But the lectern is identified via it's description - being wood - so in effect he is saying "the wooden lectern is necessarily made of wood". — Banno

Where do lecterns exist ?

Kripke gives the example of "here is a lectern" as a description of something made of wood, something that can only be known a posteriori and is an essential property.

However, what happens when we move from the demonstrative pronoun to the definite article.

There is no single property that lecterns have. Some are made of wood, some of metal, some have a flat base, some a legged base, some are grey in colour, some brown, etc. But as Wittgenstein pointed out, objects such as lecterns do have a family resemblance, such that a human observer can judge the difference between a lectern and a non-lectern.

As lecterns have no essential property, then lectern is more like a rigid designator than a description, as Mary as a name is a rigid designator, having no properties.

If lecterns exist only as a family resemblance between "this lectern" and "that lectern", and family resemblances is a human judgement, how can lecterns exist in the world, unless family resemblance is also something that exists in the world ?

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.

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.

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.

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.

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".

I tried to include a reference to Kant's philosophy of mathematics and a priori intuitions, but I know Banno isn't a fan.

Hence any private mental stuff is irrelevant to the meaning of "two". — Banno

I'm sorry about the length of reply.

Buying two apples needs both private concepts and public names

Does meaning is use have implications for the status of numbers
I agree that the meaning of "two" is how the word "two" is used. But what is the implication for the status of numbers ?

Objects are publicly named in performative acts
Prior to the interaction between me and the shopkeeper, it is necessary that we both have the same chart. Alongside the picture of one apple the name "one", alongside a picture of two apples the name "two", alongside the picture of an apple the name "apple", etc.

However, it could well have been that alongside a picture of one thing was the name "red"
and alongside the picture of two things was the name "yellow", but we can assume that in some prior performative act by someone in authority, a picture of one thing had been named "one" and a picture of two things had been named "two", thereby establishing a public language.

I wake up hungry and have the image of two apples in my mind. I compare the image in my mind to the pictures on the chart, and see the name "two". I go into the shop, tell the shopkeeper "two apples", who looks at the chart, and by comparing the picture on the chart to the image of what is in the bin, is able to give me two apples.

The number "two" is redundant in this transaction
In fact, the number "two" is redundant in this transaction. I could just have shown the shopkeeper the picture of two apples. Numbers may be convenient, in that the number "two hundred" is more convenient than a picture of 200 things, but fundamentally, within this transaction, what can be done in numbers could equally well have been done in pictures.

Perhaps this is the point of Hartry Field's nominalism, an opponent of the Quine-Putnam Indispensability Argument for mathematical Platonism. Field rejects the claim that mathematical objects are indispensable to science, arguing that it is possible to reformulate scientific theories in such a way that mathematical objects are replaced by relationships.

The transaction couldn't happen without private concepts
What is fundamental in using numbers is our ability to compare two images, either a memory of an image with a picture on a chart, or a picture on a chart with an image of something in the bin. Yet it is inevitable that the image of two apples in my mind, the picture of two apples on the chart and the image of two apples in the bin will be different. A judgement will need to be made that two things having some differences and some similarities both fall under the same concept, in that we have the concept apple even though no two apples are the same. It is an inherent human ability to be able to look at several different things and discover a commonality within them, and discover that they fall under the same concept.

The transaction would not have been possible if either me or the shopkeeper had no concept of either an apple or the number two, in that without concepts we would be still sitting in the corner of the room motionless. It may well be that my private concept of "two" is actually three, and the shopkeeper's concept of "two" is actually four, but we will never know, and is in a sense irrelevant. What is essential is consistency of concept, in that yesterday when I saw "two" my concept was of three, today when I see "two" my concept is of three, and tomorrow when I see "two" my concept will still be of three.

It is true that for the transaction to proceed, no reference is ever made to our private concepts, in that the shopkeeper does not need to know my private concepts of either apple or two, but it is equally true that the transaction could never have happened if either of us had no private concept of either apple or two. The process of buying two apples needs both a private aspect and a public aspect. As regards the private aspect, each participant must have a private concept of both two and apples, and as regards the public aspect, there must have been a priori performative act by someone in authority linking a picture of an apple to the name "apple" and linking a picture of two objects to the name "two".

Concepts don't exist in a mind-independent world
As regards the public aspect, two objects are linked to the name "two". What exactly is this link? It is the same problem Achilles had with the tortoise. When the tortoise started to move his castle diagonally, Achilles said that that move wasn't in the rules. The tortoise replied "where is the rule that I have to follow the rules". Similarly, there is the public rule that what is pictured is given the name it is linked to, such that when an apple is linked to "apple", then "apple" means apple, and when two objects are linked to "two", then "two" means two objects. But as the tortoise would say "where is the rule that a name means what it is linked to"

These linkages are relations, and as relations don't ontologically exist in a mind-independent world, then neither do these linkages. But as we do perceive linkages in the world, and as these linkages don't exist in the world, they can only exist in our minds, meaning that things like apples and two can only exist in our minds.

How is the our concept of apple related to our word "apple", and our concept of two related to our word "two". In On Denoting, Russell argued that words such as "apple" and "two" are not referring terms, in that they are not referring to an individual having its own existence, but is in fact describing those properties or parts that it is composed of. As Russell wrote "Every proposition which we can understand must be composed wholly of constituents with which we are acquainted", where those things we can think about directly are sense data, universals, relations and oneself. Similarly concepts such as apple and two are not referring terms, referring to an individual having its own existence, but in fact describe the properties or parts that it is composed of and with which we are directly acquainted. Therefore, our concepts and words do the same job in describing the properties they are composed of and which we are directly acquainted.

The process of buying two apples needs both a private and public aspect
In summary, the process of buying two apples could not happen without both a private and public aspect. If either me or the shopkeeper had no private concept of either apple or two, we would remain motionless in the corner, unable to act. If either apple or two had not been publicly named in a performative act "apple" and "two", I wouldn't be able to communicate with the shopkeeper.

Regardless of what X is (in this case metaphor) I can't see this as anything other than bullshit. — khaled

Bye.

I would say a mind requires variation to exist and not the other way around, for there must be variation before a mind capable of distinguishing variation exists (specially when such a mind collects information by detecting changes in the environment through the senses of its body). If there is variation and there is "stuff" then there are patterns automatically. — Daniel

I agree that within a mind-independent world variations exist, and it is these variations that a sentient being observes as patterns. However, "pattern" is a word that exists in language, and the question is, what exactly does this word correspond to in the world it is describing.

My starting position is my belief that elementary particles and elementary forces do exist in a mind-independent world of time and space. These elementary particles and forces combine to form what we know as patterns, rocks, water, etc.

What we see in the world as a whole is a set of parts. In a sense, a "part" is a metaphorical rather than real entity, in that parts have parts which have parts, etc until we arrive at the elementary particles.

In treating a pattern, rock, water as a whole made up as a set of parts, in accepting that the parts exist mind-independently, the question is, does the whole also exist mind-independently, or only in the mind of an observer.

I agree that a water molecule surrounded by water molecules will behave differently to a water molecule surrounded by rock molecules, ultimately because the behaviour of an elementary particle is affected by the elementary forces acting upon it, and it is this difference in behaviour that eventually accounts for what we observe as patterns, water, rocks, etc.

One doubt I have that patterns, etc exist mind-independently (though I have another) stems from the problem of naming. For example, a sentient being can judge when a rock is worn away and becomes a pebble, in that a sentient being can judge the difference between a rock and a pebble. But if rocks exist mind-independently, and pebbles exist mind-independently, when a rock is slowly worn away to become a pebble, at what stage does the set of molecules change from existing as a rock to existing as a pebble. I agree that as outside observers we could judge, but what is there in a mind-independent world to make that same judgement

Similarly for patterns, as a pattern slowly becomes a non-pattern. Midway between a set of molecules existing first as a pattern and then as a non-pattern, what in a mind-independent world can determine that the set of molecules has changed from existing as a pattern to existing as a non-pattern. My belief is that if there is nothing in a mind-independent world that can determine when a pattern becomes a non-pattern, then neither can there be anything to determine when something exists as a pattern rather than a non-pattern.

Basically, "patterns", "rocks" and "water" exist as names within language, and as Bertrand Russell pointed out in On Denoting, names don't refer to an individual having an independent existence, but are definite descriptions, quantificational expressions, of the parts that make them up.

And what are these "laws of nature" exactly in your view? Given that you do not believe patterns exist ontologically. — khaled

The phrase "laws of nature" is a metaphor.

The problem of trying to describe literal truths in the world using language is that language is inherently metaphorical. For example, just taking the sentence "Patterns we see in nature are inevitable if things move and the laws of nature are constant", the following words are metaphors - patterns, we, see, in, nature, are, inevitable, if, things, move, and, the, laws, of, constant.

If the meaning of "two" is a private concept in my mind, and is different to a private concept in your mind, then you and I literally do not share the same concept of two. — Banno

It could well be, as in theory no one other than me knows what's in my mind. However, in practice, as we share more than 99.9% of our DNA, and we both have the same ancestor, "mitochondrial Eve", I would infer that our private concepts are very similar.

So those private aspects of the concept two make no difference, and it is only the public aspects that have a place in our affairs. — Banno

I agree. Elaborating, given something in the world that has been given the communal name "two", it may well be that my private concept of this something is actually three and your private concept of the same thing is four.

However, when I see something named "two" and have the private concept three, I will interact with the world in a particular way. Consistency is important, in that the next time I see something named "two", even though my private concept is still three, I will interact with the world is the same way as before. As you say, as regards my interactions with the world, " those private aspects of the concept two make no difference".

Do the rings of a tree give us information or just facts and from there it takes an intelligence to make the facts meaningful information. — Athena

I would say that the rings of a tree give us facts and from there it takes an intelligence to make the facts meaningful information.

As Wittgenstein wrote in Tractatus: i) “The facts in logical space are the world” and ii) "A logical picture of facts is a thought"

not only are patterns instantiated in nature, but nature is also receptive to patterns — Pantagruel

Patterns we see in nature are inevitable if things move and the laws of nature are constant.

If a particular event ends as it began, for example, the earth travelling around the sun, given the constancy in the laws of nature, and all things being equal, the same event will happen a second time, and a third, etc, and this is a pattern.

Nature is receptive to patterns in that at one time the metronome didn't exist in nature, but once a part of the natural world exhibits a pattern in its behaviour.

Does your mind create the concept of 2? Does the concept of 2 cease to exists when you stop thinking about it? — Art48

My mind creates my private concept of something in the world publicly named as "two".

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".

My mind has created my private concept two, someone else has created their private concept two. But as we are both part of the same community, the public concept "two" continues to exist even if I stop thinking about it.

Because numbers have objective properties. — Art48

Some aspects are objective, others subjective

The something that I have observed in the world about which I have the concept two is objective in the sense that it exists independently of me. Because the public name "two" has been attached to this something, the concept "two" is objective in the sense that it exists independently of me within the community. As regards my private concept two, it is objective in the sense that it somehow exists within my physical brain, but it is also subjective in the sense that no one else can ever know my private concepts.

Numbers don't refer to individuals, they describe the parts of the individual

In the world is something that has been given the public name "two" about which I have the private concept two. Starting with two things in the world each of which exists, the question is, when brought together, does a new existence come into being, where this new existence has each thing as a part. Does the number two exist as a new whole in addition to the existence of the two parts that make it up ? Not according to Hume, Kant, Frege or Russell.

As the problem of numbers involves language, Bertrand Russell's On Denoting may shed light. For example, in the sentence "the author of Waverly was Scott", the phrase "the author of Waverly" is not a referring term, in that it doesn't refer to an individual having an independent existence. It is a quantificational expression, a definite description of a set of properties that makes up "the author of Waverly". Frege and Russell believed that existence was not the first-order of an individual, but the second-order of a concept.

Similarly, the phrase "the number two" is not a referring term, in that it doesn't refer to an individual having an independent existence, but rather is a quantificational expression, a definite description of the separate parts that makes up what is known as "the number two".

In language, the phrase "the number two" doesn't refer to an individual having a unique existence, but is a description of the separate parts that make up what is known as "the number two".

Why can't your 2 be greater than your 3? — Art48

It cannot

I observe something in the world that has the public name "one" and I have the private concept one. I observe something different in the world that has the public name "two" and I have the different private concept two. I observe "one" added to "two", and when observing this new something, I have the private concept three. As my concept of three has resulted from an addition to my concept of two, my concept of two cannot be "greater" than my concept of three.

it seems to me concepts exists outside spacetime. — Art48

I may be misunderstanding what you mean by "outside spacetime". I think of "spacetime" as what we exist in, the three dimensions of space and one dimension of time. I think of a chair as being inside a room and the moon as being outside a room. How can my concepts, which I believe exist somehow within my brain, within the three dimensions of space and one dimension of time, be outside spacetime ?

In the mind-independent world there exists an interface between different behaviours (of groups of particles - i.e., rock and water); the existence of the interface requires a distinction between the groups of particles that form the interface (or there would not be an interface); this distinction materializes in the behaviour of the particles that make up the interacting surfaces. — Daniel

Yes, an outside observer of the water and rock can see that molecule A behaves differently to molecule D, because molecule A is part of water and molecule B is part of rock.

Yet, within the mind-independent world of molecules A, D, etc, excluding any external observer, no single part can have any information within itself about its behaviour, as behaviour is an external property of a part.

As no single part can have information within itself about its behaviour, no single part can have information within it that its behaviour is due to being a part of one pattern, such as water, or another pattern, such as rock.

OK, if the number 2 is in spacetime, where is it? And when? — Art48

It exists in the mind as a concept, and it exists when I think about it, in the same way that government, love, apple, despair, mountain, etc exist in the mind as concepts.

It helps that there is a regularity in nature, and our numbers can model that regularity.

Even if numbers did exist outside our space-time, not only would we not know about them but also we wouldn't be able to access them. But as we do use numbers, accounting for the success of science and mathematics, the numbers we use must exist within our space-time.

Taking a simple example, an abacus can manipulate numbers, yet the abacus neither needs to nor would be able to access anything outside its own space-time.

But what is outside of spacetime? Abstract objects like thoughts and numbers................The status of abstract objects is an open philosophical question. The answer I accept is that they exist outside of spacetime. In particular, mathematical objects exists outside space time — Art48

I usually use "exist" for both cases................where "exists" applies to things in spacetime, and "subsist" applies to abstract objects. — Art48

I will never look at my calculator in the same way again

In order for my calculator to have access to numbers, if numbers exist outside space-time, then my calculator during a calculation must also exist in part outside space-time.

The interesting question is that once the calculation is finished, how the calculator is always able to return to this world at the same time and location it left.

If we could discover how this happens, we could perhaps manipulate the return of the calculator to a slightly different time and space, thereby creating a Tardis-like machine.

The implications of numbers existing outside space-time are certainly truly staggering.

I suppose that's one view of abstract objects. Another view is that they exist subsist outside spacetime. — Art48

How is two plus two equals four subsisting outside space-time different to two plus two equals four existing outside space-time ?

No, everything that exists has a pattern/arrangement. — khaled

You wrote "I believe that what exists is matter, and patterns of matter."

The Cambridge Dictionary defines arranges as "to put a group of objects in a particular order" and pattern as " a regular arrangement of lines, shapes, or colours"

They have in common the concept particular order or regular arrangement.

If I understand correctly, you are saying that as everything in a mind-independent world is in a particular order or regular arrangement, then there is nothing that is not in a particular order or regular arrangement.

However, no single part can be in a particular order or regular arrangement, only the whole, the set of parts.

If everything in a mind-independent world is in a particular order or regular arrangement, either each part has information that it is a part of of a particular order or regular arrangement, or the whole has information that its parts are in a particular order or regular arrangement.

How ?

But the relations between two groups of things may depend on the regularity of the patterns they (the things) form within their groups, independent of their awareness about each other patterns — Daniel

Keeping with your terminology, accepting that trying to explain a mind-independent world using metaphorical language is inherently problematic, and using "aware" in the sense of having information.

If two things in a mind-independent world have no "awareness" about each other, then how can each thing be "aware" that it is part of a pattern that includes the other thing.

I was asking what exactly you think is THE formal definition of "exists" in philosophy — busycuttingcrap

As the SEP article on Existence notes that the question of existence raises deep and important problems in metaphysics, philosophy of language, and philosophical logic, it's highly unlikely that I could come up with one.

Or that the pattern is simply irregular. ABABABABAB is a pattern. ABABBABBAABA is also a pattern. The second being irregular. It is our judgement that it is irregular. But both patterns exist. — khaled

You say that "All patterns exist independently of anything", inferring that before sentient beings there were some things that existed as a pattern and some things that existed as a non-pattern.

It is true that with hindsight a sentient being can judge which was a pattern and which was a non-pattern.

But in the absence of a judgement by a sentient being, either at that time or subsequently, what determines that one thing exists as a pattern and and another thing exists as a non-pattern, particularly when patterns may be regular or irregular.

Electrons do not have a set location, and they definitely exist in a mind-independent world. — khaled

Electrons are not abstract entities, in that they have a mass and exist in a cloud surrounding an atomic nucleus. It is not that the position of an electron cannot be measured, rather, if you know precisely where a particle is you don't know what direction it is going.

How can something that doesn't ontologically exist be discovered as opposed to imagined? — khaled

I didn't create or imagine this image, but discovered it on the internet. The ever-ascending stair doesn't exist in the world, even though that is what I observe. What I observe is an illusion, in the same way that patterns I discover in the world are illusions.

We have the ability to notice the abstract patterns that exist (indepencently of us). — khaled

I agree that patterns exist in the mind. The question is, do patterns ontologically exist in a mind-independent world.



A pattern as a whole is a regularity in the parts that make it up. I have no doubt that parts do exist in a mind-independent world, such as elementary particles and elementary forces. What I doubt is that sets of parts in a mind-independent world have an existence as a whole in addition to the individual parts.

We see a pattern in the rocks of the Giant's Causeway, even though the parts are not exactly regular. How regular does a pattern need to be for us to judge it as a pattern. If the distance between the parts varies by 1mm, the whole is definitely a pattern. If the distance between parts varies by 1cm, the whole is probably a pattern. If the distance between parts varies by 10cm, the whole may or may not be a pattern. If the distance between parts varies by 1 metre, the whole is definitely not a pattern.

As no pattern is exactly regular, whether the set of parts makes a pattern is determined by the judgement of the observer. There is nothing within the set of parts that is able to judge whether the whole that they are part of is a pattern or not. No part can judge whether it is part of a whole or not. The whole cannot judge that it is a whole made up of parts.

If patterns did ontologically exist in a mind-independent world, then as no pattern can be exactly regular, something within either the parts or the set of parts as a whole would have to have judged whether it was a pattern or not. Without recourse to the existence of a god sitting in judgement as to whether a set of irregular parts was a pattern or not, I don't see this as a possibility.

We judge whether the image is of a duck or rabbit, there is no information within the image that determines one way or the other. We judge that the pebbles make a pattern, even though they are neither regularly spaced nor sized, the pebbles cannot make that judgement. We judge when an object such as an apple is no longer an apple, the apple is no judge. We make a judgement in the Sorites Paradox when a heap of sand becomes a non-heap of sand, the sand cannot make any such judgement.

The mind judges when an irregular set of parts makes a pattern or is a non-pattern. If patterns did exist in a mind-independent world, then the problem would be in finding a mechanism within the mind-independent world that determines whether an inevitably irregular set of parts is a pattern or non-pattern.

Those geometric patterns emerge through natural processes — Athena

I do not see how it can account for relations that have been in effect before being found — khaled

We look at the Giant's Causeway and see patterns in the rocks and adjacent water. The question is, do these patterns, and the relationships between their parts, ontologically exist in the mind-independent world or only in the mind of the observer.



One of my problems with the ontological existence of patterns in a mind-independent world, and the relations between their parts, is where exactly do they exist.

When looking at the image, we know that A and B are part of one pattern and D and E are part of a different pattern.

But within the mind-independent world, where is the information within A that it is part of the same pattern as B but not the same pattern as D. If there is no such information, then within the mind-independent world, patterns, and the relations between their parts, cannot have an ontological existence.

One could say that patterns and relations have an abstract existence, in that they exist but outside of time and space. This leaves the problem of how do we know about something that exists outside of time and space. I could say that I believe that unicorns exist in the world but outside of time and space, but as I have no knowledge of anything outside of time and space, my belief would be completely unjustifiable.

One could say that the force experienced by A due to B is sufficient to argue that as A and B are related by a force, this is sufficient to show that A and B are part of the same pattern. However, even though A may experience a force, there is no information within the force that can determine the source of the force, whether originating from B or D. This means that there is no information within the force experienced by A that can determine one pattern from another.

Question: Sentient beings observe patterns in a mind-independent world, but for patterns to ontologically exist in a mind-independent world, there must be information within A that relates it to B but not D. Where is this information?

How do we decide it is wrong? If the pattern doesn't ontologically exist, if it depends only on our minds, then what exactly makes it wrong? If there is no "right" answer in the thing being observed itself, then how can there be wrong answers? — khaled

A pattern cannot be right or wrong. What we infer from a pattern may be right or wrong.
If I notice the pattern that the sun has risen for the last one hundred days in the east, I may infer that tomorrow the sun will again rise in the east. My inference may be right or wrong, not the pattern that I have observed.

Nothing you've presented so far actually shows that relationships ontologically existing creates any problems — khaled

It affects your thesis that "I believe that what exists is matter, and patterns of matter" in the event that patterns of matter don't ontologically exist in a mind-independent world.

There are significant consequences in the event that patterns of matter and the relations within patterns don't ontologically exist in a mind-independent world, in that for example things that we know as "apples", "The North Pole", "mountains", "tables", "trees", etc don't exist in a mind-independent world but only exist in our minds.

Those geometric patterns emerge through natural processes — Athena

Yes, what we see as patterns have emerged through natural processes in nature millions of years before there was any sentient being to observe them.

I would say that we discover patterns in nature rather than create them in our minds, as it is in the nature of sentient beings to discover patterns in the world around them.

However, any discussion is complicated by the metaphorical nature of language, in that the words "emerge", "natural", "nature", "create", "processes", "discover" and "mind" are metaphorical rather than literal terms. Trying to describe literal truths in a mind-independent world using language that is inherently metaphorical is like trying to square the circle.

In order for something to be discovered, it must exist first no? — khaled

When we observe the Giant's Causeway, which existed before sentient observers, we discover a pattern in the relationship of the parts.

It is in the nature of sentient beings to discover patterns in what they observe, and it may well be that different sentient beings discover different patterns from the same observation.

That you discover a duck and I discover a rabbit in the same picture does not mean that either exists in what is being observed.

When we discover a pattern or a relation, we are discovering an inherent part of human nature, not something that ontologically exists in a mind-independent world.

The relation "Have a gravitational pull towards each other" has always been in effect, even before we detected it. Every physical law has always existed even before we detected it, and every physical law fits the definition of a pattern (which is why we can represent it mathematically). — khaled

Patterns and relations exist in the mind of an observer of a mind-independent world

The Moon circled the Earth before humans existed, and in our terms, there was a pattern in how the Moon circled the Earth and there was a relation between the Moon and the Earth.

A pattern needs a relation between parts. I agree that patterns and relations exist in the mind, but do patterns and relations exist in a mind-independent world, because it affects your thesis that " I believe that what exists is matter, and patterns of matter".

Force is a different concept to relation, in that there may be a temporal relation between two masses yet no force between them. Two masses on either side of the Universe will have a spatial relation yet there be no force between them. There may be a relation between a mass and my concept of the mass yet no force between them. Force should be treated differently to relation.

My belief is that patterns and relations don't exist in a mind-independent world, for the reason that there is nowhere for them to exist.

Consider a system of two masses each experiencing a force as described by the equation F = Gm1m2/r2, the equation of universal gravitation. Mass m1 moves because of a force due to m2, and in our terms there is a relation between m1 and m2 and there is a pattern in the movement of m1 expressed by the equation.

Consider mass m1 experiencing a force. An external observer may know that the force on m1 is due to mass m2 at distance r, yet no observer could discover from an internal inspection of m1 that the force it was experiencing was due to m2 at distance r. Problem one is that the force from a 1kg mass at 1m would be the same force as a 4kg mass at 2m, giving an infinite number of possibilities. Problem two is that mass m1 can only exist at one moment in time, meaning that no information could be discovered within it as to any temporal or spatial change it may or may not have experienced.

Similarly, no internal inspection of m2 could discover any relation with m1. Similarly, no internal inspection of the force on m1 could discover any relation with mass m2, and no internal inspection of the force on m2 could discover any relation with mass m1. No observation internal to the m1, m2 system could discover any relation between m1, m2 and the force between them. Relations cannot be discovered intrinsic to the system m1, m2 because relations don't exist intrinsic to the system m1, m2.

An outside observer of the system m1, m2 may discover the relation F = Gm1m2/r2 because the relation is extrinsic to the system m1,m2. An extrinsic observer of the system m1, m2 would be able to relate the movement of m1, m2 to a force between them determined by the equations F = Gm1m2/r2 and F = ma. The observer would be aware of a relation between m1, m2, and being aware of a relation would be aware of a pattern.

As the relation F = Gm1m2/r2 is not intrinsic to the system m1, m2, by implication, the laws of nature are not intrinsic in a mind-independent world. Similarly, as the relation F = Gm1m2/r2 may be discovered by an outside observer of the system m1, m2, by implication, the laws of nature being extrinsic to a mind-independent world exist in the mind of an observer.

In summary, relations and patterns are extrinsic to a mind-independent world, and exist in the mind of someone observing a mind-independent world.

What does "'exist' in a formal sense" even mean here? — busycuttingcrap

You wrote: "And colloquially, to say that something exists only as a concept in your mind is simply a different way of saying that something doesn't exist (consider: a conspiracy theory, an imaginary friend, etc)"

As colloquial is defined as informal speech, "exists in a formal sense" contrasts with "exists in a colloquial sense".

You say that in an informal colloquial sense, the sentence "Santa Claus does not exist" means that although Santa Claus exists as a concept in the mind, he doesn't exist in the world.

Contrasted against this, in a more formal academic sense, the sentence "Santa Claus does not exist" is misleading, in that although Santa Claus doesn't exist in the world, Santa Claus does exist as a concept in the mind.

However, I am not even sure that in informal colloquial speech people would say that fictional characters don't exist, otherwise people wouldn't make such significant emotional investment in fictional characters within books and films.

Why would justifying the existence of relations be a task for my view specifically? — khaled

It wouldn't be if "patterns of matter" existed only in the mind, but you also say that "All patterns exist independently of anything", and " The pattern of a quadrilateral would exist even if no one discovered shapes with 4 sides", inferring that patterns also exist in a mind-independent world.

I agree that all material things have a location, and when we observe material things we can observe a relation between them, so relations do exist in the mind. So, patterns exist in the mind.

But how do we know that the relation we believe we observe between material things in the world
doesn't actually exist in the world , but is, in a sense, a projection of our mind onto the world. And if relations don't exist in a mind-independent world, then neither do patterns exist in a mind-independent world.

I'm thinking about the problem of "relations" as described in the Stanford Encyclopedia of Philosophy - Relations, which discusses (1) Rejection of both properties and relations. (2) Acceptance of properties but rejection of relations. (3) Acceptance of relations but rejection of properties. (4) Acceptance of both properties and relations.

All patterns exist independently of anything. — khaled

A pattern is a repeated relationship between its parts. If there was no relation between the parts, then the pattern wouldn't exist.

For patterns to exist, relations must exist. How do you justify the belief that relations exist, ie, that relations ontologically exist.

I believe that what exists is matter, and patterns of matter. — khaled

Assuming that matter can exist mind-independently, do patterns of matter exist only in the mind or can they exist mind-independently ?

No, I don't see any contradiction in saying that there does not exist a plump old man living at the North Pole delivering presents to children on Christmas, but that there does exist a body of literary/oral traditions involving such a character..............And colloquially, to say that something exists only as a concept in your mind is simply a different way of saying that something doesn't exist (consider: a conspiracy theory, an imaginary friend, etc) — busycuttingcrap

Perhaps the problem is that one moment you use "exist" in a formal sense and then the next moment in a colloquial sense without making it clear, because otherwise, it seems that you are saying that something that exists doesn't exist.

to say that something exists only as a "concept in a mind", and not in reality or the world, is just another way of saying that that something doesn't exist. — busycuttingcrap

Isn't your position contradictory, when you say: "something exists only as a "concept in a mind" is "another way of saying that something doesn't exist".

If something exists, it exists. The fact that something exists does not mean that it has to exist everywhere.

Frege held rather, that existence is a second order predicate: a property of concepts, not individuals. — Heracloitus

Good old Frege and Russell :100:

non-existent things like fictional characters don't exist. — busycuttingcrap

I agree that non-existent things don't exist, and that there shouldn't be a special category of existence for non-existent things. If we accept Bertrand Russell"s On Denoting, then I also agree that Santa Claus is not a referring expression, but rather a quantificational expression.

For Russell, existence is not a first-order property of individuals but instead a second-order property of concepts.

Santa Claus is a fictional character, and as a fictional character doesn't exist in the world, but as we are discussing Santa Claus, Santa Claus must exist as a concept in our minds.

To argue the blanket statement "fictional characters don't exist", accepting that fictional characters don't exist in the world, you must also be able to argue that fictional characters don't exist as concepts in the mind.

That's one, but here's the thing Saint Nicholas was a real person. I don't know how to deal with that (historical) fact and how it relates to Santa Claus. — Agent Smith

The real Saint Nicholas has many miracles attributed to his intercession, is said to have calmed a storm at sea, saved three innocent soldiers from wrongful execution, and chopped down a tree possessed by a demon.

The fictional Santa Claus is said to bring children gifts during the late evening and overnight hours on Christmas Eve. Either toys and candy or coal or nothing, depending on whether they have been "naughty or nice".

It is the nature of language that the real can become indistinguishable from the fictional, and vice versa.

If I may help you to grasp the point here... People can and do use the same kinds of words (e.g. names) for the purpose of referring to people or objects in some contexts and for the purpose of non-referring word-use in others. — bongo fury

"Apple" and "dragon" are concepts that exist in the mind. Concepts are fictional in the sense that they don't exist in the world - in the belief that neither abstracts nor universals ontologically exist in the world.

An "apple" can be instantiated in the world, but a "dragon" cannot be - even though a model of a "dragon" can be instantiated in the world.

"Apple" can refer to either a fictional concept in the mind or an actual instantiation in the world. "Dragon" can only refer to a fictional concept in the mind.

"Apples" and "dragons" both exist, but in different senses.