fredonly wrote:ThatGirlAgain wrote:
If one defines God as simply the reason for existence (whatever that term entails) it becomes difficult to talk about the existence of the reason for existence. And talking about the reason for existence not existing gets a little weird. It may be that existence is absurd – there is no reason. But that raises the question of why there should be the possibility of order. I don’t mean the ID godidit kind of incidental order but the fact that the universe is in the whole an orderly place. It is possible to make up laws that describe its behavior pretty well. If the universe is absurd, why should this be the case? But I am an ignostic. I don’t believe we can ever properly answer questions like that. But we can set logical limits on what can be and what cannot be. Thus my little game of an omnipotent God not being the god of the Bible on ‘engineering’ grounds.
As with most words, “reason� is ambiguous. In the present context, consider Leibniz’ principle of sufficient reason:
There can be found no fact that is true or existent, or any true proposition without there being a sufficient reason for its being so and not otherwise, although we cannot know these reasons in most cases.
In the above sense, “reason� does not imply
intent, but this is how some people interpret it - if they’re predisposed to believe that there is a sentient being that is behind it all. Leibniz is really just describing causality, with a little twist. A
cause is also a
reason, . But if something is uncaused, it still has a reason (this is the twist): the necessity of its own existence. A necessary truth is one that could not have been otherwise; its negation is a contradiction. A contingent truth is one that could be otherwise; under different circumstances it would not be true. A necessary entity is one that exists necessarily; it couldn’t NOT exist. A (generic) first cause is necessary, because in the absence of a first cause – there would be no existence.
The concept of a necessary being leads one into deep and muddy waters. I am not arguing that one today, in either direction. But it does raise the question that gives some theists the hives.
Is God – and now I mean the personal God of theists – dependent on logic or exempt from it? Will touch on that again below.
In the meantime I agree that a sentient being behind it all is not necessarily implicit in a first cause argument.
fredonly wrote:
ThatGirlAgain wrote:
I thought I had explained why a first cause must be infinite. But apparently not very well. Sorry.
You
did, but it has 2 problems: 1)it is only meaningful if an actual infinity
can exist. 2) you assume that a first cause has infinite power by default. This seems ad hoc.
My argument was that a non-zero but non-infinite potentiality requires an explanation. Why is it exactly what it is and not something else? One might resort to the absurdist answer (not intended pejoratively BTW) that it just is that way with no explanation needed. But this fails to take into account that this violation of sufficient cause comes equipped with apparently unbreakable sufficient cause built in. The universe is an orderly and lawful place in which thing s happen for reasons. The rules of the game are quite weird from the mundane human point of view but there
are rules. What that elaborate set of rules derives from is unexplained.
Quantum Theory is sometimes raised as proof of the absence of sufficient cause but this is an error. QT fully incorporates causality. And the results are
statistically deterministic even if they do not meet intuitive expectations derived from experience in the human level world.
The existence of rules of the game suggests we should avoid absurdism. How then do we explain the precise nature of the world we live in. It could have been something else. Why is it the way it is? A first cause that is only capable of this must be constrained in some way. What constrains it? There must be something prior to it. So it is not the first cause after all. Is the previous cause constrained in any way? Then there must be something prior that constrains it. One can either have an infinite sequence of increasingly less constrained causes or a single genuine first cause that is unconstrained in its capabilities, i.e., infinite. Either way you get infinity. Do you have a way of having a world under specific constraints that could have been otherwise without ending up with infinity?
There is of course the theist way: a conscious personal God with the ability to arbitrarily choose. But what leads such a God to make this specific choice? Same problem again.
fredonly wrote:
ThatGirlAgain wrote: Something exists so a (hypothetical) first cause must have non-zero power. But for it to have a specific finite power implies that there is a reason for limiting it to exactly that power. Something must be prior to the first cause to establish that limitation. There might be a succession of causes but ultimately there must be either an infinite first cause, one which is not limited by anything prior, or an infinite succession of finite causes that have their values for possibly absurd reasons. The sum of power in that succession would be infinite. Either way I do not see how to get away from infinity.
To restate the problem: you have not made a case for getting TO infinity. There are absolutely no examples of an actualized infinity existing in nature. Infinity is a product of the imagination, an abstraction that has certain mathematical properties. Abstract existence is a far cry from actualization in the real world.
I do not see that I need to get TO infinity if I have shown a way of coming FROM infinity. The non-existence of actualized infinities in nature is not an obstacle. First of all it may not be the case.
The most successful known laws of fundamental physics, Quantum Theory and General Relativity, both lead to infinities in their calculations. QT circumvents the problem via Quantum Electrodynamics (QED) in which mathematically illegal operations are used to cancel out the infinities. This is called renormalization. (It is suspected that Richard Feynman, inveterate prankster that he was, chose the name QED to thumb his nose at mathematicians.)
But no one has yet been able to formulate a replacement for QT that eliminates the infinities from the start. There has been much speculation and profligate generation of abstruse theory building but no real results yet despite decades of work.
The infinities are inherent in GR and cannot be eliminated by mathematical trickery. Renormalization is not possible. Yet the most exotic prediction of GR and one that leads directly to these infinities – black holes – are now the stock in trade of astronomers in explaining the phenomena they observe.
It may be that the universe is in fact infinite in extent. We can only observe out to the event horizon, the limit of from how far off light could have reached us since the beginning of the universe. We do not know how much more of it there may be. The accelerating expansion of the universe suggests a hyperbolic space-time, which is necessarily infinite. But the existence of a ringer like dark energy still allows a physically finite universe.
The existence of actual physical infinities has not been definitively ruled out. Nonetheless my argument is about causes prior to the universe. Physical infinities need not exist
within the universe. It is the fact that the world is finite – that is, limited in certain ways – is what leads to the concept of an infinite prior cause.
fredonly wrote:
ThatGirlAgain wrote: That is an assumption that the finite is logically prior to the infinite. The infinite might be logically prior. Remember my point above about why a finite thing should be exactly as finite as it is.
"Logically prior" is too weak a relationship. What's relevant here is "temporally prior," time progresses sequentially. You are simply ASSUMING infinity, not making a case for an actual infinity existing. The fact is, there IS no such case.
“Temporally prior� is problematic in contemporary physics. In relativity simultaneity does not exist. The order of events is not necessarily the same for two observers and the time interval between the events is very likely different. Time does not flow at the same rate for all observers. It is dependent on relative motion and gravitational field strength. (GPS satellites must take this into account.) In intense gravitational fields such as black holes, an observer falling in will see time progress normally (assuming he/she is not destroyed by side effects). An observer outside will see that falling observer
never reach the black hole. Hawking et al. speculate that at the beginning of the universe the time dimension goes ‘sideways’ like the surface of the Earth at the poles. Kip Thorne even claims to have shown that General Relativity allows backward time travel and dares anyone to debunk his math in a professional peer-reviewed physics journal.
In the quantum world time may even be stranger. The non-intuitive results predicted by John Bell seem to rule out local causality. One proposed solution to preserve locality involves ‘advanced waves’, influences that
go backward in time. Advanced waves are predicted by Maxwell’s theory of electrodynamics but have never been observed. And at the shortest distances, QT predicts that the meaning of time just goes away.
Logical causality sounds like a better safe haven than temporal progression. Things happen for a reason.
What happens may seem strange to us who have live our lives in an ‘ordinary’ world. But things are not causeless.
fredonly wrote:
ThatGirlAgain wrote:
fredonly wrote:
However, taking the days and counting them one by one, infinity is never reached. We have simply defined a
processs that has no endpoint. This demonstrates that the concept of infinity entails incompleteness; infinity can never be reached, because one more can always be added. An infinite past implies that an infinite number of days have completed; but this is an incoherent concept because infinity entails incompleteness and potential; the past has no potential and the past is completed.
In the Einsteinian worldview, the universe is a monobloc. It is legitimate to talk about the entire four dimensional space-time continuum. But current cosmology indicates that time will never end, that the universe will expand forever. In the Einsteinian view, an actual infinity exists.
The Einsteinian view is a mathematical model intended to describe some aspects of reality. You are mistaking the model for the reality. Einstein originally assumed the universe was infinite in both space and time. Physicists do not always make the best metaphysicists.
I believe you are mistaking ordinary everyday experience, which is not well supported by scientific investigation, for metaphysical necessities. Scientific investigation has demonstrated that the world is round, contradicting the intuitive expectations of the uninformed. The roundness of the world is not merely abstract. It is real with real consequences. Einstein’s theories have real
everyday consequences. The computer you type on incorporates several technologies that arose from relativistic quantum theory. Before relativity was incorporated, QT did not work well. As mentioned above, GPS satellites must take General Relativity into account to work right. Einstein’s theories describe the real world despite their non-intuitive character. We must take them seriously.
fredonly wrote:
ThatGirlAgain wrote:
As a side note, Aristotle thought the idea of nothingness so distasteful that he assumed the world must have existed forever. It must have been a hard decision because he also disliked infinity. If one imagines a world that has already existed forever, one is dealing with an actual infinity. The past has happened and leaves traces in the present. It cannot be treated as only potential.
Note that your starting point is IMAGINING an infinite past, again – an unjustified assumption. Try and justify it.
It was Aristotle’s starting point not mine. My point was that whichever way he turned, Aristotle bumped into either nothingness or infinity. There
is something and not just nothingness. Why the exact nature of that something and not something else?
fredonly wrote:
ThatGirlAgain wrote: fredonly wrote:
I’ll add that when someone uses the phrase, “an infinite number of…� there’s a problem, because “infinite� is not a number, it’s a process. You cannot have an infinite number of hotel rooms (as in Hilbert’s paradox), but you can keep adding rooms to your hotel potentially forever.
As an aside, and to ward off a common objection, I’ll mention that there are also two uses of infinity in mathematics. The first is in calculus, which utilizes infinities and infinitesimals. I’ve been in discussions in which this type of infinity is presented as being a completed infinity. But that is a misinterpretation. The infinities used in calculus are
limits, which in the real world are just hypothetical, but for which mathematical patterns can be identified and utilized for important calculations.
The other use of infinity in mathematics is in Cantorian set theory. The fact that we can depict an infinite set like this: {1, 2, 3, …} gives the illusion that we have contained an infinity, but that’s not the case. It’s just a handy means of mathematically manipulating series of numbers (or objects) that are hypothetically infinite. The fact that the set of all positive even integers can be mapped one-to-one to the set of all positive integers demonstrates that there is a non-real-world aspect to the infinities represented in sets. Consider Bertram Russell’s Tristram Shandy paradox, which shows the problem with this sort of mapping:
Tristram Shandy is an author writing an auto-biography. Unfortunately, he writes very slowly; each day of his life takes him a year to write about.
The Tristram Shandy paradox asks: If Shandy continues at this rate for eternity then will his book ever be finished?
Using the rules of mapping sets, it would appear that in an infinite amount of time, he will finish. But in the real world, there is no point in time at which Shandy will actually be finished; in fact, he gets further and further behind. As the days proceed toward infinity, the number of days Shandy is behind grows larger. The lesson is that the real world doesn’t map into an infinite set, except in terms of hypotheticals; actual completed infinites cannot exist.
Again you are
assuming that the finite is logically prior to the infinite.
I again take issue with your term “logically prior� since it ignores the fact that events occur in time. It is self-evident that time proceeds sequentially in discrete units of finite duration. The past consists of a set of such discrete units of time, call them “days.� How can there be infinitely many days prior to today? We would never reach today, because it is impossible to complete an infinity.
Time and its nature is an aspect of the physics of this universe. Even Augustine came to that conclusion. Time did not exist ‘before’ the universe. In that case, ‘before’ when applied to causes
of the universe cannot mean
temporally prior. It can only mean
logicallyprior.
fredonly wrote:
ThatGirlAgain wrote:
In Set Theory, the cardinal number of a set is fundamental. The cardinal number of the set of the rational numbers and the algebraic real numbers is � null. It is what it is no matter what infinite subset you wish to invoke. (The infinite ordinal ω is another matter. One can do consistent arithmetic with it including adding to it.) Before one dismisses Set Theory as nonsensical do not forget that one can generate all of mathematics from it. And although one cannot demonstrate the consistency of arithmetic by finitistic methods, one can do it using properties of transfinite cardinals.
Set Theory is not nonsensical, but it deals with abstractions, not the real world. A “cardinal number� is not a number. It’s a descriptor that identifies the type of set it maps into. A set with cardinality of aleph-null can be mapped into the set of natural numbers. That’s all it means. You are making the very mistake I described, the fact that there are mathematical uses of infinity, and means or representing this concept on paper, gives you the illusion that infinity can exist in the real world. Give me an example of an actual (not potential) infinity.
Numbers themselves are only abstractions. When you count on your fingers, you are counting different things. The thumb and the index finger are not the same. The number you are counting exists only in your head, not in the real world. Cardinal numbers are abstractions? So are integers.
If there are no physical infinities – and remember my discussion above – it is a consequence of the universe being limited in some fashion. What limits it? Is that also limited? What limits
that? The universe just
is without reason? Then where does its internal reasonableness come from?
fredonly wrote:
ThatGirlAgain wrote:
BTW the Tristam Shandy paradox is not valid. It simultaneously (and sneakily) assumes unending infinity and an end to the process.
It assumes no such thing, it just asks a question. It succeeds in demonstrating the problem of mapping mathematical infinities into the real world. The cardinality of the set {days of Shandy's life} is aleph-null; the cardinality of the set {documented days of Shandy's life} is also aleph null. But the mathematical operation of mapping is atemporal, conceptually simultaneous. But the real world is temporal, which Cantorian set theory doesn't deal with.
The Tristam Shandy paradox assumes an end at which a comparison can be made between the days lived and the days written about. There is no such end. No paradox arises there. Viewed in their entirety the cardinality of the set of days written and the set of days lived are both aleph null in accordance with the precepts of set theory. You cannot compare ordinality with cardinality. They are not the same. And BTW set theory as moved way beyond Cantor. ZFC might even get supplanted by something like NBG, which resolves the ‘set of all sets’ issue by formally defining classes.
fredonly wrote:
ThatGirlAgain wrote:
A mapping set involves cardinality, not ordinality.
Exactly correct, but “cardinality� is nothing more than a mathematical concept –it doesn’t map into the real world, as I just discussed.
Neither do ordinal numbers, as I just discussed. Stop using ordinality and I will stop using cardinality. And again, all of mathematics can be derived from set theory, and cardinality is the heart of set theory.
fredonly wrote:
ThatGirlAgain wrote: The Thompson’s Lamp problem makes the same mistake. In both cases there is no end. That is what infinity means.
That’s exactly what I’m saying, and is exactly why the past cannot be infinite:
1)Infinity means there is no end (ThatGirlAgain and I agree on this premise)
2) Time proceeds in one direction from past to present to future (physicists call this the arrow of time; it is a self-evident property of time)
3)The past has ended (the past, as viewed from our present moment of time, is a done-deal).
4) Conclusion: the past is not infinite (follows from 1, 3)
I did not say the past was infinite. Aristotle did. Contemporary physics holds that the universe has finite history. (Contemporary
speculation is another matter, involving achievable past (and future) infinities like eternal inflation or universes born in black holes. But not today, OK?)
The arrow of time is by no means self-evident. It is merely our everyday experience. The laws of physics are time-symmetric. They work the same forward and backward. At the quantum level one cannot distinguish a direction in time. This so called arrow of time is usually justified by the Second Law of Thermodynamics (SLOT). But for that to yield the results we see today requires continuous sources of low entropy. Why do they still exist in a 13 billion year old universe? Why is there fossil fuel to provide our energy? Because plants and animals got their energy from the Sun. Where does the Sun get its energy? From thermonuclear reactions in its core. Why do they happen? Because gravity compresses the Sun that much. Nuclear power plants? The uranium they ultimately depend on (plutonium is made from uranium) did not exist at the beginning of the universe. It was formed in supernovas. Why did those supernovas happen? Gravity. Every example of the low entropy you can find ultimately derives from gravity. SLOT is an artifact of the nature of the universe, not a fundamental law.
A question: why is gravity always down? Why is there no anti-gravity? Because all the mass-energy of the universe has a positive sign. Negative mass-energy would push instead of pulling. (In GR terms, space-time would bend the other way.) Why does the universe have only positive mass-energy? Everything else seems to come in plus and minus forms. Physicists see no reason why negative mass-energy is impossible. It just does not happen. Why? What
constrains the universe in this way? Does that constraint have a prior constraint? And so on…
fredonly wrote:
The mere fact that we can define an abstract entity, such as infinity, does not imply that it actually exists in the real world. Abstract algebra deals with other abstract entities (such as rings and fields) – but no one would ever suggest these exist I the real world.
The assumption that a real world, actual infinity exists is just as logically flawed as the assumption that a god exists. Both "god" and "infinity" can be conceptualized, their properties can be identified, and both concepts exist as intangible abstractions in our minds, but that doesn't imply they exist in the real world. You have assumed infinity exists and proceeded to draw conclusions from that. A Christian assumes God exists and draws conclusions from that. But there are no good arguments for the existence of either.
My definition of ‘God’ given someplace upstream is simply a shorthand term for the reason things exist.
I have not assumed infinity exists. I cannot see any way around it existing at the – let’s call it metaphysical level. The (presumed) absence of physical infinities
within the universe is not applicable to what can be
outside the universe. And throwing away the “outside’ possibility leads to an absurdism that somehow goes away once the universe is here.
As I mentioned briefly in this thread and argued at greater length elsewhere, my take on things is that the required infinity (unconstrainedness) is neither a single omnipotent entity sitting outside the universe nor an infinite regression of successfully more powerful ‘first’ causes’. My infinity is a ‘sideways’ one, to speak metaphorically. Everything that can exist does simply because it is logically possible. The law of non-contradiction leads to the necessity of separate universe to isolate potential contradictions from each other. To steal a phrase (entirely out of context
) existence is prior to essence.
Where does logic come from? Is it possible to deny the necessary existence of logic? Is a source of logic needed? How does one even argue such a thing? Now you see why I am a non-religious ignostic.
Unfortunately I have come to the very end of time I can waste on this site for the near future. I think we have reached the point where we are both repeating ourselves anyway. Goodbye bye (briefly I hope) and thanks for all the fish. I will return when I can even if just for the halibut.
