Arithmetic Foundations are Tautological and Circular

[Eodnhoj7]

All arithmetic foundations are tautological and circular:

1. The subtraction of subtraction is addition through double negation.

(-1-1=-2)=(-1+-1=-2)



2. Division is further the subtraction of subtraction, as the number of times x may be subtracted until point zero is reached.

(6/3=2) = (6-3-3=0)



3. The addition of addition is the number of times x may be added to another.

(3×2=6) = (2+2+2=6)

[RCSaunders]

All arithmetic foundations are tautological and circular:

1. The subtraction of subtraction is addition through double negation.

(-1-1=-2)=(-1+-1=-2)



2. Division is further the subtraction of subtraction, as the number of times x may be subtracted until point zero is reached.

(6/3=2) = (6-3-3=0)



3. The addition of addition is the number of times x may be added to another.

(3×2=6) = (2+2+2=6)

You have only illustrated some arbitrary symbols for a humanly invented method, which mean nothing. For every digit symbol means nothing unless it is actually a modifier, as in, 1 book, or 5 apples. None of this has anything to do with the, foundations of arithmetic. The foundation of arithmetic is not arithmetic symbols or their manipulation, the foundation of arithmetic is counting, which is neither tautological and circular.

In case you haven't figured it out, addition is just a short-cut method of counting. Subtraction is a short-cut method of counting backwards. Multiplication is a shor-cut method of addition, etc. Why does everyone want to make math into some esoteric mystery?

[Eodnhoj7]

All arithmetic foundations are tautological and circular:

1. The subtraction of subtraction is addition through double negation.

(-1-1=-2)=(-1+-1=-2)



2. Division is further the subtraction of subtraction, as the number of times x may be subtracted until point zero is reached.

(6/3=2) = (6-3-3=0)



3. The addition of addition is the number of times x may be added to another.

(3×2=6) = (2+2+2=6)

You have only illustrated some arbitrary symbols for a humanly invented method, which mean nothing. For every digit symbol means nothing unless it is actually a modifier, as in, 1 book, or 5 apples. None of this has anything to do with the, foundations of arithmetic. The foundation of arithmetic is not arithmetic symbols or their manipulation, the foundation of arithmetic is counting, which is neither tautological and circular.

Counting is tautological as all numbers are variations of one. It is the repetition of key elements of a set.

In case you haven't figured it out, addition is just a short-cut method of counting. Subtraction is a short-cut method of counting backwards. Multiplication is a shor-cut method of addition, etc. Why does everyone want to make math into some esoteric mystery?

It is circular by nature, as the act of counting is a reciprocation between subject and object.

[RCSaunders]

... all numbers are variations of one. ...

I think you are forgetting that numbers were invented. They don't exist except in human minds as a way of identifying variations in one of the possible attributes of physical existents. There are variations of symbols for "one," such as the Arabic numeral 1, the Roman numeral I, the Russian word один, the Chinese word 个, and other variations in other languages. The number two, or 2, is an entirely different concept from the number one, which is why it requires an entirely different symbol.[/quote]

Perhaps you have been influenced by the logical positivists, which would explain why you have no idea what a concept is, or what a concept means. If you did know what concepts are you would never say that any number was a variation of another. You might say, that all numbers are the same kind of conceptual existent because they are all referents of the same universal concept, "number," but they are not variations of the same existents. Two is not a one with pigtails.

[Eodnhoj7]

... all numbers are variations of one. ...

I think you are forgetting that numbers were invented.
We actually don't know if numbers are invented. The manifestation of a form, which is a loop fundamentally, shares the same nature of the number line as a loop with 1 self referencing into newer and newer numbers. The act of counting is also a loop between the subject and object.

So what we understand of numbers are looping (counting) loops (form) with number being a loop inseperable from the object.






They don't exist except in human minds as a way of identifying variations in one of the possible attributes of physical existents. There are variations of symbols for "one," such as the Arabic numeral 1, the Roman numeral I, the Russian word один, the Chinese word 个, and other variations in other languages. The number two, or 2, is an entirely different concept from the number one, which is why it requires an entirely different symbol.

Perhaps you have been influenced by the logical positivists, which would explain why you have no idea what a concept is, or what a concept means. If you did know what concepts are you would never say that any number was a variation of another. You might say, that all numbers are the same kind of conceptual existent because they are all referents of the same universal concept, "number," but they are not variations of the same existents. Two is not a one with pigtails.
[/quote]

Concepts are cycling abstractions, with an abstraction being a form in the mind which may or may not align with empirical reality. What connects both abstractions and forms are their inherent forms with these forms being spatial. One, as a number for counting, cannot be seperated from the form it quantifies. In these respects we are left with the number line, with the line being a one dimensional loop as items beginning and end are the same.

[RCSaunders]

We actually don't know if numbers are invented. ...

Speak for yourself. If you're a member of some, "we," that is ignorant of the fact all knowledge methods (language, logic, mathematics) were invented by human beings your, "we," does not include me.

If there were no human beings there would be no language, not logic, and no mathematics. Most of your confusion about logic and math I think come from a belief in some kind of mystic existence of knowledge and concepts independent of human minds.[/quote]

[Eodnhoj7]

We actually don't know if numbers are invented. ...

Speak for yourself. If you're a member of some, "we," that is ignorant of the fact all knowledg6e methods (language, logic, mathematics) were invented by human beings your, "we," does not include me.

If there were no human beings there would be no language, not logic, and no mathematics. Most of your confusion about logic and math I think come from a belief in some kind of mystic existence of knowledge and concepts independent of human minds.

[/quote]

If there were no math, logic language there would be no human beings.

[Skepdick]

All arithmetic foundations are tautological and circular:

That's a feature, not a bug.

Mathematics/logic can only prove things up to isomorphism and no further.

[Sculptor]

If there were no math, logic language there would be no human beings.

Completely and palpably bollocks.
Humans predate all of these things.

[Skepdick]

Completely and palpably bollocks.
Humans predate all of these things.

Given the continuous timeline between the Big Band and NOW, could you draw a line for us? When do you think "humanity" first appeared?

For clarity's sake. Do you equate "humans" with "homo sapiens"?

For an argument can definitely be made that the appearance of written language and abstract thought is a definite event in HUMAN (different from homo sapiens) history. Why do I draw such a distinction?

Because written language happened 60 to 30 thousand years ago. Significantly after homo sapiens happened - 200000 years ago.

The ability to record/transmit the memories, experiences and knowledge of the old generation onto the new generation is an evolutionary game changer.

[Sculptor]

Completely and palpably bollocks.
Humans predate all of these things.

Given the continuous timeline between the Big Band and NOW, could you draw a line for us? When do you think "humanity" first appeared?

For clarity's sake. Do you equate "humans" with "homo sapiens"?

For an argument can definitely be made that the appearance of written language and abstract thought is a definite event in HUMAN (different from homo sapiens) history. Why do I draw such a distinction?

Because written language happened 60 to 30 thousand years ago. Significantly after homo sapiens happened - 200000 years ago.

The ability to record/transmit the memories, experiences and knowledge of the old generation onto the new generation is an evolutionary game changer.

"maths and logical language" and writing happened far later than you suggest.
The first attempts are recording meaning were all about recording the grain stores.
There was nothing of the sort before 6000 years ago.
Evidence of maths and logical language that you suggest are necessary for "humans" much later still.
I suggest that literacy is not a necessary element of humanity.
For 99% of human evolution there has been nothing of the sort
Maybe you ought to acquaint yourself with the basic facts of archaeology before you present such statements?

[Skepdick]

"maths and logical language" and writing happened far later than you suggest.
The first attempts are recording meaning were all about recording the grain stores.
There was nothing of the sort before 6000 years ago.
Evidence of maths and logical language that you suggest are necessary for "humans" much later still.
I suggest that literacy is not a necessary element of humanity.
For 99% of human evolution there has been nothing of the sort

OK. I am willing to work with your estimates/categories - there is zero value in arguing about it.

If language/mathematics/logic started 6000 years ago, when did "humans" start?

Maybe you ought to acquaint yourself with the basic facts of archaeology before you present such statements?

Maybe you want to try be less stupid and observe that irrespective of the particulars my argument remains the same.

My argument is valid irrespective of the facts. Here, let me help you!

Given the continuous timeline between the Big Band and NOW, could you draw a line for us? When do you think "humanity" first appeared?

For clarity's sake. Do you equate "humans" with "homo sapiens"?

For an argument can definitely be made that the appearance of written language and abstract thought is a definite event in HUMAN (different from homo sapiens) history. Why do I draw such a distinction?

Because written language happened ̶6̶0̶ ̶t̶o̶ ̶3̶0̶ ̶t̶h̶o̶u̶s̶a̶n̶d̶ ̶y̶e̶a̶r̶s̶ ̶a̶g̶o̶ 6000 years ago. Significantly after homo sapiens happened - 200000 years ago.

The ability to record/transmit the memories, experiences and knowledge of the old generation onto the new generation is an evolutionary game changer.

[Eodnhoj7]

If there were no math, logic language there would be no human beings.

Completely and palpably bollocks.
Humans predate all of these things.

We cannot say humans predate space as space, while a posteriori, is a priori as well. The blank slate of human assumption, where humans assume patterns through a "no-thingness", requires a subsidiary space (which we are made in an image of by nature of our means to assume) that predates time itself.

That absence of "thingness" is an absence of time, put into shorter words thus there is a higher state than the image (man) which co-creates with it.

[Eodnhoj7]

All arithmetic foundations are tautological and circular:

That's a feature, not a bug.

Mathematics/logic can only prove things up to isomorphism and no further.

If all things exist through cycles, including arithmetic, then by default it is an inherent nature of "something-ness" or "is-ness" thus not a bug.

[Eodnhoj7]

... all numbers are variations of one. ...

I think you are forgetting that numbers were invented. They don't exist except in human minds as a way of identifying variations in one of the possible attributes of physical existents. There are variations of symbols for "one," such as the Arabic numeral 1, the Roman numeral I, the Russian word один, the Chinese word 个, and other variations in other languages. The number two, or 2, is an entirely different concept from the number one, which is why it requires an entirely different symbol.

Perhaps you have been influenced by the logical positivists, which would explain why you have no idea what a concept is, or what a concept means. If you did know what concepts are you would never say that any number was a variation of another. You might say, that all numbers are the same kind of conceptual existent because they are all referents of the same universal concept, "number," but they are not variations of the same existents. Two is not a one with pigtails.
[/quote]

Tell me how the number one was invented, as it requires an isomorphism from zero with "invention" itself being subject to isomorphism. What we understand of any invention is an isomorphism from one set of cycles into another, with isomorphism itself as grounded in the ability to assume patterns (1st degree of isomorphism as Nothingness inverts to somethingness) and invert these patterns to new patterns (2nd degree of isomorphism).

Isomorphism thus is subject to its own laws as nothing is inverted to something which Inverts again between unity and multiplicity of objects. Isomorphism inverts from one state to another, thus is self referencing. From this isomorphism of isomorphism we gain recursion, thus recursion is coexistent as a law, simultaneously, with isomorphism.