In the previous post , we discussed how there is no such thing as chance in the Christian worldview. Between the publication of that post and this one, I finally got around to publishing my article on the problem of the one and the many . In this post, I'd like to expand how the problem of the one and the many is relevant when we're talking about probabilities. The problem of the one and the many If you haven't read my article already, I'll recap the problem for us here: As a general principle (in order to have knowledge of objects in the world) the world must be such that its unity and plurality are related yet distinct. As such, the expressions of unity and plurality (e.g. Winston and Porchy) in the world must themselves manifest unity (through relations of commonality (they are both dogs)) and plurality (through distinction, as they're not the same dogs). In ancient Greece (and today in some schools of thought), the one and the many are placed in dialectical opposition to each other. The one brings uniformity, and the many brings diversification. The one is a principle of pure unity, and the many is a principle of pure chance. Regarding pure unity as ultimate removes the possibility of diversity, as unity excludes it by definition. We end up with abstract universals. Regarding pure diversity as ultimate, it excludes unity and we end up with unrelated abstract particulars about which nothing can be said. If both are some true in dialectical opposition, all is chaos. Probability revisited Recall that in the previous entry we mentioned the following: Every probability we assign is a human approximation of God's ordained outcome of an event. Every coin flip has been determined when God decreed to create. He specified the predictability of the coin toss, as well as the unpredictability inherent in every specific coin toss. And, Probabilities only make sense if we have a sovereign Creator-God that harmoniously specifies predictability and unpredictabilities. If there is no regularity in the midst of irregularity, statistics become a useless subject of study. God is in control . There is no principle of pure chance over which God does not have control. Every event (whether it's an election outcome or the flip of a coin) has been ordained by God, and has been pre-interpreted by Him. In the Christian worldview, there are no brute facts that originate via a principle of chance. A coin toss Narrowing this down to the event of a coin toss, we described in part 3 how we can model a coin toss using the following probability distribution function: Moreover, in part we introduced the idea of statistical estimators. How can we determine the probability distribution above? We can do it via estimators. We want to determine the probability that a particular coin toss will land on heads, or tails. This website is pretty cool and can illustrate our point for us . Here is a screenshot of the home page: Here we can see that globally, 8,527,569 people flipped the digital coin. Of those flips, around 50,02% landed on heads, and 49,98% landed on tails. These are our empirical observations. 8 million flips are are a pretty good amount of flips to try and make some inferences from! The probability for a particular coin landing on heads can be estimated as: In a similar way, we can estimate the tails probability as 49,98% from our sample as indicated above. What about it? How is the above relevant to our line of thought? Think with me. If abstract unity is ultimate, there is no differentiation between a coin landing on heads, and a coin landing on tails. All is one.
If somehow abstract particularity is ultimate (or some principle of ultimate chance), there is no reason our estimator for the probability of a coin landing on heads to be intelligible. There is nothing that guarantees that a next coin toss will behave in the exact same way as the previous coin tosses (we'll draw on this when we introduce an attempted solution to the problem of induction ). Modelling the outcome of a coin toss assumes that there is unity between different (diverse) coin tosses so that we can determine a fixed pattern among different tosses. In this sense, a coin toss can only make sense on Trinitarian presuppositions - that is that the eternal One-and-many has created all all facts, and has ordained that there be unity and diversity in creation.