Only demonstrable mathematical truths are domonstrably true. The jury is out on everything else (except 'I think therefore I am' and 'There is something').

So essentially any number would not refer to anything either? If so what does zero refer to? What differentiates 1 from 0? — Outlander

1 can count the 0. 'One zero'.

That you feel the need to create something - what dose that express?

What is the mind activity that leads you to create art? Is it not your consciousness? — Pop

Yes, you could say consciousness. But the primary motivation is not expression, it is simply to create. I suppose expression is inevitable on some level but 'create' is the motivation. "Reflecting society" is also something that creeps in but doing art 'to reflect society' is journalism

Information is power they say, and if this summarizes the concept of art then why would anyone just give power away to someone else for nothing? There must be more to it than that alone. — kudos

I suppose the artist reveals a lot by sharing his/her thoughts but we do that anyhow.

And he believes, not based on "faith" but on evidence, that Information is the essence of reality --- of both Matter and Mind; both "invisible transcendental" Energy, and visible tangible Matter. — Gnomon

I don't think 'everything' is information because that would mean that all that exists is abstraction and I don't see how abstraction can exist without substance. If information exists it must have some kind of substance (mind?) to keep it in being. You can't have 0s and 1s by themselves. You have to store them on something, even if that something is a mind.

The idea that "Art work is information about the artist’s consciousness," is sort of difficult for me to accept without qualification. If this were true, how could there be such a thing as art work to begin with? Because there would be no necessity for the artist to share information about their consciousness beyond some type of perversion. In addition, without some contribution from outward there can be no 'cast' of art in which to apply it's form. — kudos

I don't think it is perverse to want to share something good. It is natural. Yes, there are all kinds of influences that determine 'fashion' in art: art history, other artists, the world at large etc. But the essential aesthetic is deeper than fleeting fashions. As the OP says, art is about the artist's consciousness but the form of the image (art work) is often influenced by fashion in art. Art is creativity. An Art work is a bit messier when it comes to definitions because it has so many cultural influences.

When people say 'art' they are mostly talking about the image be it a painting or piece of music or sculpture. For me art is the inner process and the image/art work is a metaphor of that process.

Interesting...sounds like you are referring to Einstein's Block Universe theory, where time is just an illusion...(?). — 3017amen

Time is a geometric shape just like any object. Time, in human experience, depends on information reaching a certain point: where the human being happens to be. Human consciousness (at least physical consciousness) is located at a point in space and time flows as information reaches this point. But what if someone's consciousness could fill the whole solar system or universe. What would time be like then?

So, Matter, Energy, and Mind are different forms of the same thing : Information. — Gnomon

But there must be substance if there is to be anything. Information by itself is abstract. There must be mind or substance to hold the information in being.

Is eternity outside of time? If it is, then when Time/Universe had a beginning, something outside of time caused Time to exist, hence a change of events preceded Time. Time would then be subordinate to a change or change in events/being or becoming, whichever you prefer. (See the 4:40 mark of the video.) — 3017amen

Time is 'in' eternity. Time is a 4-dimensional object, like any other physical object. It is the 'shape' of physical existence. This object exists in eternity but is not necessarily eternal. 'Spacetime' is a better expression.

In your view, does art include meaning, or is it separate from it? IE: are you only occupied with the meaning of art to the artist his or her self? — kudos

Not sure if you are asking me or Pop. Anyhow, for me, art is about meaning. Truth = meaning = beauty.
Beauty is truth. But a problem arises when people are asked what is beauty? The answer will be subjective. But for me, beauty is truth. But what is truth? and we are back to subjectivity.

Beauty and meaning can be shared by sharing the external, physical, work of art. But, for the artist, meaning is in the experience of creating. Art as 'expression' or 'reflecting society' (duh) are secondary things.

Art is creativity; for me the reason to create something is a conviction that it is worth creating. People say 'art is about reflecting society'. No, I don't think so, but when it does that is only incidental or secondary. Many artists create works that are different from the societies they live in. Michelangelo painted angels but in his time there were open sewers running through the streets.

I basically agree with Pop's definitions. Art is an inner process that is shared by means of the image.

There is a difference between art and art work. Art is a process whereby the artist evolves and develops in terms of consciousness. Art is an inner journey. A art work is a physical image of this inner process. This physical image can be shared with others but art as 'expression' is only incidental. One can go on this inner journey without expressing anything (ie without showing the art works to anybody). Art certainly is not about 'expression' let alone 'self expression' (what a silly notion). It is about an inner journey. That art works express something to other people is a secondary thing. It is about sharing the experience, through the image. As an artist I never think I need to express anything. But I do need to create things.

:100: :clap: :up: — Pfhorrest

SophistiCat put me on the right track...

And the consequence of that is that talk of extension in mathematics becomes fraught with ambiguity. Hence, Wittgenstein's argument that mathematical extensions must be finite, and hence his adoption of finitism, seems misguided. — Banno

Here's a thought. Draw the X axis. The segment between 0 and 1 is a physical extension in space. This segment contains an infinity of dimensionless points: ie points of zero dimension. But if you set down an infinity of these zeros side by side, you get 1 unit of length. The implication is that 0 x $\infty$ = 1.

Those symbols are just Unicode characters that you can copy/paste from anywhere — SophistiCat

Thanks. The first thread in the Logic and Philosophy of Mathematics forum (this forum) explains how to use the math tag and how to create symbols.

"This is the answer to the question"

Is it the same as the answer to this question?

Do you have any real god given rights, or are god given rights just a feel-good lie that we tell ourselves we have so as to ignore that we have none? — Gnostic Christian Bishop

Simone Weil writes about this. The Jews did not have a concept of rights in the way we do. Their concept was the justice of God. Weil points out that when Jesus was confronted they asked Him "By whose authority do you say these things?" not "What right do you have to say these things?" What mattered to the Jews was the authority of God, not rights. Rights are invented by statesmen. They are a codification of what was originally understood, by the Jews, as justice that comes from above.

There are two spacetimes, quantum spacetime and physical spacetime. Quantum spacetime is an n-dimensional spacetime (it has been suggested n = 10 or 11). Physical spacetime is 4-dimensional. This effectively means there are two universes.

The physical universe is an emergent property of the quantum universe of energy. It is 'conjured up' from quantum spacetime.

The reason is because the EU only contains the generating sources, but as soon as those things are generated, they enter the PU where they are subject to the laws of PU. One can regard the EU as a collection of brute facts, that live outside of the framework of the PU — bizso09

This one reason why quantum physics is confusing: When there is an n-dimensional event in the quantum universe that event is reduced from n dimensions to 4 dimensions so n - 4 dimensions of information are lost. Moreso, a quantum event is registered in the physical universe as a physical trace effect. eg a spot on a photographic plate is a trace effect. But these trace effects are necessarily physical 4 dimensional objects in the phsical universe while the event that caused them is an n-dimensional event in the non physical universe of energy. So physicists are reduced to trying to measure an n-dimensional event with a 4-dimensional ruler. No wonder quantum physics is weird.

How does energy become matter and then manipulate itself? — Benj96

If energy is an expression of mind that is an easy one; Is it more correct to say mind manipulates energy and therefore matter?

How does it observe itself and ask questions about itself? Why does it have the capacity to love and hate?

Again, mind and energy may be much the same thing. If energy is mind then energy is what is traditionally termed 'spirit'.

X ∈ X'

X' ∉ X' — SophistiCat

By the way, is how do I type these set symbols? Latex? Is there a guide?

Edit: Found it. $\in$ Logic and Philosophy of Mathematics sub forum

Ok, I'll put it this way. List the sets that are not members of themselves as

a₁, a₂, a₃, ...

X is going to be {a₁, a₂, a₃, ...}

But for some i,

a_i = {a₁, a₂, a₃, ...} = X

So the sets in question are-

a₁, a₂, a₃, ...a_i...

= a₁, a₂, a₃, ...{a₁, a₂, a₃, ...}...

So X is to be defined as {a₁, a₂, a₃, ...}\a_i

= X\{a₁, a₂, a₃, ...} = X\X

That is, X is defined as not being a member of itself.

Don't worry about the notation. X is defined as not being a member of itself, that is all.

No, that's not how it works.

X = {{x}, {y}, {z}}

X' = {{x}, {y}, {z}, {{x}, {y}, {z}}}

X ≠ X'

X ∈ X'

X' ∉ X' — SophistiCat

No, I am saying IF X is included in X then

X = {{x}, {y}, {z},... {{x}, {y}, {z}}}

But IF X is not included

X = {{x}, {y}, {z},...}

I am only saying this to clarify things. But by definition X is NOT included so

X = {{x}, {y}, {z},...}

Precisely X = {{x}, {y}, {z},...}\{{x}, {y}, {z}}

{x}, {y}, {z} and {{x}, {y}, {z}} are different sets so excluding the set {{x}, {y}, {z}} does not exclude {x}, {y}, or {z}

No!

The paradox asks if X is a member of X. — SophistiCat

Let 'All sets that do not contain themselves as members' be

a = {x}
b = {y}
c = {z}
d = ... and these sets go on for as long as is necessary, e, f, g, h,...

Set X = {{x}, {y}, {z},...}

Suppose for some set h, h = {X}

I am saying X = {{x}, {y}, {z},...}\h

That is, X = {{x}, {y}, {z},...}\{X}

There may be h such that h = {X} or there may not.

I am saying X\h regardless and this is the definition of X.

In simple language X = "All sets that do not include themselves as members, except {X}"

You seem to be assuming that {X} is included in X but by definition it is not.

Or suppose Set V = {{x}, {y}, {z},...{X}}

Set X = V\{X} and there you have it.

If we define things as follows it might make it clearer-

a = {x}
b = {y}
c = {z}

Set X is the set of sets a, b, c so

Set X = {{x}, {y}, {z}}

If X is included

X = {{x}, {y}, {z}, {{x}, {y}, {z}}}

If X is not included

X = {{x}, {y}, {z}}

So X\X is {{x}, {y}, {z}} which is what I originally meant by X\X or X\{X}

Your notation is confusing. If you want to say that a is a member of X (a ∈ X), you would write that as

X = {a, ...}

which is not the same as

X = {{a}, ...}

{a} is a singleton set with a as the sole member. — SophistiCat

Yes, but X is a set of sets so X = {{a}, {b}, {c},...} but {a, b, c, ...} might be correct too as long as the logic of what I'm saying holds up. Link: https://truebeautyofmath.com/lesson-4-sets-of-sets/

I'm not seeing how you can "without X" and still have any X left - in terms of the notation. — tim wood

It is not 'without X' it is 'without {X}' as a set. {X} is not the same as X, my bad notation in the beginning notwithstanding. X\{X} is every set in X but not the set {X} itself.

X\{X} = {{a}, {b}, {c},...} but not {X}, regardless of whether {X} can be a member of X.

Excluding {X} is not the same as excluding X.

The paradox asks if {X} is a member of X but I am disposing of the paradox by defining X as X\{X} so there is no contradiction.

I get, "the set of all sets that do not contain themselves as subsets" = "the set of all sets that do not contain themselves as subsets" and/but excluding "the set of all sets that do not contain themselves as subsets." And that looks like the empty set. — tim wood

Yes, you are correct. Since we are talking about sets of sets, a better notation would be-

Set X = X\{X}

Set X₂ = (X U {X})\{X₂}

Set X₃ = (X₂ U {X₂})\{X₃} and so on.

Apologies for the sloppy notation.

There is no need to redefine the set. — EnPassant
But that's what you did. — Banno

No, I am saying there are infinite collections of things that are not a set.
See this link https://math.stackexchange.com/questions/24507/why-did-mathematicians-take-russells-paradox-seriously

Is it correct to rewrite this as X = X\X ? Can you translate into English? — tim wood

The paradox asks the question "Is X a member of itself?"

Let's say Set X = {{a}, {b}, {c},....}

If {X} is a member of X then

Set X = {{a}, {b}, {c},....{X}}

If {X} is a not member of X then

Set X = {{a}, {b}, {c},....}

But I am excluding {X} regardless of whether it can be a member of itself.

So Set X = {{a}, {b}, {c},....}

{X} can only be a member of itself according to the definition of X. I am explicitly excluding {X} from being a member of itself by definition. X\{X} excludes {X} as a member, not as the entire set.

Then I unite Set X with {X} in

X₂ = (X U {X})\{X₂} (See my next post)

Since the paradox shows that X is a kind of 'pathological' set we don't know where to put it.
I am creating X₂ and putting it in there. Then the process is repeated infinitely so that all relevant sets can be contained. The result is an infinite progression of sets that contain "All sets that are not members of themselves" And this entity turns out to be an infinity of sets, each nested within the other.

(It may also be that every X_i contains every X_j but not {X_i} but I have not got this far with it yet.)

{a} is a subset of A, B and C, but not a subset of X. — SophistiCat

Subset is transitive: If A is a subset of B and B is a subset of C, A is a subset of C.

{a} is a subset of {A} and {A} is a subset of {X} ---> {a} is a subset of {X}

No, {a} is not "in" A,B,C,... — jgill

{a} is a subset of A and A is a subset of X therefore {a} is a subset of X

Also, when it comes to set of sets, {a} can be an element.

Ok, change it to 'subset'. Post edited.

"I am having some trouble thinking of any well-defined set that does contain itself. Help?" — jgill

Set A = {a, w}
Set B = {a, x}
Set C = {a, y}

Set X = the set of sets that have {a} as an subset.

Set X = {A, B, C,...}

{a} is in X (because {a} is in A, B, C,...)

therefore X contains X

Well, a set is an unordered collection of individuals. The unordered collections of individuals that do not contain themselves is an unordered collection of individuals; therefor it is a set. — Banno

There is no need to redefine the set. All that is needed is to see that there are collections that are not single sets - as the paradox implies. I think Russel's Paradox is superficial and I never believed it "undermines mathematics" which strikes me as an unjustifiably dramatic statement.

In fact it is a trick question because of the way it is stated: "The set of all sets that do not contain themselves as subsets." Why are they calling it a set? I don't think something can be called a set unless it can be demonstrated to be such. And the paradox shows that it cannot be a set. The entity should be defined as "All sets that do not contain themselves as subsets" There is no ambiguity in stating it this way and intuitively I feel that such an entity is possible. But what is it if it is not a set?

If the logic of my first post is correct it is an infinite collection of sets, each nested within another.
What seems to be the case is that there can be infinite sets that are not simply a set. I say this, not because of my reasoning but also because Russel's solution involves something similar: an infinity of "types", each nested one within the other. But it may be possible to resolve the issue with sets alone (Russel's solution seems very artificial and contrived)

But the real question I am asking in my first post is: Is the logic I am using coherent? I don't see anything wrong with it, unless you can.

My largest uncertainty is not understanding what space-time is. If I think about it, it rather sounds like we are describing trajectories. Space... doesn't seem to exist. Does it? What is space? It's simply a dimension as far as I can tell (ie distance, relationship etc). Time is a measure of change. — Graeme M

Time is often defined as change but this is a weak definition; change is evidence of time but not a definition of it. (Space)time is a geometry according to which change happens. That is, time is the way change happens; it is the order according to which change happens. In physical spacetime general relativity describes how change happens. G.R. describes the geometry of time and how things happen in it. That geometry is time.

You say there is an object in universe A. But if an object is to exist space must exist and space must be coherent/mathematical. A non mathematical universe would be chaos. It would not be possible to move from a to b firstly because there would be no coherent space between a and b and secondly, there would be no space for an object to occupy. Chaos is chaotic beyond imagining

If the objects you are talking about are coherent objects the space within and around them must be coherent and laws would simply be a description of the shape of this space. Once you have space you have law/mathematics.

I don't know, but it's difficult to say that math is entirely made-up when it's so useful in scientific theories. Quantities of things exist, so does topography and function. — Marchesk

Here is a thought. Write the squares of numbers like this-

1 squared = 1
2 squared = 4
3 squared = 9 etc.

Now, you can plot this sequence of squares on a graph as a quadratic curve, the curve of x^2.

The question is, how can a flat piece of paper receive this concept of squared numbers so faithfully? How is it that it is possible to translate a thought about numbers onto a graph in flat space?

This can only be possible if there is a natural correspondence between mind and space. If mind and space were utterly different it would not be possible to create an image of mathematical ideas on a flat space. But if there is a natural correspondence between mind and space what is it? The only common factor I can think of is mathematics. That is, mind and space must be intrinsically mathematical.

More or less true in set theory, a particular branch of mathematics. My area was complex analysis and when I deal with the concept of infinity it is in the sense of unboundedness of sequences or processes. — jgill

Yes, but the limit can be defined independently of time.

Whether being and conscious awareness ("thinking") are the same is an interesting question. Again I find Heidegger a very interesting resource on these issues. I don't want to make this about Heidegger -- I have another thread for that -- but needless to say your question is a good one. — Xtrix

Suppose we define philosophy as 'knowing the world'. Then a cat is a philosopher because the cat, through consciousness, knows the world. And knows it in ways we cannot easily imagine. I don't want to be facetious but extend this to human consciousness; don't we know the world through consciousness? If you eat an apple you know what an apple is in a way that the intellect will never explain to you.

But we 'sophisticated' people in the 21st century are addicted to 'reason' and are conceited about any kind of knowledge that does not come from 'reason'. Reason is abstract, consciousness is concrete. Which is more truthful about the world?

I think it's a very weak relationship. That way you can equate St. Teresa of Jesus with Albert Einstein. It seems to me much more what separates them. — David Mo

Only, perhaps, in the way that the elephant's foot is very unlike its ears. They are both 'elephant stuff'. The non physical 'world beyond' is equally a quantum world and a divine world. The universe is immense and looks different from different angles. The Platonic realm and Teresa's world and quantum energy fields my well be the same world.

Setting side those never ending debates, what does it mean for a constructionist to be able to offer a proof for any conjecture involving an infinite sequence, such as any number greater than two is the sum of two primes? — Marchesk

It seems to me that a pure constructionist cannot even admit that there are an infinity of natural numbers. Induction proves that there are and many mathematical proofs rely on induction. But this comes back to what we mean by 'exist' in relation to numbers in a Platonic sense. What does 'exist' mean?

One unresolved question in philosophy is why there is something rather than nothing. We don't know but we know there is something. This necessary something that is, before all created things, is what is, eternally. This eternal substance is existence. It is not that this necessary something has the property 'existence' it is existence because existence cannot be a property. So, if numbers exist, they must be intrinsic to existence. And since it takes Mind for numbers to exist, existence must be Mind, if numbers are in existence. The only eternal mind in which numbers can exist is God's Mind.

What all this means is that existence, mind, and God are three names for the same thing.
In this context I am using the word 'existence' to mean that which necessarily is.

So how does a constructionist handle such a number? Do they deny that the set of all numbers is properly mathematical? — Marchesk

Kummer, Cantor's arch enemy, was a kind of constructionist and denied the reality of real numbers. I guess they just don't agree. The question here is What does 'real' mean when we are talking about (what seem to be) abstractions? What does 'exist' mean in the context of numbers existing?