## Search found 794 matches

- Thu Oct 15, 2015 1:40 am
- Forum: Logic and Philosophy of Mathematics
- Topic: After Reimann
- Replies:
**49** - Views:
**4078**

### Re: After Reimann

A.start with the natural numbers described by N B. remove all composites made by 2 prime numbers. C. remove all composites made by 3 prime numbers. D. ........... E. At each stage we generate a new sequence and function to describe it , the natural numbers with gaps. F. at each stage we approach P,...

- Thu Oct 15, 2015 1:22 am
- Forum: Logic and Philosophy of Mathematics
- Topic: The Axiom Of Identity *Challenged*
- Replies:
**232** - Views:
**18111**

### Re: The Axiom Of Identity *Challenged*

If we declare that a set A has no order and that its the same set regardlss of order we get into the infinite regress i was talking about. 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 Extensionali...

- Thu Oct 15, 2015 12:10 am
- Forum: Logic and Philosophy of Mathematics
- Topic: The Axiom Of Identity *Challenged*
- Replies:
**232** - Views:
**18111**

### Re: The Axiom Of Identity *Challenged*

See the underlind above. How can those two a's be equal when they differ in "order" or any respect. Yaaaaawn. Oh that's a perfectly good question. The answer is that order is not an inherent part of the definition of a set. So the set {a,b,c} has no order on it at all. It's exactly the same set as ...

- Wed Oct 14, 2015 11:50 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: The Axiom Of Identity *Challenged*
- Replies:
**232** - Views:
**18111**

### Re: The Axiom Of Identity *Challenged*

Check my edit.Moyo wrote: wtf is meaningless too.

- Wed Oct 14, 2015 11:27 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: The Axiom Of Identity *Challenged*
- Replies:
**232** - Views:
**18111**

### Re: The Axiom Of Identity *Challenged*

Is implicit in every system but it contains a viscious infinite regress. I think the word you're looking for is viscous , "having a thick, sticky consistency." ps ... Ok that was just intended as a little pun ... but I see you are the OP of this thread and I want to see if I can shed any light on t...

- Mon Oct 12, 2015 10:34 pm
- Forum: Political Philosophy
- Topic: Who should be denied choice?
- Replies:
**44** - Views:
**3980**

### Re: Who should be denied choice?

Why not, many of them are our elected leaders.Philosophy Explorer wrote: Do you count, e.g., the criminally insane as belonging to general society?

PhilX

- Fri Oct 09, 2015 1:08 am
- Forum: Articles in Philosophy Now
- Topic: Would My Zen Master Fail Me For Writing This Article?
- Replies:
**1** - Views:
**569**

### Re: Would My Zen Master Fail Me For Writing This Article?

"This article is available to subscribers only."

I have let go of my attachment to reading it.

The Tao you can subscribe to is not the true Tao. Or so I've heard.

I have let go of my attachment to reading it.

The Tao you can subscribe to is not the true Tao. Or so I've heard.

- Fri Oct 02, 2015 11:17 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Axioms and postulates
- Replies:
**5** - Views:
**1048**

### Re: Axioms and postulates

if there was a difference a couple of thousand years ago, there isn't today. And an axiom is no longer something that we see is true by observation. Rather, it's a statement accepted without proof in order to get a particular deductive system off the ground. The standard axiomatic system for all mat...

- Tue Sep 29, 2015 12:36 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Comparing infinite sets
- Replies:
**5** - Views:
**1747**

### Re: Comparing infinite sets

It occurs to me that I owe a much more clear explanation of the chain of cardinal arithmetic showing that the set of curves in the plane has the same cardinality as the real numbers. I shall do this now. There are three things we need to know. 1) If X and Y are sets, the set of functions from Y to X...

- Mon Sep 28, 2015 8:12 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Comparing infinite sets
- Replies:
**5** - Views:
**1747**

### Re: Comparing infinite sets

This is my second in a series of posts reviving @PhilX's old posts on infinity in order to clarify some issues of philosophical interest and importance. The first thread in this series is http://forum.philosophynow.org/viewtopic.php?f=26&t=15446, and it wouldn't hurt to read that one first if you ha...

- Fri Sep 11, 2015 5:19 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Proving that the difference between any two anagram numbers is always a multiple of nine
- Replies:
**59** - Views:
**5845**

### Re: Proving that the difference between any two anagram numbers is always a multiple of nine

Here's the proof that the difference of anagrams is divisible by 9. First, note that x = x0 + x1 * 10 + x2 * 10^2 + ... + xn * 10^n (writing xn or sometimes x_n to mean "x_subscript_n") and likewise y = y0 + y1 * 10 + y2 * 10^2 + ... + yn * 10^n. Note that since the x_i's are just a rearrangement of...

- Thu Sep 10, 2015 12:22 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Is infinity all black and white?
- Replies:
**5** - Views:
**1096**

### Re: Is infinity all black and white?

@PhilX, I resurrected this months-old thread because you have a lot of similar questions about transfinite cardinals in this and other threads and I wanted to unpack some of these issues if you're still interested. The question of whether every infinite set is cardinally equivalent to an Aleph is ac...

- Tue Sep 08, 2015 11:54 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Differential calculus defined by differences - what more meaningful ?
- Replies:
**12** - Views:
**1439**

### Re: Differential calculus defined by differences - what more meaningful ?

A quick Google search will show that this author is a well-known crank. Regarding calculus, he clearly has never seen the proper formalization of the concept of a limit. He has an Amazon book if anyone wants to send him money.

- Tue Sep 08, 2015 11:43 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Does the center of a disk exist?
- Replies:
**22** - Views:
**3140**

### Re: Does the center of a disk exist?

a) Case of a physical disk. You can't precisely find or define the center to arbitrary precision because of measurement error. And any physical rotational mechanism is imperfect and has some amount of wobble. So there is no stationary point in a physical spinning disk. b) Case of a mathematical disk...