Fallacy of "can God make a rock not even he can lift?"

@Reconstructo,

Reconstructo;132140 wrote:

Aren't there an infinite amount of numbers between 0 and 1?

Given any natural number, there is a rational fraction of one divided by that number, which is greater than zero and less than one. So, if there is an infinite number of natural numbers, then there is an infinite number of rational fractions greater than zero and less than one.

@Mephistopheles phil,

This question cannot be answered as its terms can not be defined. But it's a nice way to pass the time. I guess that answers the question.

Quote:

6.362 What can be described can happen too: and what the law of
causality is meant to exclude cannot even be described.

Quote:

6.375 Just as the only necessity that exists is logical necessity, so
too the only impossibility that exists is logical impossibility.

Quote:

4.064 Every proposition must already have a sense: it cannot be given a
sense by affirmation. Indeed its sense is just what is affirmed. And the
same applies to negation, etc.

@ughaibu,

ughaibu;132155 wrote:

Given any natural number, there is a rational fraction of one divided by that number, which is greater than zero and less than one. So, if there is an infinite number of natural numbers, then there is an infinite number of rational fractions greater than zero and less than one.

Sounds like an exact quote from the paper. :p

@Emil,

Emil;135849 wrote:

Sounds like an exact quote from the paper. :p

Academic slang is so anonymising.

@ughaibu,

ughaibu;132155 wrote:

Given any natural number, there is a rational fraction of one divided by that number, which is greater than zero and less than one. So, if there is an infinite number of natural numbers, then there is an infinite number of rational fractions greater than zero and less than one.

Yes, and yet these are all the same number. 3 is a modification of 1. But both are quantities, or unities. The number line is a tempered continuum.

There is only one number, modified by only one operator. From this all the rest is made. Pure logic reduces to tautology and contradiction. As Wittgenstein proved in TLP. And math is a form of logic.

See my blog for more. Hegel also knew this, at least about logic.

@Reconstructo,

Reconstructo;135851 wrote:

Yes, and yet these are all the same number. 3 is a modification of 1. But both are quantities, or unities. The number line is a tempered continuum.

It's only a continuum if you include irrational numbers.

Reconstructo;135851 wrote:

There is only one number, modified by only one operator. From this all the rest is made.

How do you make transcendental numbers? or random reals?

@ughaibu,

ughaibu;135852 wrote:

It's only a continuum if you include irrational numbers.

You can't. So yes it's a pseudo-continuum, but we can squeeze in all that we want. Irrationals are only known to the degree that they become rational. This realization is what Hegel did to Kant. The unknowable is also unspeakable. The uncountable cannot be thought. Wittgenstein realized this to. In fact he is blowing my mind.

If you like math, read this book & it will slay you. First link is online. Second is download.

Tractatus Logico-Philosophicus (online version)
Tractatus Logico-Philosophicus by Ludwig Wittgenstein - Project Gutenberg

@Reconstructo,

Reconstructo;135854 wrote:

You can't.

I refer you to post 117.

@ughaibu,

ughaibu;135852 wrote:

It's only a continuum if you include irrational numbers.How do you make transcendental numbers? or random reals?

pi is only a number to the degree that it is known. Of course professional mathematicians have their reasons for calling it a number, just as they do infinity. But the essence of number is quanity, and irrationals are not quantities. We can never actually know the irrationality of pi. We can only deduce it, never conceive it. We can not write down an irrational number. Only a rational symbol for an algorithm that does not halt automatically.

---------- Post added 03-04-2010 at 06:40 AM ----------

Reconstructo;132140 wrote:

Aren't there an infinite amount of numbers between 0 and 1?

I say that this is true, but only to the degree that we can deduce such a thing.

---------- Post added 03-04-2010 at 06:42 AM ----------

Quote:

Putting two infinite sets into one-to-one correspondence is an infinite task, and we don't pretend that we can do it (that is, finish it) in finite time.

same deal. it's an expectation, not the achievement of infinity, or numerical irrationality. both are illogical.

@Reconstructo,

Reconstructo;135856 wrote:

professional mathematicians have their reasons for calling it a number, just as they do infinity

There is no number called infinity by mathematicians.

@ughaibu,

ughaibu;135860 wrote:

There is no number called infinity by mathematicians.

Good! But the symbol is sometimes used. I study the core of math, and am now moving away from that, satisfied that I understand it, to some of the more complex math. I'm fascinated by the use of limits in calculus, and also by topology. In both fields we encounter the transcendental limits/structure of the human mind. Pure truth. Bring it on.

@Reconstructo,

Reconstructo;132140 wrote:

Aren't there an infinite amount of numbers between 0 and 1?

fractions, not real numbers though.

@Reconstructo,

Reconstructo;136318 wrote:

Bring it on.

Okay, here's a nice consequence of infinity. A and B are two agents who perform simultaneous supertasks. A supertask consists of a series of tasks each performed when half the remainder of a finite period of time has elapsed, in other words, an infinite number of tasks are performed in a finite time. Both A and B have an infinite number of balls, sequentially labeled 1,2,3..... and a jar of infinite capacity. A's tasks consist of putting the ten balls with the lowest numbers, that haven't been in the jar, into the jar and removing the lowest numbered ball from the jar, so, at time one A puts in balls 1-10 and removes ball 1, at time two A puts in balls 11-20 and removes ball 2, etc. B's tasks consist of putting the nine lowest numbered balls into the jar, but skipping all multiples of ten, and appending a zero to the number of the lowest numbered ball in the jar, so, at time one B puts in ball 1-9 and appends a zero to ball 1 so that it reads 10, at time two B puts in balls 11-19 and appends a zero to ball 2 so that it reads 20. At all times during the running of the supertask, the jars have identical contents, but when the supertask is complete, A's jar is empty and B's jar contains an infinite number of balls, each of which has a number that ends with an infinite string of zeroes.

@Krumple,

Krumple;136364 wrote:

fractions, not real numbers though.

yes, but that's not really of the essence. let's just say rational. there i still an infinity of rational numbers twixt any two rational numbers. our notation allows for this as our notation if logarithmic. "3" is a simple instruction to place a labeled and stabilized quantity on the number line, which is a euclidean line. so is "2343435667.5657567867745645."

To the people mocking God and feeling safe about it ... seems a prudent person might want to be sure He does not exist first ... and you can't be certain He does not can you? Here is a brain teaser for you; can you sneeze with so much force that you get about a 9 pound booger out your nose? Well, yes it just might be possible for a braniac given a few erudite adjustments. But your head would cave in before you could eat it. am i right? Isn't that a hoot? Thought some might have a sense of humor and laugh. You made me laugh at the simpleton anti-God question. Did you imagine those billions who believe in God were going to tear their hair out over that one? Here is one for you to ponder with logic: the word "supernatural" ; another one: is there an end to the universe? if we fall off a flat earth would we eventually bounce off the end of the universe? and why might it be illogical to assume a single or UNIverse? or if we send an object on a journey toward a single point on the edge or end of the UNIverse and it eventually makes it to that so called end where would it go then? There seem to be many such things that defy human understanding. Why even try to use human logic for such things? Sorry, forgot for a moment that there a ga-zillion theories on how the universe is or is not expanding into nothing or into itself. So many answers and too few real unique honest questions. Let those you admire most tell you what to think? Close your mind and rule out anything you can't touch or weigh or comprehend? Sorry, that would be illogical and un-philosophical as well as intellectually primitive or dishonest imo.

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Fallacy of "can God make a rock not even he can lift?"

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