- Thread starter Loren
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-Dan

Also, the human brain may have archetypes, unconcious appreciation of what would become numbers. The earliest tracable numbers are thought to be notched in stone. Before that, maybe they were sheep, or whatever had value to early man. Mating sheep became more sheep before they were called "three" (or a greater number of) sheep.

The more elementary the mathematics, the more profound it may be, both likely beyond counting. Recall Alfred North Whitehead and Bertrand Russell trying unsuccessfully to explain 1+1=2 in three volumes of

What makes this desirable? They also lack satellites.Today,, "the Piraha, an Amazonian tribe, lacks number words."

I've heard this argument before and its compelling. Unfortunately, its also completely untrue.Recall Alfred North Whitehead and Bertrand Russell trying unsuccessfully to explain 1+1=2 in three volumes ofPrincipia Mathematica!

How close did Whitehead's and Russell's proof come to argue that 1+1=2, as is widely reported? It is not hard to find many sources on the subject agreeing, with reasonable evidence, that

Truth can be evasive, both in mathematics and politics. Does there exist any absolute proof at all, as Whitehead and Russell missed over decades? I guess my point is that there is none.

How close did Whitehead's and Russell's proof come to argue that 1+1=2, as is widely reported? It is not hard to find many sources on the subject agreeing, with reasonable evidence, thatPrincipia. attempted simple addition, specifically 1+1=2. Where is there a respected and understandable refutation of the "completely untrue " belief?

Truth can be evasive, both in mathematics and politics. Does there exist any absolute proof at all, as Whitehead and Russell missed over decades?

At the earliest, of these there was just prelogic.

Object representation followed, begetting the ability to reckon and thus one need for symbology.

I would say that these had selected specializations in the brain, adapting parallel to language in general.

Its very difficult for me to refute a claim which has no basis in fact. What "argument" should I use to refute it? If I tell you that Hitler was actually a time traveler and was best friends with Harriet Tubman, how would you refute it? What source would you find that even mentions Hitler, time travel, and Harriet Tubman? That doesn't make it true.How close did Whitehead's and Russell's proof come to argue that 1+1=2, as is widely reported? It is not hard to find many sources on the subject agreeing, with reasonable evidence, thatPrincipia. attempted simple addition, specifically 1+1=2. Where is there a respected and understandable refutation of the "completely untrue " belief?

More importantly, the onus is not on me to refute your claim. It is on you to prove it. Feel free to link one of those "many sources". Keep in mind your original claim was the following:

I'm interested to see a credible source which claims that they did not understand arithmetic or were unable to prove that 1+1 = 2.Recall Alfred North Whitehead and Bertrand Russell trying unsuccessfully to explain 1+1=2 in three volumes ofPrincipia Mathematica!

Even in mathematical discovery, there is a "leap of faith" between known math and the unknown, even between 1 and itself. That example too reflects what is "math without symbols."

Do I understand all of the relevant thousands of pages of

If I asked Whitehead and Russell why does 1+1=2, I surmise that they would start with axioms, and that even in their logic there might be some subjectivity, such as what a "number" is.