Yeah, well, you know: horse, water. Smart horse drinks, stubborn horse won’t unless it’s chilled Perrier.

I'm sorry about the length of reply. — RussellA

I'm not. I agree with . Well done.

But I see some issues.

I might start with Russell's theory. Russell's logical atomism, as you so well describe it, involved working up from simple atomic statements setting out things of which we are directly acquainted, using Frege's logic. Philosophical analysis for Russell was a process of breaking down complex propositions into their constituent parts, and then reassembling them. By doing this, he argued, we could identify the truth of any proposition by looking at its separate components.

Wittgenstein, in PI, argued that what counts as a simple was dependent on the task at hand. The same thing can be simple in one context, but complex in another. The task of analysis is to understand the context and the language game at play. He argued that there was no fixed set of atomic propositions, and that the task of philosophy was not to break things down into their component parts, but rather to describe the complex interaction of language and context.

There are also the more involved criticisms of Russell's theories deriving from Kripke's Possible World Semantics. We might set those aside in this context, noting that it is not clear that Russell's work on denoting solves the syntactic and epistemic issues it was supposed to.

So we have here two differing approaches to the nature of the apples being purchased at our grocer. On the one hand we have Russell's view that the apple consists in a concatenation of "constituents with which we are acquainted", something like "Green or red and round and waxy and smooth and tart or sweet". On the other hand we might set out the nature of an apple by setting out the roles it might play as we go about our daily activities: The thing we pick, sell, bite, stew, bake in a pie and so on.

We have a similar divergence of approaches to the numbers. On the one hand we might have Russell's failed attempt to build arithmetic from logic by creating a set of axioms and definitions that could be used to construct mathematical proofs. He failed in this endeavour, as his work contained paradoxes that undermined the logical consistency of the system. These paradoxes showed that the foundations of mathematics could not be reduced to pure logic, and that mathematics contained elements of self-reference that could not be reconciled within a logical framework.

On the other hand we have accounts of how numbers are used in our everyday practices, which can include, for the mathematicians amongst us, quite complicated and sophisticated machinations. Numbers are to be understood not by setting up definitions from first principles, but by learning to make use of them.

Now comes an argument in favour of the second of these alternatives. Suppose Russell had met with more success, and been able to produce a definition of two that did not lead to inconsistency. How would we judge that what his definition sets out is in fact the number two? How would we verify tha this definition was accurate?

We would verify his definition by comparing it to our use of the number two, checking that what Russell defines is indeed adequate for the everyday tasks we set for that number. We would verify or falsify his definition by comparing it to our use of "two". after all, any stipulated definition is evaluated by comparison with the empirical facts of language use.

That is, the use of the number two has priority over any contrived stipulation.

Hence Wittgenstein's approach may claim some priority over Russell's.

So what are we to make of the supposed private concept of two? There is after all some appeal to your 'I compare the image in my mind to the pictures on the chart, and see the name "two"'. What do we make of the image in your mind?

The picture that holds us captive is of a concept of "apple" held before the mind, as an object of desire. Supposedly we make use of that concept in order to pick the apple from the pear, to construct our list of fruit for the grocer, or to argue on philosophy forums. But what is it?

The picture is of a piece of mental furniture. A page with "Green or red and round and waxy and smooth and tart or sweet" written next to the word "Apple" and a picture, near at hand for the homunculus to check in order to make sure he has his concept right.

But you might agree that such a notion of "concept" is far too passive. The concept of "apple" is what we use when we pick apples, when we sell and buy them, when we make a pie; it is interactive, showing itself in the vast range of activities in which it is involved.

Indeed, the argument used above applies here: How would we tell that the homunculus' page was correct? Only by comparison to what we do with apples.

And here the thought is that, if there is such a concept of "apple", it is a back-construction; it is something we began to build when mum cut up the thing she bought at the shop and served it for lunch, saying "Eat your apple", that we added to when we climbed an apple tree to reach the apples that were not blown, and now rely on for philosophical purposes.

Our interactions with the apple preceded and put in place any essentialist definition.

The concept of apple is not a list, but a family resemblance of our interactions with apples.

And those interactions are public.

So if there is a private concept of "apple", it is only there because of your public interaction with apples in the wide world. The private concept is public.

This approach also serves to sort the dilemma found in supposing that either concepts are in the mind or in the world. The dilemma relies on picturing concepts as mental furniture. If instead the concept "apple" is seen as what we do with apples in the wide world, then the question of whether they are in the world or in the mind dissipates. "Apples" are just our interactions with those things.

So again we can go back to

Imagine at a particular place and time in the world there is something. The public name "two" is attached to this something by the authorities. From my observation of this something, in my mind I have the private concept two. Someone else observing the same thing will also have the private concept two. However, it may well be that my private concept two is different to their private concept two, but as we are both part of the same community, we will both name our private concepts as "two". — RussellA

and see that

...those private aspects of the concept two make no difference — RussellA

Thanks again for an excellent reply.

It's the public communication that seems paramount to me.
I need to communicate what I want to the seller.
I can simply point to an apple by referencing my stored image of one. I can then hold up two fingers or take the two apples myself and hand them to the server or I can say 'two' or I can even communicate some indication of 'repeat' or 'again' after I point to an apple and want to indicate 'two.'
It seems to me that its the public communication that matters between me and the seller.

Would I need the concept of 'two,' if I had no-one to communicate with?
Does it matter what my private concept of two is when I have to communicate it to another?
My goal is to get two apples so my goal is to communicate that to the server in a way that achieves my goal and broadly satisfies/ is acceptable to the servers notion of two apples.
Whole numbers are either 1 or multiple replicates of 1. That matches my private concept of 'two.'
You might conceive 'two' to be its own amount, rather than as multiples of 1.
'Can I have two apples please?'
'Can I have an apple and then can I have another apple?'
Both would have the same result but the second one is just a bit less efficient.
If there are 'private' notions of what 'two' is, I don't think they matter as much as your personal ability to communicate 'two,' publicly.

I had an Uncle who I used to go drinking with. He would often go to the bar and order a small packet of peanuts. After he finished them he would go get another bag and then once more.
He did this routine on many occasions. So of course people would ask him, with some incredulity and annoyance, why he did not just 'f******' ask for three bags of peanuts? He would just say 'that's just me!'
Maybe he had some strange private notion of 'three,' which clashed with the public notion of three.

On the other hand we have accounts of how numbers are used in our everyday practices, which can include, for the mathematicians amongst us, quite complicated and sophisticated machinations. Numbers are to be understood not by setting up definitions from first principles, but by learning to make use of them. — Banno

This is really not the case, as the process of learning mathematics is more complex than what you represent it as. At the most basic, fundamental level, we simply learn usage, as you say. But then as we progress in our education, we must enter into a learning of abstract concepts. At this point there is a change, so that the student's mind evolves from learning simple operations of using numbers, to learning specific rules for use. That is actually a big difference, and you might see that it aligns roughly with the difference between arithmetic and mathematics.

The point here is that we cannot accurately make blanket statements like yours, " Numbers are to be understood not by...but by...", because "numbers" in the sense of arithmetic, and "numbers" in the sense of mathematics, is two different uses of the word.

We would verify his definition by comparing it to our use of the number two, checking that what Russell defines is indeed adequate for the everyday tasks we set for that number. We would verify or falsify his definition by comparing it to our use of "two". after all, any stipulated definition is evaluated by comparison with the empirical facts of language use.

That is, the use of the number two has priority over any contrived stipulation. — Banno

In light of the difference described above, this statement is very problematic. In the higher levels of mathematics we are definitely taught to follow stipulations, axioms, while in the lower levels of arithmetic we are taught to follow demonstrated usage. The difference marks the development of the student's mind from practical application, to the understanding of theory. The understanding of theory is based in the learning of rules, rather than a simple learning of use.

The result is that within mathematics we have a sort of struggle, or disequilibrium between theory and practise. You say that practise has priority over theory (your statement "the use of the number two has priority over any contrived stipulation"), but this is not really the case. Mathematics, being a high level abstract form of logic, proceeds in the opposite way, theory is prior to practise. This is obvious in the history of modern math, theory precedes the application, and therefore shapes practise.

The difficult issue is that the theory must be derived from somewhere, and it is common practise in the development of mathematical axioms, to produce axioms which are derived as a description of common usage. This creates the appearance that usage has priority over theory.

That presents a problem which I've pointed to numerous times on this forum, of which many members are ignorant, and even actively deny. If the proposed axioms are meant to be a description, or representation of usage, and they are not an accurate representation, then falsity is allowed to enter into mathematics. Mathematics is such that the rules must be followed, and the rules are given priority over usage, so rules which are supposed to be representations of usage, which are faulty representations, must be followed, thereby allowing self-deception within mathematics. Usage appears to have priority over theoretical rules, because the theory appears to be a description of usage. But in reality, the theoretical rules are what shape usage, and that this is true is evident from the fact that faulty descriptions may be used as rules.

So we have here two differing approaches to the nature of the apples being purchased at our grocer. On the one hand we have Russell's view that the apple consists in a concatenation of "constituents with which we are acquainted", something like "Green or red and round and waxy and smooth and tart or sweet". On the other hand we might set out the nature of an apple by setting out the roles it might play as we go about our daily activities: The thing we pick, sell, bite, stew, bake in a pie and so on. — Banno

I agree that Russell's work on denoting is not without criticism, and Wittgenstein's meaning as use, the language game and family resemblances are important aspects. But perhaps both are needed to arrive at an understanding of the process of buying two apples.

The mind and the language it uses need both Russell's elementary concepts and Wittgenstein's compound concepts

The elementary concepts of "logical atomism" and the compound concepts of "meaning as use"
At the moment , it seems to me that apple as a thought in the mind and "apple" as a word in language may be understood as a combination of the elementary concepts of Russell's logical atomism and the compound concepts of Wittgenstein's meaning as use, in that neither is sufficient by itself, but each provides an essential part of the whole.

Elementary concepts
Following Russell, there are things with which we are directly acquainted: green or red, round or square, rough or smooth, tart or sweet, hot or cold, acrid or fragrant, loud or quiet, etc, and the mind can judge the difference between these binary opposites.

In Kant's terms, trying to add a chilled Perrier moment, the human ability to judge between such binary opposites is an a priori intuition, an epistemic condition, an innate ability we are born with. It is the product of 3.5 billion years of life evolving in synergy with the world within which it finds itself, an Enactivist understanding whereby a person's understanding of the reality they observe in the world has been determined by the evolution of life within the world before they were born. Sentient life is a physical expression of the world it finds itself within. IE, the function of schools is not to teach children how to distinguish between green or red, round or square, etc as these abilities are innate, but without these innate abilities, being taught more complex concepts would be impossible.

Compound concepts
Given these simple concepts we can then combine them in various ways into compound concepts. Any combination is possible, but some combinations are more useful than others. For example, I have discovered that the combination round, sweet and red/green is of particular use, in that I have discovered that the apple is beneficial to my existence in the world. For convenience, rather than keep saying "pass me the thing that is round, sweet and red/green", I could name it "apple" and say "pass me the apple". I could equally as well have named it "camel", and said "pass me the camel", with the intended meaning pass me the apple, but as it has turned out, in the English language, something round, sweet and red/green has been named "apple".

But any possible combination of elementary concepts can be named, regardless of whether the particular combination is useful or not. For example I could name the combination green, square and smooth as "grasquim", not something that I have ever discovered to be useful to me.

The "apple", as a compound concept, exists as a relationship between the elementary concepts round, sweet and red/green. "Grasquim", as a compound concept, exists as a relationship between the elementary concepts green, square and smooth. As Russell in On Denoting showed, neither "apple" nor "grasquim" refer to an individual having its own existence, but describe the parts, the properties, that make it up. As both "grasquims" and "apples" have the same existence as a set of properties, if we said that "grasquims don't exist", then we would have to say that "apples don't exist", and if we said that "apples exist", then we would have to say that "grasquims exist". But Russell's On Denoting overcomes this problem in that neither "grasquims" nor "apple" are subjects that are predicated as either existing or not existing, rather, they are descriptions of a set of properties, not individuals being referred to.

It may well be that the "apple" plays an important role in our daily activities, and the "grasquim" plays absolutely no role in our daily activities, but both "apple" and "grasquim" have a meaning, in that "apple" means round, sweet and red/green and "grasquim" means green, square and smooth.

When Wittgenstein says "meaning as use", " meaning" can be interpreted in more than one way. In one sense of meaning, the "grasquim" has meaning even though it has no use. In another sense of meaning, the "grasquim" has no meaning because it has no use, in the same way that someone could say " travelling to Mars doesn't mean anything to me", knowing that they will never travel to Mars. Perhaps Wittgenstein's "meaning as use" refers to the second interpretation.

Kripke criticised Russell's Descriptivist Theory using a modal and epistemic argument
As regards the epistemic argument, Kripke pointed out the flaws in Russell's treatment of compound concepts as being able to be known a priori, inferring that compound concepts such as "government" can be known a priori, which is certainly not the case. Kant is different, in that Kant treats elementary concepts as being a priori, not compound concepts, which is certainly the case, in that humans are born with the innate ability to distinguish green from yellow, for example.

As regards the modal argument, Kripke said names should be rigid designators, true in all possible world. This requires that the elementary concepts building up a compound concept must be necessary rather than contingent, in that "apple" is true in all possible worlds, providing the elementary concepts building it up are round, sweet and red/green and not round, sweet, red/green and on the table.

Both Russell's "logical atomism" and Wittgenstein's "meaning as use" are needed
In summary, humans for survival and development within the world need both compound concepts and the elementary concepts they are built from. Some compound concepts mean more to us than others because of the use we can make of them, in that the "apple" means more to us than "grasquim", ie, Wittgenstein's "meaning as use"

Yet, we wouldn't have compound concepts without the elementary concepts they are built from, the constituents with which we are acquainted, as it were those fundamental indivisible atoms on which the rest of matter is made, where such atoms have been discovered through logical reasoning rather than intuitive feeling, ie, Bertrand Russell's "logical atomism".

Ok, but I take exception to compound conceptions. I know what is meant by it, but I think it a misunderstanding. Some thing, with a set of properties in the form of conceptions subsumed under it, is still represented only by its own conception.

Ok, but I take exception to compound conceptions. I know what is meant by it, but I think it a misunderstanding. Some thing, with a set of properties in the form of conceptions subsumed under it, is still represented only by its own conception. — Mww

I can have the concept of a single thing such as the colour yellow, or I can have the concept of an apple, which is a set of things, round, sweet and red/green.

When just looking at something round, my concept will be of something round, when just tasting something sweet, my concept will be of something sweet, when just looking at something red/green, my concept will be of something red/green.

However, what happens when I experience all of these things at the same time, something round, sweet and red/green, ie, an apple ?

Either i) I experience a single concept made up from a set of concepts, a unity of apperception, or ii) I will experience a set of concepts, discrete and separate ?

By "compound concept" I mean compound in sense i) rather than sense ii).

However, there may be a more technical term than elementary concept and compound concept.

I) works just fine:

“… But the conjunction of representations into a conception is not to be found in objects themselves, nor can it be, as it were, borrowed from them and taken up into the understanding by perception, but it is on the contrary an operation of the understanding itself, which is nothing more than the faculty of conjoining à priori and of bringing the variety of given representations under the unity of apperception. This principle is the highest in all human cognition.…”

All that presupposes “I think” has some irreducible meaning. Whether we actually do think or not, is irrelevant, insofar as the very seeming of it requires an account.

The chief difficulty with Platonism is that while proposing a distinct type of reality of mathematical entities, it must then explain how this reality interacts with everyday things. — Banno
Good question What do you think of the following explanation for explaining interaction? . . . .
In this view, mathematical entities are not a distinct type of reality. They are ideas, just like “tree.” — Art48

My tentative explanation of how Ideas interact with Real things is similar, but based on a philosophical simulation of Quantum & Information Theory. The dual entities are distinct only in the sense that the same mind can distinguish between a Thing and the idea of the Thing. Real & Ideal things are conceptually distinctive, but not epistemologically exclusive -- they are not in parallel worlds, but in the same world. You don't have to go out of this world to create an imaginary replica of a physical object.

Plato's Ideals are often portrayed as existing in some aethereal heavenly realm. But they are differentiated from mundane Reality only in the sense that mental Meta-Physics is distinct from material Physics. The human brain is physical, and interacts (communicates) with its own material body via electro-chemical signals (material information). Meanwhile, the brain also interacts (communicates) with its own ideas via something like Quantum Signal Processing : conversion of physical processes to mathematical ratios & algorithms.

In other words, specific physical energy patterns are converted into coded information functions -- in this case, the function we call "imagination" or "conception". This transformation from physical Energy to Meta-physical Information happens within the holistic system of a Person, not in some parallel world.
Of course, the detailed "how" is far over my pointy little head. So, this is just a crude macro description of the micro mechanics of Thinking. Perhaps it could only be really/ideally understood by a Mathematical Physicist. :smile:

PS__The Brain deals with Material neuro-logical patterns while the Mind works with Logical/Mathematical patterns : inter-relationships.

Quantum Signal Processing is a Hamiltonian simulation algorithm
https://en.wikipedia.org/wiki/Quantum_signal_processing

The Hamiltonian of a system specifies its total energy—i.e., the sum of its kinetic energy (that of motion) and its potential energy (that of position)
https://www.britannica.com/science/Hamiltonian-function

...perhaps both are needed... — RussellA

A half-way position. I think Wittgenstein's approach can wholly replace Russell's. Here are two follow-on points.

You say

...the function of schools is not to teach children how to distinguish between green or red, round or square, etc as these abilities are innate — RussellA

But I think this a bit too fast. While a baby has the potential to distinguish many colours, that potential is developed and reinforced over time by their interaction with the world. They learn to treat green and red differently because treating them differently has different results. The difference between red and green has public consequences. If the difference between harlequin green and neon green had similar consequences, she might learn to differentiate them before red and green. We know from studies of colour names across cultures that what counts as a significant difference in colour is at least partly dependent on where one grows up. While we are born with the potential to differentiate many colours, the ones we actually differentiate are dependent on our culture and environment. If it made no difference to us if the apple was red or green, we might well never make the distinction.

The capacity to differentiate colour is there, but it is trained by our interaction with others.

It follows that what is to count as an "elementary colour" is not entirely innate, but learned by interaction with the world. Similarly, what counts as an elementary concept, a simple, is dependent on one's interactions with the world, including other people, and language.

But we can go further and see that what counts as a simple in one case might not be a simple in another. Take a look at this example from Wittgenstein.

Is it the colours here that are the simples? Or are the colours irrelevant, and the fact that there are squares instead of circles what is important? Or that the grid is three by three, and not two by four? The point is that what is significant here is far from clear until one understands what is at stake.

One of the major differences between the Tractatus and the Investigations was Wittgenstein's realisation that what is to count as a simple is dependent on the task at hand. The meaning of "simple" varies with use.

For more on this, see The Dismantling of Logical Atomism, and

Wittgenstein there called into question whether a single, unequivocal notion of simplicity or a final state of analysis can be found (e.g., secs. 46–49, 91), and questioned the utility of an ideal language (sec. 81). Wittgenstein also called into question whether, in those cases in which analysis is possible, the results really give us what was meant at the start: “does someone who says that the broom is in the corner really mean: the broomstick is there, and so is the brush, and the broomstick is fixed in the brush?” (sec. 60). — Kevin Klement

The capacity to differentiate colour is there, but it is trained by our interaction with others. — Banno

Just a tidbit of info: innateness usually includes capabilities that develop through some sort of engagement. For instance, walking upright is an innate feature of humans, but there are needed structures that won't develop until walking is attempted. The physical stress of trying to stand triggers their development.

This meaning of innateness goes back at least to Leibniz.

Is it the colours here that are the simples? Or are the colours irrelevant, and the fact that there are squares instead of circles what is important? Or that the grid is three by three, and not two by four? The point is that what is significant here is far from clear until one understands what is at stake. — Banno

Maybe one of the most profound passages in Investigations that seems most do not appreciate. It dissolves away much of philosophy’s pretentious foundations.

Yep.

There's a need to tie all this back to @Art48's OP. I lost track of the argument somewhere along the line. Seems he is treating quantum wave functions as the mathematical simples from which everything is derived. I suppose that's one view...

I think of consciousness as what is aware of the sensations. — Art48

That seems to me to be a reification; I'd call consciousness the act (activity) of having sensations, thoughts, and so on; a more active notion than taking it as a thing that does the experiencing. A step further form the homunculus.

I'd call consciousness the act (activity) of having sensations, thoughts, and so on; a more active notion than taking it as a thing that does the experiencing. A step further form the homunculus. — Banno

How does this step us away from the homunculus? If consciousness is an activity then there must be something which is doing that activity. It cannot be the human body which is performing this activity because there is no observable act of the body which could be called the act of being conscious. So the thing which is performing this act of consciousness must be something other than the body, but it sure appears to be within the body. Therefore we are lead from consciousness is an act, to the homunculus as the actor.

...there is no observable act of the body which could be called the act of being conscious. — Metaphysician Undercover

I hope you are never called upon to perform first aid.

I'd call consciousness the act (activity) of having sensations, thoughts, and so on — Banno

Can’t be the act of; it is only that to which the unity of all our representations belong, such that it is then possible for them all to be my representations, which, in turn, makes explicit a singular self, which gives “I think”. Consciousness does not act; it is merely indicates a relative quality of being acted upon.

The activity of the having of sensations is a function of physiology, the exchange of the affect of the sensation to the representation of it, is intuition, the object of which is phenomenon.

The act of having thoughts is understanding, the representations of which are conceptions, the objects of which are judgements.

“…. this principle of the anticipation of perception must somewhat startle an inquirer whom initiation into transcendental philosophy has rendered cautious….”

The problem is that you refer to a number of very different acts "sensations, thoughts, and so on", and conclude that they comprise a single act called "consciousness". Don't you think that the unification of these vastly varying acts requires something like a "homunculus"? Or do you appeal to magic as the source of such a unification?

All that presupposes “I think” has some irreducible meaning. Whether we actually do think or not, is irrelevant, insofar as the very seeming of it requires an account. — Mww

I know that I can think of an apple and I know the concept of an apple, therefore thoughts and concepts must exist.

Kant Critique of Pure Reason A108 - "Just this transcendental unity of apperception, however, makes out of all possible appearances that can ever come together in one experience a connection of all of these representations in accordance with laws. For this unity of consciousness would be impossible if in the cognition of the manifold the mind could not become conscious of the identity of the function by means of which this manifold is synthetically combined into one cognition."

Consciousness, the unity of apperception in the mind is mysterious.

It seems that when the mind perceives a whole, which may be a set of parts, the mind is able to concurrently perceive each possible combination of parts as a unity, where each unity is distinct and irreducible. For example, the mind when perceiving a set of parts such as circular, sweet and red/green is able to perceive these parts as a distinct unified whole, an apple, and having a unity, irreducible. It will also be the case that when the mind perceives each possible combination of parts making up the whole, such as circular and sweet, the mind will also treat that combination as a distinct unified whole, and having a unity, irreducible

Similarly, each thought, such as the thought of an apple, is a distinct unified whole and as a unified whole is not only irreducible but has meaning.

….the unity of apperception in the mind is mysterious. — RussellA

Ain’t that the truth. Especially since mind is itself merely a conceptual placeholder for whatever’s going on upstairs. Gotta call it something, right? Calling it something isn’t enough, in that it still needs be explained what the hell it’s for, what it’s doing, and how do we know all that.

I prefer reason over mind, myself.
————

….each thought (…) is a distinct unified whole and as a unified whole is not only irreducible but has meaning. — RussellA

Agreed, but the ultra-moderns will insist each thought is reducible to its meaning, which is directly related to its communal, collective use. Without, of course, a strict methodology by which that actually happens.

Because they don’t like metaphysics, they kill it.

The problem is that you refer to a number of very different acts "sensations, thoughts, and so on", and conclude that they comprise a single act called "consciousness". Don't you think that the unification of these vastly varying acts requires something like a "homunculus"? Or do you appeal to magic as the source of such a unification? — Metaphysician Undercover

So the homunculus is only a logical problem if we're using it to explain something about consciousness. Otherwise it's no more a problem to refer to consciousness as a thing than it is to refer to gravity that way.

Insisting that consciousness is a set of actions implies knowledge about the nature of consciousness that we just don't have at present. There's no good reason to adopt that pretense.

I think Wittgenstein's approach can wholly replace Russell's — Banno

Russell and Wittgenstein fundamentally differ in that Russell's logical atomism requires both knowledge by acquaintance and description, whereas for Wittgenstein's meaning as use, knowledge by description is sufficient.

The question is, is it possible that Wittgenstein's approach includes knowledge by acquaintance.

I don't think it does. As he wrote in On Certainty, the proposition "here is a hand" is more about how the proposition is used rather than making an empirical claim about hands in the world. It may be objected that Wittgenstein's language games are circular, in that the meaning of the word comes from the game. As there is no external link, there is one problem of how to choose between different games, and another problem that there is no allowance for discourse between different games. For example, an atheist using one language game may not be able to criticise a religious believer using a different language game. A particular language game within a particular society may well be coherent, but such a language may not correspond with the world that the society lives within.

IE, Wittgenstein's language game of knowledge by description includes no link to knowledge by acquaintance.
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The capacity to differentiate colour is there, but it is trained by our interaction with others. It follows that what is to count as an "elementary colour" is not entirely innate, but learned by interaction with the world. Similarly, what counts as an elementary concept, a simple, is dependent on one's interactions with the world, including other people, and language. — Banno

Russell distinguished between two ways of thinking about things. He made the contrast between knowledge by acquaintance and knowledge by description, those things we think about directly and those things we think about indirectly. Knowledge by acquaintance includes sense data, universals, relations and oneself. As regards universals, he wrote "Not only are we aware of a particular yellows, but if we have seen a sufficient number of yellows and have sufficient intelligence, we are aware of the universal yellow"

The question is, are Russell's universals in fact not innate but learned by interaction with the world. If so, then Russell's knowledge by acquaintance becomes part of Wittgenstein's knowledge by description

I don't think they are. Consider those elementary concepts such as green or red, round or square, rough or smooth, tart or sweet, hot or cold, acrid or fragrant, loud or quiet, etc. I may have learnt many things over the past few years, but my perception of green, for example, one of these elementary concepts, has remained constant throughout my life. I certainly may have learnt more about the occurrences of green within the world, grass is green, traffic lights become green etc, but my innate ability to see green has not changed since the day I was born.

I agree that even in the absence of green I have the potential to see green, but this potential hasn't been taught, it was something I was born with. It is true, however, that I had to be taught that the name of my elementary concept of green is "green". It is also true that even though I have the potential to see green, I have to interact with the world, otherwise there would be no green for me to see. .

My ability to see green is innate, though I can learn by interactions with the world its occurrences in the world and can learn by interactions with other people its name.

IE, Elementary concepts such the innate ability to see the colour green cannot be learnt by description within a language game.
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One of the major differences between the Tractatus and the Investigations was Wittgenstein's realisation that what is to count as a simple is dependent on the task at hand. The meaning of "simple" varies with use. — Banno

We can call our perception of the colour green a "simples". Is Russell correct in treating such a simple as independent of context and as knowledge by acquaintance or is Wittgenstein correct in treating such a simple as being dependent on context and as such knowledge by description.

In fact, Russell and Wittgenstein are talking about different things. Russell's simples are within the philosophy of the mind and epistemology, where such simples have neither meaning nor can be true or false, Wittgenstein's simples are within language, can have meaning and can be either true or false. As noted by the SEP article on Wittgenstein's Logical Atomism "The so-called “colour-exclusion problem” is a difficulty that arises for the Tractatus’s view that it is metaphysically possible for each elementary proposition to be true or false regardless of the truth or falsity of the others (4.211)."

Wittgenstein's simples as being within language cannot be independent of the context they are within, as Wittgenstein explains, whilst for Russell, simples in existing independently of meaning, truth and falsity can be independent of any context they are in.

IE, Wittgenstein's approach of knowledge by description within language cannot include Russell's knowledge by acquaintance outside of language.

In summary, Wittgenstein's approach cannot wholly replace Russell's, as Wittgenstein's approach doesn't include knowledge by acquaintance, which Russell's does.

The quintessential language game involves the builder calling "slab!' and his apprentice bringing a slab. It is clear that the language game involves interaction with slabs. More generally, language games are embedded in the activities of the participants. It would be a misunderstanding to think of language games as disconnected from the world. Rather, and in contrast, a language game involves participation in a social activity embedded in the world.

That strikes me as a much better starting place than a supposed passive absorption of impressions.

I'll not enter into a competition between Wittgenstein's logical atomism and Russel's. Both fall to the expediency of what counts as a simple. That ought be clear from the SEP articles. What is to count as a simple depends on the task in hand.

Back again to to the begining, and

Imagine at a particular place and time in the world there is something. The public name "two" is attached to this something by the authorities. From my observation of this something, in my mind I have the private concept two. Someone else observing the same thing will also have the private concept two. However, it may well be that my private concept two is different to their private concept two, but as we are both part of the same community, we will both name our private concepts as "two". — RussellA

In place of this I offer a picture of "two" as part of a family of activities that we engage in together. What is significant in these activities is what is shared, since the activity is that sharing. What is not shared, is not part of that public activity, and so of no significance.

So the homunculus is only a logical problem if we're using it to explain something about consciousness. — frank

I really don't see why the homunculus is a logical problem, maybe you could explain this problem for me. I realize consciousness presents us with a problem, but I think it's more of a problem of premises rather than a problem of logic. If the homunculus is inconsistent with some other premise, maybe it's the other premise which is the problem.

I really don't see why the homunculus is a logical problem, maybe you could explain this problem for me. — Metaphysician Undercover

The idea of a Cartesian theatre is subject to the development of an infinite regress if we imagine that the stream of data coming into the CNS is being witnessed by an internal person.

. I realize consciousness presents us with a problem, but I think it's more of a problem of premises rather than a problem of logic. — Metaphysician Undercover

You know, it's really that we're at the very beginning stages of even theorizing about the nature of consciousness. We're still grasping for conceptual tools while wondering if such a science is even possible.

If the homunculus is inconsistent with some other premise, maybe it's the other premise which is the problem. — Metaphysician Undercover

Yes, the faulty premise is that the psyche is a full fledged being that is somehow independent of the body and the body's environment. For a lot of reasons, we know that can't be what's happening. The homunculus fallacy is just part of that.

In place of this I offer a picture of "two" as part of a family of activities that we engage in together — Banno

I agree that "two" is part of a family of activities that we engage in together, but where did "two" originate, allowing us to use it in our activities.

In answer to the question what are objects such as apples and what are numbers such as two, I can refer to the Standard Model, Kant's Critique of Pure Reason, Russell's On Denoting and Wittgenstein's Tractatus and Philosophical Investigations.

Within the Standard Model, in the world are fundamental particles, fundamental forces, time and space.

We are born with certain innate abilities, which have evolved over 3.5 billion years, elementary concepts such as the ability to distinguish between time and space, green or red, round or square, rough or smooth, tart or sweet, hot or cold, acrid or fragrant, loud or quiet, etc. In Kant's terms, from the Critique of Pure Reason, these are a priori pure and empirical intuitions. His term for the mind's ability to combine distinct parts into a unified whole is known as unity of apperception. Given innate elementary concepts, we can then discover correspondences between them and what we observe in the world.

From Russell's On Denoting, these innate elementary concepts may be combined by the mind into compound concepts. For example, the elementary concepts circular, sweet and red/green may be combined into the compound concept of apple.

From the Picture Theory of Wittgenstein's Tractatus, it may be discovered that these elementary and compound concepts in the mind correspond with what can be discovered in the world, and once a correspondence has been discovered, that concept can be named. For example, in discovered that our elementary concept of red corresponds with pictures of red in the world, we can name this concept "red".

From Wittgenstein's Philosophical Investigations, these named elementary and compound concepts can then become part of a coherent language. For example, in the statement "an apple has the properties circular, sweet and red/green in colour".

Using the above, an object, such as an apple, is a set of related properties, such as circular, sweet and red/green. But as relations don't ontologically exist in the world, apples can only exist in the mind. Similarly, a number, such as two, is a relation between two individuals. But as relations don't ontologically exist in the world, the number two can only exist in the mind. Therefore, objects such as apples and numbers such as two exist only the mind as compound concepts.

In answer to the question posed in the OP, We Are Math?, the answer is yes, we are math.

The idea of a Cartesian theatre is subject to the development of an infinite regress if we imagine that the stream of data coming into the CNS is being witnessed by an internal person. — frank

This proposed internal regress is bogus. The Cartesian dualism holds that the supposed "internal person" is non-material, therefore its method or mode of witnessing the data cannot be represented as a stream of data which needs to be witnessed again. Therefore the propose infinite regress is actually broken at the very first step, and only created by a strawman representation which does not properly represent substance dualism.

Yes, the faulty premise is that the psyche is a full fledged being that is somehow independent of the body and the body's environment. For a lot of reasons, we know that can't be what's happening. The homunculus fallacy is just part of that. — frank

How do you understand "independent" here? Does it simply mean not dependent on? Obviously it is completely unrealistic to present the two substances of substance dualism as completely independent of each other, and no form of dualism actually makes this claim. Platonic dualism for example, places the material as dependent on the immaterial, as the immaterial is understood as prior in time to the material.

So representing the homunculus as "independent of the body" is not necessarily a faulty premise. If we adhere to Platonic dualism, the homunculus could be properly independent of the body (not dependent on it), while the body is dependent on the homunculus. Further, since the homunculus is supposed to be of a completely different substance the infinite regress is avoided.

The question then can be apprehended as an issue of how the homunculus can observe, and interact with the material world. This interaction is understood through the concepts of intention, final cause, free will, and choice. When we understand that the homunculus is not dependent on the material body, we have the premise required to apprehend these concepts, because we establish the order of necessity in its proper one-way representation, as required by the one-way nature of time. Time makes necessity a one way direction.

The homunculus is prior in time to the body, such that the existence of the body is dependent on the homunculus, as the effect is dependent on its cause. But the reciprocal relationship is not one of necessity. The cause is not dependent on the effect. Nor is a cause necessarily an effect, because this would produce the dreaded infinite regress which we must avoid. The body has a relation with the homunculus which is a relationship of necessity, the homunculus is necessary for the existence of the body. But the homunculus has a relationship with the body which is not a relationship of necessity, the body is not necessary for the homunculus. The body therefore is contingent, and its posteriority in time, from the perspective of the homunculus, makes its existence better described or understood in terms of possibilities. This is what allows for the reality of the freedom of choice, and the reality that the internal homunculus is better described in accordance with the principles of dualism as the operator of the body, rather than the passive "sitting inside your head looking out" which Banno stated.

It's just clear that who you are is culturally and chemically mediated. Whether you are a lawyer or a gangster, that stuff depends on your environment. Was there lead in the water you drank as a child? Did you inherit schizophrenia? Were you sexually abused? Was your father a billionaire? Did you become a heroin addict?

You'll be a very different person in each of these cases, with very different emotions and cognitive functioning. This leads us to ask what the homunculus is supposed to be.

You'll be a very different person in each of these cases, — frank

I’ve had a dozen occupations, both professional and incidental, yet I’m still just lil’ ol’ me.

Can the interest which makes one good at something, and conversely the lack of it that makes him not so good, be predicated on cultural or environmental influences?

I’ve had a dozen occupations, both professional and incidental, yet I’m still just lil’ ol’ me. — Mww

There are certain kinds of childhood trauma that result in dissociative personality disorder. People who have that don't report what you do.

The fact that you do indicates that you didn't have that trauma, and your short term memory is being stored properly. A lot of this happens when you're asleep. That's just the tip of the iceberg of environmental, cultural, and biological elements that go hand in hand when your sense of self. So it's just hard to imagine how your self could be independent of your body.

Can the interest which makes one good at something, and conversely the lack of it that makes him not so good, be predicated on cultural or environmental influences? — Mww

Sometimes. If you teach a girl that females are bad at math, voila, she doesn't put any effort into it, and subsequently sucks at it.