Philosophy Now Forum

Eodnhoj7 wrote: ↑Tue Jan 28, 2020 3:17 am We don't know if numbers are man made considering they are tied to forms; All numbers are loops of 1 self referencing, they loop between the subject and object when counting, and all forms have a shape that loops when tracing beginning and end points. It's all loops.

Scott Mayers wrote: ↑Tue Jan 28, 2020 5:29 am

Eodnhoj7 wrote: ↑Tue Jan 28, 2020 3:17 am We don't know if numbers are man made considering they are tied to forms; All numbers are loops of 1 self referencing, they loop between the subject and object when counting, and all forms have a shape that loops when tracing beginning and end points. It's all loops.

You are running into the dilemma in common with most of us who think deep on these issues.

Are numbers premised in counting yes or no?

Set theory attempts to divorce their relationship to 'number' by utilizing 'cardinality' labels to define them. They do this by asserting some set as having some cardinality rather than a 'count' of members because they don't want to be biased to assuming numbers in order to prove them. As such, the following are said to have an identical 'cardinality':

{X}, {8}, {dirty rags}, {a}, ....

To count is to manifest a set of one thing which exists in many variations.

Then they label this concept, "one" or "oneness". To be possibly clearer, they might say, using the above examples, that what makes or defines the following statement 'true' (or 'agreed to among two or more people'):

{X} = {8} = {dirty rags} = {a} = ...{(any single member)} is "one(ness)" or "unit".

For other concepts built upon this, they can make an axiom about PAIRS of member ship and replacement of symbols (or objects). This might be an axiom that asserts the following is agreed to be able to construct a new set:

Axiom of Duple member creation of sets: {(any concept/symbol/object), (any concept/symbol/object)} exists if some {(any concept/symbol/object)} exists.

This BEGS an agreement between people.

The numbers as symbols are themselves arbitrary. But many presume that numbers are ONLY the symbols and lack a coinciding reality of comparison such that if there were no comparison, then there could be no actual 'count' that the symbols represent.

Given nothing, say what could be in this set: {}, we can then have a set by the "Axiom of Duples", { {}, X}, wher X can be anything. With a 'substitution' axiom, we might permit the "X" to be replaced by anything, including the set it is contained in such as,

Let X = { {}, X}. Then

{ {}, { {}, X} } is an agreed set that exists.


May I ask if you have directly studied any set theory system (a particular one, that is, not just an abstract understanding of them in general)?

I tends toward an abstract understanding.

Eodnhoj7 wrote: ↑Tue Jan 28, 2020 7:07 pm

Scott Mayers wrote: ↑Tue Jan 28, 2020 5:29 am

Eodnhoj7 wrote: ↑Tue Jan 28, 2020 3:17 am We don't know if numbers are man made considering they are tied to forms; All numbers are loops of 1 self referencing, they loop between the subject and object when counting, and all forms have a shape that loops when tracing beginning and end points. It's all loops.

You are running into the dilemma in common with most of us who think deep on these issues.

Are numbers premised in counting yes or no?

Set theory attempts to divorce their relationship to 'number' by utilizing 'cardinality' labels to define them. They do this by asserting some set as having some cardinality rather than a 'count' of members because they don't want to be biased to assuming numbers in order to prove them. As such, the following are said to have an identical 'cardinality':

{X}, {8}, {dirty rags}, {a}, ....

To count is to manifest a set of one thing which exists in many variations.

Scott Mayers wrote: ↑Thu Jan 30, 2020 1:30 am

Eodnhoj7 wrote: ↑Tue Jan 28, 2020 7:07 pm

Scott Mayers wrote: ↑Tue Jan 28, 2020 5:29 am

You are running into the dilemma in common with most of us who think deep on these issues.

Are numbers premised in counting yes or no?

No, not in formal set theories. They treat elements (members of sets) as arbitrary symbols and just relate other sets by 'cartesian products' (an ordered relationship between two sets identical to the x-and-y axes in graphing relations and functions. [Why it is also called the "Cartesian plane".] They define a "one-to-one" relation and just arbitrarily label this as having a "common Cardinality" by a mere variable. Any and all sets with the same count will have the same Cardinality. This can then be given the traditional 'number symbol' that expresses this family of sets.

But 'order' first needs to be set up as well.

Cartesian products are still counting positions, all counting is ground in a position as the object being counted is a position of a set of phenomena (for example an orange is a set of particles and qualtities in specific positions.)

Set theory attempts to divorce their relationship to 'number' by utilizing 'cardinality' labels to define them. They do this by asserting some set as having some cardinality rather than a 'count' of members because they don't want to be biased to assuming numbers in order to prove them. As such, the following are said to have an identical 'cardinality':

{X}, {8}, {dirty rags}, {a}, ....

To count is to manifest a set of one thing which exists in many variations.

All numbers that are finite share the feature of 'oneness'. The usual word, "unique" defines this property to everything and everything acts as its own 'unit'. Both words are begging but differ in that they are treated as 'qualities' rather than 'quantities'.

A qualtity is still quantifiable.

I prefer defining it different and am still working on a set theory that can express it as such.

Scott Mayers wrote: ↑Thu Jan 30, 2020 10:35 pm Eodnhoj7,

Take anything, no matter what it is, whether it is a single thing or group of things, whether it is unique or not, whether any parts of it (as a whole or collection of things) and label it "P"

P is a 'unit' concept because we can now use the label, "P", to act as a comparative thing to measure.

This may seem odd to assert simplistically but anything 'finite' is itself able to act as a 'unit' in this way. This is the first step to defining numbers without using number directly. P would be the actual reality to which the label, "P", acts as the artificial (man-made) factor we initially mean by a "unit" thing. Note that even whatever concept you might think of that is not necessarily itself finite, like an action, is also able to be something we can label 'finitely' and treat it as a 'unit'.

So when symbolizing the initial number we usually label with the symbol, "1", it is itself just a unit variable that we just prefer universally for the same thing we used "P" for above. As long as we CAN at least imagine some fixed (finite) concept, that represents a unit too. So both the thing taken and the label you assign to represent them are real and act as the first 'number' if you use it for counting or measure. We don't call these concepts 'numbers' in other contexts because we may not be using them for mathematical reasons. But they exist.

Numbers are thus both artificial (symbol assignments) and not artificial (the finite concept real or imagined of something assumed taken or collected).

[I can answer more of what you asked above but think it might help to take one step at a time. You raised the concept of 'one' in another thread and this needs to be first established and agreed to before we can consider other numbers beyond the initial 'one'.]

Scott Mayers wrote: ↑Thu Jan 30, 2020 10:35 pm Eodnhoj7,

Take anything, no matter what it is, whether it is a single thing or group of things, whether it is unique or not, whether any parts of it (as a whole or collection of things) and label it "P"

P is a 'unit' concept because we can now use the label, "P", to act as a comparative thing to measure.

This may seem odd to assert simplistically but anything 'finite' is itself able to act as a 'unit' in this way. This is the first step to defining numbers without using number directly. P would be the actual reality to which the label, "P", acts as the artificial (man-made) factor we initially mean by a "unit" thing. Note that even whatever concept you might think of that is not necessarily itself finite, like an action, is also able to be something we can label 'finitely' and treat it as a 'unit'.

So when symbolizing the initial number we usually label with the symbol, "1", it is itself just a unit variable that we just prefer universally for the same thing we used "P" for above. As long as we CAN at least imagine some fixed (finite) concept, that represents a unit too. So both the thing taken and the label you assign to represent them are real and act as the first 'number' if you use it for counting or measure. We don't call these concepts 'numbers' in other contexts because we may not be using them for mathematical reasons. But they exist.

Numbers are thus both artificial (symbol assignments) and not artificial (the finite concept real or imagined of something assumed taken or collected).

[I can answer more of what you asked above but think it might help to take one step at a time. You raised the concept of 'one' in another thread and this needs to be first established and agreed to before we can consider other numbers beyond the initial 'one'.]

Eodnhoj7 wrote: ↑Fri Jan 31, 2020 2:31 am

Scott Mayers wrote: ↑Thu Jan 30, 2020 10:35 pm Eodnhoj7,

Take anything, no matter what it is, whether it is a single thing or group of things, whether it is unique or not, whether any parts of it (as a whole or collection of things) and label it "P"

P is a 'unit' concept because we can now use the label, "P", to act as a comparative thing to measure.

This may seem odd to assert simplistically but anything 'finite' is itself able to act as a 'unit' in this way. This is the first step to defining numbers without using number directly. P would be the actual reality to which the label, "P", acts as the artificial (man-made) factor we initially mean by a "unit" thing. Note that even whatever concept you might think of that is not necessarily itself finite, like an action, is also able to be something we can label 'finitely' and treat it as a 'unit'.

So when symbolizing the initial number we usually label with the symbol, "1", it is itself just a unit variable that we just prefer universally for the same thing we used "P" for above. As long as we CAN at least imagine some fixed (finite) concept, that represents a unit too. So both the thing taken and the label you assign to represent them are real and act as the first 'number' if you use it for counting or measure. We don't call these concepts 'numbers' in other contexts because we may not be using them for mathematical reasons. But they exist.

Numbers are thus both artificial (symbol assignments) and not artificial (the finite concept real or imagined of something assumed taken or collected).

[I can answer more of what you asked above but think it might help to take one step at a time. You raised the concept of 'one' in another thread and this needs to be first established and agreed to before we can consider other numbers beyond the initial 'one'.]

I understand what you are claiming but the number as attached to a phenomenon and the number as a symbol both have forms, all forms have shapes, and all shapes when traced either are a loop or begin and end with the same point.

A number cannot be seperated from a form, we reason through forms and forms are inseperable from the phenomenon.

Skepdick wrote: ↑Sat Feb 01, 2020 12:37 pm

Scott Mayers wrote: ↑Thu Jan 30, 2020 10:35 pm Eodnhoj7,

Take anything, no matter what it is, whether it is a single thing or group of things, whether it is unique or not, whether any parts of it (as a whole or collection of things) and label it "P"

P is a 'unit' concept because we can now use the label, "P", to act as a comparative thing to measure.

This may seem odd to assert simplistically but anything 'finite' is itself able to act as a 'unit' in this way. This is the first step to defining numbers without using number directly. P would be the actual reality to which the label, "P", acts as the artificial (man-made) factor we initially mean by a "unit" thing. Note that even whatever concept you might think of that is not necessarily itself finite, like an action, is also able to be something we can label 'finitely' and treat it as a 'unit'.

So when symbolizing the initial number we usually label with the symbol, "1", it is itself just a unit variable that we just prefer universally for the same thing we used "P" for above. As long as we CAN at least imagine some fixed (finite) concept, that represents a unit too. So both the thing taken and the label you assign to represent them are real and act as the first 'number' if you use it for counting or measure. We don't call these concepts 'numbers' in other contexts because we may not be using them for mathematical reasons. But they exist.

Numbers are thus both artificial (symbol assignments) and not artificial (the finite concept real or imagined of something assumed taken or collected).

[I can answer more of what you asked above but think it might help to take one step at a time. You raised the concept of 'one' in another thread and this needs to be first established and agreed to before we can consider other numbers beyond the initial 'one'.]

What a mess. You are mixing up concepts and vocabulary from three distinct theories/languages, and because you are being careless you are committing a Type error.

Skepdick wrote: You are confusing the [/Unit-type (1:Type) with 1:Integer.

### Conventions

Category Theory (CT)
Logic (L)
Type Theory (TT)
Set Theory (ST)

The Initial Object (CT) corresponds to Falsity (L) corresponds to Empty set (TT, ST).
The Terminal Object (CT) corresponds to Truth (L) corresponds to the Unit Type (TT, ST)
For more clarity see: https://ncatlab.org/nlab/show/computati ... itarianism

So lets start with a set-theoretical Mathematical universe which contains nothing but an Empty Set (or in the language of Logic: a Universe which contains only a Falsehood, or in the language of Category Theory: Category with only an initial object)
In such a Universe there is no way to arrive at truth (Units?, Terminal Objects?) - that would be (literally) Absurd. The Principle of Explosion. From falsehood anything follows. Which is why the Absurdity Type can be declared as follows:

In the language of Category Theory:
let x: initial object
let y: terminal object
f: x -> y

In the language of Logic:
False -> True

In the language of Type Theory/Set Theory: f :: ∅:Type -> 1:Type

So if the ∅:Type producing a 1:Type is equivalent to the Absurd() function, then what function can we use to get an actual 1?

The only way out of this mess is to introduce a new function into the Mathematical Universe. A function which constructs an Integer:1 from a ∅:Type

There is one and only one function which starts with the ∅:Type and produces 1:Integer (N.B **NOT** 1:Type - any function that starts with ∅:Type and produces 1:Type is equivalent to the Absurd function).

What we need is g :: ∅:Type -> 1:Integer

That function is called counting. What would such a function end up counting? The only thing that exists in the Mathematical Universe before us: falsehoods/empty sets.

Question: How many empty sets exist?
Answer: count(∅:Type) = 1:Integer

This is generally how all Proof by Abstract nonsense goes...

References:

Logic:
https://ncatlab.org/nlab/show/falsehood
https://ncatlab.org/nlab/show/true+proposition

Category Theory:
https://ncatlab.org/nlab/show/initial+object
https://ncatlab.org/nlab/show/terminal+object

Type Theory:
https://ncatlab.org/nlab/show/empty+type
https://ncatlab.org/nlab/show/unit+type

Scott Mayers wrote: ↑Sun Feb 02, 2020 9:03 am

Eodnhoj7 wrote: ↑Fri Jan 31, 2020 2:31 am

Scott Mayers wrote: ↑Thu Jan 30, 2020 10:35 pm Eodnhoj7,

Take anything, no matter what it is, whether it is a single thing or group of things, whether it is unique or not, whether any parts of it (as a whole or collection of things) and label it "P"

P is a 'unit' concept because we can now use the label, "P", to act as a comparative thing to measure.

This may seem odd to assert simplistically but anything 'finite' is itself able to act as a 'unit' in this way. This is the first step to defining numbers without using number directly. P would be the actual reality to which the label, "P", acts as the artificial (man-made) factor we initially mean by a "unit" thing. Note that even whatever concept you might think of that is not necessarily itself finite, like an action, is also able to be something we can label 'finitely' and treat it as a 'unit'.

So when symbolizing the initial number we usually label with the symbol, "1", it is itself just a unit variable that we just prefer universally for the same thing we used "P" for above. As long as we CAN at least imagine some fixed (finite) concept, that represents a unit too. So both the thing taken and the label you assign to represent them are real and act as the first 'number' if you use it for counting or measure. We don't call these concepts 'numbers' in other contexts because we may not be using them for mathematical reasons. But they exist.

Numbers are thus both artificial (symbol assignments) and not artificial (the finite concept real or imagined of something assumed taken or collected).

[I can answer more of what you asked above but think it might help to take one step at a time. You raised the concept of 'one' in another thread and this needs to be first established and agreed to before we can consider other numbers beyond the initial 'one'.]

I understand what you are claiming but the number as attached to a phenomenon and the number as a symbol both have forms, all forms have shapes, and all shapes when traced either are a loop or begin and end with the same point.

A number cannot be seperated from a form, we reason through forms and forms are inseperable from the phenomenon.

I agree to what I follow you saying. It truly is hard if not impossible to separate the two. Once an assignment is made, the meaning of the symbol is tied to what it refers to inseparably. Since the actual object being pointed to is itself a 'symbol of itself', this justifies identity and 'truth' where we use logic as a means to seek agreement among two or more people. Everything is just 'containers' of something when you get to the deep level of metalogic.

Since we cannot define anything without becoming circular, you just begin at the bottom level with a container (a symbol) you assume that you cannot open nor determine what is inside. It can be absolutely nothing, something specific, or an infinity of thing imaginable or not. The container itself can be containing the outside world as a perfect point, like inverting everything inside out, or even just 'reflecting' our reality.

Thus you can postulate it as that "P" I used as a symbol and then only deal with symbols themselves (and why the first-order logics are also referred to as "symbolic logic").

For Propositional logic, the container is a proposition that acts to speak of some reality in a sentence that is itself another 'container' but specified for language about reality. For Set theory, the set is what this container holds of assumed objects conceived or not. Boolean algebras focus on assigning a values assumed to be LINKED to something else, like a proposition or an object, etc.

The reality cannot be separated from the symbol either because that is all we can actually interpret about reality outside of us. We just have to assume our sensations as is without questioning and so postulate/assume it.

Eodnhoj7 wrote: ↑Sun Feb 02, 2020 4:48 pm

Scott Mayers wrote: ↑Sun Feb 02, 2020 9:03 am

Eodnhoj7 wrote: ↑Fri Jan 31, 2020 2:31 am

I understand what you are claiming but the number as attached to a phenomenon and the number as a symbol both have forms, all forms have shapes, and all shapes when traced either are a loop or begin and end with the same point.

A number cannot be seperated from a form, we reason through forms and forms are inseperable from the phenomenon.

I agree to what I follow you saying. It truly is hard if not impossible to separate the two. Once an assignment is made, the meaning of the symbol is tied to what it refers to inseparably. Since the actual object being pointed to is itself a 'symbol of itself', this justifies identity and 'truth' where we use logic as a means to seek agreement among two or more people. Everything is just 'containers' of something when you get to the deep level of metalogic.

Since we cannot define anything without becoming circular, you just begin at the bottom level with a container (a symbol) you assume that you cannot open nor determine what is inside. It can be absolutely nothing, something specific, or an infinity of thing imaginable or not. The container itself can be containing the outside world as a perfect point, like inverting everything inside out, or even just 'reflecting' our reality.

Thus you can postulate it as that "P" I used as a symbol and then only deal with symbols themselves (and why the first-order logics are also referred to as "symbolic logic").

For Propositional logic, the container is a proposition that acts to speak of some reality in a sentence that is itself another 'container' but specified for language about reality. For Set theory, the set is what this container holds of assumed objects conceived or not. Boolean algebras focus on assigning a values assumed to be LINKED to something else, like a proposition or an object, etc.

The reality cannot be separated from the symbol either because that is all we can actually interpret about reality outside of us. We just have to assume our sensations as is without questioning and so postulate/assume it.

To view it as a container is to view the phenomenon as a loop. Containers within containers leaves a Russian Mirror doll effect and we are left with the constant of all forms as loops. This loop is the constant symbol.

Scott Mayers wrote: ↑Sun Feb 02, 2020 5:20 pm

Eodnhoj7 wrote: ↑Sun Feb 02, 2020 4:48 pm

Scott Mayers wrote: ↑Sun Feb 02, 2020 9:03 am
I agree to what I follow you saying. It truly is hard if not impossible to separate the two. Once an assignment is made, the meaning of the symbol is tied to what it refers to inseparably. Since the actual object being pointed to is itself a 'symbol of itself', this justifies identity and 'truth' where we use logic as a means to seek agreement among two or more people. Everything is just 'containers' of something when you get to the deep level of metalogic.

Since we cannot define anything without becoming circular, you just begin at the bottom level with a container (a symbol) you assume that you cannot open nor determine what is inside. It can be absolutely nothing, something specific, or an infinity of thing imaginable or not. The container itself can be containing the outside world as a perfect point, like inverting everything inside out, or even just 'reflecting' our reality.

Thus you can postulate it as that "P" I used as a symbol and then only deal with symbols themselves (and why the first-order logics are also referred to as "symbolic logic").

For Propositional logic, the container is a proposition that acts to speak of some reality in a sentence that is itself another 'container' but specified for language about reality. For Set theory, the set is what this container holds of assumed objects conceived or not. Boolean algebras focus on assigning a values assumed to be LINKED to something else, like a proposition or an object, etc.

The reality cannot be separated from the symbol either because that is all we can actually interpret about reality outside of us. We just have to assume our sensations as is without questioning and so postulate/assume it.

To view it as a container is to view the phenomenon as a loop. Containers within containers leaves a Russian Mirror doll effect and we are left with the constant of all forms as loops. This loop is the constant symbol.

I WAS going to say the same thing but forgot the name of the dolls and so left it out. [They are called, "Matryoshka dolls", by the way.] The 'loop' is just one possibility of these containers because on the lowest level we just either presume we cannot open them or define them as 'empty' (even if it may not be actually 'empty' because it doesn't matter when you can't actually open them.]