Skeptics "reasoning" applied to mathematics

[Brant Gaede]

Everyone thinks he knows something. She knows she does.

--Brant

[Daniel Barnes]

Stephen writes:

>Do readers here think that the Epicurean argument is sufficient to defeat Hume's argument?

I suppose it depends on whether you think that "that the senses cannot be refuted." I think the senses clearly can be mistaken, as we debated on another thread. I agree with the Popperian non-authoritarian theory of knowledge. That is, there is no final, authoritative source of knowledge, including the senses (which are nonetheless generally reliable).

The fact that we realise an optical illusion is an illusion is an example of just what Hume is saying: we "correct the first judgment, deriv'd from the nature of the object, by another judgment, deriv'd from the nature of the understanding". In other words, an example of a refutation of sensory information via reason, which in turn lets us "see" the reality of the situation.

>What further failings of this particular Humean argument are exposed by Rand's metaphysics and epistemology, beyond the failure signaled by Lucretius?

The failings appear to be in Lucretius' argument, it appears to me. Likewise I do not know of anywhere that Rand successfully answered Hume; she admitted she had not even begun to think about the problem of induction (at least by the time of the ITOE), let alone answer it.

Where in your opinion does she expose Hume's errors, and which ones?

[Guyau]

Daniel, you write: "The fact that we realise an optical illusion is an illusion is an example of just what Hume is saying: we 'correct the first judgment, deriv'd from the nature of the object, by another judgment, deriv'd from the nature of the understanding'."

That is not the end of the new corrective examinations, according to the argument of Hume that I quoted above. For any judgment you take as true---say your judgment that you are sitting---Hume bids you consider how often you've made mistakes in the past. Then your present judgment should be uncertain. Now, think of that newly become uncertain judgment that you are sitting, and consider how often you've made mistakes in the past. Then your present uncertain judgment should be even more uncertain. Repeat again and again, and the original judgment, however certain at the start, becomes, under this scrutiny of reason, entirely uncertain.

That is Hume's argument from local reasonable corrigibility to complete skepticism.

What is wrong with that argument?

Hume's skeptical arguments concerning the rationality of induction are another matter. They are not what Hume is arguing in the argument above.

I have treated Hume's arguments concerning induction elsewhere, bringing Rand's philosophy into the analysis and resolution of his errors on that topic. That is in my 1991 essay "Induction on Identity" in V1N3 of Objectivity, which you may now read at Objectivity Archive (www.objectivity-archive.com). I will show the ABSTRACT for that essay below, for you to see if you would like to check it out. But right here, I'm trying to understand what all is wrong with Hume's argument for general skepticism given above.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

ABSTRACT

"Induction on Identity" by Stephen Boydstun

Part 1 - Volume 1, Number 2, Pages 33-46

The Aristotelian and Leibnizian roles of non-contradiction and identity in metaphysics and in deductive logic are reviewed. Beyond those roles, Boydstun proposes that Rand's existential law of identity can fully justify inductive inference.

The two types of induction articulated by Aristotle are rehearsed. These are the abstractive induction and the ampliative induction. Rand had noted that the integration of facts into concepts is a type of induction. This is abstractive induction à la Rand, and Boydstun resolves this type into two components: the bare recursive induction we use in mathematical induction and the ampliative induction needed for the construction of concepts adequate to the concrete existents in the world.

Part 2 - Volume 1, Number 3, Pages 1-56

Boydstun examines the critiques of the rationality of induction put forth in the fourteenth century by Nicolaus of Autrecourt and in the eighteenth century by David Hume. The stage for Nicolaus was set by Ockham. On this stage were the metaphysical and logical platforms for arguing that there can be no logically necessary connection between distinct existents. Nicolaus' hour on the stage articulates how to hold fast to identity, non-contradiction, and the existential presentations of immediate perception, while barring any logically justifiable inference to the existence of material substance. Boydstun disputes Nicolaus' account of our experience of substance and of our rational inferences to the existence and character of substance not directly experienced. The defense of our knowledge of substance here marshals logical considerations, findings of modern developmental psychology, and the history of modern science.

Hume's accounts of our experience of cause and effect and of our reasonings to cause or to effect are closely examined and roundly criticized. Various statements of the law of causality in the history of philosophy are recounted and assessed, with due consideration of modern physics. A version of the law of causality logically supportable by Rand's rich principle of identity is formulated. It does not require that in a given circumstance a given kind of thing could do only the same single thing on repeated trials. It is argued also that Rand's principle of identity is the broad base of Mill's methods of induction and of the hypothetico-deductive method of science.

Beyond the corrected law of causality, Boydstun formulates a "principle of substantive propagation." This is an application of Rand's principle of identity to all alteration and constancy in time. He argues that the principle of substantive propagation is a fundamental justified justification for our inductive causal inferences and indeed all of our modes of scientific explanation. He concludes with a proposal of how predication can be cast as a triple-identity abstract form, a derivative of Rand's fundamental thesis that existence is identity.

Edited May 3, 2007 by Stephen Boydstun

[Dragonfly]

That is not the end of the new corrective examinations, according to the argument of Hume that I quoted above. For any judgment you take as true---say your judgment that you are sitting---Hume bids you consider how often you've made mistakes in the past. Then your present judgment should be uncertain. Now, think of that newly become uncertain judgment that you are sitting, and consider how often you've made mistakes in the past. Then your present uncertain judgment should be even more uncertain.

I can't follow that step. That you may conclude on the basis of errors in the past that your present judgement isn't certain either is logical, but why should it be even more uncertain? That somehow suggests that your errors in the past are added or multiplied, but I see no reason for that. The opposite is more likely, namely that increasing knowledge will make it more likely that the last judgement is correct, like in the process of trial and error, or honing in on a target, your judgements are in general no random statements, but based on accumulated knowledge.

[BaalChatzaf]

If Fermat had a proof of his theorem, as he claimed, it didn't take hundreds of pages. So if a shorter proof could be found, that would be interesting to say the least.

--Brant

Most likely, Fermat did not have a correct proof of his theorem (it was actually a conjecture until Wiles nailed it down). It is highly unlikely that mathematical proposition that required some very high powered techniques would yield to elementary methods (Fermat did not even have analysis or calculus). To this day, no one has come up with a valid elementary proof of FLT.

Bob Kolker

[Guyau]

Dragonfly,

I am pleased to see that you think Hume's argument must be incorrect and that you will join us in diagnosing its failures.

I quite agree with your counter to Hume's argument. I think, however, he can just dig in his heels, and say that no matter how solid we have made some judgment by corroboration with other experience, it remains that one has made errors in the past and could be making one now, in one's well-supported judgment. And when one realizes that, the well-supported judgment is more uncertain than before. He will insist that one must, by reason, take the now more uncertain judgment and recall again that one has made errors in the past, and this multiplies the fractional probabilities of correctness on and on down to zero. Yes, he is taking the probabilities of correctness to be multiplied, as you will see from his full text in this section, if you have it handy.

Consistent with your objection, I would add that it is not a requirement of reason that one consider in some vague hand-waving way that one may be making an error. Reason in Rand's sense requires that one consider the specific and particular ways that one might now be making an error. Existence is identity, specific and particular. Errors are part of existence.

Stephen

Edited May 3, 2007 by Stephen Boydstun

[Daniel Barnes]

Dragonfly, I agree with Stephen's counter to your counter. Hume can just dig his heels in. But we can see how this can be easily overcome later.

In terms of Stephen's objection,

>I would add that it is not a requirement of reason that one consider in some vague hand-waving way that one may be making an error. Reason in Rand's sense requires that one consider the specific and particular ways that one might now be making an error.

But there are any number of ways humans might err; through emotional bias, through carelessness, through lack of imagination, through repetition dulling awareness, overfocus on detail ("not seeing the forest for the trees"), through missing a step in reasoning without realising it, through a simple sensory lapse, and of course, the famous Rumsfeldian "unknown unknowns"..and so on. These possibilities are present at all times in human intellectual endeavour; that is to say, these possibilities are real. They cannot be dismissed as mere "handwaving", but are important caveats to all our knowledge. All these errors have led to serious problems in countless situations. How much more "specific" and "particular" do they need to be?

After all, we may, and do, put an immense amount of effort in to consider the "specific" and "particular" ways one might now be making an error, but from this it does not follow that we have not erred. Further, from acknowledging the above, what does follow is not that as is often claimed, we are somehow helpless or prevented from acting, but merely that we should always act with some caution, bearing our limitations in mind.

Does this mean we can't know anything? Only if you mean "knowledge" in a kind of Platonic sense; that which is absolutely certain and eternally immune to any possibility of overthrow or correction. This is the kind of knowledge Humeanly impossible, to coin a phrase...;-)

However, if you mean "knowledge" as that which is hypothetical, that which always contains at least the possibility of being false, then I agree, Hume's various objections (and his checking of the checking of the checking in the quest for "absolute certainty" etc) become disposable. This is perhaps what Rand was shooting for with her resort to oxymorons such as "contextual certainty", "contextual absolute" etc

I suspect some strong underlying agreement here, despite the radical divergence between this position and Rand's rhetoric. Stephen, Fred Seddon recently formulated Rand's theory of knowledge in just such a hypothetical sense: that one may know P, but P may be false. Would you agree this is an accurate summary?

If so, how does Rand's theory of knowledge differ in any important way from a skeptic such as Karl Popper's, who also maintained one may know P, yet P may be false?

Was Rand really a skeptic, yet, with no little irony, did not know it?

>I have treated Hume's arguments concerning induction elsewhere, bringing Rand's philosophy into the analysis and resolution of his errors on that topic.

Many thanks, I will read your article with interest. As Rand clearly stated she didn't solve the problem of induction, so perhaps once again, with no little irony, she solved it without knowing it?...;-)

[Guyau]

Hi Daniel,

Rand's conception of knowledge would not square with a conception in which one could know that P, but P is false. Rather, her conception is more in the classical mold, such as you find upheld in Nozick's 1981 Philosophical Explanations: To know that P requires that P be true, plus further conditions that must be satisfied.

In Rand's system, her philosophical axioms are not simply ultimate hypotheses. On this, check out my article "Ayn Rand Society 2005 - Paper 1" at RoR.

Karl Popper was not a skeptic in the philosophical sense that Hume means, neither a mitigated skeptic nor a radical skeptic. Likewise, Popper's American predecessor, Charles Sanders Peirce, was not a skeptic.

Stephen

Edited May 3, 2007 by Stephen Boydstun

[Daniel Barnes]

Stephen:

>Rand's conception of knowledge would not square with a conception in which one could know that P, but P is false. Rather, her conception is more in the classical mold, such as you find upheld in Nozick's 1981 Philosophical Explanations: To know that P requires that P be true, plus further conditions that must be satisfied.

Yes I would tend to agree. I strongly criticised Fred Seddon's interpretation myself, but nonetheless was curious to see what others thought, in case I was wrong.

I, along with many others, would definitely call Karl Popper a skeptic, and a radical one, and put his Critical Rationalism firmly in the skeptical tradition of critical enquiry. But this is a merely terminological disagreement, and unimportant.

[Michael Stuart Kelly]

Although less technical than the discussion of Hume now underway, I made a post on another thread that I believe has bearing here.

I am becoming increasingly aware of two types of knowledge: the philosophical and the scientific. Although this might sound superficial, there are some fundamentals I have discerned.

Let's call philosophy the identification of entities at the mid-range level of observation. This means at the level of observing the world with eyes, ears, nose, tongue, skin, and the other organs of primary awareness (for things like gravity), with a brain to process and identify it all, and without any instruments. There is only one basic means of obtaining this knowledge: observation and using both induction and deduction. (There is seed-like pre-wiring in the brain for things like affects for some basic knowledge, but that is not what I am discussing here.) Induction is more basic for this form of knowledge (philosophy) due to the size limitations of information input and survival requirements of our very beings.

When philosophy tries to use deduction from principles to explain many things other than entities, you often get absurdities like postulating that the universe is finite or that there is ultimately a basic "stuff" at the bottom of the reduction chain. Neither of these things are known as fact, yet going the philosophy route, I have seen them both postulated as absolute truths. Both expansionism and reductionism can go on infinitely as far as I am able to discern.

I am reading OPAR right now and I have come across where Peikoff postulated a basic "stuff" at the bottom while scoffing at it as if it were a replacement for philosophy, calling this basic stuff "puffs of existence." How does he know that he will get to a bottom? He doesn't. Here merely projects from a philosophical principle that what he does know about all entities is that they have a specific size.

Then we get to scientific knowledge, which uses induction to derive hypotheses, but deduction to carry out the work of breaking up parts of entities, verifying their properties and forming new ones. This entails devising instruments to vastly expand our mid-level forms observation both outward and inward. This has produced outstanding results. Science is deduction heavy, but the truth is that without induction, there would be no formation of intelligent hypotheses. In fact, you do see this problem in the science world at times with some absolutely bizarre experiments, the outcome of which any child would be able to predict. This gets really wacky when induction is removed from experiments of social behavior.

I have seen the science be-all-and-end-all itch need to be scratched and some strange theories formed like the big bang or the string theory drawn up to explain the start of the universe from principles belonging to subparticles. These are and can be nothing but speculations based on selectively massaging data and math.

I have yet to see anything from this approach that convinces me so far on how subparticles decide to stop interacting to create new stuff and a complete entity finally gets formed. (I speak metaphorically for simplicity of understanding.) What causes them to stop? This especially gets tricky with life. Why stop at one point and get a tiger or a bacteria, for instance, instead of another and get a super-duper tiger or bacteria with many more characteristics? But the fact is that specific entities with specific characteristics not only get formed, they are formed as a fact and we encounter them as they are, not as they were before being formed.

The "deductive knowledge only" approach is not of much use when a man encounters a tiger in the woods. He knows from induction that all tigers eat people if they are hungry, so he runs like hell and survives. His knowledge is correct and absolutely true for that purpose. Yet going the scientific route only, you put aside the danger and wonder if all tigers eat people and how to test for falsifiability.

Dum-da-dum-dum. End of query.

(To be fair, if you use induction, make provisions against the danger and have a sufficient number of enemies at hand that you have captured, you can test this knowledge for falsifiability. I don't know what use that knowledge would be if it is found that one tiger or another does not eat a person when hungry and when your enemy is offered to it on a plate, but I suppose it is possible to make the experiment and prove something, sort of.)

Both forms of knowledge not only complement each other, they are both essential to survival and to further understanding the universe. I see proponents of each side constantly clash with each other by mixing up the different functions. Science states that so long as we can keep reducing elements, we cannot know anything for sure and all knowledge potentially can be overturned. This is true. Technology is proof. Philosophy states that we must be able to know some things with absolute certainty about entities in order to survive at all. Tigers will always eat people when they are hungry if nothing else is available and a person is at hand. Your life depends on you knowing that if you ever come across a tiger.

Both positions are correct.

The mistake I see is science-trumps-all people trying to use knowledge arrived at deductively and tested under controlled conditions to replace and invalidate entity-level knowledge. It can't. Tigers eat people regardless of any falsifiability experiment. And the philosophy-trumps-all people constantly make huge mistakes through oversimplification by applying entity-level knowledge as absolute to reduced parts (or even to agglomerations on a macro level), thus going to the absurd length of telling science that what has been observed doesn't exist.

One can point to logical fallacies in both positions. But the truth of the matter is that one form of knowledge is not more important than the other as a universal law—only specific items of knowledge can be compared. Philosophy and science overlap and complement each other. Sometimes philosophy holds more weight (like fundamental axioms) and sometimes science turns entity-level knowledge on its head, like quantum physics. The world is a better place for human beings because of knowing both.

I think that a true defense of reason will postulate the proper identification and use of both methods, induction and deduction, without this silly competition.

Michael

[Rodney]

complement

[Dragonfly]

I have seen the science be-all-and-end-all itch need to be scratched and some strange theories formed like the big bang or the string theory drawn up to explain the start of the universe from principles belonging to subparticles. These are and can be nothing but speculations based on selectively massaging data and math.

String theory is certainly highly speculative, but that is not true for the big bang, that is a theory that is very well verified. Where did you get the notion that scientists are "selectively massaging data"? Can you give any example in this case? Or is it just Peikoff's bullshit that you have swallowed?

[Michael Stuart Kelly]

Can you give any example in this case? Or is it just Peikoff's bullshit that you have swallowed?

Dragonfly,

Nah. It comes from the fact that there is no possibility of making any controlled conditions to falsify. Beginning of universe speculation is nothing but speculation by the very nature of human limitations. Maybe one speculation is better than another because of a higher degree of deductive conformity with observations of other things, but it is still speculation.

Does anyone have any kind of real proof that the universe started at some point?

Michael

[Michael Stuart Kelly]

complement

Rodney,

Thank you. I looked it up and changed my post (in both places). That's one that fell through the cracks and I had not learned yet.

Michael

[James Heaps-Nelson]

Can you give any example in this case? Or is it just Peikoff's bullshit that you have swallowed?

Dragonfly,

Nah. It comes from the fact that there is no possibility of making any controlled conditions to falsify. Beginning of universe speculation is nothing but speculation by the very nature of human limitations. Maybe one speculation is better than another because of a higher degree of deductive conformity with observations of other things, but it is still speculation.

Does anyone have any kind of real proof that the universe started at some point?

Michael

There is good evidence, not proof: the 3 degree Kelvin background radiation that is uniform throughout the sky, the overabundance of light elements like hydrogen and helium and the Hubble redshift. It is somewhat unfortunate that the Big Bang theory has reached such a level of dogma that dissident astronomers such as Halton Arp have been persecuted, but it is not an untestable theory like superstrings.

Jim

[James Heaps-Nelson]

By the way, Michael, if you are interested in such topics as superstrings and some other esoteric theories, there is a terrific book out for the layman which lays out modern physics from Maxwell to Einstein through the most recent theories, it is Warped Passages by Lisa Raymond. She is a highly accomplished physicist and gets the science right.

Jim

[Michael Stuart Kelly]

Jim,

I looked it up and skimmed a couple of articles: The Big Bang Theory from an old Nasa site. From the article:

The big bang was initially suggested because it explains why distant galaxies are traveling away from us at great speeds. The theory also predicts the existence of cosmic background radiation (the glow left over from the explosion itself). The Big Bang Theory received its strongest confirmation when this radiation was discovered in 1964 by Arno Penzias and Robert Wilson, who later won the Nobel Prize for this discovery.

Although the Big Bang Theory is widely accepted, it probably will never be proved; consequentially, leaving a number of tough, unanswered questions.

I have no problem with "tough, unanswered questions." That is a perfectly scientific statement as I know it and respect it.

Here is another: Big Bang Theory - An Overview. From the article:

According to the standard theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. What is a "singularity" and where does it come from? Well, to be honest, we don't know for sure. Singularities are zones which defy our current understanding of physics. They are thought to exist at the core of "black holes." Black holes are areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squished into infinite density (a mathematical concept which truly boggles the mind). These zones of infinite density are called "singularities." Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something - a singularity. Where did it come from? We don't know. Why did it appear? We don't know.

. . .

According to the many experts however, space didn't exist prior to the Big Bang. Back in the late '60s and early '70s, when men first walked upon the moon, "three British astrophysicists, Steven Hawking, George Ellis, and Roger Penrose turned their attention to the Theory of Relativity and its implications regarding our notions of time. In 1968 and 1970, they published papers in which they extended Einstein's Theory of General Relativity to include measurements of time and space.1, 2 According to their calculations, time and space had a finite beginning that corresponded to the origin of matter and energy."3 The singularity didn't appear in space; rather, space began inside of the singularity. Prior to the singularity, nothing existed, not space, time, matter, or energy - nothing. So where and in what did the singularity appear if not in space? We don't know. We don't know where it came from, why it's here, or even where it is. All we really know is that we are inside of it and at one time it didn't exist and neither did we.

[Go to the link for the footnotes.]

That word, singularity, is one hell of a word, isn't it? Why does it sound like God to me? Maybe because it is a concept for something that exists but does not exist? And something that is nothing, but which created all the rest? That's a pretty shaky premise if that is the end-point of deducing things from observation wedded to the Theory of Relativity.

How about getting back to some fundamentals? When science is used to prove that something can be nothing, it has stepped outside of human knowledge and entered religion or the worst there is in philosophy.

And look at that itch I talked about above being scratched! After all those "we don't know" statements to give the appearance of objectivity, look at the very last line of the quote:

"All we really know is that we are inside of it and at one time it didn't exist and neither did we."

All we really know??? What is this guy talking about? If he had written "All we really SPECULATE is that we are inside of it and at one time it didn't exist and neither did we," that would have been correct. This is a perfect example of science trying to be philosophy.

And for the record, I am not getting this notion from Peikoff. His thesis is to debunk all of cosmology to prove the superiority of philosophy. My thesis is to make use of both forms of knowledge: philosophical and scientific to complement each other.

Here is the Wikipedia article: Big Bang. This article was way too long for me to do anything by skim it under my present time constraints, but here is a quote that did jump out at me:

Huge advances in Big Bang cosmology have been made since the late 1990s as a result of major advances in telescope technology as well as copious data from satellites such as COBE, the Hubble Space Telescope, and WMAP. Cosmologists now know many of the parameters of the Big Bang model quite precisely, and have made the unexpected discovery that the expansion of the universe appears to be accelerating (see dark energy).

Accelerating? Hmmmm...

I have a proposal. Let's call it the MSK Outsucker Hypothesis. Instead of the universe expanding from a core that never existed (a "singularity"), how about it being sucked outward in all directions as if it were in a bell jar or globe? That would be one explanation for the acceleration. What sucks it (or draws it) doesn't have to exist, either, and we can call it a "totality." I am sure some calculations can be made to prove this.

Michael

[James Heaps-Nelson]

Michael,

I'm certainly willing to accept the tough, unanswered questions language. The Big Bang is among theories that describe the what, but not necessarily the how and the why. Should that be surprising? Also a singularity is simply scientific language for describing an object that is so massive that gravity has overcome the strong nuclear force and shrunk the object to an infinitesimal size. Do we know what is in there? Of course not, we'll never know, however astronomers view these objects all the time.

Jim

[Dragonfly]

Nah. It comes from the fact that there is no possibility of making any controlled conditions to falsify.

Falsifying a theory doesn't necessarily need controlled conditions. We know for example quite well what happens in the sun and in other stars and we can predict how they'll evolve, even if we are not able to put a star in a laboratory under controlled conditions. One of the most solidly proved theories is the theory of evolution; we may quibble about details of the mechanism, but the evidence that evolution has happened on earth from single cells to complex animals like humans (theory of common descent) is so overwhelming that only an idiot can doubt it, even if we are not able to test "macro"-evolution under controlled conditions, as we just don't have the time for it.

Beginning of universe speculation is nothing but speculation by the very nature of human limitations. Maybe one speculation is better than another because of a higher degree of deductive conformity with observations of other things, but it is still speculation.

In biological terms: you are confusing evolution with abiogenesis. We know fairly well what happened in the big bang after a very tiny fraction of a second, but what happened "before" the big bang or the question if there even is a before, is of course speculative. But what happened afterwards is solid science.

[Michael Stuart Kelly]

Also a singularity is simply scientific language for describing an object that is so massive that gravity has overcome the strong nuclear force and shrunk the object to an infinitesimal size.

Jim,

I can accept that—that some of these points exist within the universe.

But that's not what I read. I read that the whole universe was squeezed into a singularity as a starting point. Did I misunderstand that? If not, this means and can only mean that this singular singularity existed outside of the universe, so there was another universe in which it existed. Otherwise it would not have existed. That's not only poor science, that is poor philosophy as well.

Excuse me for saying the emperor has no clothes on with this kind of theory, but there it is. We get to the point of God—if God created the universe, who created Him? If the universe once fit into a singularity, where did that singularity fit? We are not within the realm of knowledge anymore. We have moved into the realm of arbitrary opinion.

I see no reason whatsoever to postulate a beginning of time from a time without time and that kind of contradiction except as daydreaming. I do find value in the calculations, as in the black holes within the universe. I don't find value in using them to promote daydreams as "plausible" fact, as in a universe before this one holding a singularity of all that will be. Why not call it Heaven and be done with it?

Michael

[Michael Stuart Kelly]

We know fairly well what happened in the big bang after a very tiny fraction of a second, but what happened "before" the big bang or the question if there even is a before, is of course speculative. But what happened afterwards is solid science.

Dragonfly,

What I read was not solid science, but solid calculations from the Theory of Relativity.

Michael

[Dragonfly]

What I read was not solid science, but solid calculations from the Theory of Relativity.

And the theory of relativity is solid science.

[James Heaps-Nelson]

Michael,

It's nothing too hard to imagine. Suppose all of the matter in the universe had enough mass to overcome its outward expansion and gravitationally attract back together. It would form a supermassive object very much like a black hole that contained everything in the universe. Now, what would happen from the resultant explosion (or by star analogies: supernova)?

Jim

[Michael Stuart Kelly]

It's nothing too hard to imagine.

Jim,

Neither is God.

Michael

[Michael Stuart Kelly]

And the theory of relativity is solid science.

Dragonfly,

So? So have been other theories in the past like Newtonian physics. That doesn't make them explain things like quantum physics.

Is the Theory of Relativity the proper standard for proving that the universe had a beginning?

Michael