Show #1- Short Intro Video:
This is just a short intro video to the 3.5 hour S&S show I did entitled “Calculus for Christ” whereby I went over how I use Bayes Theorem in determing Christianity is true and/or endorsed by God. I introduce the main video (as well as 2 hour After show) and reveal some minor errors I made in the shows.
YouTube Video = https://www.youtube.com/watch?v=mCySuwR3MGc
Rumble Video = https://rumble.com/v377cy5-calculus-for-christ-short-intro-video.html
Audio Only Link = https://podcasters.spotify.com/pod/show/real-seeker-ministries/episodes/Calculus-for-Christ–Short-Intro-Video-e282k3a
Show #2- Main Discussion Show:
Alrighty, gear up for your math lesson today, this is the main show of “Calculous for Christ” on the S&S podcast. Join Atheists David Johnson, Darren Lute, Bryan Portier, Andrew Knight and Theists Mak Attack and Tyler Vela (along with my good self) as I go over how to use Bayes Theorem to prove christianity.
YouTube Video = https://www.youtube.com/watch?v=uVWT15FF-9Y
Rumble Video = https://rumble.com/v377o5f-calculus-for-christ-main-discussion-show.html
Audio Only Link = https://podcasters.spotify.com/pod/show/real-seeker-ministries/episodes/Calculus-for-Christ–Main-Discussion-Show-e282k63
Show #3- S&S After Show:
YouTube Video = https://www.youtube.com/watch?v=OuyyWTVAwgM
Rumble Video = https://rumble.com/v377w5m-calculus-for-christ-s-and-s-after-show.html
Audio Only Link = https://podcasters.spotify.com/pod/show/real-seeker-ministries/episodes/Calculus-for-Christ–SS-After-Show-e282l5r
Show #4- Calculus for Christ- The GRAND Finale (Atheist David J. Changes His Mind);
Alright, well we got one last show in the series Calculus for Christ, this one is the grand finale where I fulfill my promise to go over my method with David J. using a practical example.
David chose to evaluate the hypothesis that the God of the Bible is NOT an Omni-God given his assessment of the evidence for and against. In the end, David agrees with me that my Bayes-ish method is a valid way to determine truth even if it is not his own preferred method.
YouTube Video = https://www.youtube.com/watch?v=dM09XNNtQYc
Rumble Video = https://rumble.com/v38jafs-calculus-for-christ-the-grand-finale-atheist-david-j.-changes-his-mind.html
Audio Only Link = https://podcasters.spotify.com/pod/show/real-seeker-ministries/episodes/Calculus-for-Christ–The-GRAND-Finale-Atheist-David-J–Changes-His-Mind-e287dpc
Recommended Sources (for further study);
a) My Previous Argument for God from Universe contingency;
See my full & NOW COMPLETED Cosmological Argument Write-Up in the attachment here =
b) Evidentialism vs. Pragmatic Encroachment Theory;
d) Old 4A Ask an Atheist Anything Show with Andrew Knight on Atheist’s Burden of Proof;
STANFORD PEER-REVIEWED PAPER ON BAYES THEOREM = https://plato.stanford.edu/entries/bayes-theorem/
Also confirming Subjective Probabilties are used with Bayes and Rational to do so = https://plato.stanford.edu/entries/bayes-theorem/#3
Proscenium/4A (Ask an Atheist Anything) Shows- Dale Guest Stars
Real Seeker Ministries 
I have no idea what was wrong with me when I went over the background evidence vs. evidence part of the S&S After show- I was entirely wrong in how I defined them. Look the prior probability looks at the probability that the hypothesis God exists/doesn’t exist is intrisically true/false without or before evidence = a priori whereas the a posteriori prob is the “dirext evidenxe” relevant to the truth of the hypothesis. So this kind of deal with things like the plausibility or implausibility/incoherence of God as a concept or perhaps argueing God is not the simplest hypothesis or I liked Andrew’s first example perhaps argueing God is imporbable to exist a priori because the hypothesis that He exists doesn’t make testable predictions or perhaps argueing the God is not simple but too complex to be the best explanation- stuff like this. Any appeal to evidence is a posteriori reasoning and thus are direct evidences.
Now, just to be clear whether you put something into the background or evidential category makes no difference to Bayes’ resutls as we are multiplying all the factors at the end of the day, so for practical purposes, it doesn’t really matter for the purposes of my Bayes-ish approach to work and give good results for the overall probability
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I just wanted to add that I think what Andrew was saying around the 1 hour 5-9 min mark or so of the Main Show about the equal probabilties on both sides- I think what he was having in mind was more the Odds Form of Bayes where we get a ratio of the liklihood of one hypothesis relative to another and perhaps if two hypotheses then it’s 50/50 for the prior prob but if 3 hypotheses or 4 then it is 33% or 25% prior prob respextively. I’m not 100% sure this is what he was saying, but I think what he was talking about makes more sense in light of the Odds Form of Bayes rather than the version of Bayes I was using.
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A fan of S&S says this ;
Bayes is good when you’re dealing with clearly quantifiable data like large bodies of cross-reffed statistics. You can’t derive those kind of clearly quantifiable data from biblical sources without presupposing the reliability of those sources, which obviously creates contention that can’t be resolved by the Bayesian calculations themselves.
So it seems to me that you’d do well to establish a good, solid theory defending the use of Bayes to make probability calculations from faith-based data and that establishes limiting criteria for those data. That way, you’d have a solid theoretical grounding that actually justified the use of Bayes in this context, plus you’d circumscribe the terms of the argument to prevent it running all over the place as occurs when people (quite rightly) start nit-picking the contentious details you’re plugging into your calculations.
Such a theoretical justification doesn’t have to run to thousands of pages – it could be argued for in the space of about 8,000 words. And if it was worked out carefully enough, and road-tested with some solid critical feedback, you could end up with a serious academic paper that might make a genuine contribution to the existing debate about the use of Bayes for faith-based data.
I REPLIED THUSLY,
Hi Tom, thanks for your thoughtful feedback here. In terms of using Bayes for religious propositions/hypotheses, to be honest many scholars have already done the work that you suggest I do here and so I think Bayes use for subjective nont frequentist based probability values (such as in religious matters) has already been well justified at this point (see for example the section on “The Role of Bayes’ Theorem in Subjectivist Accounts of Evidence” (ALSO Section 4 too) in the Stanford Encyclopedia article on Bayes Theorem. So I think that work has already been done really, but I do agree with you and Andrew that it’s of course better to have real quantifiable or frequetnist stats to work with as probabilities; unfortunately for most things in life those kinds of numbers just aren’t available and yet thankfully we are rational in making subjective probability judgements nonetheless.
Think about this for a second- I take it that you have concluded that Christianity is false. OK what are your reasons for that and let’s say you cite whatever your negative evidences against the truth of Christianity are. OK, but surely you’ve heard of the positive reasons in favour of it like the historical evidence for the resurrection and considered those as well. You say, yes I have. And so you came up overall that Christianity is probably false. Yes you say. OK great, please show me your statistical calculations that ever PhD mathmetician in the world would agree with proving that Christianity is probably false. I don’t have that, all I did was subjectively consider all the factors and make an overall subjective assessment of the truth/falsity of the hypothesis on the basis of all the evidence I’m privy to on my end. And then I say but that isn’t rational and you’re opinions agaisnt Christianity can just be dismissed as subjective then.
What I want to say is no, you may indeed be rational despite the lack of statistical calculations on your part (along with the vast majority of rational agents who make decisions about hypotheses on the basis of evidence every day). Proper statiscal calculations arent’ needed, as rational agents are able to rationally intuit or infer their level of credences for a propostion on the basis of the evidence without needing to do the stats all the time. Now, all I do is that I provide a quantification to those rational intuitions/inferences that all of us make every day when we assess a given set of evidences in relation to the truth/falsity of some proposition and then use Bayes as a useful tool to provide me with an objective basis to put all the pieces together in making my overall judgement. That’s all I’m doing, I did the same thing you did when you concluded Christianity is false or God doesn’t exist or evolution is true, or the Earth is round, etc., but I just did so better and more objectively.
I hope that makes sense as otherwise, you are basically dismissing most everything you and I and pretty much everyone else on Earth beleives or disbleives as being entirely subjective and irrational unless and until they do statiscal calculations- no one does that, no scientist or logician in the world demands that we need do that to make rational assessments.
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An Unbeleiver and Phd Math expert responded to my Bayes-ish method, here is what he said against me;
“I plan to post on the broader concerns I have with Dale’s approach which will be along the lines of those expressed by David and MA. But I first want highlight 3 technical errors of increasing consequence and then some further comments about priors, beyond those I’ve voiced over the years.
The first surrounds uncertainty and significant figures. Dale’s outputs are often expressed in terms of 4 significant figures (c.f. 53.14%) and yet the inputs have less (2 in the case of 75%, 1 or 2 in the case of 50%) and hence give an unwarranted picture of precision. But there are strict rules that should be followed to deal with significant figures during calculations and these are there to ensure result don’t provide a false confidence. In short, one should not generate more significant figures via mathematical machinery than are significant figures in the input. (See this video series for details: https://www.khanacademy.org…. Dale’s 53.14% may well be properly expressed as 50% which would land him as a pure agnostic.
Around the 25 minute mark, Dale brought up the “Fallacious Atheist Version” slide and declared the Ai term to be fallacious. This may or may not be correct depending on how Cavin defined the term. In the general form of Bayes representing multiple competing hypotheses rather than just two (as Dale presents), there is indeed a series of Ai terms, the number of which determined by the number of competing hypotheses. Cavin may have just been using Ai to represent all the different terms although mathematicians would normally using a summation sign to make this explicit. Either way, Cavin is correct in that if there are multiple hypotheses these need to be accounted for. Dale and WLC want to simplify things by just having the binary hypotheses (e.g. R and ~R) but the ~R should be decomposed into a set of mutually exclusive alternative hypotheses.
Around the 48 minute mark, we are introduced to the “Bayes-ish Approach”. Dale doesn’t like the conditionals in Bayes proper, so for some reason he thinks he can invert them and still have a valid form. You can’t do this. Bayes theorem is derived from the axioms of probability according to strict logical rules. One can’t just choose to ignore this underlying framework and manipulate terms willy-nilly. What Dale has done is to effectively convert the prior terms in the true formulation to their squared values. In doing so, there is one and only one value of the priors where this doesn’t result in erroneous results, that being the contentious 50-50 prior. In that case, all the prior terms cancel one another. But for any other values of the prior, the results are going to be erroneous. (EDIT: I skimmed the follow-up show and noted the unexpected result. The Dalean not the Bayesian framework is the likely issue.)
As was voiced on the show, Bayes calculations built on uncertain priors are next to worthless. Sure, we can use a default 50-50 when one is without data but one should not want to take actions based on the posteriors. One would never produce health policy for example without solid priors. 50-50 may indeed be the default if you don’t have the background information, but the honest approach is to say the prior is undefined and say we simply don’t know. It’s only if forced to make a call, such as being a government official who has to make up some numbers at the behest of a politician, that one goes forward with 50-50. But it’s all fiction.
On the resurrection specifically, Dale uses 50-50 instead of empirically derived values because it it is granted the status of a “religion authenticating event”. This seems to be post hoc. One can’t boost the priors based on the subsequent knowledge that a religion arose. I’d like to know how the resurrection became a religion authenticating event without post hoc rationalization. What is the signal from heaven where the priors suddenly escalated from infinitesimally small to 50-50? Furthermore, if we are to believe most Christian theologians, the individual resurrection of Jesus was not expected, rather a general resurrection. So if we can infer anything about the mind of God, the prior probability of Jesus’ resurrection was definitely well below 50%.
The priors game in this context is all smoke and mirrors. Four significant probability measures, despite 100s of pages of analysis and calculations, is unfortunately just cargo cult epistemology. It is not a path to truth…
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My Reply to the PhD Math Guy Anthony66;
Hello Anthony 66,
First off I want to thank you very much for your respectful (non-insulting) and substantive feedback- I think yours means most of all given you are a PhD Math guy. I take seriously your criticisms given your expertise even if I don’t agree in the end.
1. Your first objection is as follows;
DALE’S REPLY:
First of all, I tried to go to the link you provide but it doesn’t work for some reason. Next, I was unaware that there were any rules on this front, but I’m not sure why this is an issue at all to be honest, if I give no decimal places, then rounding my % value would be 53% not 50%, so I’m afraid I don’t understand, even given your rule, why a 53.14% would round down to a 50% and not a 53%- would you be able to explain this in your next reply (and even though I’m unable to reply I will read it).
Additionally, you explain why this is a rule, namely so the “result don’t provide a false confidence”, but it doesn’t do this at all, I know full well what my final results are based on and I’ve always been transparent with everyone as what it represents and what the inputs are as well. So I don’t deny this may be a rule I had no idea about, but I don’t find this to be anything that really takes away from my work- OK fine, instead of 53.14%, say I was 53% at the time of my conversion and the problem is solved.
2. Next you say,
DALE’S REPLY:
I’m inclined to go along with you on this as I’ve seen experts argue both ways on this front. That said, the just two hypotheses in my Bayes-ish approach represents the fullness of ~R (meaning it does represent a simple way to decompose those elements and sum them in the way you want anyways- just in my more direct and intuitive way) and so I don’t think this matters as much given I’m not using conditional probabilities and Bayes proper method which this criticism applies to.
But just a question for my understanding of Bayes proper, if the Ai is the right way to go about assessing ~R in Bayes proper, then shouldn’t we also sum all of the multiple Resurrection hypotheses too- such as if we add up Dale Allison’s Spiritual Rez hypothesis and all the Pro-Shroud Resurrection hypotheses (based on different forms of radiation, electromagnetic, etc.)- what is to stop me from slightly tweaking the Resurrection hypothesis to come up with 1000 Resurrection hypotheses all of which need to be added to the calculation in the same way you demand we do with all the mutually exclusive possible ~R hypotheses. Heck, I could artificially inflate pro-Rez hypotheses by saying Jesus rose his right arm first vs. left arm vs right leg vs. left leg and boom there we’ve got 4 very probable Rez hypotheses based on the conditional probabilities added into the mix and so on and so forth.
Just a sincere question as these things I struggled with back in 2014 and it’s why I choose not to use conditional probabilities and go for the Dalean way I use now. So if you would clarify that for me, that would be great.
3. Finally you say,
“
UPDATE- The unbeleiving Math expert was kind enough to respond with helpful information based on my questions- for those following along- here is what he said;
“Dale,
I noticed on your site this morning your response. Please note I’m not an atheist.
1. Hopefully I’ve fixed the link now – I need to remember to leave a space between the hyperlink and any closing parenthesis. Hopefully the material will make sense but as you’ll learn, the question that needs to be answered is how many significant figures are in your inputs. If 60% means a value between 59.5-60.5 then you have 2 significant figures and this is what your final calculation should contain. If on the other hand, it means 55-65 then you have 1 significant figure and so your 53.14% should be rounded as 50%.
The complicating issue here is that significant figures are primarily applicable to physical measurements where there is typically upward and downward measurement uncertainty. As I understand things, you typically use an upper or lower bound in your calculations, so things are little bit more complicated. I guess you’ll need to ask the question of when you assess a belief in the 60-70% range and you choose say the 60% value, does the 60 signify a sure value that is definitely greater than 59 (therefore 2 SF) or does it only signify greater than 50 (therefore 1 SF)? Perhaps we can dive deeper after you watch the videos.
Bryan speaks about error bars or stadnard deviation in the results +/- and so maybe you are saying 53% – 3% = 50% or something, but again my error bars are worked into each indivdual objective input already and in terms of the overall probability is irrelevant as there are no error bars given God prevents me from having any undue confusion. So what I get, is what I get and that is what I base my decision on- there are no +/- to deal with.
This is a very strange assertion. If you go back after this and recalculate and erroneously arrive at 45% and deconvert, do you believe God will say to you on judgement day, “It’s OK Dale, I know you forgot to carry the one and so rejected me again.” Or does God protect the real seeker from technical error?
2. Practically, if there are multiple competing hypotheses, one typically isolates the strongest contenders. Remember the priors must sum to 1 so 1000 low prior hypotheses are going to struggle to make an impact on a hypothesis with a strong prior. But if one is going to bake off H against ~H, one must definitely keep in mind that ~H may represent multiple hypotheses.”
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UPDATED AGAIN- MY REPLY TO ANTHONY’S REPLY;
“Hi Anthony,
1. I’ve watxhed your videos on signifixant figures and yes I understand what you are saying now. Again, I don’t think this is really an issue for my method even if I’m doing some sort of faux pas in using no decimals but then rounding to two decimal places in the end. To answer your question when I have a range of 65-75% let’s say and then I input a 65% into Bayes, yes I’m treating these as sure values, so in other words it’s me saying I’m 65.00% so I with the decimal in place, the video said that indicates it is meant as a precise number (or sure number). Again, obviously, we know this number represents my subjective credences and is not some objective measure in the same way meauring a km is, but still I’d say these are meant to be precise numbers that precisely measure my degree of subjective credences.
The only reason I give more significant figures in my answer is simply because I didn’t know of any rules against doing so and when you plug those inputs in, the calculator gives many decimal places and so I arbitraily said I would round to 2 decimal places to be more accurate but without having to write down 13 or so decimals in some cases. So again, I understand there is this rule to go with the least number of signficant figures via the inputs, but the 53.14% is still accurate to where I am and even more so than the 53.%. So I feel fine using it so long as I explain what it represents and how I got there, I don’t think it gives a false level of precision even if it does initially- I use that as an “in” so to speak as it usally does peek interest as to how I got that number, but once explained- well take a look at this Board, literally no one has my back or supports my method on here as they all understand that my numbers simply reflect subjective credences and from there they (wrongly imo) proceed to dismiss the overall result.
That said, I agree with you that when I use the 53.14% as an ice-breaker, there is a responsiblity on my part to be clear, once probed, as to what that represents andhow I arrived at that in a way that they understand.
1.b) As to your question about God and undue confusion- yes, that is precisely what I’m saying- if I got 49.4% or 49% asmy overall probability, then given God doesn’t allow undue confusion, I would disbelieve and I expect a Real Maximally Great Being not to blame me for that decision. So yes, I’m consistent there. I understand some who want to have what I called the “Agnostic range”- for me I arbirarily put that at 45.%-55.% and so anything in that range one is able to either believe/disbelieve accordingly or raitonall choose to suspend judgement on the basis of a std deviation or as Bryan says the +/-, but given the no undue confusion factor, I now don’t allow for that (at least in the overall result) as ultimately Evidentialism states we follow the evidence and apportion our beleifs/disbeliefs accordingly and a 49.% mean the proposition is improbable just as a 51.% means it’s probably true. So given God’s role in preventing undue confusion with these kinds of religious propositions at least, I’m much more a purist on that front.
2. OK thanks yeah that makes sense to me with the summing to 1 bit there. But again, it does seem very counter-intuitive there as it seems like saying adding up crappy evidences somehow proves the hypothesis is true (no that is like stacking leaky buckets on top of each other and pretending they hold water), but somehow with mutile failed hpyotheses these do potneitally add up to something that can hold water, but I understand you are “filling up the space” to get 100% and all these hypotheses represent the gap of 100%-the% of the R hypothesis (or the sum of R hypotheses)- same thig I do really.
3. Great, amazing. All I care about is whether the results were correct in terms of what I wanted and used to make my decision and it seems you are now affirming that I was doing that properly. But I take your point that I may be using some of the terms in the wrong way, not totally sure how but esentially yes I’m getting the stength of the hypothesis given all the evidences and background evidences and so OK yes you got me correctly there.
The only thing I don’t understand is why you say I’m using Bayes proper as to do that, don’t I have to use conditional probabilities along the lines of Pr(E|H) not Pr(H|E) for example and same deal on the ~H side as well? Again, either way I don’t really care so long as the math is achieving what I want it to do and on that front, you seem to be saying, “Yep, it works” now 🙂
4. That is fascinating about the Bayesian network approach, I wish you were able to complete that research as I would have liked to see it and wrap my head around it, even if in all liklihood I probably would not have understood it. That said, yes I think you are totally right that trying to obtain statistical probabilties for hypotheses like God raised Jesus from the dead or God exists just aren’t possible to do and thus God, if He exists, must allow for humans to make rational decisions on other bases and I just make the argument that assigning subjective probabilties to reflect our own subjective credence levels based on the evidence/arguments for and against and then plugging those into Bayes to get the overall % given those inputs is one of those valid ways. I think it’s also valid to do the same with just the subjective credence levels based on that same evidence/arguments without any % values being assigned or using Bayes at all but the former is simply superior as it provides more protection against bias and subjective factors that aren’t conducive to truth.
That is all I argue, I’ve never pretended that my % values represent anything more than that as Darren falsely alludes to above in the posts, no the only thing I say is that my subjective % values/credences are objectively rationally justified/reasonable and/or warranted (or technically warrantedish); this doesn’t deny that others may have different values that are also the same vs. some others whose credences are not raitonally justified/reasonable or warranted such as the guy who dibeleives in the Holcaust (thinks only a 20% prob it happened given the same evidence)– that guy has his own subjective credence level reflected by the 20% he may assign, but we all know that he ain’t a reasonable person and is thus unwarranted in his opinion on this particular issue. So yeah, I allow for Permissivism to be true in our Fallen World and thus differing subjective credence levels are rationally permitted by me depending on the strength or weakness of the given evidence- some are warranted/justified/reasonable and some are not.
P.S.- I have a rather unique take on the Uniqueness Thesis vs. Permissivism debate in Epistemology whereby I am technically a Uniqueness proponent, but THE only correct subjective credence level (% value) would be the one that God has in any given situation (including any hypothtical ones whereby God is limited to just the evidence a human has or is aware of or something) and thus only HIS subjective divine credence level is the one that is warranted. However, in a Fallen world, humans rarley, if ever, have the same credence leve as God and thus why we see so many different credence levels in this world. Yet as per Permissivism, I do want to say that people are still rational or reasonable and/or “warranted” depsite these differences and so my unique solution is that God, prevents or restricts the ranges that a reasonable person will get on any given issue and this is what I call the “reasonableness range” (or the range of being “warranted-ish”) of subjective credences. I think this applies to any and all propositions outside of the religious ones where I think one must be a reasonable Real Seeker for God to restrict the noetic effects of sin and obviously that is where I argue God doesn’t allow for any “undue confusion”.
So my belief is that on the key religious beliefs related to our ultimate purposes at least, God musn’t allow undue confusion as per my Premise #9. But I also beleive that even outside of religious propositions, it seems to me that God also seems to prevent or restrain the effects of sin on our cognitive faculties for most “reasonable persons” so that most understnad that 1+1=2 or that the Earth is round (given our evidence today at least), or that is it rational to infer the truth of natural selection for example.”
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