The most baffling mystery of all

[Syntax]

Changing the parameters? You stipulated that I can reach into the box with my hand and make the selection myself. If there would be a layer of plastic, I would be able to discover that, break through it and shake the balls to get a true statistical sample.

You assume that there is a “soft, plastic layer” in reality, which prevents us from making a correct assessment of part of reality.

I don’t “assume” anything more than you do. In fact, your own implicit background assumption is that there is no plastic layer and everything in the box is equally accessible. But you don’t know this. And you went ahead and performed this experimet anyway, leading you to your faulty results.

The point is that *you *don’t know every ball is equally accessible because you can’t see inside the box, just as none of us can “see” all possible cases for all possible events in the universe. So we are limited by:

(1) The numbers of cases actually observed.
(2) Our 5 senses, 3 dimensions of space, and 1 dimension of time.

What is the reason for this assumption? What are the supporting pieces of evidence for it? Or are you just speculating?

By the same token, what is your reason for your assumption that everything in the box is equally accessible? What evidence did you provide me for thinking this is true? Are you just speculating? After all, you can’t see everything in one God-like vision inside the box:shrug:

The larger question for you is this: what reason do you have for thinking that whenever you notice a *constant regularity *you have also found a *causal relationship *between events?

Suppose there are ten coins in my pocket and I pull out 9 quarters. Does that mean it more likely that all ten coins in my pocket are quarters? Not at all.

What is the “problem of induction” you refer to? If it would be the lack absolute, 100% certainty, then you are fighting a windmill. No one states that.

There are different ways this problem is formulated, but any formulation comes down to the same issue. There are plenty of references for you that can be found here:

plato.stanford.edu/entries/induction-problem/

 

[djeter]

It would be a good idea to check out JPII’s Faith and Reason as well to help you understand how these two things are intimately tied together for us Catholics.

http://payingattentiontothesky.files.wordpress.com/2010/02/fide-et-ratio-cover.jpg?w=450&h=651

Me to the rescue. Reading Selections from *Fides et Ratio *here

payingattentiontothesky.com/2010/02/23/fides-et-ratio-%e2%80%93-john-paul-ii-part-i/

Parts One and Two. With topic headings and good stuff emphasis

dj

 

[Thing]

It pops up every time God’s supposed benevolence is discussed. The atheists bring up some questions about it, and the believers will start a barrage of their rationalizations. A few examples: God outsources his helping hand to humans, who are mostly unequipped to handle the problem or God does not want to reveal his existence, because such revelation would make it harder not to believe in him, or maybe why should God “pamper” us? Lots of other nonsensical answers. None are rational, of course.

My amazement stems from their utmost reluctance to admit: “they believe in God’s benevolence on blind faith, they need no evidence for it”. Why do they try so desperately create a rational basis for their belief? After all Jesus himself endorses blind faith when he says: “blessed are the ones who have not seen, yet believe”. This is the quintessential blind faith. Are they somehow secretly “ashamed” of their blind faith? Why would they shun Jesus’s words? Do they secretly believe that (blind) faith is somehow “lower” than cold, hard reason?

They should have their answer ready, wearing it proudly as a badge of honor: “we have our (blind) faith, we believe even in the face of evidence to the contrary - as Jesus endorsed”. Personally, I would find such an answer worthy of respect. Not intellectual respect, mind you, but respect for their honesty nonetheless. It would be much more praiseworthy to have your belief, and stick to it, than coming up with feeble rationalizations, which would not convince a child. Just say: “Jesus said it, I believe it, that is the end of it”. This advice comes free of charge. Use it.

If God is real then His existance can and will be rationally argued; for everything He made points to its maker - Him.
If God is not real then one must rationally argue why, despite your ‘evidence to the contrary’, there are so few atheists in the world.

For passing by, and seeing your idols, I found an altar also, on which was written: To the unknown God. What therefore you worship, without knowing it, that I preach to you:

 

[Syntax]

Changing the parameters? You stipulated that I can reach into the box with my hand and make the selection myself. If there would be a layer of plastic, I would be able to discover that, break through it and shake the balls to get a true statistical sample.

You assume that there is a “soft, plastic layer” in reality, which prevents us from making a correct assessment of part of reality.

I don’t “assume” anything more than you do. In fact, your own implicit background assumption is that there is no plastic layer and everything in the box is equally accessible. But you don’t know this. And you went ahead and performed the experiment anyway, leading you to faulty results. So you are limited by:

(1) Your assumption that you’ve accessed all 1000 balls.
(2) The numbers of actually observed cases.
(3) Your own 5 senses, 3 dimensions of space, and 1 dimension of time.

What is the reason for this assumption? What are the supporting pieces of evidence for it? Or are you just speculating?

By the same token, what is your reason for your assumption that everything in the box is equally accessible? What evidence did you provide me for thinking this is true? Are you just speculating? .

What is the “problem of induction” you refer to? If it would be the lack absolute, 100% certainty, then you are fighting a windmill. No one states that.

Well it is certainly not a “statistical problem” that you continue to make it out to be. There are plenty of references that can be found here:

plato.stanford.edu/entries/induction-problem/

 

[warpspeedpetey]

Yeah, I don’t know why this is so difficult to understand. The problem of induction is NOT a statistical problem, but RDaneel continues to construe it this way.

because it undercuts his cherished belief.

like many atheists, he thinks we are scared of numbers and can thus confuse the issue with them.

it all goes back to having the courage of your convictions. no courage. no conviction.

 

[Syntax]

You are misquoting or misunderstand the rule of succession. Here is the link to it:

I beg to differ. If you think I’ve misunderstood the Laplace’s Rule of Succession, then show me where. Don’t just make this accusation and not defend it.
R Daneel;6390698:

As a matter of fact, since the time of Laplace there were some advances in mathematics. Read up upon the Central Distribution Theorems here: en.wikipedia.org/wiki/Central_limit_theorem

Though I am not a mathematician, the numbers don’t scare me because I already understand how the concpet works. You need to pay attention what the article itself says right from the start with the bold-faced pieces being relevant to this discussion:

…the central limit theorem (CLT) states conditions under which the mean of a **sufficiently large **

number of independent random variables, each with finite mean and variance, will be approximately normally distributed (Rice 1995).

2 issues:

(1) CLT only works for finite domains.
(2) The question for the theorem is: how large is “sufficiently large” in order to secure some degree of certainty? “Sufficiently large” is totally unspecified.

So there is no way of telling whether this theorem is applicable to all cases

 

[Syntax]

The central distribution theorem proves mathematically, beyond any doubt whatsoever that when we increase the number of experiments the difference between “p” and “k/n” - “abs(p - k/n)” converges to zero. Thus it proves that more experiments will increase our confidence in the null-hypothesis. This theorem does not say anything about any specific “p” or “k” or “n”. It proves the method that undertking more experiments will justify our increased certainty (which will never reach 100%) in our null-hypothesis.

No, it doesn’t “prove” anything. You say the CLT is a way of “proving” our undertaking experiments to achieve increased certainty are justified. Ok, so CLT justifies what we think is a reliable way of achieving degrees of certainty.

But how do we know CTL itself is *empirically *justified? It’s apparent you are presupposing some undefined notion of what constitutes “reasonable empirical belief” here. So why is it empirically reasonable to believe that CLT itself is empirically justified? See next:

the uniformity of nature…cannot be “proven” in a deductive fashion, but our confidence in its veracity keeps on increasing - as justifed by the Central Distibution Theorems. I ask you again: what is the rational underpinning for your skepticism here?

Here is a quote dealing with how the very Problem of Induction relates to the Central Distribution Theorems from Stanford Encyclopedia of Philosophy. I highlighted the central issue in bold below. And if you fully read this piece about CLT in the full context of that article, you will understand the problem at stake. Very simply put, CLT depends on the prior assumption that the domain of sampling is finite and also presupposes an UNDEFINED notion of what is to count as “sufficiently large numbers of instances.”

plato.stanford.edu/entries/induction-problem/

Likelihood ratios are a way of comparing competing statistical hypotheses. A second way to do this consists of precisely defined statistical tests. One simple sort of test is common in testing medications: A large sample of people with a disease is treated with a medication. There are then two contradictory hypotheses to be evaluated in the light of the results:

h0: The medication has no effect. (This is the null hypothesis.)
h1: The medication has some curative effect. (This is the alternative hypothesis.)
Suppose that the known probability of a spontaneous cure, in an untreated patient, is pc, that the sample of treated patients has n members, and that the number of cures in the sample is ke. Suppose further that sampling has been suitably randomized so that the sample of n members (before treatment) has the structure of n draws without replacement from a large population. If the diseased population is very large in comparison with the size n of the sample, then draws without replacement are approximated by draws with replacement and the sample can be treated as a collection of independent and equiprobable trials. In this case, if C is a group of n untreated patients, for each k between zero and n inclusive the probability of k cures in C is given by the binomial formula:

P(k cures in C) = b(n, k, pc)
= ( n
k ) pck(1 − pc)(n − k)

If the null hypothesis, h0, is true we should expect the probability of k cures in the sample to be the same:

P(k cures in the sample | h0) = P(k cures in C)
= b(n, k, pc)
= ( n
k ) pck(1 − pc)(n − k)

Let kc = pcn. This is the expected number of spontaneous cures in n untreated patients. If h0 is true and the medication has no effect, ke (the number of cures in the medicated sample) should be close to kc and the difference

ke − kc
(known as the observed distance) should be small. As k varies from zero to n the random variable

k − kc
takes on values from −kc to n − kc with probabilities

b(n, 0, pc), b(n, 1, pc), …, b(n, n, pc)
This binomial distribution has its mean at k = kc, and this is also the point at which b(n, k, pc) reaches its maximum. A histogram would look something like this.

Distribution of k − kc
Given pc and n, this distribution gives the probability that the observed distance has the different possible sizes between its minimum, −kc, and its maximum at n − kc; probabilities of the different values of k − kc are on the abscissa. The significance level of the test is the probability given h0 of a distance as large as the observed distance.

A high significance level means that the observed distance is relatively small and that it is highly likely that the difference is due to chance, i.e. that the probability of a cure given medication is the same as the probability of a spontaneous, unmedicated, cure. In specifying the test an upper limit for the significance level is set. If the significance level exceeds this limit, then the result of the test is confirmation of the null hypothesis. Thus if a low limit is set (limits on significance levels are typically 0.01 or 0.05, depending upon cost of a mistake) it is easier to confirm the null hypothesis and not to accept the alternative hypothesis. Caeteris paribus, the lower the limit the more severe the test; the more likely it is that P(cure | medication) is close to pe = ke / n.

This is not the place for an extended methodological discussion, but one simple principle, obvious upon brief reflection, should be mentioned. This is that the size n of the sample must be fixed in advance. Else a persistent researcher could, with arbitrarily high probability, obtain any ratio pe = ke / n and hence any observed difference ke − kc desired; for, in the case of Bernoulli trials, for any frequency p the probability that at some n the frequency of cures will be p is arbitrarily close to one.

 

[warpspeedpetey]

I give you a hint: the two players are under no obligation to show one and two fingers at exactly 50% of the time. From here on you can find the correct answer. If you are still baffled, just ask, politely.

im all for fun math games, but if you always hold up 1 then i will also, if you always hold up 2 then i will also. thats to my advantage. unless you make your choices random, i dont see how you benefit.

so please tell me the correct answer.

There are two kinds of “ignores”, the hardware and software ignores. The hardware is to push the “ignore” button. I use the software method (and I never stated otherwise).

there is only 1, the button you push. this is another false statement.

The fact that you don’t understand the difference is your problem, not mine.

there is no difference, because there are not 2 different kinds of ‘ignore lists’. this is another false statement.

I admit weakness here. I read your posts, because I find them amusing.

thank you.

Your level of ignorance of truly “catholic” proportions,

that may be a true statement, but then why do you keep dodging real arguments like the problem of induction, the epistomological arguments?

why do you keep making statements that i can easly demonstrate are false?

coupled by your obnoxious, abrasive and taunting style is funny.

yes, i know it is.

But then again, I have a strange sense of humor. So keep on entertaining me.

will do, i wouldnt want to disappoint.

 

[warpspeedpetey]

**Come on, at least be intellecually honest about your own posts. **

see the post immediately above this one

 

[Sarpedon]

Yes, we do. You demonstrated that God cannot benefit from our existence - which is somewhat disputable since God wishes or desires our worship - so he gets something out of the deal. But what about us? If God is benevolent, then he would not create us if we were not better off existing, rather than non-existing. So you analysis still lacks until you can show that any existence is always better than nonexistence. If existence and non-existence would be equally “good”, God would have no reason to choose either one. If non-existence is better, then God would not create us. So your analysis demands to show that existence is in and by itself is more desirable than non-existence.

I’d like to clarify that God’s perfect nature doesn’t mean He is indifferent- God doesn’t change per se in response to us, but his fixed nature is such that He desires to give us love and all the things that come with it. Our obedience or disobedience does not change that fixed nature. We can conclude from God’s necessarily perfect nature that He cannot benefit from us, but that does restrict God from choosing to give good things to us of His own accord without benefiting Himself. Indeed, such an arrangement fits in nicely with the deducible and necessarily selfless act that God undertook in creating us.

I do not need to demonstrate that existence is better from non-existence simply because we can proceed from the fact that we exist and the prior determined reality of God’s existence. God exists, and He is ultimate, perfect, uncaused, and self-sufficient. We also exist, and God is the necessary source of our existence. The fact that God is self-sufficient and perfect and the fact that we exist means that God must have given us existence even though He cannot benefit from our existence.

I don’t have to prove that we are better off existent than non-existent. Merely observing the reality of our existence is enough to conclude that God undertook at least one selfless act. Given that selfless benevolence is easily conceivable and observable, and selfless evil is barely conceivable and not clearly observable, it makes sense to attribute God’s necessarily selfless act to benevolence rather than evil. It is not necessary to establish that existence is better off than non existence, simply because we can conclude from the fact our our own existence that God undertook at least one selfless act, and selfless benevolence makes much more sense than selfless evil.

 

[Syntax]

You explicitly introduced the “probability of 50%” into the discussion, and now you wish to disown it? Come on, at least be intellecually honest about your own posts.

That’s right…ecause raising the probability of a hypothesis beyond 50% 1st depends on deciding whether or not induction is a reliable source of reasoning for all cases, within which only a very limited amount we’ve actually found to “work.”

 

[Syntax]

You explicitly introduced the “probability of 50%” into the discussion, and now you wish to disown it? Come on, at least be intellecually honest about your own posts.

That’s right…because deciding whether or not raising the probability of a hypothesis beyond 50% actually occurs first depends on deciding whether or not induction is a reliable source of reasoning for all cases, within which only a very limited amount we’ve actually found to “work.” Induction, in turn, relies on the assumption that nature is uniform. And this is the very assumption you are presupposing, *not *establishing, by arguing that CLT supports inductive reasoning. So CLT depends on an assumption which has NEVER been empirically established!

 

[R_Daneel]

That’s right…because deciding whether or not raising the probability of a hypothesis beyond 50% actually occurs first depends on deciding whether or not induction is a reliable source of reasoning for all cases, within which only a very limited amount we’ve actually found to “work.” Induction, in turn, relies on the assumption that nature is uniform. And this is the very assumption you are presupposing, *not *establishing, by arguing that CLT supports inductive reasoning. So CLT depends on an assumption which has NEVER been empirically established!

I am trying to touch on all of your points in this segment.

First, I asked you a question:

You assume that there is a “soft, plastic layer” in reality, which prevents us from making a correct assessment of part of reality. What is the reason for this assumption? What are the supporting pieces of evidence for it? Or are you just speculating?

You neglected to answer this, and instead you threw back the question at me:

By the same token, what is your reason for your assumption that everything in the box is equally accessible? What evidence did you provide me for thinking this is true? Are you just speculating?

In my circles it is bad form to refuse to answer and instead asking the same question back. If you **had **answered the question, and **then **asked it back, it would have been perfectly all right. I have observed that you guys use this “technique” every time when you are unable to provide an answer. It just gives the impression of dodging, to hide the fact, that you have nothing to say.

To answer your specific example: I am not allowed to peek into the box, but I am allowed to put my hands into it. Therefore I am able to count the balls and see if there really are one thousand balls in them or only a hundred. If I count a thousand, then my analysis is correct. If I can count only a hundred, then you are exposed as a cheat.

However, I am going to answer yours. The reason is the same as before. I trust my senses, and I trust the much maligned principle of ***accepting ***the uniformity of nature. The reason for this trust is that the principle has never let me (or anyone else) down. What reason do you have for your mistrust? By the way, your mistrust is only in your words, not in your actions. I am willing to bet (again!) that you would never put your hand into a hot flame and “hope” that this time the flame will not burn you. You count on the uniformity of nature just as much as I do (and everyone else does).

So, again, and this time, please answer me: “what are your specific reasons to assume that it is possible that nature is not uniform”?

You also said:

Though I am not a mathematician, the numbers don’t scare me because I already understand how the concpet works.

There is no reason to be “scared”. But don’t assume that reading a few pages on the net will give you qualification to speak of complex mathematical concepts - which take years to master. First, the Central Limit Theorems (observe the plural) are pure mathematical theorems - and there are quite a few of them. Indeed the one mentioned in the quoted articles is the most well-known, because it offers a great insight into the strange and beautiful fact that many, small independent variables will result in a normal distribution. But there are other ones, too, less known, but equally well established.

Then you say:

No, it doesn’t “prove” anything. You say the CLT is a way of “proving” our undertaking experiments to achieve increased certainty are justified. Ok, so CLT justifies what we think is a reliable way of achieving degrees of certainty.

But how do we know CTL itself is empirically justified? It’s apparent you are presupposing some undefined notion of what constitutes “reasonable empirical belief” here. So why is it empirically reasonable to believe that CLT itself is empirically justified?

You gotta be kidding. Why and how could and should a purely mathematical theorem be empirically verified? You may dispute that the application of the theorem needs to be substantiated, but the theorem itself is beyond dispute. However, if you wish to say that this particular theorem is not applicable, you should give reasons for that assertion.

In the answer I gave you to your 1000 balls question I showed you the result (pure, mathematical result) that the more experiments we perform, the smaller the discrepancy we find. That is undisputable again - and it **proves **the principle that increasing the number of experiments will decrease the uncertainty. This mathematical proof can be verified by actually undertaking the experiments - which was done, many times. But such verification is not really necessary. One does not dispute that all even numbers are divisible by two, just because it is impossible to verify empirically that all even numbers are actually divisible by two.

To be continued below:

 

[R_Daneel]

Your next post was:

That’s right…because deciding whether or not raising the probability of a hypothesis beyond 50% actually occurs first depends on deciding whether or not induction is a reliable source of reasoning for all cases, within which only a very limited amount we’ve actually found to “work.” Induction, in turn, relies on the assumption that nature is uniform. And this is the very assumption you are presupposing, not establishing, by arguing that CLT supports inductive reasoning. So CLT depends on an assumption which has NEVER been empirically established!

Well, well. I wonder if you would care to apply your reasoning to other branches of science. You might dispute the laws of logic, because the laws of logic cannot be proven logically. Or you might dispute mathematics, because its axioms cannot be proven mathematically. Here is a surprise for you: no branch of science can prove or verify its very foundation. They are all accepted as true, because they are either obvious, or because they work. The axioms of mathematics are arbitrary, but the ones we accepted are not only consistent, but also happen to be applicable to natural sciences - they are useful.

The **principle of induction **is not provable, or verifiable. Indeed, it may lead one to incorrect results, as in the example: “all swans we have so far observed are white, therefore it is reasonable to assume that all swans are white”. It is a typical example of faulty induction - which will be refuted by observing one black swan - but it cannot be refuted by empty speculation! So what? The principle does not assert that there will be no faulty results, but it allows the process to incorporate these new observations and modify the original hypothesis (to wit: all swans are white). Using another example, the duck principle: “if it looks like a duck, walks like a duck, quacks like a duck, tastes like a duck, it is very probably a duck”.

Observe again: it does not say “… then it is a duck” - it merely says: “… then it is very probably a duck”. There is no absolute certainty, there cannot be any absolute certainty, and guess what - no one cares. It is still the best method available, it cannot be improved upon, it keeps on working. And its built-in possibility of error is also taken care of, by keeping to be aware of the possibility of error, and allowing the modification of the theories, if and when it is necessary. Only some ivory-tower philosophers try to undermine the process by pointing to some “errors”, which are already acknowledged and accounted for. In other words: “where is your black swan?”…

Now, I answered your points, and I am going to ask you another question. Do you have a better solution, which would eliminate the perceived “errors” in the inductive method? Let us know. Be specific. And don’t dodge this time.

 

[R_Daneel]

im all for fun math games, but if you always hold up 1 then i will also, if you always hold up 2 then i will also. thats to my advantage. unless you make your choices random, i dont see how you benefit.

so please tell me the correct answer.

Sure. The two players choose their own strategy. Player “A” chooses 1 finger with a probability of “p” and player “B” chooses one finger with a probability of “q”.

The expected payoff from player “A”'s (he wins if 2 or 4 fingers are visible) perspective is:

z = 2 * p * q + 4 * (1 - p)*(1 - q) - 3 * p * (1 - p) - 3 *(1 - p) * q.

Since the game is a zero-sum game (whatever one player loses, the other one wins) the expected payoff for “B” is -z.

If you rearrange the above polynomial (which is a trivial undertaking) you can see that if player “B” chooses one finger with 7/12 probability and thus chooses two fingers with 5/12 probability, he has an 8.33% advantage. Player “A” can do no better, if he chooses the same probabilities, his disadvantage is also 8.33%. With any other strategy “B” will win more and “A” will lose more.

If both “A” and “B” would make both “p” and “q” equal to .5, then your first answer would be correct. But that is not the optimal startegy. So, if “A” accepts this game, he will lose all his money.

This example shows that “common sense” or “intuition” are dangerous tools when it comes to problems of statistics and probability. I advise everyone: “calculate, don’t speculate”. Both “common sense” and “intution” are wonderful starting points, but they must be precise. And the precision can only be assured by calculation.

there is only 1, the button you push. this is another false statement.

Only according to your opinion. To give you an example, I do not need to wear earplugs (hardware protection), I can tune out annoying external noises by a “software” method, by not hearing them. This is pretty unique, most people are unable to disregard noises. I guess, I am just lucky.

Personally, I find the “ignore” button rude and impolite, because it presupposes that the other person cannot ever contribute anything useful and is unable to change his arrogant, taunting and obnoxious behavior to become contrarian, argumentative, and yet polite and civilized. Maybe it is my fault, but I keep on hoping, even if it does not happen in specific cases. In a non-rational fashion, I let my previous, positive results guide me. I was able to “tame” quite a few, and while never agreeing, a polite conversation could be conducted.

 

[R_Daneel]

I’d like to clarify that God’s perfect nature doesn’t mean He is indifferent- God doesn’t change per se in response to us, but his fixed nature is such that He desires to give us love and all the things that come with it. Our obedience or disobedience does not change that fixed nature. We can conclude from God’s necessarily perfect nature that He cannot benefit from us, but that does restrict God from choosing to give good things to us of His own accord without benefiting Himself. Indeed, such an arrangement fits in nicely with the deducible and necessarily selfless act that God undertook in creating us.

I do not need to demonstrate that existence is better from non-existence simply because we can proceed from the fact that we exist and the prior determined reality of God’s existence. God exists, and He is ultimate, perfect, uncaused, and self-sufficient. We also exist, and God is the necessary source of our existence. The fact that God is self-sufficient and perfect and the fact that we exist means that God must have given us existence even though He cannot benefit from our existence.

I don’t have to prove that we are better off existent than non-existent. Merely observing the reality of our existence is enough to conclude that God undertook at least one selfless act. Given that selfless benevolence is easily conceivable and observable, and selfless evil is barely conceivable and not clearly observable, it makes sense to attribute God’s necessarily selfless act to benevolence rather than evil. It is not necessary to establish that existence is better off than non existence, simply because we can conclude from the fact our our own existence that God undertook at least one selfless act, and selfless benevolence makes much more sense than selfless evil.

Seems like we are at an impasse. There are three possibilites: 1) existence is always preferable to non-existence, 2) existence is not always preferable to non-existence, and 3) neither existence nor non-existence matters.

From the assumption that God is benevolent, and from the fact that we exist it follows that 2) or 3) are not an option. Therefore it must be the case that 1) must be true. But to prove this you cannot use God’s benevolence, because it would be a circular argument.

 

[Sarpedon]

Seems like we are at an impasse. There are three possibilites: 1) existence is always preferable to non-existence, 2) existence is not always preferable to non-existence, and 3) neither existence nor non-existence matters.

From the assumption that God is benevolent, and from the fact that we exist it follows that 2) or 3) are not an option. Therefore it must be the case that 1) must be true. But to prove this you cannot use God’s benevolence, because it would be a circular argument.

I’m not making an assumption that God is benevolent. The order works like this:

1. We exist
2. God exists as the perfect, self-sufficient, unchanging, and ultimate being
3. God cannot improve in perfection since He is by nature perfect
4. Therefore, God cannot improve in perfection from us. Therefore, He cannot benefit from us
5. But we exist, and our existence necessarily comes from God as the only self-existent being.
6. Therefore, God undertook at least one act that did not benefit Himself in any way, and therefore we can conclude that God undertook at least one selfless act.

I have not assumed that God is benevolent at any point in this sequence. I have simply deduced from God’s necessary nature and the fact of our own existence that God acted selflessly in regards to our own creation.

1. Now, and only now, do we examine whether God is benevolent. We know God acts selflessly. From our own experience, we can conclude that selfless benevolence makes more sense than selfless evil.

Benevolence does not seem to require any element of self-benefit. We can easily imagine some heroic person or being acting in such a way that they sacrifice everything for some noble end. There is nothing unusual or striking about this.

In contrast, evil does seem to require an element of self-benefit. We cannot easily imagine someone intentionally practicing evil when they have nothing at all to gain from it.

Therefore, it makes more sense to attribute benevolence to God’s necessarily selfless act.

 

[warpspeedpetey]

Only according to your opinion. To give you an example, I do not need to wear earplugs (hardware protection), I can tune out annoying external noises by a “software” method, by not hearing them. This is pretty unique, most people are unable to disregard noises. I guess, I am just lucky.

no, there is only the software ignore list. its not my opinion it is the bare fact of the forums.

 

[Syntax]

In my circles it is bad form to refuse to answer and instead asking the same question back. If you **had **answered the question, and **then **asked it back, it would have been perfectly all right. I have observed that you guys use this “technique” every time when you are unable to provide an answer.

No, there’s no hidden “technique” here…sheesh. My stupid illustrative example was “rigged” against you from the beginning because you weren’t understanding the problem of induction. I had to “dumb it down” for you–and you STILL don’t get it. Of course how the example is set up isn’t flawless, that’s why I told you right from the start to “give me a rough estimate” and “not to bother crunching all the numbers.” “Cheating” is not the same thing as “illustrating.” You just feel cheated.

To answer your specific example: I am not allowed to peek into the box, but I am allowed to put my hands into it. Therefore I am able to count the balls and see if there really are one thousand balls in them or only a hundred. If I count a thousand, then my analysis is correct. If I can count only a hundred, then you are exposed as a cheat.

No. I didn’t say “you are able to count the balls.” I only said that you know there are 1000balls in the box, that “you are able to withdraw 100 finding that they are all black, and that you can repeat this very same experiment however many times you like. So what are the contents of the box?” I didn’t cheat you. You just simply didn’t know the contents of the box because I STIPULATED you couldn’t look inside it.

The example is just an analogy designed to show our own cognitive limitations to the actual empirical world, the limitations provided by our own senses, and the limitations provided by what are called “scientific auxiliary hypotheses.”

Whenever a hypothesis is tested against the tribunal of sense-experience, that hypothesis is always accompanied by a set of implicit background assumptions that are being tested too. And some of these assumptions scientist will too often discover they are implictly holding which is determining the faulty results of their failed experiments. So they go back and revise their auxiliary assumptions before they decide to reject the actual hypothesis they are testing. This is part of that interplay between verification and falsification–neither of which holds absolute epistemic sway over their actual scientific practices in real life.

However, I am going to answer yours. The reason is the same as before. I trust my senses, and I trust the much maligned principle of ***accepting ***the uniformity of nature. The reason for this trust is that the principle has never let me (or anyone else) down.

Yes, the key word is “trust.” The trust has to do with utility, not mathematical or empirical demonstration–simply because no “proof” or probability assignment is available. We would first have to establish that all possible cases are just like all actually observed cases, precisely what we haven’t done.

What reason do you have for your mistrust?

I don’t typically mistrust my senses. But I don’t have any reason for thinking the inductive method used to reach the accepted scientific theories of today is any more reliable than the same method used to reach the false scientific theories of the past. So how reliable is it, really?

By the way, your mistrust is only in your words, not in your actions. I am willing to bet (again!) that you would never put your hand into a hot flame and “hope” that this time the flame will not burn you. You count on the uniformity of nature just as much as I do (and everyone else does).

Of course. What’s your point? We still cannot empirically demonstrate the uniformity of nature. And as far as I know the laws of gravity could cease to exist tomorrow and there would be nothing I could do about it.

So, again, and this time, please answer me: “what are your specific reasons to assume that it is possible that nature is not uniform”?

Simply because it is not been demonstrated that it IS uniform. This “possibility” is purely epistemic and is a function of my ignorance, just as thinking it is possible that nature takes its course according to deterministic laws is a function of my ignorance.

There is no reason to be “scared”. But don’t assume that reading a few pages on the net will give you qualification to speak of complex mathematical concepts - which take years to master.

I am not assuming this. I’ve had CLT shown to me many time by several professors and colleagues who deal with probabilities and statistics all the time. So I even though I have a rather basic understanding of how these theorems are supposed to work, I assure you that none of them solves the central problem of induction.

First, the Central Limit Theorems (observe the plural) are pure mathematical theorems - and there are quite a few of them. Indeed the one mentioned in the quoted articles is the most well-known, because it offers a great insight into the strange and beautiful fact that many, small independent variables will result in a normal distribution. But there are other ones, too, less known, but equally well established.

Sure. But all the Bayesians that I know in my department will tell you that neither the CLT nor Bayes’ Theorem can solve the problem of induction.

 

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You gotta be kidding. Why and how could and should a purely mathematical theorem be empirically verified?

That might have been a misnomer on my part. I don’t think any mathematical theorem could *or *should be empirically substantiated. But if any of these mathematical theorems are presupposing induction, then yes, they must face the tribunal of experience since inductive reasoning presupposes that necessity exists in nature. You can’t just “hope” that a mathematical theorem will always be applicable to nature, even if it has been in the past, simply because you have no mathematical or empirical reason to suppose that nature will be the same in future as it has been in the past.

You may dispute that the application of the theorem needs to be substantiated, but the theorem itself is beyond dispute.

I am not sure if the theorem itself is “beyond dispute.” That’s for mathematicians to decide. But it certainly seems mathematically reasonable to believe that it is.

However, if you wish to say that this particular theorem is not applicable, you should give reasons for that assertion.

I didn’t say the theorem is not applicable. I only said that as far as we know it **has been **applicable, but we have *no reason *to believe that it will **always be **applicable.