Excuse me. I was being silly.
Nonetheless, there is some truth to it, but I guess it doesn’t fit in to the discussion. Sorry for the interruption.
Excuse me. I was being silly.
Nonetheless, there is some truth to it, but I guess it doesn’t fit in to the discussion. Sorry for the interruption.
i have to disagree with you here. nothing is independent of materiality. the principle of noncontradiction, for example, could just be “not so” in a different sort of universe. that we can’t speak meaningfully of such a universe does not mean that no such universe is possible. this is simply how our universe operates, and we do our best to describe it.
[British General] Stop it.[/British General]
Keep it simple…
take 2 Apples add 2 more how many do you have?
4! :eek:
I think the maths of this problem has been thoughly covered, so I would like to take a moment to consider the language of this problem.
The = sign gets translated into several different words.
(+ sign similarly has various wordings, some I use below, but none are problamatic, unlike the synonyms for the = sign.)
equals : Good word, but doesn’t really give the meaning of the sign just the name of it
becomes : This is sometimes used, but is bad, this leads to the (Platonic I think) conjecture that “How comes 2 and 2 becomes 4, what is this and (plus) such that somehow things have changed from 2 + 2 into 4?”
is the same as : This is a long old phraise, but it gets to the heart of the matter. 2 plus 2 is the same as 4, there is no sence of change from one state to the other, both states are the same.
Unfortunately, computing has taken the ‘becomes’ meaning and has run with it giving us coding structures such as x=x+1 just to add to confusion of the = sign.
When we say x = y, we mean that every property that x has, y also has, and every property that y has, x also has. I don’t think anyone is really confused by the used of = as assignment operator in programming.
Agreed. Though the myth that the book is about 1+1=2 has surely been given legs by the fact that the CUP’s standard abridgement *Principia Mathematica to 56, in print since 1962, more or less culminates with *54.43. From that, there’s only about 20 pages to the end of the main text. While Whitehead was dead, the abridgement was presumably approved by Russell.
[Though about a quarter of the abridgement is the original introduction, which had mainly been written by Russell and which is a brilliant example of his skill at technical exposition. So he may have been biased in agreeing what to include.]
Why is there 10 basic numbers??
Because we have ten digits on our hands. It’s not as stupid an answer as it seems…there had to be something as the base, and ideally something not tiny, and not massive. It was fairly predictable that the ‘winner’ would be the one which corresponded with what we reach when we count on our fingers.
However, IIRC, not all societies have always used Base 10…was it the Greeks who used Base 60, hence our division of the hour into sixty minutes? Somebody who knows what they’re talking about can take over…
It was the Babylonians that used the sexagismal (base 60) system.
One thing I’m not clear about - nowadays, we’ve formalized the natural numbers using Peano’s axioms. It’s presented as if that’s how we started, historically; but of course we knew that 2+2=4 way before Peano was even born. Upon what we were basing that?