[1) Refuting an Atheist - Happy Easter!, 2) Probability]
Properly speaking, when we deal with mathematic odds, many times when it is used one could estimate many of component probabilities differently.
But mathematical probability deals basically with previous probability of outcome. And that "probability of outcome" often enough has some kind of aleatoric factor in it.
It does not directly tell us of other kinds of probability, more important, but less exact.
Saying someone will throw dice, probability of getting a five is 1/6 - if it is one die of the d6 model which usually is meant when we speak of dice. If you use the kind of dice used on RPG, and use a d10 instead, the probability of a five is just one in ten. And if we speak of getting the sum five, throwing two normal dice (2d6)?
4/36 or 1/9.
So, getting five is differently probable, supposing dice unloaded, according to whether you throw for it with 1d6, with 1d10 or with 2d6 looking for the sum. That is, probability of aleatoric outcome depends on what equipment you have.
You can on the other hand not determine probability of any of these equipments from its having resulted once in a value 5.
That kind of probability is not mathematic and statistic. It is either incalculable, basically, or its calculation depends on what you know about the player. Is he a honky tonk blue collar worker or an RPG geek? In the first case, you are nearly sure the value 5 was either 1/6 or 1/9. In the second case it could also have been very easily 1/10.
So, can one calculate equipments from values?
A value 5 is not incompatible with any of these equipments. A value 12 could for instance be either max value (1/36, like min value 2) of sum of 2d6, or one of the 100 values of 2d10. But it definitely supersedes both 1d6 and 1d10. At 13, there is no 2d6 either. It might once again be one value out of 100 with 2d10, or it might be a value of 3d6. There are theoretically 216 different outcomes, with minimum 3 as 1/216 and maximum 18 also as 1/216, but mid values rising in probability (that is why 3d6 is often used to get ability scores).*
And of course, a 13 as 1/100 (1 possibility on 2d10) has a less probable previous probability on that equipment than a 13 as 36/216 or 1/6 (36 possibilities on 3d6). But if you heard it was 13 as 1/100 cases (one possible value on 2d10) you would have no way to consider the information given improbable in hindsight just because previous probability was less to hit precisely 13 in the one way than in the other. Both ways clearly do include 13 in outcomes.
However, you can safely exclude the dice equipments 1d6, 1d10 and 2d6, once you know a value 13 was hit.
So, suppose you had reckoned on fact of a known value being 5 that equipment was either 1d6 or 2d6 or just possibly weirdest case a 1d10, and you hear of a score 13, which is impossible on those equipments. Unless you know what game it is and know the rules exclude any dice equipment where 13 is a possible outcome, you really cannot, you really ought to consider it might be a 3d6 or a 2d10.
But all this time we are dealing with aleatory probabilities. What if artistic intention is involved? Well, then we are in a totally other world. Probability of each artistic detail depends clearly on how it fits according to artist's taste within the general framwork of the work of art. If I ever found an ancient text including the word sequence: ... ETLUVXNONLOQVI ... but lacking the rest, I will be pretty sure one sentence ends in "... et lux," while next begins with "Et loqui ..." for each of which there are a few possibilities that make grammatical sense. But if I come across "et lux non loqui" on the internet, I will take it as a google translate, that is as an incompetent translation made by a machine having no grasp on meaning, for a text which might be English "and light not to speak". In other words, a way to get across very indirectly to a Latinist someone wishes him to have x "and also light to shut up", in other words a request for omertà. In Latin, there is hardly any good syntactic context for a single phrase "et lux non loqui". What you wish someone is usually accusative and lux has an accusative distinct from the nominative, and whatever it is, if it is qualified by an English infinitive, negated or not, it cannot be qualified by a Latin one, but needs another construction, since Latin infinitives and infinitive phrases can only occupy the roles of a nominative or an accusative noun.** Similarily, if I find words like a girl looking into a grimoire while performing a task set for her, I'll be more likely to consider it a part of C. S. Lewis' scenario in which Narnia is a world where magic is sometimes licit for human actors, like the morality of The Amulet or other E. Nesbit stories, but transposed OUT of this world where C. S. Lewis knew very well it is highly illicit, than as part of Tolkien's scenario in which even a previously presumed to be innocuous magic ring turns out, very pessimistically, to be not just illicit to use, but very deplorable if used anyway. In other words, even if I had not read all of the Narniad and Silmarillion, The Hobbit and LotR, I would rather place it in the Narniad (where Lucy takes this risk in The Voyage of the Dawn Treader) than in the Tolkien Legendarium (where the ring of Bilbo turns out to be the ring of an Antichrist figure or incarnate Devil figure and where looking into a Palantir is only possible for the king who has the moral stamina of an exorcist, but very dangerous to anyone human else, including the very noble and learned Denethor, and even to Saruman, who was nevertheless an angelic being, in the scenario).
So, before we can decide whether a miracle is "probable", what we need to decide is not whether the chances of it happening are previous to it so great or so small, but rather if there is equipment for it in the universe. And since a miracle is not an aleatory event, but a highly intentional one, if the one who wields it (supposing there is one) is likely to have such an intention. We get to moral rather than mathematical probability.
But, we can on the other hand say that if any miracle is at all certain, the universe has someone in or about it who has the ability to perform such.
And that also goes for anything which would be impossible on materialistic terms.
If you identify a phenomenon as thought as bypassing all purely materialistic explanations, like a value 13 bypasses all versions of 1d6, 2d6 or 1d10, you have identified conscience as a phenomenon perhaps concretely in us interdependent with, but not ultimately dependent on matter. And that leaves a possibility open for which physical laws applicable to matter only are no effective block.
Also, one can go the other way and identify the value "a group clearly believes its founder, whom living members knew, to be physically risen from the dead" as being a value like 13 to 1d6 to the equipments of error and lying.
In other words, probability as understood by Pascal has nothing to say against the existence of God or the Resurrection of Christ.
As we Roman Catholics have today had Dominica in Albis, and as this year it coincides with Orthodox celebrating Easter Sunday, I insist: Christ is Risen. He is Truly Risen.
Hans Georg Lundahl
Bpi, Georges Pompidou
I Sunday after Easter
* 1. Roll 3d6 for each ability score.
2. Write down the bonus / penalty for each score.
|Ability Score||Bonus / Penalty|
Cited from: BASIC FANTASY BEGINNER'S ESSENTIALS
** Yes, an Accusative with Infinitive may well occupy the role of a nominative: "me non loqui nec scribere malis videtur bonum esse." But after lux, you need sth with genitive, dative or ad phrase of gerund: "lucem non loquendi, lucem non loquendo, lucem ad non loquendum", not a pure accusative or nominative.