So point me to a mathematical framework where Infinity + 1 != Infinity.
Better still explain to me why the universe is bound to that particular framework and that is possible that there have existed infinite events before this one.
I’m not sure why that would be necessary. I’m not making any claims about the existence or non-existence of infinite causal chains. If anything I would say that I can think of no reason why they could not possibly exist. In fact, I find the idea that there are only a finite number of causal events before the present time much more difficult to sustain intuitively, but that’s neither here nor there.
In any case, I don’t see why the universe would need to conform to any particular mathematical model in order for an infinite causal chain to be possible. And for that matter, the question still stands of what exactly the nature of “Infinity + 1” has to do with the idea of an infinite causal chain.
Our point isn’t to say that the universe is bound to particular mathematical framework X. Our point is that you haven’t established that the universe is bound to alternative mathematical framework Y, and thus can’t automatically argue that facts about Y translate directly into facts about the universe.
Also, it’s not actually clear to me why “infinite + 1 = infinite” should imply anything about the impossibility of an infinite causal chain, but ok… (On edit, I am glad to see that Stealth Potato has already made these same two points)
The controversial assertion is that “There cannot be an infinite causal chain” is somehow logically mandated. Let’s examine that assertion this way: Consider the statement “It is not possible that there is some e1 which is caused by some e2 which is caused by some e3 and so on ad infinitum”. What is the logical form of this statement? Is “caused by” a logical term in itself, with respect to which we are entitled by force of pure logic to make special, otherwise-unlicensed deductions, or is “caused by” just any binary predicate? If the latter, then the logical form of this statement cannot be any finer-grained than “It is not possible that there is some e1 in relation R with some e2 in relation R with some e3 and so on ad infinitum”; but this logical form certainly isn’t logically mandated (not all instances of it are true; e.g., if the binary relation was taken to be that of “___ is a smaller integer than ___”, the statement would be contradicted by the possibility for the sequence <e1, e2, e3, …> to be <1, 2, 3, …>).
So if “It is not possible that there is some e1 which is caused by some e2 which is caused by some e3 and so on ad infinitum” is logically mandated (i.e., holds true on account of its logical form alone), then part of that logical form must include the specific fact that the binary relation being discussed is causation and not something else; i.e., we must be using a logic with built-in rules for reasoning about causation.
Well, standard deductive logic doesn’t contain any such rules. [We could of course appeal to another logic of our choice or construction which has such rules worked into it, but, naturally, nothing will come out of it other than what we’ve specifically put into it… anyone who isn’t already inclined to accept the necessary finitude of causal chain is unlikely to be tricked into accepting principles in a logic of causation which will allow such a conclusion.]
The weird thing about this is that you seem to be saying “I believe” should be the default position, and one can only principledly resort to “I don’t believe” when evidence is brought in its favor. Why should belief rather than lack of belief be the default?
[Note, lest there be any ambiguity, that I mean to keep “I don’t believe X is true” distinguished from “I believe X is false”]
Here is an axiomatic definition of operations on infinities.
0 * infinity = 0.
1 * infinity = infinity
infinity + infinity = infinity
0 + infinity = infinity
-1 * infinity = -1.
n + infinity = infinity, for any real or natural n.
infinity - infinity is undefined.
why undefined?
Say we have two real numbers, n and m, m <> n. since
n + infinity = m + infinity by our sixth axiom, if
infinity - infinity = 0, we’d be able to subtract infinity from both sides, leading to
m = n, a contradiction.
So operators under this system work a bit differently than under the natural or real numbers.
I assume this is not new - I didn’t try to search for anything similar, but just made this up for amusement value.
Actually I know it is not new, since Cantor did it, but I haven’t read that for so many years that my rapidly rotting brain has ejected it.
OK then, let’s go back to the definitions:
In order to excape the need for a first cause, an infinite chain of causes was posited. This chani, by definition, is unable to be regressed through, otherwise it would be possible to arrive at some starting point. However if it is impossible to regress through the chain from this point, it must also be impossible to progress through it to reach this point in the causality chain. This is the problem. It is necessarily contradictory to posit a chain of events that is possible to progross and not regress through.
I read the above argument, and I still do not see why you believe it can exist. All you seem to be saying is that I haven’t proved that it doesn’t, which is neither here nor there.
I would say that neither “I believe” or “I don’t believe” are the default. I think “I don’t know” is the only true thing one can say about an arguement for which there is no evidence. It is just not a very useful position.
Calculon.
Hooray; so you acknowledge that we can discuss addition of infinity as a coherent mathematical concept. Have fun playing around with and tweaking your system. (Your system differs in some ways from the ones I had been trying to mention earlier, but no matter, as long as you have your own motivations and applications for the definitions. I would just note that taking -1 * infinity to be -1 is rather odd and I’m not at all sure why you did so.)
Why would, in passing through a causality chain, the universe need to go through a first point upon the chain?
The following is a model of a universe with an infinite causality chain:
Joe was born in 20 B. C. and named after his father; this was caused by his father Joe being born in 40 B.C. and named after his father; this was caused by his father Joe being born in 60 B.C. and named after his father; and so on, with the years stretching back without end. There was no first year; there was no first Joe to be born.
Is there anything logically inconsistent about this? It certainly has a mathematical model, at least if we do not impose extra constraints on what the binary relation of causation can be like. So, if there’s something logically inconsistent about this, it must be because there’s something logically special about causation… which isn’t the case unless we specifically work that into a logic designed to enforce it.
So, would you then say that the future is not infinite? Because it is just that kind of thing – unbounded by an upper limit. However, how does saying that the future is not infinite not entail that there is some farthest point in the future, i.e. that the future actually is bounded by an upper limit?
I do agree that not endeavour that has a start will ever reach any kind of infinity; however, in arguing for infinite causal chains, I am pretty explicitly saying that they cannot have a start. Thus, the whole notion of ‘regressing through it’ doesn’t really apply, since it assumes a start from the outset, which also assumes that it isn’t actually an infinite causal chain.
So would, to you, the argument ‘there is a god, therefore, there is a god’ be a proof of god’s existence? You cannot show that the premise is false, and the conclusion follows trivially. However, I would say that there is much reason to challenge the premise anyway.
The fundamental problem here is that you are defining the chain in the opposite way in which the effects flow. Remember that in saying there is an infinite chain you are saying effectively that the universe “started” (even though that makes no sense in this context) at some point in the point at the other end of the chain, and then progressed to this point now. And there-in lies the problem. What you have to show is not that you can go from now to an infinite point in the past, but that you can go from an infinite point in the past to now. For that is what we are saying has happened.
If as you define it, there is no starting point in the chain, if no matter how far through the chain you regress there is always an infinite amount of points left, that same property would have to hold as you move the other way through the chain. No matter how many points forward you moved there would likewise have to be an infinite number of points to move through until you got to now. Since then you can never get to the current event, such a chain cannot exist.
Calculon.
Let me clarify: To challenge an argument you must either show that a premise is false, or that the conclusion does not logically flow form the premises. In this case I would say that the argument is invalid because the premise is the conclusion, and therefore is not connected to it in any meaningful way.
Simmerly the arguement:
- Russel Crowe is Australian
- Russel Crowe has an Oscar
- Paul Hogan is Australian
Therefore:
Paul Hogan has an Oscar
is invalid because while all of the premises are true, the conclusion does not flow from the premises.
Calculon.
If as you define it, there is no starting point in the chain, if no matter how far through the chain you regress there is always an infinite amount of points left, that same property would have to hold as you move the other way through the chain. No matter how many points forward you moved there would likewise have to be an infinite number of points to move through until you got to now. Since then you can never get to the current number, such a chain cannot exist.
Spot the difference!
Identity is not a meaningful connection? Of course, the argument is tautological, but if, as you seem to claim, there is no need for a substantiation of premises, it’s a perfectly valid deduction, since, if the premise is truly arbitrary in that way, there’s nothing to keep me from making it the conclusion.
But well, if you insist, it’s trivial to reformulate the argument:
(1) god exists if roses are red
(2) roses are red
-> therefore, god exists
Would you say I have now proven god’s existence? Or can you disprove my premise (1)?
And not to prod you, but are you going respond to my somewhat lengthy post directed to you on the last page? I fully appreciate if you don’t have the time right now, but I’d nevertheless like to hear your opinion on a couple of the points I made.
I admit, I have not read through the entire thread. But here, since it seems to be relevant, is a link to an explanation/discussion of the Aquinas arguments under discussion:
It’s by Peter Kreeft, a professor of philosophy who has written books on Thomas Aquinas (A Summa of the Summa) and Christian apologetics.
I don’t think it brings anything new to the thread that hasn’t been said before, and I don’t think it’ll win anybody over who isn’t alredy convinced, but it does lay things out fairly clearly.
Personally, though I believe in God I find these particular arguments less than decisive. An uncaused universe-as-a-whole is hard to swallow, but no more or less so than an eternal, Unmoved Mover. I know things don’t just pop into existence by themselves at the normal scale of human experience, but I can’t say for sure that they never could have, even at a subtomic level. And an infinite chain of causes stretching backwards through time seems impossible, but I hesitate to trust my intuition to tell me what really is impossible.
The difference is that no-one is claiming that you an process through an infinite set of numbers. Do you claim, for instance, that it is possible to add all natural numbers? The claim that the universe is eternally existant requires both that:
- An infinite chain of events exists
- That the enitre chain has been processed through to reach the current point.
It is point two, necessary in the definition of an infinite universe that I have a problem with. This point is not necessary if you just want to say that an infinite number series exists. Saying that the universe is eternally existant is like saying that you have found the sum of all natural numbers, not just that those numbers exist.
Calculon.
An infinite amount of events happening does seem extremely unlikely. Unless you have an infinite amount of time in which they can occur.
I would say that in this context identity is not significant. Becuase the conclusion is the premise, the conclusion cannot flow from the premise.
With your new arguemnt, if I was being flippant I would say that not all roses are red cite, and so premise 2 is faulty, but then you would just re-phrase it to “one or more roses are red”. Even still if you think about it you can construct an argument against premise 1. An example may be:
- Since God is, by definition eternal, anything that demonstrates the existence of God must be true for all known time.
- There was a time in the past when red roses did not exist.
Therefore:
Red roses cannot prove the existence of God.
That argument may or may not be a good one (especially since I am tired), and I am not sure I even accept premise 1 myself, but at least it adds to the conversation. Just merely stating, without reason, that you don’t believe an argument because a premise feels wrong is really just a cop-out.
Calculon.
BTW, I am sorry if you feel I am ignoring you, but a lot of people are replying to me, and I was feeling overwhelmed with the number of different topics that were in play. I felt that the only way I could really continue this was to focus on one or two points at a time. Perhaps you could pick one point to start with, and we can hash them out one at a time?
To be clear, this is not the definition of “God”, but a presumed aspect of the god you worship. Other gods are worshipped, and other people have different ideas about the god you worship.
Oh, I don’t know about that; everything follows from itself, so if I’m allowed to assume everything, plainly, everything follows.
Yet having to accept every premise means to have to accept faulty logic: if one premise is not proven to hold, the whole argument is not proven to hold, though it could be by validating the premise; if one premise is unprovable, the whole argument is invalid (or valid only under the assumption that the premise holds, i.e. when taken the premise as an axiom). Logic is a great framework for deductive reasoning, but it still suffers from garbage in, garbage out. Thus, the proponent of some argument will have to demonstrate the validity of his premises if they are called into question (just like you called the validity of my premise into question); otherwise, the premises are accepted as axioms, and can be just as well rejected.
As for my mammoth-post, feel free to just take on the points in the order they are in the post, one at a time, if you wish; I don’t think there’s really any that necessitate earlier answering than others.
I don’t see the evils “caused by religion” as necessarily a religious problem. And I think that many of the “No reason to believe in God,” “You’re an idiot if you do,” “I’ve seen no evidence so YOU shouldn’t believe either,” camps are often just as irrational. They seem to demand utmost logic, but I’ve see no evidence that they have passed beyond the “god doesn’t exist” premise.
Ok, so you’ve decided to be an athiest. God doesn’t exist. Great. Now what? Shout it loud and vehemently? Or think for a second about what it means you should do with your life? Let’s say you’ve actually decided to logically follow this assumption to a conclusion…
God doesn’t exist. What do this mean about the reason for existance. Naturally, (pun intended,) it means the only reason to exist is to survive to pass on your genes, and to give those offspring the best possible chance of survival, i.e. resources. Now, nature has developed many ways to do this that all work, but it wasn’t decided rationally, and they developed for the survival of a species, not individuals. The human species cooperated to survive, but this wasn’t always to the benifits of individuals. Rationally, you want YOUR genes to survive. And the best result for an individual always comes when everyone else cooperates, and he is free to do whatever he wants. You want others to follow the rules: (not kill YOU, not take YOUR stuff,) but you realize that if you have other people’s stuff, you would be better off. (as long as there are no consequences, so you always look for that opportunity where the risks are minimal and rewards high.)
Possibly, the best athiest ever was Genghis Khan. (doesn’t even matter whether he believed in a diety, belief is irrelevant to being a good athiest.) He amassed a vast empire of resourses to rear his children, forced everyone else to cooperate to his survival, and then produced offspring so prodigiously, that 1 in every 200 people on the planet appear to be decended from him.
Other good athiests? Your Carnegies, your Rockefellers, people who built vast fortunes on shady dealings then turned respectable. People who lobbied to SET the rules to their advantage, like the bankers of today who let others take the risk, walked away with 100s of millions in personal wages, and now are getting more money as “bail outs.”
Oh, and another way to be a good athiest, get the best possible outcome for yourself? (and the reason I don’t see the “evil of religion” as necessarily a religious problem,) Set up a religion, (or get to the top of an existing one.) You’re not going to be sent to jail for bilking your “flock,” as your system can’t be disproven. You can get them to give you millions, promote the societal cooperation you need, and do whatever you want. Even if you’re caught impregnating another man’s wife, there are almost no repercussions, except having to walk away with your millions. boo hoo.
Many of the athiests, and I believe I’ve seen Der Trihs among them, speak out against these religious leaders as examples of bad theists. But, I just see them as examples of good athiests.
That only applies if you’re going to speak out so vehemently against irrationality. You better have thought through your own position, rationally.
Now, I’m a firm believer in irrational beliefs. The placebo effect is an IRRATIONAL belief in the power of medicine above and beyond what it is actually capable of. And as medicine improves and our belief in it increases, the effect becomes more and more profound. If you believe that medicine can do more for you than it actually can, you have a much better chance to survive.
But many vehement athiests seem to have one of the worst irrational beliefs: an irrational belief in what science can accomplish. Don’t despair, many scientists are ignorant of the limits of science, but an irrational belief in its capabilities doesn’t allow it to accomplish things it actually can’t. And a logical, scientific theory of the universe can never be complete.