The Problem with Atheism

Topic: The Problem with Atheism (Read 205134 times)

Re: The Problem with Atheism

Reply #400 – 2014-07-01, 12:33:52

Quote from: Barulheira on 2014-07-01, 10:51:12

I possibly got it wrong. 2+2=4 is falsifiable because joining 2 things and 2 other things and getting something other than 4 things would prove it false. It couldn't be more simple.

2+2=4 is always an immutable given. When you join two things with two another and you get something else than four, the problem is not with 2+2=4, but with the way you go about joining things.

You are right that you got it wrong. But you got it definitely wrong, not possibly. See, even that statement of yours needed correction.

Re: The Problem with Atheism

Reply #401 – 2014-07-01, 12:50:20

2+2 = 4 for sure

falsifiable is something like Buttered cat paradox .

[video]http://www.youtube.com/watch?v=Z8yW5cyXXRc[/video]

Re: The Problem with Atheism

Reply #402 – 2014-07-01, 13:00:41

Quote from: ersi on 2014-07-01, 12:33:52

2+2=4 is always an immutable given.

Quote from: Sparta on 2014-07-01, 12:50:20

2+2 = 4 for sure

You can create many kinds of mathematics, including mathematics where 2+2 are not 4 but something else.
What's required is that any new form of mathematics keeps on being logically coherent at it's entire inner structure.

1+1=2 it's only a postulate. Then, Arabs invented zero, a major breakthrough.
Zero it's a very curious thing with strange properties, the first being that it doesn't exist, therefore turning things a bit problematic as for example when simply trying to divide by zero.

(I know that many of you knows all this but others may not.)

Re: The Problem with Atheism

Reply #403 – 2014-07-01, 13:13:10

1+1 = 2

unless for satirical purpose

1+1 = 3

use condom

Re: The Problem with Atheism

Reply #404 – 2014-07-01, 13:24:11

Quote from: Belfrager on 2014-07-01, 13:00:41

Zero it's a very curious thing with strange properties, the first being that it doesn't exist...

Absent people, which numbers do exist?

Re: The Problem with Atheism

Reply #405 – 2014-07-01, 14:18:29

wait, what ?

Numbers never exist?

Re: The Problem with Atheism

Reply #406 – 2014-07-01, 14:22:10

1. No.
2. I'm not convinced yet. Let's try another way.
2+2=3 is falsifiable? Yes or no?

Re: The Problem with Atheism

Reply #407 – 2014-07-01, 14:50:23

Quote from: Barulheira on 2014-07-01, 14:22:10

2. I'm not convinced yet. Let's try another way.
2+2=3 is falsifiable? Yes or no?

In math, statements are true or false, not falsifiable the way they are in empirical experiments. True mathematical statements are true by virtue of deductive proof. The same way, false statements are false by virtue of deductive proof. Deductive proof is a technical term in logic, something you should study some day.

Mathematics stands by virtue of internal coherence and consistency, and sustains all other sciences the same way. There's no probability or inductive assumption involved at all.

Empirical experiments are off the screen altogether when mathematics is considered, whereas empirical experiments vitally depend on mathematics. The dependence is precisely one way.

Whether you are convinced by this or not, it changes nothing in this. Nobody's convictions or opinions have any effect on mathematics, the nature of deductive proof, or truth.

Re: The Problem with Atheism

Reply #408 – 2014-07-01, 17:31:55

Quote from: Belfrager on 2014-07-01, 05:00:41

Then, Arabs invented zero, a major breakthrough.

If by "invented" you mean "borrowed from India"...

The "existence" of numbers is problematical, for some. But, note, Jaybro isn't a Nominalist -- he's a contrarian! A serious excursion into the ontological status of numbers would better fit the Mysticism thread...

Quote from: ersi on 2014-07-01, 06:50:23

True mathematical statements are true by virtue of deductive proof.

And the axioms of the particular system, which perforce must be "justified" in some other manner.

Re: The Problem with Atheism

Reply #409 – 2014-07-01, 17:44:20

Quote from: ersi on 2014-07-01, 14:50:23

Mathematics stands by virtue of internal coherence and consistency, and sustains all other sciences the same way. There's no probability or inductive assumption involved at all.

Empirical experiments are off the screen altogether when mathematics is considered, whereas empirical experiments vitally depend on mathematics. The dependence is precisely one way.

Not so fast Ersi. It turns out to be extremely useful in mathematics and science to say that this equation, x2 + 1 = 0, has a solution. There is no real number to solve this equation, so math has made up a complex number, once called an imaginary number, so that there is a solution. The magic number "i" is used where √-1 = i.

Just briefly, the behavior of some differential equations depends upon whether the roots of a certain quadratic are complex or real. If they are complex, then certain behaviors can be expected. These are often used just to get the solutions that one wants, but they are indispensable in many thousands of applications today.

As an analogy, suppose you have a normal carpenter’s hammer and it does everything you need it to do around your house just fine. Then one day you need to drive a big thick nail into hard wood. You try the hammer, but it’s not sufficient to do the job and you have no other hammer to do the job. What you need basically is more leverage to drive the nail in, so you attach an extension onto the hammer and it works perfectly to drive in the big nail. If you now tried to use the hammer with the extension to drive a simple nail in the wall, it can no longer do the job well because it doesn't suit the task and makes holes in the wall. Therefore, you simply remove the extension and the hammer is usable again for what you normally need. Complex numbers are analogous to the hammer with the extension (complex hammer), they are useful for some tough jobs, but not for everything. I used them in school to solve differential equations involving AC electricity—it works!!

Re: The Problem with Atheism

Reply #410 – 2014-07-01, 18:16:58

I've heard it remarked that God created the natural numbers, Man the rest...

Note: Gödel's Theorems referred to the natural numbers only, So, it's God's fault!

Re: The Problem with Atheism

Reply #411 – 2014-07-01, 18:39:04

Quote from: OakdaleFTL on 2014-07-01, 17:31:55

Quote from: ersi on 2014-07-01, 06:50:23
True mathematical statements are true by virtue of deductive proof.

And the axioms of the particular system, which perforce must be "justified" in some other manner.

The axioms are justified either as a separate case of proof or they are necessary presuppositions, consistent with and foundational to the logic. In either case there's no departure from the same logic.

Quote from: jseaton2311 on 2014-07-01, 17:44:20

As an analogy, suppose you have a normal carpenter’s hammer and it does everything you need it to do around your house just fine. Then one day you need to drive a big thick nail into hard wood. You try the hammer, but it’s not sufficient to do the job and you have no other hammer to do the job.

Good analogy. It describes you well. Disproving God or even arguing about God is a totally different task than anything that science of your definition can do. You even explicitly admitted that science never approaches truth and cannot give propositions to which one could safely commit oneself. Therefore either you keep hammering hopelessly, even if optimistically, or choose the appropriate tool to the task.

Btw, what you said about math is nothing new of course. From positive numbers, negative numbers logically follow. From full numbers (or whatever the English term is), fractions logically follow. From rational numbers, irrational numbers logically follow. Imaginary unit is within the same chain, subject to the same laws of thought. It's the same logic all along, following from itself necessarily. Philosophy is the same way. No science can limit it.

Quote from: OakdaleFTL on 2014-07-01, 18:16:58

I've heard it remarked that God created the natural numbers, Man the rest...

I like this one:
"God exists since mathematics is consistent, and the devil exists since we cannot prove the consistency." -- Morris Kline

Re: The Problem with Atheism

Reply #412 – 2014-07-01, 19:04:10

I, too, like that, ersi!
About your parade of logical followings, I'd want to say -instead-that our simple logic permits such extensions... Not that it requires or impels them. Our experience (including our musings) are their motive, no?

In like manner, we find that while we can extend or alter our simple logic what we get then are systems that routinely fail to make sense. For instance, dropping the Law of the Excluded Middle...

Quote from: ersi on 2014-07-01, 10:39:04

The axioms are justified either as a separate case of proof or they are necessary presuppositions,

Meaning what exactly? That one can't get by without them? Then they should be made explicit, no? But, so far, every attempt to do so ultimately fails -- because some terms have to be left undefined.

Mathematics is not as malleable as Natural Language. But it is more like it than is comfortable to admit! (Still, that shouldn't be surprising.)

Re: The Problem with Atheism

Reply #413 – 2014-07-01, 19:15:32

Quote from: OakdaleFTL on 2014-07-01, 19:04:10

About your parade of logical followings, I'd want to say -instead-that our simple logic permits such extensions... Not that it requires or impels them. Our experience (including our musings) are their motive, no?

Consistency or coherence remains the main theme though. For some thinkers, such as myself, consistency is necessary. Others say it's natural. For you it's permissible

Fair enough. Everyone describes it as their experience dictates...

Re: The Problem with Atheism

Reply #414 – 2014-07-01, 19:26:21

Quote from: ersi on 2014-07-01, 11:15:32

Consistency or coherence remains the main theme though [etc.]

Indeed. And I'd agree too that they all come to the same thing... How else could it be?

(Well, ask a mystic -- if you'd want an answer to that question!)

Would you, ersi, consider abstract algebra and set theory part of mathematics?

Re: The Problem with Atheism

Reply #415 – 2014-07-01, 19:51:38

Of course. And topology too.

Re: The Problem with Atheism

Reply #416 – 2014-07-01, 19:59:19

Good! Believe it or not, I prefer discoursing with those who share many of my preconceptions and predilections; otherwise, the likelihood of "mere" misunderstanding is too great...

Re: The Problem with Atheism

Reply #417 – 2014-07-01, 22:10:52

Quote from: ersi on 2014-07-01, 18:39:04

From rational numbers, irrational numbers logically follow. Imaginary unit is within the same chain, subject to the same laws of thought. It's the same logic all along, following from itself necessarily.

The complex number i, where i2+1=0 does not exist at all in the traditional mathematical system. There does not exist a number, positive or negative, rational or irrational that when squared equals a negative number, that's why i was originally referred to as imaginary. It is not imaginary at all, it simply doesn't exist is our mathematical system.

Quote from: ersi on 2014-07-01, 18:39:04

From rational numbers, irrational numbers logically follow.

﴾͡๏̯͡๏﴿ O'RLY? Virtually all numbers are irrational you know, there are just a scant few rational numbers in comparison. Which one, logically follows which?

Quote from: ersi on 2014-07-01, 18:39:04

From positive numbers, negative numbers logically follow.

﴾͡๏̯͡๏﴿ O'RLY? Not in the binary system which uses only 0 and 1, neither of which are negative.

Re: The Problem with Atheism

Reply #418 – 2014-07-01, 23:33:49

Quote from: OakdaleFTL on 2014-07-01, 17:31:55

A serious excursion into the ontological status of numbers would better fit the Mysticism thread...

Yes and no, it depends. I see nothing of mystical at numbers, be it natural, integers, rational, real or complex numbers.

The only place for joining numbers with mystical approaches would be at the pre socratic philosophers for whom numbers had "magical" properties the same way footprints followed steps or shadows were connected with objects. Or prime numbers, much more "pure" than the rest.
But no one pays attention to the pre socratics these days.

Re: The Problem with Atheism

Reply #419 – 2014-07-02, 01:22:47

Quote from: Belfrager on 2014-07-01, 15:33:49

But no one pays attention to the pre socratics these days.

Not quite true: Among other things, some pre-Socratic Greek Stoics did creditable work on what we now call the sentential calculus; that the logic of the syllogism eclipsed it is a fact of history that I think retarded both science and logic/mathematics… This, in much the same way as Roman numerals made mere calculation an arcane art! A bad notation makes thought harder than it needs to be… (Yes, I do think that the "modern" first-order predicate calculus should have been recognized and formalized in the Middle Ages. Instead, we had to wait until 1879…

) (Popper himself said this.*)

Quote from: Belfrager on 2014-07-01, 15:33:49

The only place for joining numbers with mystical approaches would be […]

Do numbers "exist" before they are constructed? Was the square root of two (or negative one) an entity before someone considered them?
Consider π: We do really know that it is an irrational and transcendental number. (Don't we?) And that it is merely the ratio of a circle's circumference to its diameter… (Not an unusual nor certainly bizarre notion!) Why is it thus?

You may scoff at such questions. But not everyone does; indeed, some great mathematicians have not. And -you'll forgive me for saying so- a lot of people would likely reject most of mathematics; specially, if they understood it!

——————————————
Have you recanted your belief in Platonic ideas, and accepted the Nominalism of common sense?

_______________________
* @Sparta: You'll like this, if you have enough English to read it… Section XI is the most important! (If for no other reason, than that an American of my generation has immediate and conflicting emotions about "Chapter Eleven" filings… I mention this lame joke because I only decided to take your posts seriously after you quoted Popper!

)

Re: The Problem with Atheism

Reply #420 – 2014-07-02, 02:10:31

Quote from: OakdaleFTL on 2014-07-02, 01:22:47

Consider π: We do really know that it is an irrational and transcendental number. (Don't we?) And that it is merely the ratio of a circle's circumference to its diameter…

I want to inject a simple observation that's not at all relevant to what you are discussing here, but the ratio of a circle's circumference to its diameter is a largely irrelevant property in geometry. We should be using the value that is equal to approximately 6.28—the ratio of a circle's circumference to its radius. Some mathematicians propose that pi should be changed to equal 6.28, whereby circumference C would equal πr and some have proposed the use of a whole new term called tau, which equals 2π. Tau has been gaining popularity, they even have a Tau Day celebration at some math events.

Re: The Problem with Atheism

Reply #421 – 2014-07-02, 02:31:35

Quote from: jseaton2311 on 2014-07-01, 18:10:31

Tau has been gaining popularity, they even have a Tau Day celebration at some math events.

That goes a long way toward explaining your scientism, James!

You're a Faddist, through and through…
Why not base our number-system on Tau (or Pi or e…)? It'll just be a slight inconvenience of notational obscurity! (Quick now: What's the unit chosen times itself? Then, how does one coach the Peano Postulates? Or does one get a new mathematics? I'm calling BS on you, here!)

Re: The Problem with Atheism

Reply #422 – 2014-07-02, 02:48:57

All work and no play, makes Oakdale a dull boy.

Re: The Problem with Atheism

Reply #423 – 2014-07-02, 03:45:50

To the poet (and the savant), work and play are the same!

I spent 10 hours today dealing with a six year-old and a four year-old… And then their mother! I'm entitled to some recreation that involves my interests and experience.

Re: The Problem with Atheism

Reply #424 – 2014-07-02, 03:53:40

Quote from: jseaton2311 on 2014-07-01, 22:10:52

Quote from: ersi on 2014-07-01, 18:39:04
From rational numbers, irrational numbers logically follow. Imaginary unit is within the same chain, subject to the same laws of thought. It's the same logic all along, following from itself necessarily.

The complex number i, where i2+1=0 does not exist at all in the traditional mathematical system. There does not exist a number, positive or negative, rational or irrational that when squared equals a negative number, that's why i was originally referred to as imaginary. It is not imaginary at all, it simply doesn't exist is our mathematical system.

If it's not imaginary, but doesn't exist, what is it then? In the end, you just like to throw words around. You are making no sense, you have no aim and no point to make. You simply have a fascination for things that you think is somehow not traditional or not in "our mathematical system". At the same time you equally irrationally reject concepts that don't fit your box. And this has been going on for a long while, well, all the time really.

Quote from: jseaton2311 on 2014-07-01, 22:10:52

Quote from: ersi on 2014-07-01, 18:39:04
From rational numbers, irrational numbers logically follow.

﴾͡๏̯͡๏﴿ O'RLY? Virtually all numbers are irrational you know, there are just a scant few rational numbers in comparison. Which one, logically follows which?

Since you have no logic and no system, even the question doesn't follow.

Quote from: jseaton2311 on 2014-07-01, 22:10:52

Quote from: ersi on 2014-07-01, 18:39:04
From positive numbers, negative numbers logically follow.

﴾͡๏̯͡๏﴿ O'RLY? Not in the binary system which uses only 0 and 1, neither of which are negative.

It's because in the binary system the concepts of positive and negative don't apply. If you had any systematic reasoning, you would have seen this far away.

If you were a theist, you would be of the sort who is fascinated with tooth fairies and easter bunnies because you like to think that you have some extraordinary ideas, while rejecting little red devils because those are nasty and ugly. And rejecting transcendental god too, because you cannot wrap your mind around that one. But instead you prefer to be called atheist with these self-same ideas and the self-same line of methodless reasoning.