Reasoning and Randomness

Question

What is the relation between reasoning and randomness or more specifically finding any relation between logic and stochastic processes? Why does it work so well, I wonder. For instance, prices in economic studies may move in random ways such as the daily perturbations of the prices of commodities, but there also appear to be meaningful patterns, particularly in terms of supply and demand. It is believed that some prediction from hypothesis is held to be scientific, and not same as foretelling future, so there must be a line between the two.

How does logic and reasoning suss out the difference between guessing or supernatural prediction and mathematical or scientific prognostication when dealing with randomness?

If it is random do we use deductive and if it is non random do we use inductive ? — quanity, Aug 09 '22 at 19:22
You're looking for three terms: deterministic, probabilistic or stochastic, and random. The first is associated with deductive inference, the second with inductive, and the last in its extreme form is sort of a mathematical ideal that's hard to get out of the physical world even with expertise in PNRG construction. — J D, Aug 09 '22 at 19:26
Most topics of scientific study require inductive methodologies and rely on statistical correlations, eg the efficacy of pharmeceutical compounds. In deep philosphical topics, one might hear dispositions as a traditional term to talk about longitudinal properties. https://plato.stanford.edu/entries/dispositions/ — J D, Aug 09 '22 at 19:30
@JD Hi So foretelling future based on past data is different from predicting from a hypothesis/premises — quanity, Aug 09 '22 at 19:33
@JD btw deterministic and predictable are two different things (eg. chaos is deterministic but unpredictable) — quanity, Aug 09 '22 at 19:38
Sometimes, yes. Bayesian inference is one method of foretelling, and classical probability another. A hypothesis may use an algebraic equation, or it may be a rational intuition or even divine religious experience. A hypothesis is just a fancy word for reasoned guess. What the reasoning is makes all the difference. In most studies, sophisticated statistical and probabilistic theory is used. PCA, linear regression, Bayesian priors etc. The closer a correlation is to + or -1, eg, the stronger the claim to deterministic our causal relationship https://en.wikipedia.org/wiki/Statistical_inference — J D, Aug 09 '22 at 19:40
Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/138402/discussion-between-quanity-and-j-d). — quanity, Aug 09 '22 at 19:43
@JD Is backtesting inductive reasoning https://www.google.com/url?sa=t&source=web&rct=j&url=https://en.m.wikipedia.org/wiki/Backtesting&ved=2ahUKEwiX04HD5Lz5AhW2RWwGHX8iCyoQFnoECCUQAQ&usg=AOvVaw0Zm418iJ3QCU7C2Q8cpE0e — quanity, Aug 10 '22 at 17:22
Yes. Statistical predictive models draw probabilistic conclusive. No certainty, no deduction. — J D, Aug 10 '22 at 17:28

Ted Wrigley · Answer 1 · 2022-08-10T19:43:51.530

Random events tend to cancel out over time, leaving only the expected effect. This is called the Law of Large Numbers in probability: that the average of a large number of random trials will tend towards the expected value of a single trial. The expected effect can be a number of different things — an average value (as with a coin flip), a linear or curvilinear tendency (as with a growth model), a chaotic system that shows self-similarity and repetitive recurrence (such as weather or stock market patterns) — but the end result is that randomness tends to reduce to noise that filters itself out.

There are probability distributions that don't work so nicely, meaning that in certain cases random events will tend to magnify and obscure any underlying pattern. But many practical cases fall under the Central Limit Theorem; they tend towards a normal distribution and fall under the Law of Large Numbers.

Reasoning and Randomness

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