Philosophy Now Forum

The answer is that symbols cannot be referred to within a system as symbols, but only as elements of the formal system. Thus, saying that "(a,a) means that the first 'a' is before the second 'a' " is a meta-statement, outside the system. You do realise that your point is really just a poi...

Why not build the whole system of relations on the same basis that this "=" is. It seems that if we can do this we avoid arbitrariness and acheive consistency. The whole system of cartesian products and orderd pairs are an unnecesary frameworkthen and we can build mathematics without the ...

... The whole system of Cartesian products and ordered pairs are an unnecessary framework then and we can build mathematics without the suspect (because it doesn't involve computation) theory of sets. ... I thought pretty much that Mathematics was already built before set theory came about? Set the...

All we are doing is making the primes predictable and finding how this induces the natural numbers to behave. we do have some theory's that correlate primes with naturals so inverting them would be easy. Once we have enough of these theorems we see how the inverted naturals are behaving each time an...

Reality can be desribed as a "group" minus the identity element. Since the axiom of identityy is a=a i.e. leave "a" unchanged, and as we can see its giving us problems , we could search for an algebraic structure that handles identity in a more sophisticated way that circumvents ...

Lets plot the prime numbers evenly on a line and call it axis A. Then get another axis B and put it perpendicular to form a plane. On that plane exists all the numbers made by multiplying two prime numbers. Can you give an example to say what you mean? So on the A axis we have the prime 7, say. The...

The answer is that symbols cannot be referred to within a system as symbols, but only as elements of the formal system. Thus, saying that "(a,a) means that the first 'a' is before the second 'a' " is a meta-statement, outside the system. You do realise that your point is really just a poi...

Why not build the whole system of relations on the same basis that this "=" is. It seems that if we can do this we avoid arbitrariness and acheive consistency. The whole system of cartesian products and orderd pairs are an unnecesary frameworkthen and we can build mathematics without the s...

Lets plot the prime numbers evenly on a line and call it axis A. Then get another axis B and put it perpendicular to form a plane. On that plane exists all the numbers made by multiplying two prime numbers. If we were to draw a line or a circle on this plane the functional description would be very ...

Lets do this slowly

say we have a set A = {a;b;c}


In what way is that element "a" the element "a".

Why ! but by the axiom of identity.or in other words a=a . AKA (a,a).

Get the limit of M(n). M(n) is the mother function that generates the child functions which at one end are N(n) and at the other P(n). The partial functions don't converge in any way I can think of. You need to say exactly how to determine the limit. If you could do that, you'd have something. I'm ...

Get the limit of M(n).

M(n) is the mother function that generates the child functions which at one end are N(n) and at the other P(n).

... There's a bit of notational confusion here. A is the set, 'a' is one of its elements. So given the set A, we form the collection {(a,a) : a is an element of A}. That collection, which is a subset of A X A, is the equality relation. ... I'm interested in this wtf, how can there be a CP of a sing...

You don't accept the Axiom of Extensionality, which says that two sets are the same if and only if they have exactly the same elements? If you deny Extensionality, then you are rejecting modern set theory. You are free to invent your own set theory, but you are not saying anything meaningful about ...

The golden prize in number theory is to get a function P(n)=p(n) Were P of n gives us the nth prime number. Here is a sketch of how we may do it. We know that n ranges over the natural numbers. The natural numbers do have a simple function to obtain the nth natural number..simply N(n)=n We also know...