Arithmetic Foundations are Tautological and Circular

[Sculptor]

"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.

Given the easy accessibility of these facts, the only person who is "stupid" here is yourself.
You have NO argument.
There are still humans in the world that have no knowledge or interest in your criteria- this does not make them less human.

[Skepdick]

Given the easy accessibility of these facts, the only person who is "stupid" here is yourself.

The contents of your mind aren't on the internet.

The question: Do you equate "humans" with "homo sapiens"?

Is directed at you, not Google.

You have NO argument.

You are very observant. What I do have is questions, not arguments.

In so far as you are using the word "human" and you know what a "human" is - when did humans first appear on Earth?

There are still humans in the world that have no knowledge or interest in your criteria- this does not make them less human.

You are stretching for a strawman.

[Sculptor]

Given the easy accessibility of these facts, the only person who is "stupid" here is yourself.

The contents of your mind aren't on the internet.

The question: Do you equate "humans" with "homo sapiens"?

Is directed at you, not Google.

You have NO argument.

You are very observant. What I do have is questions, not arguments.

In so far as you are using the word "human" and you know what a "human" is - when did humans first appear on Earth?

There are still humans in the world that have no knowledge or interest in your criteria- this does not make them less human.

You are stretching for a strawman.

The statement in contention which you defended was "Eodnhoj7 wrote: ↑Sat Jan 18, 2020 12:59am If there were no math, logic language there would be no human beings."

I'm happy to learn you are not defending this.

As for what is "human" and what is homo sapiens, that also is fairly easy to find on the Internet.
HS is a subset of humans which also includes HE and HN.

It is widely judged that the branch of evolution we call "human" began after the time of "Lucy". Although Lucy is regarded as a Homonid, she does not get the taxonomic "homo".
Lucy is categoried as Australopithecus afarensis, but the next stage ,where there is more clear evidence of tool use following Lucy and that branch is called Homo Habilis. This literally means handy.

So the appearance of humans is at least 4.5 million years ago.
But this is evolution. Things change gradually. So there is no exact time and would depend on whatever arbitrary characteristics you would choose.

[Skepdick]

As for what is "human" and what is homo sapiens, that also is fairly easy to find on the Internet.

If I wanted the answer that's on the Internet - I would ask the internet.

I am asking you because the answer I am looking for is in your head, not on the Internet.

HS is a subset of humans which also includes HE and HN.

It is widely judged that the branch of evolution we call "human" began after the time of "Lucy".

So you are using "human" to mean "genus Homo", not "species Homo Sapiens".

It can mean either.

So the appearance of humans is at least 4.5 million years ago.

Genus - yes.
Species - no.

But this is evolution. Things change gradually. So there is no exact time and would depend on whatever arbitrary characteristics you would choose.

I know that. Which is precisely why I asked YOU the question: When did "humans" start?

Read: where do YOU draw the line? And I am happy with an answer to the nearest 5000 years.

[Scott Mayers]

I can't exactly follow the OP on this but still understand the concern. In another way of looking at this as a question, what particular 'first order' logics would be most basic and how can you link the others in a way that builds strictly upon the last without being circular?

For instance, I see the following logics that come across as 'circular' in that where one attempts to teach one, it assumes at least one or more of the others: Boolean, Propositional, Predicate, and Set Theory.

Of these, many can easily connect Predicate to Propositional by just EXTENDING it with Quantifiers. But is Boolean a subset of those or does it stand separately as its own distinct logic? Should we instead begin with Set theory first and then define the others through it. Notice that most Set theories presume Predicate (which includes Propositional within it) in a formal (non-naive) way of developing it.

The way most teach things today are 'circular' because they are taught in distinct areas that cannot be complete without being sure that other related subjects aren't synchronized and may be potentially impossible to do.

[Eodnhoj7]

I can't exactly follow the OP on this but still understand the concern. In another way of looking at this as a question, what particular 'first order' logics would be most basic and how can you link the others in a way that builds strictly upon the last without being circular?

For instance, I see the following logics that come across as 'circular' in that where one attempts to teach one, it assumes at least one or more of the others: Boolean, Propositional, Predicate, and Set Theory.

Of these, many can easily connect Predicate to Propositional by just EXTENDING it with Quantifiers. But is Boolean a subset of those or does it stand separately as its own distinct logic? Should we instead begin with Set theory first and then define the others through it. Notice that most Set theories presume Predicate (which includes Propositional within it) in a formal (non-naive) way of developing it.

The way most teach things today are 'circular' because they are taught in distinct areas that cannot be complete without being sure that other related subjects aren't synchronized and may be potentially impossible to do.

All arithmetic foundations are tautological and circular:

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

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

****All negates numbers, as subtractive, when cycled back on themselves results in addition as a negative and a negative are additive by nature. You cannot seperate the positive or the negative from a number as they are functions by nature. Positive is addition, negative is subtraction.



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)

The subtract of a negative number, multiplied results in the number of times subtraction occurs.

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

(3×2=6) = (2+2+2=6)

Multiplication is the number of times a number is added to another, times is the summation, hence addition of the natural numbers.

[Scott Mayers]

I can't exactly follow the OP on this but still understand the concern. In another way of looking at this as a question, what particular 'first order' logics would be most basic and how can you link the others in a way that builds strictly upon the last without being circular?

For instance, I see the following logics that come across as 'circular' in that where one attempts to teach one, it assumes at least one or more of the others: Boolean, Propositional, Predicate, and Set Theory.

Of these, many can easily connect Predicate to Propositional by just EXTENDING it with Quantifiers. But is Boolean a subset of those or does it stand separately as its own distinct logic? Should we instead begin with Set theory first and then define the others through it. Notice that most Set theories presume Predicate (which includes Propositional within it) in a formal (non-naive) way of developing it.

The way most teach things today are 'circular' because they are taught in distinct areas that cannot be complete without being sure that other related subjects aren't synchronized and may be potentially impossible to do.

All arithmetic foundations are tautological and circular:

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

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

****All negates numbers, as subtractive, when cycled back on themselves results in addition as a negative and a negative are additive by nature. You cannot seperate the positive or the negative from a number as they are functions by nature. Positive is addition, negative is subtraction.



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)

The subtract of a negative number, multiplied results in the number of times subtraction occurs.

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

(3×2=6) = (2+2+2=6)

Multiplication is the number of times a number is added to another, times is the summation, hence addition of the natural numbers.

You just repeated your OP without additional reflection on what I said. Your examples are incorrect. Double negation is an identity relation. Adding of negative numbers is about 'INVERSE' operations and are non-identical.

While you no doubt have a possible correct intuition of some understanding about what you mean, you are not using the language within any known logic system correctly. Your examples above are 'defining' expressions and thus are only 'tautological' by begging the definition as 'true'.

"2 = 1 + 1" is defining what the symbols used here mean. But it is only 'tautological' by postulating the expression is 'true'. Then to state it as 'true' (universally) when you assumed this statement true (particular to the system defining it), become 'circular' as a fallacy because you are assuming an extension of this idea to ALL POSSIBILITIES, not merely the created system or language.

[Eodnhoj7]

I can't exactly follow the OP on this but still understand the concern. In another way of looking at this as a question, what particular 'first order' logics would be most basic and how can you link the others in a way that builds strictly upon the last without being circular?

For instance, I see the following logics that come across as 'circular' in that where one attempts to teach one, it assumes at least one or more of the others: Boolean, Propositional, Predicate, and Set Theory.

Of these, many can easily connect Predicate to Propositional by just EXTENDING it with Quantifiers. But is Boolean a subset of those or does it stand separately as its own distinct logic? Should we instead begin with Set theory first and then define the others through it. Notice that most Set theories presume Predicate (which includes Propositional within it) in a formal (non-naive) way of developing it.

The way most teach things today are 'circular' because they are taught in distinct areas that cannot be complete without being sure that other related subjects aren't synchronized and may be potentially impossible to do.

All arithmetic foundations are tautological and circular:

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

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

****All negates numbers, as subtractive, when cycled back on themselves results in addition as a negative and a negative are additive by nature. You cannot seperate the positive or the negative from a number as they are functions by nature. Positive is addition, negative is subtraction.



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)

The subtract of a negative number, multiplied results in the number of times subtraction occurs.

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

(3×2=6) = (2+2+2=6)

Multiplication is the number of times a number is added to another, times is the summation, hence addition of the natural numbers.

You just repeated your OP without additional reflection on what I said. Your examples are incorrect. Double negation is an identity relation. Adding of negative numbers is about 'INVERSE' operations and are non-identical.

The relationship of negative numbers to eachother shows the first act of addition.
To subtract negativs numbers from eachother results in addition. You cannot subtract -2 from -3 without adding them. The subtraction of negative numbers is additive by nature.

While you no doubt have a possible correct intuition of some understanding about what you mean, you are not using the language within any known logic system correctly. Your examples above are 'defining' expressions and thus are only 'tautological' by begging the definition as 'true'.

That is because the logic systems are grounded in natural language, not the other way around. The logical system which could Express this is either limited or does not exist. I cover this in several threads, specifically the assumptive logic thread.



"2 = 1 + 1" is defining what the symbols used here mean. But it is only 'tautological' by postulating the expression is 'true'. Then to state it as 'true' (universally) when you assumed this statement true (particular to the system defining it), become 'circular' as a fallacy because you are assuming an extension of this idea to ALL POSSIBILITIES, not merely the created system or language.

Tautologies are one thing expressed in a new manner. The arithmetic functions behave circulary, for example division is the number of time subtraction occurs until zero is reached. It is a second degree of subtraction, or the subtraction of subtraction. It is a variation of subtraction.

Your example of 2 = x reflects alot more than just 1+1. It reflects 2+0, 3+-1, 4+-2, etc. as infinitum. So yes it is a tautology but so is 1+1=2, 2-0=2, 3-1=2, etc.

[Scott Mayers]

My own background is strong in logic. When you test to determine the completeness of any system, you want to be sure to have all possible situations covered and this is done by assuring each of all possibilities are 'tautologous' and cover the domain. So I don't know what you believe that you are asserting or adding to the field. (?)

In computing, addition is adding of complements (a single 'negation'). A double negation just turns the number back to its original (an identity function).

You open this thread and IMPLY that the foundations are also 'circular' as though this was a flaw or fallacy in reasoning of math. The 'circularity' is not a flaw unless one attempts to convince something MORE than the system's domain is 'true' (or 'false').

I think you just have a different way of communicating and the onus is on you to adapt to the language of the audience OR are required to present your logic. That would take a book to write and place the burden upon the audience to do a lot of voluntary homework. Thus, it would be better if you try to adapt to some conventional logic that is shareable. But given you are limited to colloquial conversation, even that might be too much. Instead, state some proposed 'thesis' statement. [Example form: "I believe that...X...because...Y..."0] I don't know what you are stating without this kind of expression.

[Scott Mayers]

As to my point about how the formal proof of one system tends to assume another logic on the 'first order' level, this tends to be 'circular' because one system requires some prior metalogic to prove the logic you are 'testing' and thus cannot necessarily be closed with respect to their dependency upon a collection of systems.

For instance, to prove the Propositional Calculus, you usually need some prior assumption of the validity of a set of boolean truth-functioning tables. Formal Zermelo-Frankel Set theory relies on assuming Predicate logic which is itself dependent upon Propositional logic to prove 'closed' (i.e. 'complete'). Boolean algrebra requires trusting Set theory. Boolean systems include 'multivariables' but requires the first stage is to assume a binary 'set' of values, for instance, and a 'set' of operations declared to be used.

So my question is which metalogic system is most basic an doesn't require another system of logic ASSUMED in order to prove it complete?

[Skepdick]

In computing, addition is adding of complements (a single 'negation'). A double negation just turns the number back to its original (an identity function).

That's not normative - it's a design choice. Double negation need not be an identity function. Also Logical and arithmetic negation aren't the same thing...

https://repl.it/repls/GorgeousRigidDriverwrapper

Code: Select all

print(1) #=> 1
print(not 1) #=> False
print(not not 1) #=> True

But then again - it doesn't only apply to numbers....

https://repl.it/repls/GlisteningBewitchedRoutine

Code: Select all

print(None) # => None 
print(not None) # => True
print(not not None) # => False

Double-negation is constructive.

[Sculptor]

As for what is "human" and what is homo sapiens, that also is fairly easy to find on the Internet.

If I wanted the answer that's on the Internet - I would ask the internet.

I am asking you because the answer I am looking for is in your head, not on the Internet.

HS is a subset of humans which also includes HE and HN.

It is widely judged that the branch of evolution we call "human" began after the time of "Lucy".

So you are using "human" to mean "genus Homo", not "species Homo Sapiens".

It can mean either.

\If you don't like the answer - why ask the question?

So the appearance of humans is at least 4.5 million years ago.

Genus - yes.
Species - no.

Genus yes, species yes.
"sapiens" no

But this is evolution. Things change gradually. So there is no exact time and would depend on whatever arbitrary characteristics you would choose.

SO what?

[Eodnhoj7]

My own background is strong in logic. When you test to determine the completeness of any system, you want to be sure to have all possible situations covered and this is done by assuring each of all possibilities are 'tautologous' and cover the domain. So I don't know what you believe that you are asserting or adding to the field. (?)

In computing, addition is adding of complements (a single 'negation'). A double negation just turns the number back to its original (an identity function).

You open this thread and IMPLY that the foundations are also 'circular' as though this was a flaw or fallacy in reasoning of math. The 'circularity' is not a flaw unless one attempts to convince something MORE than the system's domain is 'true' (or 'false').

I think you just have a different way of communicating and the onus is on you to adapt to the language of the audience OR are required to present your logic. That would take a book to write and place the burden upon the audience to do a lot of voluntary homework. Thus, it would be better if you try to adapt to some conventional logic that is shareable. But given you are limited to colloquial conversation, even that might be too much. Instead, state some proposed 'thesis' statement. [Example form: "I believe that...X...because...Y..."0] I don't know what you are stating without this kind of expression.

Double negation is two fold. If I have a fallacy and negate it with another fallacy:

1. The fallacy is negated and results in a positive truth value, ie the fallacy of circularity is negated resulting in an authority statement.

2. The fallacy continues to exist due to slippery slope, thus circularity is also a fallacy.

3. Circularity is both a fallacy and not a fallacy, therefore a fallacy is only a negative limit, ie the argument is limited because it is circular but not invalid.

4. The same applies for all double negation: -(-A) --> (A & -A)

[Eodnhoj7]

As to my point about how the formal proof of one system tends to assume another logic on the 'first order' level, this tends to be 'circular' because one system requires some prior metalogic to prove the logic you are 'testing' and thus cannot necessarily be closed with respect to their dependency upon a collection of systems.

For instance, to prove the Propositional Calculus, you usually need some prior assumption of the validity of a set of boolean truth-functioning tables. Formal Zermelo-Frankel Set theory relies on assuming Predicate logic which is itself dependent upon Propositional logic to prove 'closed' (i.e. 'complete'). Boolean algrebra requires trusting Set theory. Boolean systems include 'multivariables' but requires the first stage is to assume a binary 'set' of values, for instance, and a 'set' of operations declared to be used.

So my question is which metalogic system is most basic an doesn't require another system of logic ASSUMED in order to prove it complete?

There isn't one, all contexts are assumed and context is inescapable, this thread addresses this:

Highest Abstraction for Logic and Math?
viewtopic.php?f=26&t=28138

[Scott Mayers]

As to my point about how the formal proof of one system tends to assume another logic on the 'first order' level, this tends to be 'circular' because one system requires some prior metalogic to prove the logic you are 'testing' and thus cannot necessarily be closed with respect to their dependency upon a collection of systems.

For instance, to prove the Propositional Calculus, you usually need some prior assumption of the validity of a set of boolean truth-functioning tables. Formal Zermelo-Frankel Set theory relies on assuming Predicate logic which is itself dependent upon Propositional logic to prove 'closed' (i.e. 'complete'). Boolean algrebra requires trusting Set theory. Boolean systems include 'multivariables' but requires the first stage is to assume a binary 'set' of values, for instance, and a 'set' of operations declared to be used.

So my question is which metalogic system is most basic an doesn't require another system of logic ASSUMED in order to prove it complete?

There isn't one, all contexts are assumed and context is inescapable, this thread addresses this:

Highest Abstraction for Logic and Math?
viewtopic.php?f=26&t=28138

I said I do not follow your own language or thought process so will not participate further than my comment about metalogic 'circularity'. Thank you.