This re-instated what passes for faith in humanity

[Occhidiangela]

Ghostiger:

The prosecution rests.

By your own works are you convicted. After all that protesting, the Passive Aggressive act continues and we get four posts on one page that fail to identify who you are addressing. I note your PM has either been disabled or is too full for accepting new PM's.

Fine, back to public rebuttal of your wheeze.

You have inverted a concept. Authorship is so protected in Science because people want the fame of being associated with cleverness rather than to prove cleverness by association with the name.

Of course there are some exception, ussually involving money, but they are exceptions.
[right][snapback]98103[/snapback][/right]

Neither sounds good to me.

In essence Thor is just a a multitude of dark matter varieties.
Both are just making up a filler with no evidense, for a gap in knowledge.
Dark matter theory is more elegant than Thor theory much in a the same one 1 stain is cleaner that filth on an entire carpet.


I think common sense is making a surprise attack on cosmology in the last 2 years though.
People are suggesting exspansion of space can be described by the General Theory of Relativity just as the contraction with gravity can.(and some local movement for nearby space).
This seems obvious to me, but maybe Im missing something.

This post has been edited by Ghostiger: Dec 27 2005, 09:19 PM

Well its quite possible I underestimated the degree of that money sullies science.
I should known better I guess, I left science because it was appearent to me I could never handle the money politics of modern science and I was not so brilliant that people would throw money at me no matter what.(I dont mean to imply at any other large industry in America has less politics.)

That was nonsese.

It would be analogous if you had said "Wouldnt it be a miracle if my hammer could know why I use it to pound a nail."

Note that Jester referenced the comment to which he replied, even if he didn't note the poster who made the comment. That modest effort aided clarity. It made his reply make sense. It is your adamant refusal to make that modest effort that incited this whole critique.

"It's worth keeping in mind that all humanistic legends and fantasies maintain internal consistancy to mirror the world we live in, not unlike much of theorhetical science."

You've lost me here. Are you claiming that all legend and fantasy is consistent? Or is there some subset that is?

Does fiction have falsifiability? Specificity? Is Odysseus subject to contrary evidence?

I don't think any of those things are true. But if that's not what you're claiming, then I don't know what you're claiming.

-Jester

QED

Occhi

[kandrathe]

Why would this be? I would think that if one posits a being capable of creating the phenomenal world itself it would be contradictory to posit that the same being wouldn't also be capable of interfering with it.
[right][snapback]98209[/snapback][/right]

Suppose "God" is not bound by the laws of this universe. We may be as art works, compared to the painter. How many universes are there? How much more complex is the designer from the design? Perhaps the interference is done minimally in a way that is consistent with our comprehensions, and only echos of that interference register to us a "mysteries" indicative of there being a painter.

"Stephen Hawking's God" excerpts below from Margaret Wertheim's PBS TV programme 'Faith and Reason.'

Anthropic Principle

A controversial cosmological principle that the observable universe, as it is, must be compatible with our powers of observation, or else we would not be able to observe it.  Exponents of the principle will often point out that the universe appears to be “fine tuned,”or delicately balanced in its basic physical processes, to allow for the existence of carbon-based life.  Although there are many versions of the principle, usually one can distinguish between (a) the Weak Anthropic Principle, which affirms simply that the existence of human life itself implies that nature must be consistent with having evolved carbon-based life, and (B) the Strong Anthropic Principle, which is concerned with the possibility of alternative universes, yet goes on to state metaphysically that our observable universe must be the only kind of universe capable of evolving human-like creatures as observers.

Only a small range of possible values for the universal constants (such as the mass of an electron) are consistent with the presence of life as we know it. The significance of such apparent fine-tuning of the universal constants is disputed by those who regard it as trivial and those who argue from it to the necessity of life in the universe.

The impetus and tradition for Darwins work was from a long line of "Natural Theology" of the type done by Sir Thomas Aquinas. So, the concept of trying to look at the universe and find revelations of God is not a new one. I think it is clear that Darwinian, and other theories fall short to explain much of the universe, and so in the gap of a cohesive "truth" many people resort back to the old ways of explaining the complex as evidence of a designer. As a truth seeker, I find that a bit of a cop out.

The cosmological argument has also received much critical scrutiny from the time of Kant on, and it must now be accepted that what we know about the universe can never demonstrate whether it has a cause, or whether its existence is ultimately inexplicable.

The demise of natural theology, and its partial rebirth as ‘a philosophical theology or new style natural theology’ are well analysed by John Macquarrie.  The central point to note is that those authors claiming to revive natural theology tend to do so in a way which is ‘descriptive instead of deductive’

But, again in reference to my prior post, we humans seem to need a consistent belief system and also a desire for the pursuit of truth. As old, supposedly empirical truths are debunked and new empirical truths emerge, we disrupt belief systems, and cause much anxiety. There are some convincing philosophical arguments on why Theism may be the most probable explanation for the universe, such as The Justification of Theism by Richard G. Swinburne or the apologetic works of C. S. Lewis as another example. But, again, these are philosophical appeals to a belief system, and are not science.

Science, in it's reliance on the observable, experimentable, and repeatable may never be able to explain most things in our universe. I think we need to allow room for the use of science, and mathematics as a tools for discovering "truths", as well as allow for attempts to fit these truths into the belief systems of cultures. The danger lies in mistaking philosophy for science.

[Doc]

The danger lies in mistaking philosophy for science.
[right][snapback]98334[/snapback][/right]

Um... Some philosophy is science, to some degree. The science of how we think, why we think. It may just be the most complex issue of all, when you consider all of the baggage that goes with it. Some might even argue it is because we have philosophical natures that we strive so much toward scientific reasoning, as human beings. The two are deeply intertwined, like it or not, and I dare say that one could not exist with out the other.

I uh, just wanted to toss that in to the mix. I am not even sure what it is I am trying to say, but your last line really rubbed me the wrong way. I am not even sure why it did.

I'll go back to eating jelly beans now and watching this most facinating exchange. I am rather enjoying this thread.

[kandrathe]

...
I uh, just wanted to toss that in to the mix. I am not even sure what it is I am trying to say, but your last line really rubbed me the wrong way. I am not even sure why it did.
...
[right][snapback]98335[/snapback][/right]

Well, certainly in the idea that any endeavor of the mind, including science, is a philosophy, I agree.

The philosophy of science is a discipline that deals with the system of science itself. It examines science’s structure, components, techniques, assumptions, limitations, and so forth.

I guess what I'm getting at is the mistaken process of many ID researchers who (just as Sir Thomas Aquinas did) start at the desired conclusion, then derive the supporting evidence of the conclusion, make the mental argument from evidence to conclusion, then describe thier theories as proven. This is not neccesarily a bad philosophical approach, but it is not a scientific approach.

[Thecla]

Forgive my puckishness: but shouldn't we also know what is meant by "a," "thing," "is," "than," and "itself?"

Then forgive mine for saying that your original comment ("So what is infinite can be larger than what is infinite? You find no contradiction in stating that a thing may be larger than itself?") struck me as showing some lack of understanding about the mathematics of infinity, and in serious need of defining your terms. ;)

There is a least infinite cardinal number?

Yup: it's aleph_0, the cardinality of the natural numbers.

Doesn't this claim present two problems:
1) If aleph-0 is itself finite, then infinity can now be defined as a finite number plus 1, and thus must be itself finite, and not infinite?

Actually, we only defined when two sets have cardinal numbers that are equal (in one-to-one correspondence), less than or equal (in one-to-one correspondence with a subset) or greater than or equal. It doesn't make sense in general to add cardinal numbers.

There is another different type of infinite number, called the ordinal numbers, which one can add. They look something like this:

1, 2, 3, 4, ... w, w+1, w+2, ... w+w , ....

Here w (omega) is the first infinite ordinal number, which comes immediately after all the natural numbers. Unlike a finite number, it has no immediate predecessor (i.e. if n < w then there is always another ordinal number m such that n < m < w), which is why your argument in 1) doesn't apply to w.

2) If aleph-0 is itself infinite, then infinity is not infinite in that it is larger than any number, as here is an infinite number that has a greater?

Here you utterly lost me in philosophical pyrotechnics. ;)

Regardless, I see from brief browsing that the idea of trans-finite numbers and aleph-null appears to rest upon the continuum hypothesis that is not just un-proved, but considered un-proveable

The concept of cadinal numbers doesn't rest on the continuum hypothesis at all -- quite the reverse, in fact. Once you've given a precise and meaningful definition of the cardinal numbers, you can ask questions about them. In particular, having shown that c = 2^{aleph_0} -- the cardinality of the continuum (the real numbers) -- is strictly greater than the cardinality aleph_0 of the integers, one can ask if there's another cardinal number between these two. The continuum hypothesis is the statement that there isn't.

What Godel and Cohen proved in the mid-20th century is that this probelm can't be answered within the terms of the standard axioms of set theory (assuming -- as pretty much everyone believes -- that these are not self-contradictory). If the axioms of set theory and the continuum hypothesis are consistent, then the axioms of set theory and the negation of the continuum hypothesis are also consistent. It's one -- and perhaps the most stricking -- example of the dilemma between incompleteness and consistency that enters the foundations of mathematics once one introduces the infinite.

But why can't one make a one-to-one correspondence between these fractions and a set of natural numbers

One can put the fractions in one-to-one correspondence with the natural numbers e.g. put all (positive -- which makes no difference) fractions in a square:

1/1 2/1 3/1 4/1 ...
1/2 2/2 3/2 4/2 ...
1/3 2/3 3/3 4/3 ...
1/4 2/4 3/4 4/4 ...
....

and count them starting at the top left corner down diagonals, neglecting repeats (i.e. 1/1 2/1 1/2 1/3 (2/2) 3/1 4/1 3/2 2/3 1/4...)

So the set of fractions has the same cardinality as the set of integers, and smaller cardinality than the set of real numbers.

[Doc]

What would a philosophy flavoured jelly bean taste like?

I suspect that it would be sickningly sweet, followed by a creeping bitter after-taste.

[wakim]

It doesn't make sense in general to add cardinal numbers.
[right][snapback]98339[/snapback][/right]

I wish I'd known that before I had the hubris to add 2 + 2 in expectation of meaningful result.

With more seriousness, I doubt I can master the particular field of abstract mathematics that you speak of fast enough to respond to your statements in a meaningful manner; and when I speak I find that I lose you in what appears to be "philosophical pyrotechnics." Allow me to try to explain clearly:

My difficulty is that it would seem that you claim a class of numbers neither finite nor infinite in its properties: not infinite in that it is bounded, yet not finite in that it has no upper limit. This strike me as contradictory, as what is bounded is bounded by limits, and what is unbounded is unlimited:

If some set of items is infinite, a property I would assume one should rightly attribute to the natural numbers, then how can its members be numbered, or bounded, or limited? (How many natural numbers are there? Infinite. What is the largest natural number? There isn't one.) If some other set of items is also infinite, a property that I would assume one should rightly attribute to the divisibility of any continuous interval, then how can its members be numbered, or bounded, or limited? (How many divisions are there in a continuous interval? Infinite. What is the smallest division? There isn't one.)

It would seem that to compare one of these infinite sets to another one introduces language that denotes difference between magnitudes of infinity; yet if infinity is unbounded, unlimited, and un-numbered, then how can one assign magnitude to it? But perhaps it isn't magnitude, but correspondence that is introduced? Correspondence between what? Correspondence between the magnitude of the quantity. What is the magnitude of the quantity? Infinite. Magnitude cannot be assigned to infinity, but perhaps it isn't magnitude, but correspondence that is introduced? Correspondence between what? ...

[Thecla]

I wish I'd known that before I had the hubris to add 2 + 2 in expectation of&nbsp; meaningful result.

Fair enough. (Especially since my previous statement was wrong, and one can add cardinal numbers after all. My mistake. :) )

With more seriousness, I doubt I can master the particular field of abstract mathematics that you speak of fast enough to respond to your statements in a meaningful manner; and when I speak I find that I lose you in what appears to be "philosophical pyrotechnics."

If you're going to talk about "infinity" then I'm afraid you have no alternative other than to understand something about how it is defined in mathematics; otherwise what you say is liable to degenerate into meaninglessness, and what seems counter-intuitive or contradictory may just turn out to be an unexpected property of infinite numbers.

My difficulty is that it would seem that you claim a class of numbers neither finite nor infinite in its properties: not infinite in that it is bounded, yet not finite in that it has no upper limit. This strike me as contradictory, as what is bounded is bounded by limits, and what is unbounded is unlimited:

For example, if I interpret you correctly, you don't like the fact that for every natural number there is a natural number which is larger than it (the natural numbers have 'no upper limit') yet there is a number that is larger than every natural number (the natural numbers are 'bounded'). That isn't a contradiction, however; that's how it works.

Of course, any number that is larger than every natural number cannot itself be a natural number -- it must be an infinite number. This means one has to define, as Cantor did, what one means by an infinite number and show that this statement is true. Much of our intuition goes out the window when dealing with infinite numbers, which is why it's essential to base everything on precise definitions and logical deductions from them.

It would seem that to compare one of these infinite sets to another one introduces language that denotes difference between magnitudes of infinity; yet if infinity is unbounded, unlimited, and un-numbered, then how can one assign magnitude to it?

Exactly what Cantor did was to show that in a precise way there are different 'magnitudes of infinity' (in fact, that there are infinitely many different cardinal numbers or `magnitudes of infinity') and that, for example, the real numbers are 'more infinite' than the integers or the rational numbers.

But perhaps it isn't magnitude, but correspondence that is introduced? Correspondence between what? Correspondence between the magnitude of the quantity. What is the magnitude of the quantity? Infinite. Magnitude cannot be assigned to infinity, but perhaps it isn't magnitude, but correspondence that is introduced? Correspondence between what? ...

You start with sets (say sets of numbers to be definite, but it doesn't matter) and define what it means for two sets to `have the same cardinality': namely, two sets have the same cardinality (`magnitude') if they are in one-to-one correspondence with each other.

Then you can say a set has cardinality 1 if it is in one-to-one correspondence with the set {1} with one element; cardinality 2 if it is in one-to-one correspondence with the set {1,2} with two elements,...; cardinality aleph_0 if it is in one-to-one correspondence with the set of natural numbers; cardinality c if it is in one-to-one correspondence with the set of all real numbers;... and so on.

[jahcs]

What would a philosophy flavoured jelly bean taste like?

I suspect that it would be sickningly sweet, followed by a creeping bitter after-taste.
[right][snapback]98340[/snapback][/right]

Agreed, the sweet portion would be accompanied by a gentle warming, kind of like eating a slow-acting chili pepper.




One thing to remember, for the layman, is that infinity+infinity=infinity. No need to get wrapped around the axle about it. infinity+infinty is, for most practical purposes, no bigger than infinity.

Infinity is the name given to man's attempt to wrap our little minds around something that is not definable in a finite sense. Man's quest for knowledge, exploration, and purpose hates something undefinable. We always want to see what's over that next rise, what happens if we add one to it, or what happens if we take it apart and get smaller and smaller pieces.

[--Pete]

Hi,

One can put the fractions in one-to-one correspondence with the natural numbers e.g. put all (positive -- which makes no difference)&nbsp; fractions in a square:

1/1&nbsp; 2/1&nbsp; 3/1&nbsp; 4/1 ...
1/2&nbsp; 2/2&nbsp; 3/2&nbsp; 4/2 ...
1/3&nbsp; 2/3&nbsp; 3/3&nbsp; 4/3 ...
1/4&nbsp; 2/4&nbsp; 3/4&nbsp; 4/4 ...
....

and count them starting at the top left corner down diagonals, neglecting repeats (i.e. 1/1 2/1 1/2 1/3 (2/2) 3/1 4/1 3/2 2/3 1/4...)

So the set of fractions has the same cardinality as the set of integers, and smaller cardinality than the set of real numbers.
[right][snapback]98339[/snapback][/right]

You don't even need to neglect the repeats and it still works :)

--Pete

[wakim]

If you're going to talk  about "infinity" then I'm afraid you have no alternative other than to understand something about how it is defined in mathematics; otherwise what you say is liable to degenerate into meaninglessness, and what seems counter-intuitive or contradictory may just turn out to be an unexpected property of infinite numbers.
[right][snapback]98348[/snapback][/right]

I won't quibble; I grant this.

For example, if I interpret you correctly, you don't like the fact that for every  natural number there is a natural number which is larger than it  (the natural numbers  have  'no upper limit') yet  there is a number that is larger than every natural number (the natural numbers are 'bounded'). That isn't a contradiction, however; that's how it works.
[right][snapback]98348[/snapback][/right]

You are correct. How one can resolve this contradiction, despite your friendly reassurance, I do not see.

Exactly what Cantor did was to show that in a precise way there are different 'magnitudes of infinity'...  and that, for example, the real numbers are 'more infinite' than the integers or the rational numbers.
[right][snapback]98348[/snapback][/right]

I am not yet inclined to grant differing flavors of infinity - for better reason than simply that I can recall playground arguments that ultimately devolved into meaninglessness once infinity was allowed to be treated as a number of finite magnitude: "Uh-huh." "Nuh-huh." "Uh-huh, uh-huh." "Nuh-huh, nuh-huh, nuh-huh." "Uh-huh infinity!" "Nuh-huh infinity plus one!"

I will grant, however, that if one defines "infinity" to mean something different, then naturally different conclusions will follow from that. Perhaps, until I have had the opportunity to study set-theory and thus engage its premises and conclusions more intelligently, it would suffice to return to the original question that sparked this digression and ask whether such an understanding is an application of more precision to the question than it merits?

The question was, if I recall, whether a set than contains some quantity of elements, whether infinite in magnitude or not, could exist that did not contain a first element? - "Thus, how if one claims a set of infinite items, can it not contain a first item?" The point of contention that you drew was over "So what is infinite can be larger than what is infinite? [Isn't there] contradiction in stating that a thing may be larger than itself?" This point seems incidental to the question, and I don't see why, if contested, it may not be discarded without loss to the cogency of the argument.

Perhaps you'd be inclined to grant that if one accepts infinity to mean "immeasurably great, unlimited, boundless, endless" that the point of contradiction is valid? and, in general, that a thing may not be larger than itself? and, further, ascribe the use of ambiguous language that failed to encompasses Cantor's divisions of the infinite (and thus inadvertently referred to many things as if they were only a single thing) as evidence of my finitude and not the fallacy of the argument?

[--Pete]

Hi,

I won't quibble; I grant this.
The question was, if I recall, whether a set than contains some quantity of elements, whether infinite in magnitude or not, could exist that did not contain a first element?[right][snapback]98353[/snapback][/right]

Yes. Consider the set of positive and negative integers: {. . ., -2, -1, 0, 1, 2, 3, . . .}. Without getting into advanced set theory, this set is countably infinite and yet (assuming the axiom of choice) it has no 'first' or 'last' element. A simpler example, {all flatware in your house} is a finite set that has, a priory, no ordering principle -- any element of that set could be designated 'first', or if you prefer, no element can be.

As to cause and effect and effects needing a cause, that simply leads to an infinite regression. One must either accept that, postulate a 'first cause', or give up some part of casualty. All three are perfectly acceptable philosophical grounds. But that is not the only viable viewpoint. There are many other possibilities: our 'universe' may be a bubble in something that is infinite in time; the curvature of our universe might have been sufficiently great prior to the initial expansion that time was curved onto itself so that it was infinite but bounded; our universe might still be a gravitationally bound object that expands, contracts, rebounds and goes on like that forever in both the past and future. Frankly, we haven't been doing science long enough to have more than a notion or two.

--Pete

[Drasca]

What created God?

I believe that is where all this banter will eventually lead in all of this cause and effect stuff being thrown about.

Can God microwave a burrito so hot that even He could not eat it?
[right][snapback]98277[/snapback][/right]

Or make one so good even he can't stand the after-effects?

Another fun philosophy question: Ask not why a perfect god make an imperfect universe, but why would a perfect god make a universe at all?

Why do I only like Chi Chi's hot salsa, and not most other brands (sadly not equipped to make my own).

[Thecla]

I can recall playground arguments that ultimately devolved into meaninglessness once infinity was allowed to be treated as a number of finite magnitude: "Uh-huh." "Nuh-huh." "Uh-huh, uh-huh." "Nuh-huh, nuh-huh, nuh-huh." "Uh-huh infinity!" "Nuh-huh infinity plus one!"

Well, for cardinal numbers "infinity+1" (or even "infinity+infinity") is the same as "infinity", wheras for ordinal numbers "infinity+1" really is a bigger "infinity", so I hope they were using ordinal numbers. ;) Of course, then there's infinity+2. On the other hand, 'the largest infinity' turns out to be a self-contradictory concept, but I doubt that would stop anyone on the playground ("largest infinity plus one").

I will grant, however, that if one defines "infinity" to mean something different, then naturally different conclusions will follow from that.

I certainly grant that the word "infinity" might be used in lots of different ways. But IMO all of the non-mathematical uses -- whatever their poetic, metaphysical, or religious value -- don't lend themselves well to rational argument.

The question was, if I recall, whether a set than contains some quantity of elements, whether infinite in magnitude or not, could exist that did not contain a first element?&nbsp; "Thus, how if one claims a set of infinite items, can it not contain a first item?"

I came in after that, but since you ask (WARNING: feel free to read no further unless you wish)...it really depends on what you mean: The set of integers (positive or negative) has no first element -- if by that you mean a smallest element. On the other hand, you could imagine reording them as, for example, 0, -1,1,-2,2,-3,3... and then they would have a first element (0).

The set of all real numbers also has no smallest element, with its usual ordering (or even the set of real numbers 0 < x < 1). You could imagine reording them by picking one number at a time, say as

pi, sqrt{2}, -25.1010010001..., -9/7,..

until they're exhausted (an exhausting procedure requiring an uncountably infinite number of choices), and then they would have pi as a first element; furthermore every subset of the real numbers would also have a first element (e.g. - 9/7 would be the first element of the rational numbers). The assumption that you can so order any set, however big, is called the well-ordering principle, and it's rather controversial (being equivalent to the axiom of choice).

The point of contention that you drew was over "So what is infinite can be larger than what is infinite? [Isn't there] contradiction in stating that a thing may be larger than itself?" This point seems incidental to the question, and I don't see why, if contested, it may not be discarded without loss to the cogency of the argument.

It may well be discarded -- I simply couldn't stand to see such imprecision about mathematically related concepts without responding. ;)

Perhaps you'd be inclined to grant that if one accepts infinity to mean "immeasurably great, unlimited, boundless, endless" that the point of contradiction is valid? and, in general, that a thing may not be larger than itself?

I honestly don't know whether "immeasurably great, unlimited, boundless, endless" really defines a meaningful concept, or whether -- in whatever context this definition is supposed to apply ---the statement that "a thing may not be larger than itself" is tautological, true, false, or meaningless.

[Thecla]

You don't even need to neglect the repeats and it still works :)
[right][snapback]98352[/snapback][/right]

Well, one last tiny comment: if you don't ignore repeats you get a map of the natural numbers onto the rationals, but it's not one-to-one since different natural numbers map to the same rational, so that doesn't quite prove their cardinalities are equal, only that

card(rationals) <= card(natural numbers)

Of course, since the natural numbers are a subset of the rationals the reverse inequality holds, so they're actually equal.

But, for example, if you map the real numbers into the rationals by saying that x maps to x if x is rational and x maps to 0 if it's irrational, then you get a map of the reals onto the rationals, and in that case the cardinality of the reals is strictly greater than the cardinality of the rationals.

[GenericKen]

No. Nothing that can be called science works on those principles. The internal consistency of fiction has no bearing whatsoever on the outside world. It is not, in a word, testable.

Scientific "theories" that cannot be tested *at all* are not theories. They are philosophical musings, or some such. Even M-theory, poorly understood though it is, exists for the purpose of making *testable* predictions from a description of the universe. Without that, it would just be a thought experiment. Internal consistency is merely the prerequisite for being taken seriously, and for making sensible predictions.

I have no idea what theory you're talking about in your last sentence. Intelligent Design? Also, I can only presume you're talking about Pete doing the lambasting, in which case I'd be wary about declaring his lack of knowledge. He's not the subject of elaborate conspiracy theories for nothing.

-Jester
[right][snapback]98203[/snapback][/right]

I'll quote Pete's lambasting of the Thor theory here:

Yes. Because 'Thor' can have any properties you want. And he doesn't have to follow any rules, not even homogeneity or consistency (really, the same thing, but I split them for those who still don't instinctively think in four space).

Whatever dark energy ('dark matter' is another concept that helps to describe the rotational velocity and dynamics of galaxies) is, it has to follow rules. We don't know what those rules are, yet. It may take a while to figure them out, it might take a few revisions of the theory (or even complete replacements of the theory) to get a decent map.

He asserts that the lack of internal consistancy is what seperates Science from fiction, when in fact, most good fiction (like good science) maintains internal consistancy.

What's more, though philosophical musings may be arbitrary, they're far from meaningless. In every thought is the reflection of the thinker. At the very least, it holds information critical to understanding man, and thus, the philosophies he comes up with. Just because a story is allegorical does not mean it's not real.


The real issue of division between Science and other musings is testability, as you said. However, given the far-fetched circumstances of how we might one day perhaps consider thinking of maybe testing some scientific theories like String or M-theory, you have to admit that the line between science and fiction is blurred.

[GenericKen]

Hi,
Yes.&nbsp; Consider the set of positive and negative integers: {. . ., -2, -1, 0, 1, 2, 3, . . .}.&nbsp; Without getting into advanced set theory, this set is countably infinite and yet (assuming the axiom of choice) it has no 'first' or 'last' element.&nbsp; A simpler example, {all flatware in your house} is a finite set that has, a priory, no ordering principle -- any element of that set could be designated 'first', or if you prefer, no element can be.

As to cause and effect and effects needing a cause, that simply leads to an infinite regression.&nbsp; One must either accept that, postulate a 'first cause', or give up some part of casualty.&nbsp; All three are perfectly acceptable philosophical grounds.&nbsp; But that is not the only viable viewpoint.&nbsp; There are many other possibilities:&nbsp; our 'universe' may be a bubble in something that is infinite in time; the curvature of our universe might have been sufficiently great prior to the initial expansion that time was curved onto itself so that it was infinite but bounded; our universe might still be a gravitationally bound object that expands, contracts, rebounds and goes on like that forever in both the past and future.&nbsp; Frankly, we haven't been doing science long enough to have more than a notion or two.

--Pete
[right][snapback]98354[/snapback][/right]

Well if you want to get into allegorical mathematics, 1 is really the origin of all countable numbers in additive space, as all other numbers are recursively derived from it. Given that the space is arbitrarily large, though, any number that normalizes itself can become the origin. Kinda buddhist, really.

[wakim]

“If a set that contains some quantity of elements, whether infinite in magnitude or not, could exist that did not contain a first element?”

I chose this question as an example in the hope of illustrating a principle, not as proof of that principle, just as x = 1 + x/2 may illustrate some algebraic principle, but doesn’t prove it. If, in light of set theory, the example, through some abstruse numerical postulate that I was ignorant of (and probably still am), does not illustrate the principle in question I’d be happy to withdraw it and try to find another, as needed, that can illustrate better. If you intended to answer the question posed by this example by explaining advanced set theory, I appreciate your efforts, but I haven’t mastered set theory yet; and if I am expected to do so from what has been given then please allow that my abilities have proved countably finite. If before I may pose examples that encompass numerical entities or concepts I must first learn the language of set theory, then please grant me a reasonable time to do so and evaluate the examples I had happened to give before then in the appropriate light; and should we until then not be able to agree on what “infinity” means, let’s agree to avoid illustrative examples that are predicated on a contested meaning.

Consider the set of positive and negative integers: {. . ., -2, -1, 0, 1, 2, 3, . . .}.&nbsp; Without getting into advanced set theory, this set is countably infinite and yet (assuming the axiom of choice) it has no 'first' or 'last' element.
[right][snapback]98354[/snapback][/right]

A glance at the example reveals that {. . ., -2, -1, 0, 1, 2, 3, . . .} seems to begin with negative infinity and end in infinity; yet a set infinite in both directions has no beginning and no end (if we both share this meaning of “infinity”), no first or last.

And, obiter dicta, isn't “axiom of choice” and the phrase “countably infinite” indulgences in advanced set theory?

A simpler example, {all flatware in your house} is a finite set that has... no ordering principle -- any element of that set could be designated 'first', or if you prefer, no element can be.
[right][snapback]98354[/snapback][/right]

Yet to count that same unordered set there must be a first element counted (and for it to be a finite set of elements mustn't it contain countable elements? and to accept that the elements are countable is to accept a first; for it doesn’t seem possible to count without starting to count, nor to start without starting from the first), then proceeding to a second, and so on... But isn't what is “first” here an arbitrary designation? Can't any element equally be considered as first? In the example of flatware, which was premised to be arbitrary - a premise I don’t contest - and therefore without ordering principle (and analogous to lacking cause), should it be any surprise that the first element, if existent, is found to be equally arbitrary?

If one supposed an ordered set (analogous to possessing cause - an ordering principle), shouldn't one then expect a definitive first element? To return to the example I offered, I don’t deny that it presumes cause, or that it presumes order. The example was offered only after it was first asserted that, “everything, insofar as I can tell, has a cause.” Even if I have provided an example that failed to consider the language and definitions required by set theory, the fact that the example itself, when taken out of context - order - and considered without regard to its cause, became meaningless should serve as example:

The question of: “If a set contains an infinite number of integers, mustn't in contain every quantity of integers smaller than the infinite? In other words, if a set of 100 items were examined, mustn't it also be found to contain 99 items, and 98 items, and so on? If a set of 100 items did not contain a first item, how could it contain a second?” is the original example, given explicitly under the premise that “everything... has a cause,” and further prefaced by this question of mine:

“I don't understand how everything can be claimed to have a cause, with one hand, while with the other claim that things exist without a first cause; since without a first cause there can follow no other cause, and thus things must exist as uncaused. For if no first cause exists, how can a second cause exist, or a third, or a fourth, or any higher number, let alone an infinite number? It would appear as if one who would reject a first cause for something as unreasonable, would then turn around and claim that no cause is an answer in better accord with reason.”

“[Could] a set that contains some quantity of elements, whether infinite in magnitude or not,... exist that did not contain a first element?” is only the shorter version (and given the length that this recapitulation has grown to it should be evident the virtue, and failings, of such brevity). The shift from cardinality to ordinality (in the ordinary sense of the terms – from a quantity (e.g. 1) to an order (e.g. first)) evident in the longer version was made in the context of cause and effect (an ordering principle) – a principle that this example is predicted on, not that cause and effect is proved a necessary element of all sets based upon this example. I grant that without cause the example fails, as ordinality presumes order, and order is a cause.

As to cause and effect and effects needing a cause, that simply leads to an infinite regression.&nbsp; One must either accept that, postulate a 'first cause', or give up some part of casualty. All three are perfectly acceptable philosophical grounds.
[right][snapback]98354[/snapback][/right]

I would argue that all three are not equally acceptable. All effects needing a cause creates no contradictions that I can discern, nor does accepting a first cause lead to infinite regression, and I would hope that you would agree that philosophical grounds that stand free of contradiction are preferable to those that don't, and likewise, those that don’t postulate infinite regress are superior to those that do.

To accept effects without a cause would appear to contradict the principles of scientific investigation; for who would bother to investigate the causes of things if there weren't any? To accept a chain of causality that does not have a first cause is to either admit circular cause ("this thing caused itself"), which like circular reasoning I would think most would find unsound, or to abandon the principle of caused effects. Isn’t the presumption that science will yield answers in a given circumstance predicated upon the existence of cause, and thus implicitly to deny that all philosophical positions (respecting cause) as equally acceptable?

Frankly, we haven't been doing science long enough to have more than a notion or two.
[right][snapback]98354[/snapback][/right]

If one accepts that science is an investigation of causes, it would seem that for it to investigate something that is without cause is beyond its scope. Applying a tool to find the cause of an object that is without cause would yield no information; regardless of how long one had been at it. If one accepts that there is an infinite causal chain, then that chain must be uncaused. If one accepts uncaused effects, then isn’t it beyond any field of study to find the cause of those effects?

[Jester]

What's more, though philosophical musings may be arbitrary, they're far from meaningless.

IIRC, this thread was initially about Intelligent Design being taught in science class. If something doesn't pass muster as science, it doesn't get into science class. However interesting philosophy might be, it should keep to its own turf.

However, given the far-fetched circumstances of how we might one day perhaps consider thinking of maybe testing some scientific theories like String or M-theory, you have to admit that the line between science and fiction is blurred.
[right][snapback]98390[/snapback][/right]

No. As I said, the entire point of these theories is to create a testable view of the universe. If we can't test it yet, that's really too bad, since it means they will be hypotheses for quite some time. That's a completely different thing than being untestable, or not intended for testing. There is no blurring of the line here.

-Jester

[Artega]

What created God?
[right][snapback]98277[/snapback][/right]

Being an athiest (or at least agnostic), I would say man created god. Other, past civilizations (such as the Greeks and Romans) had their own gods, conjured up to explain things that they themselves couldn't explain. They couldn't explain where fire came from, so enter Hephastus (I think) or Vulcan, depending on the civilization. Then again, I'm just recalling things that I've read somewhere, and have nowhere near the knowledge to support and enforce my views, so I could very well be wrong.

I would think the best kind of religious person would be one that can openly question his faith, yet still truly believe in it.