

It does. The Stranger is identified as a member of that circle. (216a) How do we reconcile Parmenides' denial of not-being with the Stranger's affirmation? The solution is in the dyad 'same and different' or 'same and other'. In this case, what is and is not being. — Fooloso4

Being concerned with "that which is not" is the mark of a sophist (254).

If you maintain the distinction between being and becoming then you maintain the distinction between being and not-being. As you say, becoming is not being. — Fooloso4

In the context I was using it, "not-being" was a shortened form of "that which is not". Here, you use "not being" to indicate something which is other than being. "Becoming is not being". Equivocation is a tool of the sophist.

If there is no reality about what the electron is and quantum physics is purely a functional method utilized by technological practice, how can you say that the intelligible form of the phenomenon is more real than the sensible? — Enrique

Obviously, the mathematics (intelligible form) is very reliable. Coming from the other direction, visible observation, we see material objects can be broken into parts, and we see molecules with microscopes, and theorize about atoms as material objects, and the parts of atoms, which are responsible for the bonding between atoms, as material parts. But then we cannot see where these proposed electrons (as material objects) are, so we cannot validate with our senses, that they even exist as material objects.

So the intelligible form of "the electron", is very reliable, and proven in scientific research therefore extremely real. But the "sensible form", as a particle, being a part of an object, cannot even be sensed at all, so we really cannot say that there is any reality to the "material form" of an electron. .

When the past and future interact they are causally unified such that certain events could happen and alternate events couldn't. — Enrique

This leaves out a huge portion of reality. Of the events which "could happen", there is a division between the ones which actually do happen, and the ones which don't happen. We cannot class the ones which don't happen with "events that couldn't happen", because they've already been placed in the other category, of "could happen", and this would effectively negate the category of "could happen", resulting in hard determinism.

Therefore we need a form of causation which is not the same as the causation of determinism, to allow that within the category of "could happen", some events are caused to happen, and some are not.

Another striking difference that ought to be pretty obvious is that Socrates’ philosophy serves a higher purpose which is to attain a vision of the Good, whilst the Stranger’s sophistry is for its own sake. — Apollodorus

This is an important point. Plato came across the importance of "the good" in his attempts to understand the reality of ideas. In The Republic, "the good" is described as that which makes intelligible objects intelligible, just like the sun is what makes visible objects visible. We can say :the good" is the reason for the intelligibility of intelligible objects.

Aristotle then proceeds with a much better definition of "the good". "The good" is that for the sake of which, "the end", as what is intended.

In seeking philosophical knowledge it is of the highest importance that "the good", meaning what is sought, the end, (in Aristotelian terms), or that which illuminates the ideas making them intelligible to the person (in Plato's terms), is real understanding, and truth. Without this true goal of real understanding, any goal, such as financial gain, honour, the pride of vanity, etc., might take the place of the true goal, real understanding, and serve to illuminate ideas as intelligible, instead. And the ideas which serve such goals, though they are highly intelligible to a person who has that goal, will not be intelligible to the person who has the highest, true goal of real understanding.

This is the position of the sophist. The sophist has some goal, a good, which is other than the goal of truth and real understanding. So the principles which the sophist argues appear to be highly intelligible to anyone else who has a similar goal. But these principles are seen as unintelligible to anyone looking for the real good, the true goal of real understanding. Therefore Aristotle proposed a distinction between the real good, and the apparent good.

I regard an ontological proposition that the immaterial is a fundamentally distinct substance from physical matter as fallacy.

If what has traditionally been referred to as immaterial is a distinct substance in some sense, it at least has to have causal principles in common with conventional matter by virtue of interaction, and the entire range of phenomena becomes part of one theoretical edifice modeling a single reality, which will presumably be a revised physical reality of matter in various forms. — Enrique

You seem to be neglecting the reality of time, and the division between past and future. In relation to the past, there is real 'material' truth concerning what has been. In relation to the future, there is real possibility. At any moment, my material arm might move to the right or to the left. There is no determinate truth as to where my arm will be in the next moment. This means that to speak of the material existence of my arm, on that side of the present, the future side, is to speak nonsense. But we can always speak truth about where my arm was on the other side of the present, the last moment.

We exist at the present, but there is a real incompatibility between the material existence of the past, that which has been experienced, and the immateriality of the future, that which cannot be experienced. However, we cannot say that the future is completely without substance, though it cannot be experienced because this would put it into the past. If the future was completely without substance, this would mean that absolutely anything is possible at any moment. So we can conclude that the "substance" of the future, as allowing for real possibility, is distinct, and separate from the "substance" of the past, which does not allow for possibility.

Clearly, the "causal principles" attributable to the substance of the future, which enable the reality of possibility, are not "in common" with the causal principles of the determinate matter of the past. This does not mean that the two do not interact, as they clearly do, at the present. What it means is that the causal principles which are applicable to the substantial existence of the observed past, are completely distinct, and separate from, incompatible with, the causal principles which are applicable to the substantial existence of the unobservable future.

Therefore the dream of "a single reality" where everything behaves according to a single, consistent and coherent, set of causal principles, because it is composed of a single substance, is just that, a dream. And you appear to be living in this illusion, which others have created for you, and impressed upon you, until you accepted it without appropriate scrutiny. Either that or you created the illusion yourself because you are intellectually lazy, and the true nature of reality is too complex for you to grapple with.

I don't understand the basis for calling the Stranger a Sophist. Can you point to one of the arguments he makes by way of example? — Valentinus

Socrates asks the stranger at the beginning, about the difference between engaging others in the discussion, and simply making a long speech. The stranger claims to respect this distinction. But the entire dialogue turns out to be a long speech made by the stranger. Sure, the stranger pretends to engage Theaetetus in the discussion, but it's really only to ask him to agree at certain points, it's never to ask for his opinion. You can read the dialogue without paying any attention to what Theaetetus says, and it reads like a big long speech from the stranger. So this is just a pretense, to engage Theaetetus, and that is one of the things the stranger says a sophist is, an imitator.

Further, there is throughout the dialogue, many subtle indications that Plato (in writing the dialogue) is having the stranger do exactly the things that he says are characteristic of the sophist. For example, at 254, the stranger says "The sophist runs off into the darkness of that which is not...". Then, by the end of 256 the stranger is talking about "that which is not"... "So it has to be possible for that which is not to be..."

Remember, what is stressed over and over again throughout the dialogue, is that the sophist is hard to catch, appearing just like a philosopher, but really a poser, a pretender. The dialogue has to be read very carefully to see that Plato is portraying the stranger as a sophist, pretending to be a philosopher.

Another indication is that the stranger is not named. The Eleatic school was highly regarded by the Greeks, and respected even by Socrates. Plato could not name a member of the school, and portray him as saying the things which the stranger says, because none of them would have actually said those things the way Plato presented them, so he'd be guilty of libel. The stranger from Elea is presented in a way which is less than flattering, as a sophist, and this is a serious attack on the Eleatic school, so it is disguised. As such, you might say it is itself a work of sophistry. Nevertheless, Aristotle later continued with this attack, more openly.

Is he mistaken in his opinion? If not, then what is the difference? Why is there a dialogue the Sophist and a dialogue the Statesman, but no dialogue the Philosopher. Where is the philosopher? Are they three? — Fooloso4

It's not that he is mistaken in his opinion, but the stranger behaves in a way which he himself says is the way of the sophist. In other words, Plato has the stranger describe what a sophist is like, while the stranger is behaving in the described manner.

Have you noticed how often Socrates' behaves like a sophist? Aristophanes was not simply mistaken when he called Socrates a sophist. — Fooloso4

Yes, as the stranger says, it is very difficult to distinguish the philosopher from the sophist, so just as the sophist appears like a philosopher, the philosopher will appear like a sophist. The way that they differ is that one is a pretender, an imitator.

One of the key differences mentioned is what I said above, that the sophist hides in the concept of "that which is not". It is a common ploy of sophists, mentioned by Aristotle, to produce a dichotomy of being and not being, that which is, and that which is not. Once this dichotomy is produced, there is no place for becoming, which is neither being nor not-being. This is the result of adherence to the law of excluded middle. From this platform, the sophist can "prove" all sorts of absurdities.

What is it about a sophist that you think means he must be wrong? The sophists were not all the same, to simply to be dismissed. Their arguments must be attended to, as Socrates did. It should also be noted how often Socrates incorporates parts of what the sophists he is arguing with say. — Fooloso4

Unlike philosophy which has one goal, described as a true desire to know, sophistry works toward many different ends. That's why "sophists were not all the same". But since it works toward an end, and that end is not true knowledge, as is the case with philosophy, the sophists arguments are designed toward proving whatever is seen as conducive to the end. The end is what Plato called "the good".

He was, as you said, from Parmenides' school. It was not a school of sophists. — Fooloso4

That is your opinion. The question is whether it was Plato's opinion or not. Notice my quote above, from 254, where the stranger says that the sophist runs off and hides in "that which is not". Doesn't Parmenides' school have a lot to say about "that which is not"?

In the case of the tree trunk, the distinction between the ideal and the real is easily inspectable with vision, while in the case of subatomic matter, its structure morphs at a rapid rate and in such complex orientation that we are mostly reliant on an indirect process of manipulating ideal concepts for any empirical comprehension we can achieve (though techniques such as electron microscopy give us some direct insight). But subatomic matter is no less material than a tree trunk, we simply don't have sense-perceptual insight at the subatomic scale to make this obvious. — Enrique

What subatomic physics, quantum mechanics, demonstrates, is that the reality of continuous subatomic existence is best represented as immaterial (wave function). There is no reality to where the electron, as a material entity, a particle, is at a specific time, because the evidence indicates that it does not exist as a material particle.

This is the inverse of what you say about the tree trunk. Every attempt to represent the tree trunk as an immaterial form fails, as you say, because the form of the trunk is given to us through our senses. What you are not accounting for though, is that our senses are deficient, as you probably already know, they commonly mislead us. So the form which our senses gives us of the tree trunk is incorrect, due to the deficiencies of the senses. As chemistry and physics show us, the trunk is not really as it appears to our senses. So the fact that the ideal does not match up with the tree trunk, as perceived by the senses, is because the senses misrepresent the tree trunk to us, The senses provide a much more deficient perspective than the intellect does with its ideals, so it is clearly not a case of the ideals being wrong, while the senses are right .

This is exactly the issue of Plato's cave. The common people believe that the world is as it appears to the senses, and if the intelligible principles are not consistent with what the senses give us, the intelligible principles must be wrong.. But what Plato says, is that what the senses are giving us is just a representation of the world, and the senses are far less reliable in representing the world than the intellect is. The real world is completely different from how the senses represent it to us, the sense representations being the shadows referred to in the op. Modern science confirms that Plato was absolutely right. The real world is completely different from how it appears to our senses, and the intellect demonstrates to us that the intelligible forms are far more reliable in giving us the real world, then are the senses.

There is a lot more to the dialogues than Socrates pointing out the weaknesses of the arguments of others.

I do not think it is a case of Plato dismissing the views of others, but of you dismissing the dialogues of Plato. — Fooloso4

In "The Sophist", the stranger, from Parmenides' school, is of the opinion that there is a difference between, a sophist, a philosopher, and a statesman, as three distinct intellectual capacities. What is demonstrated by Plato, is that the stranger, who thinks of himself as a philosopher, really behaves in the way that he describes a sophist. So the stranger is therefore the sophist, the namesake of the dialogue.
Why else is the dialogue called "The Sophist"?. It is clear that Plato is not supporting what the stranger is arguing, as the dialogue is presented as an example of the sophistry coming from the Eleatic school.

Humans are capable of thinking and imagining in extremely versatile ways, especially as it relates to generalized concepts (the universals you guys are talking about), but commonly refuse to or shrink away from doing so. I think this constant, arbitrary stereotyping of conceptual categories shows that rationality is without a doubt material, rooted in the body.

If the so-called immaterial is to be understood, it must be via reconfiguring physical knowledge to account for its material and physiological foundations in novel ways. — Enrique

The problem is, that when we follow "the material" all the way down, to its most fundamental constituents, as we are prone toward doing in scientific reductionist practices, we find that what is there, what supports the material world is the immaterial. So for example physics has found that immaterial wave fields are the foundation of material existence. When we encounter the immaterial at the bottom, as the foundation of all material existence, and our attitude is that the only way to understand the immaterial is as rooted in the body, then the immaterial is rendered as impossible to understand.

When this blockage toward understanding the immaterial is hit, we have no recourse but to reverse this attitude that the immaterial is rooted in the body, to account for the true fact that the body is rooted in the immaterial. When we make this reversal of attitude, all the various features of reality, like free will, and the so-called "hard problem", which are impossible to resolve from the perspective that the immaterial is rooted in the body, become highly intelligible.

But tell me again how your contradiction is a result of "different contexts". — Luke

Why should I have to tell you again? Can't you read? Oh yeah, that's been central to this whole discussion, your inability to read what is written. I see now, that when it comes to metaphysics, you have an attitudinal blockage, which is most likely the cause of your misreading of Wittgenstein.

We are discussing Wittgenstein who says in the same work: "What we do is to bring words back from their metaphysical to their everyday use." — Luke

Yes, what Wittgenstein suggests, is itself a form of metaphysics. But unless you take the time and effort required to understand the metaphysical usage of the words, you haven't the means to bring the words back.

This is easily solved. Provide an example of a token of sensation that is not present to the conscious mind. — Luke

I've done this many times already, but you refuse to acknowledge. Any token of pain which is there when I fall asleep, and also there when I wake back up, like a tooth-ache, or the pain in my toe, were the examples already given. That very same "token" of pain exists while I am sleeping and it is not present to my conscious mind. It was there when I went to sleep, and it is there every time when I wake up in the night, just like the chair in the corner of the room, so I can conclude that it must be existing, though I am not sensing it, when I'm asleep. Why would you think that there is some type of magical "token" which magically disappears, and reappears every time I fall asleep and wake back up? Obviously it is the very same tooth-ache, which I have in the morning, as I had the night before, and not a different tooth-ache, so this "token" of pain must exist during the night while it is not present to my conscious mind.

Rather than a distraction, I introduced the type/token distinction intending to help provide clarity for what could be meant by "the same sensation" or "the same chair". But we got bogged down in your continual misunderstanding and argumentation about what is a token. So you go ahead and give your metaphysical reading. — Luke

Obviously, the type/token distinction has only created confusion. We cannot even agree on what a token of a sensation might be. Wittgenstein clearly does not use that distinction, and at the quoted passage (261), he implies that we cannot make such a judgement concerning what is referred to by "S" ("that when he writes "S", he has something—and that is all that can be said").

Do you accept this, that when he says "that is all that can be said", he is implying that we cannot apply the type/token distinction here?

"One" as unity, in the sense of simple or non-composite, need not be limited. — Apollodorus

Such a sense of "One" is definitely limited. If it was not limited there would be nothing to maintain its status as simple or non-composite. That is a limitation, whatever prevents it from being a mixture.

Indeed, Plato says quite clearly that the One is not a whole consisting of parts and that it is "unlimited" (apeiron). This is precisely why there is nothing else like the One. — Apollodorus

I never saw a clear and coherent definition of "the One" in Plato, perhaps you could show me where this is stated. Nevertheless what I did see stated about the One seemed confused and incoherent, so I tend not to agree with it. I have the same problem with what Plotinus said about the One, though it seems much clearer than what Plato said, it still appears to me to be inconsistent.

The ordinal numbers are orders of numbers. It applies to anything that is ordered in some way as first, second, third.

Eidetic numbers are relations of eidos or Forms. Their order is determined by kind. — Fooloso4

So eidetic numbers look very similar to ordinal numbers to me, as an ordering of Forms. Numbers are Forms, and orders are relations. Differences of "kind" is insufficient for determining an order, because relations between the kinds is what order is.

Rest, Change, and Being are not at the same level of order and so are not counted together. — Fooloso4

I don't see how you can justify this claim. What puts being at a different level from rest and change?

Why would Plato write this long, detailed, difficult dialogue if the point is to just to dismiss the Stranger? — Fooloso4

Have you not read many Platonic dialogues? That's what he did with them. He wrote long difficult dialogues to show the faults of, and dismiss the views expressed by the people taking part in the dialogues.

Not necessarily. There is a difference between "unit" and "unity". The former refers to one among many, the latter to something that is one in the sense of simple or non-composite.

As unit, one is limited. As unity, it can be unlimited. — Apollodorus

Well, I don't accept any of this. I see no reason why a "unit" must be one among many, and not just a defined "whole", without the need for others to validate the definition. And I see no possible way that "unity" could be unlimited, as necessarily limited by that which unites.

Monism posits a One, but a One can only exist in relation to another. So 'one' already implies 'two'. — Wayfarer

As above, in the case of "unit", I do not agree that One implies two. "One", as commonly defined (as distinct from mathematically defined), is a fundamental unity, an individual, a whole. To describe, or define a unity, individual, or whole, does not require reference to others. It is only when "one" is defined as referring to the first, in an order, or succession, that there is a second implied. This is the mathematical way, based on "ordinals". But in this definition the second is not actually necessary, it is implied as possible, the possibility of something following the first. In other words, the position of the first is defined by allowing for the possibility of followers, and it does not require actual followers.

We discussed this issue in another thread on the difference between cardinal numbers and ordinal numbers. Modern mathematical theory derives cardinals from ordinals, so the primary definition of "number" places "one" as having a position in an order, thereby implying others. But this does not make "one" refer to a unit, individual, or whole, because that requires a different definition. It makes "one" refer to a position in an order.

But if this is the case, then "one" is not a unit, or individual, but a place, and we cannot truly derive the cardinal numbers in the way that mathematicians do, because they count these places as if they are objects, when by definition they are not objects but places. In reality therefore, cardinal numbers cannot be derived from ordinal numbers, because the two rely on distinct definitions of "number".

What confusion? — Luke

Your mode of argumentation, as commonly displayed, is to pay no respect for what the other person is saying, and remove phrases from their context to create the appearance of contradiction.

Here is your confusion. In one context I was speaking about instances of sensation of a token. In the other context I was replying to your talk about instances of existence of a token. You conflate these two, continuing to insist that an instance of sensation of a token is an instance of existence of a token, refusing to acknowledge the difference between these two, hence your confusion .

The definition of a token is not “encountering a token”, as you obviously think it is. — Luke

When I've spent a number of days explaining to you, the difference between encountering a token, and the existence of a token, because you ceaselessly insist that a token of sensation can only exists if it is present to the conscious mind, for you to make a statement like this is a clear indication, that you are confused.

I'm sorry if my use of words is confusing to you, but your attitude ("I'm not going to follow you in your metaphysical nonsense"), is the real reason for your confusion. We are discussing a metaphysical issue, so if you refuse to follow the metaphysics of the issue, it is impossible that you will ever understand.

Here's a proposal for another way of looking at this issue, to perhaps iron out the confusion which Wittgenstein has created with his way of writing.

Since we have no point of agreement between us as to whether "S" is supposed by Wittgenstein to stand for a token or a type, Let's start with what Wittgenstein says at 261: "that when he writes "S", he has something—and that is all that can be said". Do you agree that "S" as employed in Wittgenstein's example refers to neither a type nor a token? .Can we say that "S" refers to "something", and that's all that can be said? To say that it refers to a either a type, or a token of a type, is to jump to a conclusion, because the diarist's use of "S" has not yet been justified. What "S" is supposed to refer to is something completely private. Even to say that the diarist "has something" is a little misleading, as Wittgenstein describes at 261, because these words have meaning in our common language, "has" implying a sort of possession, and "something" implying a sort of thing.

So we can remove all this type/token distinction as a distraction, and get right down to what Wittgenstein is actually saying with the example. S refers to something private and we really can't say whether it's a type or a token, because what S refers to is 'known' only to the diarist. Of course this is a special use of 'known', because it is explained that the diarist has no real criterion of identity.

So I'll repeat what I said before. The ambiguity inherent in your preferred type/token distinction produces the confusion required for your mode of argumentation.

You know what I meant. Your pretense continues to baffle me.

but some Platonic immaterial objects are real insofar as we are affected by them. — Mww

This is an important point, as it implies that the immaterial has causal power over us, as material beings. So even if we take a materialist or physicalist perspective, which see the human being as a physical body, we have to provide the metaphysics required to account for this fact, that the immaterial has causal power over the material body.

We are discussing number which can be understood as being necessarily instantiated in diversity. If you are thinking about the so-called platonic forms of objects, like for example the form of the horse; we can be affected by the empirical form of a horse or the imagined form of a horse. When it comes to a number, say five, we can be affected by the empirical form of five, five apples for example, or we can be affected by thinking about five. When it comes to the form of the good, we can be affected by an empirical form of the good, a good action for example, or we can be affected by thinking about the good. There are diverse instances of horses, instantiation of five and examples of the good, so I'm not seeing the difference you are attempting to refer to? — Janus

Suppose you are hungry, and you move toward getting something to eat. You are affected by this immaterial idea, to get something to eat. It has causal power over your material body. The immaterial ideas of numbers have a very similar causal power over you. For example, if you have a thousand dollars in your bank account, and you need twelve hundred for your rent payment tomorrow, you will be moved toward getting another two hundred into your account. These numbers have causal power over your material body.

This is one token of a chair: “the very same chair”. You are not distinguishing two instances of chair here. — Luke

I'm not talking about two instances of chair, I can't even understand what that might mean. I am talking about two instances of seeing the very same chair. Likewise, a person might have two instances of sensing the very same sensation, or two instance of remembering the same memory, or two instances of using the very same idea of "two", and "four". How is this so difficult for you to understand?

We cannot have different instances of the very same token, by definition. A token is an instance of a type, not an instance of seeing or encountering something. — Luke

I didn't say we can have two different instances of the same token, that doesn't even make sense to me. I said we can have two different instances of encountering, or sensing the same token, like when I see the same chair today, that I saw yesterday..

It is very clear that we can have two different instances of sensing the same token, as exemplified by the token of chair. Why do you think that we cannot have two different instances of sensing the same token of pain?

But when people talk about their inner experiences, we tend to assume they are all numerically distinct, that having "the same feeling" at one time that you had at another means only that you have had two quite similar feelings. Why is that? Is it because we are physical beings, subject to time and chance?

There seems to be no logical barrier to having the same experience or the same sensation twice. But it strikes us as wrong. We believe "I have the exact same feeling I had when ..." is always literally false. What would have to be different for us to consider such a statement, like the unintentional return of the loaned book, literally true? — Srap Tasmaner

The problem is that there is a double standard here with respect to "inner experiences". We commonly believe, due to some sort of intuition, that it is impossible to have the same sensation twice, a sensation being an inner experience. So we are inclined toward believing that inner experiences are merely similar, or of the same type. But when it comes to other inner experiences like memories. we always talk about having the same memory twice. And then there is the logic of mathematics, where a significant logical structure is dependent on the assumption that the idea (another sort of inner experience) is always the same idea. So there is an inconsistency between this notion, that we cannot have the same inner experience twice, and the fundamental axioms of mathematics, which assume that we consistently work with the same mathematical objects.

What Wittgenstein seems to get backward, is that he portrays the private, inner language as naming particulars, and the public as naming types, showing an incompatibility between the two. In reality the private language is inclined toward naming types, as intuition tells us that two distinct sensations cannot be the same. But to make the private types intelligible to the public in general, we must refer to particulars. So the public language inclines us to name particulars while the private language inclines us toward naming types, and there is still the incompatibility between the two, which Wittgenstein demonstrates.

The One is Infinite or Unlimited. — Apollodorus

Isn't "one", by its very definition, a unit and therefore limited?

What is at issue is not that there are different kinds of number, but what is different about the eidetic kind: — Fooloso4

I think that this is just like the modern difference between ordinal numbers and cardinal numbers, ordinals demonstrating an order, while cardinals count a quantity.

The point is that Being belongs to a higher intelligible order. — Fooloso4

Sure but if it's a higher order than rest or motion, how does this make it not simply a third category?

Also, remember that this is the position of "the Stranger" which is being expressed, not the position of Socrates or Plato, and usually Socrates ends up demonstrating how the positions of the others are faulty. So I would not attribute a lot of significance to what the Stranger says, as it's most likely just another form of metaphysics, popular in the day, which Plato is dismissing.

You have acknowledged there is no problem with naming a single token of the sensation. — Luke

This depends on what you call a problem

If the person is naming a single token, it's as Wittgenstein clearly indicates at the end of 258 "One would like to say: whatever is going to seem right to me is right. And that only means that here we can't talk about 'right'". There is no such things as correct, in naming a single token, because this cannot be judged. The person has no criterion by which to judge whether one occurrence is the very same as another occurrence. In the case of the chair, on the other hand, we might ask someone else who observed the chair in the interim time period. So there is no problem for the person naming, just no sense in talking about the person is correct.

But the problem arises when the person attempts to justify his use of "S". Since there is no such thing as his correct use of "S", justification of his use is problematic

If it were as you claim, that he was naming a type, then there would be no such thing as him being wrong . A type is created, so whatever he names, is that type, 270. Since the person writes "S" every time, then the sensation has been placed in that class, signified by S, therefore it is of that type, which the person has called "S". The person cannot be wrong.

This difference clearly indicates that the person starts the practice by attempting to name a single instance, (what you call a single token), and it's only upon the attempt to justify his use, that he is forced to demonstrate it as a type. That there is a difference between naming a type, and naming a single object, is where the problem lies.

• The problem is in establishing the name/type of the sensation, 'S'. — Luke

This is not true. There is no problem here, "Sensation" is a term of the public language with a definition, so it is already established, no problem..

261. What reason have we for calling "S" the sign for a sensation? For "sensation" is a word of our common language, not of one intelligible to me alone. So the use of this word stands in need of a justification which everybody understands.—And it would not help either to say that it need not be a sensation; that when he writes "S", he ha something—and that is all that can be said

So, the question here is what reason do we have for calling the thing which the diarist has labeled with "S", a sensation.? Why is it a token of "sensation"?

This is why the type/token distinction is misleading you. It puts the type as prior to the token. A token is necessarily of a type. But here, Wittgenstein puts the thing, what is referred to by "S", as prior to the type. It is not a token at all, but just something being named. It's just a thing, "he has something---and that is all that can be said". So we cannot call it a token, because its classification, as a token of a sensation has not been justified.

• Your constant repetition that Wittgenstein uses the phrase "the sensation" is no support for your claims. — Luke

I gave you examples of common use, "the chair", "the hammer". Each time we use "the" in common usage it refers to a particular token. You have provided no examples of when we use "the" when referring to a type.

• It is not my claim that he refers to a more general type called "sensation", but that he refers to a type of "certain sensation" called 'S'. — Luke

Your phrase, "type of certain sensation" doesn't even make sense. It would make sense if you said "certain type of sensation", but of course that would be inconsistent with what Wittgenstein said. The simple fact is that he doesn't mention "type" at all, so your attempt to put it in there is completely out of place.

If you assume that the sensation occurs continuously, then what distinguishes one instance from another in Wittgenstein's example is every (different) day. — Luke

Clearly, what distinguishes one instance from another is the coming into the conscious mind, coming to the attention of the conscious mind. Just like when you see the very same chair twice, what distinguishes one instance of seeing it from another, is the coming to the attention of your conscious mind. I don't understand why this is a problem for you. He is giving an example of inner experience, and this is how we commonly talk about inner things like memories and ideas, they come and go from our conscious minds many times, as the same thing recurring many times, many different instances of the very same thing coming into your mind.

. Different tokens are different instances. PERIOD. — Luke

You are refusing to acknowledge that despite the fact that "Different tokens are different instances. PERIOD", we can have different instances of the very same token. PERIOD. Why is this so difficult to you?

How does that follow? It's equivalent to saying that seeing something is a creation of the act of seeing. — Luke

Why can't you understand this either? If the thing (object, or token) exists only at the precise time when it is being sensed in the act of sensation, then it must be the act of sensation which is creating its existence.

On the other hand, if the thing which is being sensed in the act of sensation continues to exist when it is not being sensed in the act of sensation, then the very same thing might be sensed numerous times.

Which part of "it's not about "encountering" something" do you not understand? I'm not going to follow you in your metaphysical nonsense. — Luke

Your refusal to even attempt to grasp some very simple metaphysical principles show me why you have such a difficulty understanding what Wittgenstein said.

That's mot how I see it. I could disagree because I think an alternative view seems the more plausible, without even necessarily being wedded to that alternative view. — Janus

But you would think that you were right to disagree, otherwise you wouldn't disagree.

I think it's way too much of a generalization, and presupposes that there was some absolute ( as opposed to contextual) truth understood in the ancient world which is beyond our understanding today, — Janus

There is something very important which has been lost. It's the way that we relate to time, summed up very well by Einstein when he says that time is an illusion. We've lost the perspective which apprehends the reality of time. That's why questions about the eternal are so important, they bring us face to face with the reality of time, when that reality has been lost to illusion.

thus one which we cannot fully understand no matter how hard we try, because we simply cannot put ourselves into the ancient mindset since we are not ancients. — Janus

This is the closed minded perspective. It's nothing more than I cannot fully understand you, because I cannot put myself in your mindset, on a larger scale. I cannot become you, and I cannot become an ancient person, but that does not mean that I cannot put myself in your mindset, or in an ancient person's mindset, to understand.

I think I understand Wayfarer's position very well and all the more so since I actually used to inhabit it. — Janus

Coming from the person who just said wayfarer's position (putting oneself into the ancient mindset) is impossible.

I think we should always be open to the possibility that we have it wrong; — Janus

But if you didn't think you were right, you wouldn't disagree. To be open to changing your mind is another matter, related to how determined you are in your belief, certitude. And if you're very open minded, then you just don't tend to disagree.

And actually what I should have said is "you act as though you think those who disagree with you must not understand," as that would be even more accurate to the situation as I see it. — Janus

Now that's a better way of putting it. But isn't it the case that when two people disagree it's mostly likely that they misunderstand each other? So there's nothing wrong with assuming that the other misunderstands. The reason for presenting arguments is to aid the other in understanding. That's what changing one's mind is, coming to understand what wasn't understood before.

You act as though you think those who disagree with you must be wrong. — Janus

Doesn't it go without saying, that when someone disagrees with you, you think the other person must be wrong? Isn't that precisely what disagreement is, a case of thinking that the other is wrong?

The problem is with number, but it is with number as understood by the Greeks, which is not the way we treat number.

Aristotle identifies three kinds of number: — Fooloso4

We have a multitude of different kinds of numbers as well, natural numbers, rational numbers, real numbers, to name a few.

To count rest, change, and being as three would be mistaken. Being is a higher order than rest and change. It is not a third thing to be counted alongside them. — Fooloso4

I don't see your point