Bayesian Reasoning: Is it reasonable?

[Cure_of_Ars]

My understanding is that Bayesian reasoning assigns a probability for the evidence against a theory but also the evidence for a theory. By doing this they claim to be able to tell how likely something is true. How can this be taken seriously in regards to things that we have little data for? Where do they get the numbers for probability? Seems to me that they are pulling numbers out of thin air.

I have seen Bayesian reasoning used in regards to a theory that there are many different worlds and that there is not a God so I think this stuff is relevant to Catholic Apologetics.

 

[SeekingCatholic]

My understanding is that Bayesian reasoning assigns a probability for the evidence against a theory but also the evidence for a theory. By doing this they claim to be able to tell how likely something is true. How can this be taken seriously in regards to things that we have little data for? Where do they get the numbers for probability? Seems to me that they are pulling numbers out of thin air.

This is not what Bayesian reasoning is. Bayesian reasoning is entirely sound. It shows how the probability of a theory being true changes in the presence of new data.

In a nutshell: P(M|D) = P(D|M)*P(M)/P(D)

where P(M|D) is the probability of the model given the data (called the posterior probability), P(D|M) is the probability of the data given the model (called the likelihood), P(M) is the probability of the model before the data (called the prior probability) and P(D) is the probability of the data (called the evidence). This result is a tautology from probability theory, called Bayes’ Theorem. Similar kinds of mathematics allow comparison of two different models.

Of course in many cases the prior probability, or likelihood of the data under various models cannot be known exactly; however, they can often be reasonably estimated, leading to a range of posterior probabilities. If there is not much data to be had, than the posterior probability will not change much from the prior.

I have seen Bayesian reasoning used in regards to a theory that there are many different worlds and that there is not a God so I think this stuff is relevant to Catholic Apologetics.

It is entirely relevant to Apologetics. In fact as far as I can see it is the biggest challenge for Apologetics. To claim proof for any model from the data (which equals 100% posterior probability) by the math you can see that the only way this can happen is if the likelihood of the data under any other possible model is zero (conversely, you must have zero likelihood to have disproof of a model). Or, you must have a zero prior probability for those models for which there is a non-zero likelihood of the data - but that’s “cheating” in a sense - the model isn’t disproven from the data but is deemed impossible a priori. All the Thomistic “proofs” for God’s existence are “cheats” in precisely this sense - alternative models are simply ruled out a priori, despite the claims to an a posteriori proof.

 

[ForwardProgress]

I know it works great for SPAM detection!!

 

[Cure_of_Ars]

Thank you for your response SeekingCatholic. This topic is clearly beyond my current knowledge base but I won’t let it stop me from asking more questions. I read somewhere that someone concluded, by use of Bayesian, that the probability of God’s existence was 50% because God exists or he doesn’t exist meaning only 2 priors (I think thats the proper term for this). Then others claimed that this was wrong because there are many different possible gods, spaghetti monster, Thor, Zeus, up to an infinite possible gods making the probability of God’s existence minute.

My question is does St. Anselm’s definition of God, "God, by definition, is that than which a greater cannot be thought” place things back to only 2 priors?

 

[SeekingCatholic]

Thank you for your response SeekingCatholic. This topic is clearly beyond my current knowledge base but I won’t let it stop me from asking more questions. I read somewhere that someone concluded, by use of Bayesian, that the probability of God’s existence was 50% because God exists or he doesn’t exist meaning only 2 priors (I think thats the proper term for this). Then others claimed that this was wrong because there are many different possible gods, spaghetti monster, Thor, Zeus, up to an infinite possible gods making the probability of God’s existence minute.

This could be an argument over what the prior probability of God’s existence should be, but it cannot be a conclusion by use of Bayesian reasoning, which would be a posterior probability.

My question is does St. Anselm’s definition of God, "God, by definition, is that than which a greater cannot be thought” place things back to only 2 priors?

Either this being exists, or he doesn’t. But that doesn’t mean the prior is 50%. If St. Anselm’s, or any other a priori argument is correct, the prior is 100%. If not, the prior might in fact be very low. Not zero, however; his existence is not logically impossible.

But the Thomistic arguments are of no help whatsoever here. Meaning, they are, in fact, cleverly disguised a priori arguments. For instance, the fact that beings are in motion is perfectly well explained by an infinite regress of motion. The Thomist must argue to a prior impossibility of such a regress.

 

[Cure_of_Ars]

I was able to find where I read the 50% probability.

Note that although this is receiving much attention now, quantifying one’s judgments for use in Bayesian calculations of the existence of God is not new. Richard Swinburne, for example, a philosopher of science turned philosopher of religion (and Dawkins’s colleague at Oxford), estimated the probability of God’s existence to be more than 50 percent in 1979 and, in 2003, calculated the probability of the resurrection [presumably of both Jesus and his followers] to be “something like 97 percent.” (Swinburne assigns God a prior probability of 50 percent since there are only two choices: God exists or does not. Dawkins, on the other hand, believes “there’s an infinite number of things that some people at one time or another have believed in … God, Flying Spaghetti Monster, fairies, or whatever,” which would correspondingly lower each outcome’s prior probability.) In reviewing the history of Bayes’s theorem and theology, one might wonder what Reverend Bayes had to say about this, and whether Bayes introduced his theorem as part of a similar argument for the existence of God. But the good reverend said nothing on the subject, and his theorem was introduced posthumously as part of his solution to predicting the probability of an event given specific conditions. In fact, while there is plenty of material on lotteries and hyperbolic logarithms, there is no mention of God in Bayes’s “Essay towards Solving a Problem in the Doctrine of Chances,” presented after his death to the Royal Society of London in 1763 (and available online at www.stat.ucla.edu/history/essay.pdf ). Scientific American

Isn’t there an infinite number of possible models that can explain any data, and I think this would apply no matter what the data is? I guess this is where the probability of the data weighs in. It seems to me that we do not have access to direct data in reference to God to be able to consider the probability of the data and because of this Bayesian calculations can’t be used in reference to God. But saying this I know that I don’t have my head wrapped around how Bayesian works.

 

[SeekingCatholic]

I was able to find where I read the 50% probability.

As I thought, this related to prior, not posterior, probability.

Isn’t there an infinite number of possible models that can explain any data, and I think this would apply no matter what the data is? I guess this is where the probability of the data weighs in. It seems to me that we do not have access to direct data in reference to God to be able to consider the probability of the data and because of this Bayesian calculations can’t be used in reference to God. But saying this I know that I don’t have my head wrapped around how Bayesian works.

Yes, but in certain questions, such as whether God exists or not, there are only two subsets of models to compare, and we can marginalize, or integrate, over all other variables. And yes we can use Bayesian calculations in reference to God with regard to the data we do have.

 

[MindOverMatter]

For instance, the fact that beings are in motion is perfectly well explained by an infinite regress of motion. The Thomist must argue to a prior impossibility of such a regress.

This is not an explanation at all. If there is no other kind of being other then physical being, then we can only suppose an infinite regress. However, this does not justify an infinite regress.

You must explain what you mean by an infinite. A true infinite has no potential, becuase it is already infinite in moments and potential. It has already expressed and infinity of time. If there is an infinite chain of events in the past, then how is it that there is such thing as tommoro? I cannot tranverse an infinite serious of events, becuase it is not a number; there is no numbers. You cannot describe an infinite, other then to say that it has no numbers. It has transversed all numbers, and so cannot be a physical being as such. There is no such thing as a physical infinite. The futures inability to reach an infinite, is proof that the past is finite, since it is impossible that the world is infinite in events and change, but finite in events and change at the same time. It is just a mathematical concept. It is like saying that something is infinetly small; it has no real meaning. Its sounds better to say that something is infinetly small then to say that all things cease to be at some point. Concepts such as Time, moments, change and potential, has no place in an real infinite, becuase they presuppose a beginning; they are all fractions of something. How can you have a fraction of an infinite? You can’t. You can have a fraction of a number such as one, or any number, but it has to be a “finite number”. An infinte regress is meaningless.

 

[SeekingCatholic]

This is not an explanation at all. If there is no other kind of being other then physical being, then we can only suppose an infinite regress. However, this does not justify an infinite regress.

Whatever the validity of your following arguments, you are still arguing to the prior impossibility of an infinite regress. The likelihood of the data (beings in motion) given an infinite regress is one. Thus the argument is a prior philosophical belief, not a conclusion based on evidence.

You must explain what you mean by an infinite.

Again, it is a logical fallacy to say that something is “meaningless” just because a certain concept (such as division) doesn’t apply to it. How do you get a fraction of God?

 

[MindOverMatter]

The concept of “transversal” implies a beginning and an end, but an infinite series has neither, thus the concept is not applicable. However, tomorrow follows after today just as 1 follows after 0, despite the fact that the series of integers is infinite.

An interger has nothing to do with objective reality. The concept of an infinite regress is being applied to objective reality.

certainly does have numbers and can be described.

In the real world, there is no number that can describe an infinite series. We have transversed all numbers, as in to say, we have gone beyond the world of parts.

What “transversing numbers” has to do with being a “physical being” is beyond me.

If there has already been an infinite series of events before this moment in time, then it is contradicting the fact that it is an infinite series. There has already been an infinite series of events, so it is impossible for there to be another event. There can be no time.

If the world does not have a beginning, it is infinite in events and change. It is not finite in events and change at the same time, even if it will eventually have an end.

If there has been an infinite series of events before this time, it is imposible that we can reach this moment without tranversing the infinite.

Again, it is a logical fallacy to say that something is “meaningless” just because a certain concept (such as division) doesn’t apply to it.

Explain why you think it is a logical fallacy. Simply saying it, only gives the illusion that you have an answer.

How do you get a fraction of God?

God has no parts. Therefore you cannot have a fraction of God. The universe has parts, which begin to exist. The question therefore applies

 

[SeekingCatholic]

If there has already been an infinite series of events before this moment in time, then it is contradicting the fact that it is an infinite series. There has already been an infinite series of events, so it is impossible for there to be another event. There can be no time.

Not true. This is mere argument by assertion. Just as if you take the (infinite) set of all negative integers, and claim it is impossible to continue the series, an infinite set of events in the past doesn’t mean there can’t be more events in the future.

If there has been an infinite series of events before this time, it is imposible that we can reach this moment without tranversing the infinite.

A logical fallacy. “Transversal” implies a starting point. Where’s the starting point? A past infinite series doesn’t have one. Reach this moment from where? You have to pick a moment in the past a finite reach ago.

Explain why you think it is a logical fallacy. Simply saying it, only gives the illusion that you have an answer.

Actually you explain it quite well yourself in your next statement.

God has no parts. Therefore you cannot have a fraction of God. The universe has parts, which begin to exist. The question therefore applies

Obviously therefore, you simply cannot negate an entity merely based on the fact a concept does not apply to it.

 

[MindOverMatter]

A logical fallacy. “Transversal” implies a starting point.

Explain.

Where’s the starting point? A past infinite series doesn’t have one. Reach this moment from where? You have to pick a moment in the past a finite reach ago.

An infinite time ago, has no number. Thats why it is illogical to conclude that there is an infinite past and then speak of finite numbers. If there is an infinite past, then there is an infinite number of events, which is in itself contradictory, since “aditional numbers” presuppose a beginning in themselves. You are claiming that the past has an “Infinite number”. Id like to know what that number is, because there is no such thing in my book. You first have to prove that there is such a thing as an infinite past, otherwise, it is completly ligitimate for the Tomist to pressupose that there is a finite number of events in the past; since there is no such thing as an infinite number; only potential infinites. The burden of proof lies on the person that has made the claim, that the past is infinite; since the past is in fact made up of numbers. Untill an infinte is proven, an infinite regress is a meaningless assertion; an illogical attempt to refute an ultimate begining. When dealing with “additional numbers”(which is what we are dealing with), it is a natural inescapable consequence that the past is finite.

I think you and i both know that there is no such thing as an infinite “number”. The past is made up of additional numbers, not intergers. If i am going to speak of an infinite past, i cannot refere to a finite time ago and then add up to this moment. I have to veiw the past in respect of an “actual infinte”. To even talk of an infinite past is to apply numbers to something that has no number at all. You cannot claim that there is an infinite number, and then say that i cannot speak of numbers; since you yourself are claiming that there is an infinite number of something. How can you get to this moment from an infinite time ago. You can’t. If you say my answer is illogical, well so is an infinite regress. You cannot have it both ways. You either have to admit that the past is finite, or admit that it is impossible to reach the present moment form an **infinite number **of moments ago.

The term “Infinte-number”, is meaningless.

Hence forth; this moment in time, is unreachable from a true infinite regress, unless you are speaking of a potentially infinite past. But that doesn’t make any sense. You can for sure, believe that there is a potentially infinite future, becuase you are counting from this point onward, an can go on indefinetly. However, it is an error to count backward from this moment, if in fact there is no beginnning, because we are coming from the past. Therefore my reasoning stands unrefuted. If there is an infinite series of events before this moment in time, then it is unreasonable that we could reach this event, becuase there has already been an infinite amount of time. That is why when we are speaking of an infinite in respect of an actual thing such as the universe, we cannot speak of it in terms of a number of things, since there is no number; like you said.

You are making the mistake of taking a potential infinite, and then reversing it into the past; but if you do that you will always reach a finite number. The past cannot be potentially infinite, unless you count backward from your relative point of veiw in time. Therefore if we are going to apply an infinite to the past, it has to be an actual infinite; in otherwords, we have to tranverse an infinite.

 

[Texas_Roofer]

My understanding is that Bayesian reasoning assigns a probability for the evidence against a theory but also the evidence for a theory…

Probability of a tree developing through evolution? (high)
Probability of a conscious developing through evolution? (very low)
Probability of diversity (in all aspects) developing through evolution? (very low)
Probability of men and woman becoming uniform through evolution? (very high)
Probability of Natural Law developing through evolution? (very low)
Etc.
Etc

So does the sum of the probabilities point toward evolution or creation?

We used Bayesian Statistics in process engineering, the concept was parts are equal so rather than statistically testing the parts to prove them equal we assumed the variation was in the machine producing parts not the parts. This meant the variation was preexisting to the machine. A convention statistical review would say all these assumptions are premature, however a conventional statistician would have needed a million dollars or more to prove through conventional methods that we really knew what we thought we knew. We knew because the Bayesian Statistics ( or logic really) allowed us to improve machines. Some pretty smart people have come to realize proving history to be 99% accurate is less important than say proving a new cancer therapy to be 75% successful. I hope this helps see you have no history to the new cancer therapy so some (Bayesian theory) will imply what they know from other therapy testing to the new therapy even though the new therapy should be different this allows a means to detect early success or failure. Later it all comes out in the wash when new therapy generates its own data which can be backwards analyzed with conventional statistics. So why do Bayesian theory at all? Well in both process (cancer and parts) limited resources (money) had to be used to improve the system so Bayesian logic increased the efficiency of the improvement process.

Hope that is not to confusing

 

[Texas_Roofer]

I was able to find where I read the 50% probability…

It is asked to every statistics students. It is a true statement, and it is a false statement, and that is why it is asked. If you know better the answer is false, if you do not know better the answer is true.

Some believe the chance to win the lottery is 50/50 either you win or you do not win. On a select 5 of 54 balls the statistician uses a 5(factorial) divide by 54(factorial) which without a calculator I think is about 55 million (do not win) to one (win)

So again it is the knowledge of inquirer which determines the degree of answer acceptable to their personal knowledge base

hope that helps

 

[Cure_of_Ars]

Thanks Texas Roofer

So would I be correct to say that Bayesian Statistics is only as good as the data we have gathered?

I can see how Bayesian Statistics can be useful in deciding what direction to proceed in science when there are many different models to try to test. It’s just not definitive in saying what is true or even what is likely because it depends on the data that we have. There is always the possibility to find data that would totally change the probability outcome of Bayesian Statistics.

 

[Cure_of_Ars]

MindOverMatter,
If there has been an infinite series of events before this time, it is imposible that we can reach this moment without tranversing the infinite.

This is only true if time in linear. If time is circular then it is possible. It would mean though that I have already been at this point in time before and that time will in affect go backwards at some point to meet back up to the beginning. Not that I believe this myself. I seems to me that at some point the universe would run out of energy unless the universe is a 100% efficient machine. But I know that it is popular to some who are trying to make a model of the universe that does not require God. Here is an example

sciam.com/article.cfm?id=the-cosmic-origins-of-times-arrow&print=true

 

[SeekingCatholic]

Explain.

“Transversal” implies a beginning and an end by definition. To transverse any path you have to specify the beginning and the end for the term to have any meaning.

An infinite time ago, has no number. Thats why it is illogical to conclude that there is an infinite past and then speak of finite numbers.

No, it isn’t. Anymore than it’s illogical to speak of finite numbers in the set of all negative integers.

If there is an infinite past, then there is an infinite number of events, which is in itself contradictory, since “aditional numbers” presuppose a beginning in themselves.

No, they don’t. We can add additional numbers to the set of negative integers, which has no beginning.

You are claiming that the past has an "Infinite number

". Id like to know what that number is, because there is no such thing in my book.

Aleph-null is of course not a member of the reals or integers, but it is still a “number”. You’re perhaps confusing a set with an infinite number of elements with “infinity” or “negative infinity” being a member of the set. The set of all negative integers has an infinite number (aleph-null) of elements; negative infinity is however not a member of the set.

You first have to prove that there is such a thing as an infinite past

, otherwise, it is completly ligitimate for the Tomist to pressupose that there is a finite number of events in the past; since there is no such thing as an infinite number; only potential infinites. The burden of proof lies on the person that has made the claim, that the past is infinite; since the past is in fact made up of numbers.

All I have to show is the possibility of an infinite past, whereas the Thomist must prove the impossibility of an infinite past. Now if the past is made up of numbers, then if you map the past to the set of all negative integers, you have an infinite past. “Infinity” or “negative infinity” is not a member of this set. There is in fact such a thing as an infinite number in this sense: aleph-null.

Untill an infinte is proven, an infinite regress is a meaningless assertion

; an illogical attempt to refute an ultimate begining. When dealing with “additional numbers”(which is what we are dealing with), it is a natural inescapable consequence that the past is finite.

No, it isn’t, and that claim was refuted above.

You cannot claim that there is an infinite number, and then say that i cannot speak of numbers; since you yourself are claiming that there is an infinite number

of something. How can you get to this moment from an infinite time ago. You can’t.

Of course you can’t, because “an infinite time ago” doesn’t exist. “Negative infinity” is not a member of the set.

If you say my answer is illogical, well so is an infinite regress. You cannot have it both ways.

Your question is illogical. You’re saying you can’t transverse the whole set from beginning to end; whereas the set has no beginning.

You either have to admit that the past is finite, or admit that it is impossible to reach the present moment form an **infinite number **

of moments ago.

Of course it’s impossible, because “an infinite number of moments ago” doesn’t exist.

Therefore my reasoning stands unrefuted. If there is an infinite series of events before this moment in time, then it is unreasonable that we could reach this event, becuase there has already been an infinite amount of time. That is why when we are speaking of an infinite in respect of an actual thing such as the universe, we cannot speak of it in terms of a number of things, since there is no number; like you said.

Your reasoning is fallacious. You are trying to use the concept of a “beginning” to a series which has no beginning.

 

[MindOverMatter]

“Transversal” implies a beginning and an end by definition. To transverse any path you have to specify the beginning and the end for the term to have any meaning…

An infinite time ago is my beginning in terms of an explanation. You are saying that there is no such a thing as an infinite number of events in the past, but there would have to be, however illogical that may seem, since the past is numbered and the present event is founded upon it. Therefore i can speak of an infinite number ago. If there is no number to the past, then how can we speak of yesterday?

"
No, they don’t. We can add additional numbers to the set of negative integers, which has no beginning.

Intergers have nothing to do with the real world and the past from which the world has arrived.

"
Aleph-null is of course not a member of the reals or integers, but it is still a “number”. …

Yes, but it is not a real number, as in representing a number of events in the real past. I never said that we cannot have a mathematical regress; i am saying that we cannot have an actual regress.

"You’re perhaps confusing a set with an infinite number of elements with “infinity” or “negative infinity”…

I think your confuesing mathematical concepts with the real world. Theres no such thing as an infinite, so how can the world come from or arrive from an infinity? It can’t.

“All I have to show is the possibility of an infinite past.”…

No you haven’t shown the possibility. To show the possibility of an infinite past, you have to suppose an infinite number of events, which is self contradictory for reasons that should be obvious by now.

“Of course you can’t, because “an infinite time ago” doesn’t exist. .”…

But it should exist, if there is an infinite number of events in the past arriving at the present moment. The past is made of events, and since we cannot look at the past as potentially infinite, then we percieve the past as an actual infinite, with numbers being added to it. Therefore we are tranversing the infinite.
Which is prescisely why it is illogical to speak of an “Infinite Past”.

"Your question is illogical. You’re saying you can’t transverse the whole set from beginning to end; whereas the set has no beginning.

You are proposing an infinte regress as a begining, which is illogical. You are saying that the past is infinite in “Number”, since we are speaking of past events which are being “added to”, numbers. If you propose an infinite regress, you have to propose and infinite number of events; it cannot be pontentially infinite. Thats why i called it meaningless, becuase its self contradictory. So if my answers seems illogical, it is only because the concept of an infinite regress is illogical in the first place.

“Of course it’s impossible, because “an infinite number of moments ago” doesn’t exist…”…

Which is precisely my point. An infinte regress is logically impossible. But according to you, an infinite number of moments ago does exist, and would have to in order for us to “arrive” at the present moment, and thats becuase the present moment is founded upon an infinite number; unless your willing to say that past isnt made of additional events.

"Your reasoning is fallacious. You are trying to use the concept of a “beginning” to a series which has no beginning.

Your reasoning has been fallacious from the outset, since you haven’t shown how it is possible in the first place for us to have an infinite chain of cause and effect before this moment. You cannot prove it or infere it by counting backward, since you will always reach a finite number. You cannot prove it by starting from an infinite, because there is no such thing as an infinite number. Such an attempt at proof would be illogical since you would have to begin from somewhere in order begin an explanation. You have begun from an infinite and merely asserted that it exists. I began from an infinite and said it impossible to arrive at this moment from a meaningless concept. Talk of intergers doesn’t cut it, and just gets really anoying, considering we are dealing with real events in real time, and you haven’t even attempted to show us how such concepts measure up with reality.

 

[SeekingCatholic]

An infinite time ago is my beginning in terms of an explanation. You are saying that there is no such a thing as an infinite number of events in the past, but there would have to be, however illogical that may seem, since the past is numbered and the present event is founded upon it. Therefore i can speak of an infinite number ago. If there is no number to the past, then how can we speak of yesterday?

There is no “infinite time ago”, and there is no “beginning”. I am saying there is an infinite number of events in the past (assuming an infinite regress to be true). But each individual event occurred a finite time ago, at a finite number of events from the present. Each individual event corresponds with an individual (finite) number.

Intergers have nothing to do with the real world and the past from which the world has arrived.

Yes, they do. We can number each event and associate it with an integer. For convenience, we can use zero as the present, and the past is either a finite, or infinite, set of negative integers.

Yes, but it is not a real number, as in representing a number of events in the real past. I never said that we cannot have a mathematical regress; i am saying that we cannot have an actual regress.

You are saying that, but you haven’t provided any proof. Why can’t the cardinality of all past events be aleph-null?

I think your confuesing mathematical concepts with the real world. Theres no such thing as an infinite, so how can the world come from or arrive from an infinity? It can’t.

I don’t know what you mean here. In the case of an infinite regress, the world didn’t “come from” anywhere; it always was.

No you haven’t shown the possibility. To show the possibility of an infinite past, you have to suppose an infinite number of events, which is self contradictory for reasons that should be obvious by now.

Where’s the contradiction, other than your mere assertion that such a thing is impossible.

But it should exist, if there is an infinite number of events in the past arriving at the present moment. The past is made of events, and since we cannot look at the past as potentially infinite, then we percieve the past as an actual infinite, with numbers being added to it. Therefore we are tranversing the infinite.
Which is prescisely why it is illogical to speak of an “Infinite Past”.

No. Just because the set is infinite doesn’t mean “negative infinity” is a member of it. There never was a T = negative infinity. If you wish to talk about “transversal” you must specify a beginning.

You are proposing an infinte regress as a begining, which is illogical.

No, I’m not proposing an infinite regress as a beginning. There is no beginning.

You are saying that the past is infinite in “Number”, since we are speaking of past events which are being “added to”, numbers. If you propose an infinite regress, you have to propose and infinite number of events; it cannot be pontentially infinite. Thats why i called it meaningless, becuase its self contradictory. So if my answers seems illogical, it is only because the concept of an infinite regress is illogical in the first place.

True, an infinite regress would contain an infinite number (aleph-null) of events. However, you have not shown why that is meaningless or self-contradictory.

Which is precisely my point. An infinte regress is logically impossible. But according to you, an infinite number of moments ago does exist,

Yes, there are an infinite number (in terms of cardinality) of moments in the infinite regress, but each of them existed a finite time ago.

and would have to in order for us to “arrive” at the present moment, and thats becuase the present moment is founded upon an infinite number; unless your willing to say that past isnt made of additional events.

The present moment is only founded on the last moment in the past.

Your reasoning has been fallacious from the outset, since you haven’t shown how it is possible in the first place for us to have an infinite chain of cause and effect before this moment. You cannot prove it or infere it by counting backward, since you will always reach a finite number.

Yes I can prove it this way, if the series has no defined stopping point. That is how series of cardinality aleph-null are defined. Of course all elements are finite numbers, just like the set of negative integers. But there is no limit to the number of elements which can be contained within the series. To prove an infinite series of past events impossible, there must be a limit on the number of events which can be contained within the series. What is it, and why?

You have begun from an infinite and merely asserted that it exists. I began from an infinite and said it impossible to arrive at this moment from a meaningless concept. Talk of intergers doesn’t cut it, and just gets really anoying, considering we are dealing with real events in real time, and you haven’t even attempted to show us how such concepts measure up with reality.

If it is possible for God the Father to eternally generate the Son then it is possible, I maintain, for Him to create an eternal universe.

 

[MindOverMatter]

There is no “infinite time ago”, and there is no “beginning”. I am saying there is an infinite number of events in the past (assuming an infinite regress to be true). But each individual event occurred a finite time ago…

Are you saing that there is no limit to past events? Why should i assume this to be true?

True, an infinite regress would contain an infinite number (aleph-null) of events. However, you have not shown why that is meaningless or self-contradictory…

There is no such thing as an infinite number, thats why its meaningless to claim that there is. We are coming from the past, not going into the past; thats why its a fallacy to count backwards and infere that it goes on for ever. You cannot know that it goes on forever; you are mearly speculating that it does, and since we can only ever reach a finite number, there is never any reason to suppose the the past is infinite. Its like me walking up a path, and complaining that it seems to go on forever, and then concluding based on no evidence, that it goes on forever; the only difference is, we are going back in time. Since we cannot actually know an infinite or infere it; then there is no reason to suppose that there isn’t a begining.

The present moment is only founded on the last moment in the past…

No. In an infinite regress, the present moment exists precisely because of an infinite number of events in the past, without which there would be no present moment. There is an actual infinite. If neither of the events where connected, and just existed, then you might have a point. But there is no such thing as an infinite number. If you saying that there has never been a beginning, then how have we reached this event? If the past extends from the present moment, and goes on indefinetly into the past, then you might have a point. But time doesn’t start from the present moment; it comes from the past. There is no fixed present, so how can you speak of integers?